**Neural Network-Based Model Reference Adaptive System for Torque Ripple Reduction in Sensorless Poly Phase Induction Motor Drive**

#### **S. Usha 1, C. Subramani 1,\* and Sanjeevikumar Padmanaban <sup>2</sup>**


Received: 22 February 2019; Accepted: 5 March 2019; Published: 9 March 2019

**Abstract:** This paper proposes the modified, extended Kalman filter, neural network-based model reference adaptive system and the modified observer technique to estimate the speed of a five-phase induction motor for sensorless drive. The proposed method is generated to achieve reduced speed deviation and reduced torque ripple efficiently. In inclusion, the result of speed performance and torque ripple under parameter variations were analysed and compared with the conventional direct synthesis method. The speed estimation of a five-phase motor in the four methods is analysed using MATLAB Simulink platform, and the optimum method is recognized using time domain analysis. It is observed that speed error is minimized by 60% and torque ripple is reduced by 75% in the proposed method. The hardware setup is carried out for the optimized method identified.

**Keywords:** induction motor; speed estimation; model reference adaptive system; kalman filter; luenberger observer

#### **1. Introduction**

An induction motor is the most commonly used motor in industries because it is reliable, robust and has low cost. Conventionally, the traction drive was operated with a direct current motor, but the maintenance cost is high. To overcome the above problem, a three-phase induction motor is used. The three- and poly-phase induction motor are modelled and analysed; the amplitude torque ripple is less in a polyphase machine. Even though the poly-phase machine has high efficiency, less torque pulsations, and higher fault tolerance due to the lack of power supply in earlier days, poly-phase has not been used. However, nowadays, due to the advancement of power electronics devices, control of the poly-phase induction motor also possible.

Since reliability is one of the important parameters to which the induction motor owes its operation, the reliability of the induction motor is improved under different operating conditions. To achieve this, the parameters of the induction motor need to be taken care of. To eliminate the design mistakes in the archetype construction and when testing the motor drive system, the dynamic simulation plays a major role in validating the design process of the system. A synchronously revolving rotor flux-oriented frame is taken as a reference, and the induction motor is modelled in it [1].

Accurate knowledge of a few of the parameters of the induction motor is important for the purpose of sensor-less vector control and the control schemes of the induction motor. If the original parameter values in the motor fail to match with the values used within the controller, it leads to the degradation of the presentation of the drive. The benefit of dynamic modelling is that it helps in understanding the behaviour of the motor in the transient and steady state in a better way [2].

The dynamic modelling comprises of all the mechanical equations including the torque and speed vs. time. The differential voltages, flux linkages, and currents between the moving rotor as well as the stationary stator can also be modelled by dynamic modelling. There are numerous schemes that show a narrow stable region for low speeds in the regenerative mode for high torques [3]. This paper focuses on analysing the parameters like flux and speed evaluations of an induction motor without a sensor using reduced order observers [4,5].

In the traction industries and electric vehicles, the induction motor is the most commonly used machine as it offers advantages like good performance, less primary cost, and low maintenance cost. Speed identification is needed for the induction motor drives [6]. However, installation of the speed sensor in the induction motor leads to disadvantages like less reliability, extra cost, large size, etc. Estimation of speed for sensorless induction motor drive can be done by various techniques. These techniques are designed by keeping the factors like accuracy and sensitivity adverse to the induction motor parameter variations in consideration [7–9].

The fault tolerance capability of Quinary phase machines is of a superior standard compared to those of the three-phase machines. The three-phase machine becomes a single-phase machine when one of the phases is short-circuited, which still allows the machine to workout but for initializations, external means are needed and must be de-rated. In the case of the open circuit of quinary phase machines, it still holds its self-start competence and runs with minimized de-rating [10].

The projected crop up through a dynamic modelling of a quinary phase induction motor on a Direct-Quadrature (d-q) axis and the speed guesstimate of the motor using two sensor-less guesstimate techniques and an evaluation is being shaped between those procedures centred on the tenets of the speed being judged. Exploration in the arena of a multi-phase machine zone has gifted significant scopes in the previous era. With the figure of conservative electrical machines unceasingly mounting, the curiosity in multiphase machines is also intensifying due to innate types such as power disbanding, better fault resilience, or lower torque ripple than three-phase machines. Quinary phase machines are more defensive than the counterparts of three-phase towards the time-harmonic element in the waveform with excitations which produce high ripples in the torque of the elementary frequency with excitations at even multiples. This paper proposes a dynamic modelling of a quinary phase induction motor and the speed guesstimation of the motor using two sensor-less method guesstimations, and a comparison is being formed with conventional methods based on the values of speed that are estimated [11].

The stationary part stimulation in a quinary phase machine creates a field with less harmonic content, so that the improved efficiency is more appreciative than in a traditional three-phase machine. In the conventional induction motor, one of the common methods for obtaining rotor speed is by using speed encoders which sense the speed signal and give the rotor speed. Besides the necessity for the extension of shaft and mounting arrangement, a speed encoder adds rate and reliability snags [12]. It is feasible to find the speed with the ease of a digital signal processor from machine terminal current and voltage.

In conventional methods, speed and rotor flux estimators are intended for sensor-less control of motion control structures with induction motors. More exactly, the estimators entail the conjunction of an adaptive speed guesstimation scheme and either a robust or standard descriptor-type Kalman filter. It is exposed that the descriptor structure of the Kalman filter permits for a direct transformation of parameter variations into coefficient disparities of the structure model, which leads to vulgarizations in the describing reservations and a stochastic guesstimation of inaccessible state variables, and the mysterious input of an electric vehicle driveline fortified with an innovative seamless clutch-less two speed transmission is being studied. However, the guesstimation is normally intricate and steadily dependent on the components of the machine [13]. Hence, sensor-less speed guesstimation techniques are being proposed to tackle these snags.

Although in the case of a flux estimator, the flux of motor cannot be measured immediately, the notion of comprehending a closed-loop structure is tranquil associable if the discrepancy flanked

by a signal replacing the stable-state data of the source flux and the wave of the evaluated flux vector is back to the input signal that is a feedback signal. This reference data is normally attainable in rotor-flux-based regulations. In this proposed method, the filter equation is altered by including a sliding hyper plane in the modified Luenberger and extended Kalman filter method to improve the performance of the system. The conventional voltage model-based reference adaptive system replaced by a neural network-based system to overcome the integration problem in the conventional method is also robust to parameter variations.

In this paper, Section 2 explains the modelling of an induction motor and speed estimation methods. The simulation results of speed guesstimation of a quinary phase induction motor using a Direct Synthesis method, Model Reference Adaptive System, Luenberger observer, and Extended Kalman Filter are discussed in Section 3. Speed deviation and Torque ripple reduction of induction motor drive in parallel using an extended Kalman filter are discussed in Section 4. Section 5 delineates the hardware implementation's induction motor drive.

#### **2. Modelling of Induction Motor and Speed Estimation Methods**

The steady-state prototype and equivalent enlarged circuit are helpful for studying steady state interpretations of the machine. This involves all the transients being skipped during the variations in stator frequency and load. Such changes that emerge in implementation include changeable speed drives [14,15]. The output of converter fed changeable speed drives in their impotence to provide large transient power. Hence, it requires estimating the changing of converter support changeable speed drives to determine the fairness of the switches of the converter and for a particular motor and their interactions to find the expedition of torque and current in the motor and converter [16–18]. The first theory assumes that the Magneto motive force generated by different phases of the rotor and stator are expanded in a sinusoidal method with an air gap, when those windings are traversed by a stable current. A suitable distribution of the windings in the area allows extending this aim. The air gap of a machine is also assumed to be invariably thick: the notching results and originating space harmonic are disregarded. These hypotheses will permit regulating the modelling of the low frequency of alternative quantities [19,20].

#### *2.1. Five Phase Induction Motor Model*

The phase voltages of the quinary phase induction machine are *Va*, *Vb*, *Vc*, *Ve*, and *Vf*. The phase angle between each phase is 72 degrees. The voltages are given by the Equations (1)–(5) respectively.

$$V\_a = V\_m \text{Sin} \ (\omega t) \tag{1}$$

$$V\_b = V\_m \sin\left(\omega t - \frac{2\pi}{5}\right) \tag{2}$$

$$V\_c = V\_m \sin(\omega t - \frac{4\pi}{5})\tag{3}$$

$$V\_{\varepsilon} = V\_{m} \operatorname{Sin}(\omega t - \frac{6\pi}{5}) \tag{4}$$

$$V\_f = V\_{\text{ff}} \operatorname{Sim}(\omega t - \frac{8\pi}{5}) \tag{5}$$

The quinary phase voltages are converted into d-q axis using the transition matrix. The transition matrix is given by Equation (6).

$$\frac{V\_d}{V\_q} = \sqrt{\frac{2}{5}} \begin{bmatrix} \cos(\omega t)\cos(\omega t - \frac{2\Pi}{5})\cos(\omega t - \frac{4\Pi}{5})\cos(\omega t - \frac{6\Pi}{5})\cos(\omega t - \frac{8\Pi}{5}) \\ \sin(\omega t)\sin(\omega t - \frac{2\Pi}{5})\sin(\omega t - \frac{4\Pi}{5})\sin(\omega t - \frac{6\Pi}{5})\sin(\omega t - \frac{8\Pi}{5}) \end{bmatrix} \cdot \begin{bmatrix} Va \\ Vc \\ Vc \\ Vd \\ Ve \\ Ve \end{bmatrix} \tag{6}$$

The d and q axis stator voltages are given by Equations (7) and (8), and the d and q axis rotor voltages are given by Equations (9) and (10) respectively.

$$V\_{ds} = R\_s i\_{ds} + \frac{d}{dt} \psi\_{ds} - \omega\_c \psi\_{qs} \tag{7}$$

$$V\_{q\text{s}} = R\_s i\_{q\text{s}} + \frac{d}{dt}\psi\_{q\text{s}} + \omega\_c \psi\_{ds} \tag{8}$$

$$V\_{dr} = R\_r i\_{dr} + \frac{d}{dt} \psi\_{dr} - (\omega\_\varepsilon - \omega\_r) \psi\_{qr} \tag{9}$$

$$dV\_{\eta r} = R\_r i\_{\eta r} + \frac{d}{dt} \psi\_{\eta r} + (\omega\_\varepsilon - \omega\_r) \psi\_{dr} \tag{10}$$

The flux linkages in the d and q axis are expressed in terms of the direct axis and quadrature axis currents in the following equations given by (11)–(16).

$$
\psi\_{ds} = L\_{1s} i\_{ds} + L\_{m\_r} (i\_{ds} + i\_{dr}) \tag{11}
$$

$$
\psi\_{dr} = L\_{1r} i\_{dr} + L\_{m\_\ast}(i\_{ds} + i\_{dr}) \tag{12}
$$

$$
\psi\_{qs} = L\_{1s} i\_{ds} + L\_{m\_r} (i\_{qs} + i\_{qr}) \tag{13}
$$

$$
\psi\_{qr} = L\_{1r} i\_{dr} + L\_{m\_\ast} (i\_{qs} + i\_{qr}) \tag{14}
$$

$$
\psi\_{dm} = L\_{m\_\star}(i\_{ds} + i\_{qr}) \tag{15}
$$

$$
\psi\_{dm} = L\_{m\_{\prime}}(i\_{ds} + i\_{qr}) \tag{16}
$$

The direct axis and quadrature axis currents in terms of flux and inductance are given by the following Equations (17)–(20).

$$i\_{ds} = \frac{\psi\_{ds}(L\_{1r} + L\_{m}) - L\_{m}\psi\_{dr}}{(L\_{1s}L\_{1r} + L\_{1s}L\_{m} + L\_{1r}L\_{m})} \tag{17}$$

$$\dot{q}\_{qs} = \frac{\psi\_{qs}(L\_{1r} + L\_{m}) - L\_{m}\psi\_{qr}}{(L\_{1s}L\_{1r} + L\_{1s}L\_{m} + L\_{1r}L\_{m})} \tag{18}$$

$$i\_{dr} = \frac{\psi\_{ds}(L\_{1r} + L\_{m}) - L\_{m}\psi\_{ds}}{(L\_{1s}L\_{1r} + L\_{1s}L\_{m} + L\_{1r}L\_{m})} \tag{19}$$

$$i\_{dr} = \frac{\psi\_{ds}(L\_{1r} + L\_{m}) - L\_{m}\psi\_{ds}}{(L\_{1s}L\_{1r} + L\_{1s}L\_{m} + L\_{1r}L\_{m})} \tag{20}$$

The electrical torque developed in the rotor of a quinary induction motor is given by Equation (21).

$$T\_{\mathcal{E}} = PL\_{m}(i\_{qs}i\_{dr} - i\_{ds}i\_{qr}) \tag{21}$$

The reference speed of the rotor is given by Equation (22).

$$
\omega\_r = \int \frac{P}{2f} (T\_\varepsilon - T\_1) dt\tag{22}
$$

#### *2.2. Modelling of Conventional Direct Synthesis*

To estimate the speed in the direct synthesis method for obtaining the rotor fluxes in the direct and quadrature axis, the voltage and the current model of rotating reference are used. Different regulation methods such as scalar regulation, field orient control approach, and regulation without a sensor are used. This method agonizes from parameter reactivity and partial presentations at a very low speed of operation. The combination of the direct synthesis method is extremely machine parameter-delicate and will move to give a less accurate guesstimation. The flux guesstimation can be done by using both the current regulation method and voltage regulation model.

The direct axis and quadrature axis rotor fluxes are given by the following Equations (23) and (24).

$$
\Psi\_{\,\,dr}^{\rm s} = \int (\frac{L\_m}{T\_r}\dot{\mathbf{r}}\_{\,\,ds}^{\rm s} - \omega\_r \psi\_{\,\,qr} - \frac{1}{T\_r} \Psi\_{\,\,dr}^{\rm s}) \tag{23}
$$

$$
\Psi\_{\
qr}^{s} = \int \left( \frac{L\_m}{T\_r} \ddot{\mathbf{r}}\_{qs}^{s} - \omega\_r \psi\_{dr} - \frac{1}{T\_r} \Psi\_{dr}^{s} \right) \tag{24}
$$

The direct axis and quadrature axis rotor fluxes are also given by the following Equations (25) and (26) respectively.

$$
\psi^{s}\_{\;\;dr} = \frac{L\_r}{L\_m} (\psi^{s}\_{\;\;ds} - \sigma L\_s i^{s}\_{\;\;ds}) \tag{25}
$$

$$
\psi^{s}\_{\ \ qr} = \frac{L\_r}{L\_{\text{nr}}} (\psi^{s}\_{\ \ qs} - \sigma L\_s \dot{r}^{s}\_{\ \ \ \ \ \ \ \ \prime}) \tag{26}
$$

The Speed Equation for the Direct Synthesis method has been derived from the following Equations (27)–(32).

$$\mathbf{V}^{\rm s}{}\_{ds} = \dot{\mathbf{r}}^{\rm s}{}\_{ds}\mathbf{R}\_{\rm s} + L\_{\rm 1s}\frac{d}{dt}\dot{\mathbf{r}}^{\rm s}{}\_{ds} + \frac{d}{dt}\boldsymbol{\upmu}^{\rm s}{}\_{dm} \tag{27}$$

$$V^{s}\_{\;\;ds} = i^{s}\_{\;\;ds}R\_{\;s} + L\_{\;1s}\frac{d}{dt}i^{s}\_{\;\;ds} + \frac{d}{dt}\psi^{s}\_{\;\;dm} \tag{28}$$

$$\boldsymbol{V}^{\rm s}\_{\,\,\,ds} = \frac{\boldsymbol{L}\_{\rm m}}{\boldsymbol{L}\_{\rm r}} \frac{d}{dt} (\boldsymbol{\psi}^{\rm s}{}\_{\,\,dr}) + (\boldsymbol{R}\_{\rm s} + \sigma \boldsymbol{L}\_{\rm s} \mathbf{s}) \boldsymbol{I}^{\rm s}\_{\,\,ds} \tag{29}$$

$$
\sigma = 1 - \frac{L^2 u}{L\_r L\_s} \tag{30}
$$

$$\frac{d}{dt}(\psi^{\varepsilon}\_{\,\,dr}) = \frac{L\_r}{L\_m}(V^S{}\_{ds}) - \frac{L\_r}{L\_m}(R\_S + \sigma L\_S S)i^S{}\_{ds} \tag{31}$$

$$\frac{d}{dt} \left( \psi^{s}{}\_{qr} \right) = \frac{L\_{r}}{L\_{m}} V^{s}{}\_{qs} - \frac{L\_{r}}{L\_{m}} (R\_{s} + \sigma L\_{s} \mathcal{S}) \dot{\mathbf{r}}^{s}{}\_{qs} \tag{32}$$

$$
\omega\_r = \frac{1}{\overline{\psi^2\_r}} \left[ (\psi^s\_{\,dr} \psi^s\_{\,qr} - \psi^s\_{\,qr} \psi^s\_{\,dr}) - \frac{L\_m}{T\_r} (\psi^s\_{\,dr} \psi^s\_{\,qs} - \psi^s\_{\,qr} \psi^s\_{\,ds}) \right] \tag{33}
$$

The stator and rotor flux are estimated. Stator voltage in the direct axis is derived in terms of flux and inductances. The rotor speed is estimated from the estimated flux in the direct and quadrature axis.

#### *2.3. Modified Luenberger Observer Technique Model*

A structure that observes the state of structure from the inference that there is no way of directly observing the states easily is called an observer. It is used to guess the unmeasurable state of a structure. Any structure that gives an evaluation of the intramural state of a stated real structure, from the survey of the given input and response of the real structure is termed as a state observer. An eloquent structure state is mandatory to solve many regulation concept technical hitches; for example, maintaining a structure using response. The regular state of the structure cannot be gritty by direct cognition in most practical cases. Instead, oblique consequences of the core state are pragmatic by way of the

structure outputs. An estimator with a closed-loop system is grounded on the axiom that by giving back the discrepancy amongst the identified output of the perceived structure and the guessed output, and perpetually amending the prototype by the signal, the error has to be miniaturized. Although, in the case of a flux estimator, the flux of the motor cannot be measured immediately, the notion of comprehending a closed-loop structure is tranquil associable if the discrepancy flanked by a signal replacing the stable-state data of the source flux and the wave of the evaluated flux vector is back to the input signal that is a feedback signal. This reference data is normally attainable in rotor-flux-based regulations. In this proposed method, a filter equation is altered by including a sliding hyper plane to improve the performance of the system.

The Luenberger observer uses the electrical model in a *ds*-*qs* frame, where the state variables are currents of stator *i s ds* and *i s qs* and fluxes of the rotor are *ψ<sup>s</sup> dr* and *<sup>ψ</sup><sup>s</sup> qr*. The rotor voltage is given by Equations (34) and (35).

$$
\mu^s{}\_{dr}R\_r + \frac{d}{dt}(\psi^s{}\_{dr}) + \omega \gamma \psi^s{}\_{qr} = 0\tag{34}
$$

$$
\dot{u}^{s}{}\_{qr}R\_{r} + \frac{d}{dt}(\psi^{s}{}\_{qr}) + \omega\_{r}\psi^{s}{}\_{dr} = 0\tag{35}
$$

From the voltage model of flux guesstimation, the rotor axis flux is given as

$$
\psi^s\_{\ \ qr} = L\_m \dot{\imath}^s\_{\ \ qs} + L\_r \dot{\imath}^s\_{\ \ qr} \tag{36}
$$

$$
\psi\_{\;\;dr}^{\;s} = L\_{m} \mathbf{i}\_{\;\;ds}^{\;s} + L\_{r} \mathbf{i}\_{\;\;dr}^{\;s} \tag{37}
$$

After eliminating *i S dr* and *i S qr* from Equations (34) and (35) with the help of Equations (36) and (37), the result is

$$\frac{d}{dt}(\boldsymbol{\psi}^{s}{}\_{ds}) = -\frac{R\_{r}}{L\_{r}}\boldsymbol{\psi}^{s}{}\_{dr} - \omega\_{r}\boldsymbol{\psi}^{s}{}\_{qr} + \frac{L\_{m}R\_{r}}{L\_{r}}\boldsymbol{i^{s}{}\_{ds}}\tag{38}$$

$$\frac{d}{dt}(\psi^{s}\_{\;\;\;r}) = \frac{L\_{r}}{L\_{m}}V^{s}\_{\;\;\;s} - \frac{L\_{r}}{L\_{m}}(R\_{s} + \sigma L\_{s}S)i^{s}\_{\;\;\;s} \tag{39}$$

$$\frac{d}{dt}(\boldsymbol{\psi}^{s}{}\_{qr}) = -\frac{R\_r}{L\_r}\boldsymbol{\psi}^{s}{}\_{qr} - \omega\_r \boldsymbol{\psi}^{s}{}\_{dr} + \frac{L\_m R\_r}{L\_r}\boldsymbol{\psi}^{s}{}\_{qs} \tag{40}$$

$$\frac{d}{dt}(\boldsymbol{\psi}^{\rm s}{}\_{qr}) = \frac{L\_r}{L\_m}\boldsymbol{V}^{\rm s}{}\_{qs} - \frac{L\_r}{L\_m}(\boldsymbol{R}\_s + \sigma L\_s S)\boldsymbol{i}^{\rm s}{}\_{qs} \tag{41}$$

$$\frac{d}{dt}(\dot{\mathbf{r}}^s\_{ds}) = \frac{(L^2{}\_m R\_r + L^2{}\_r R\_s)}{\sigma L\_s L^2{}\_r} \dot{\mathbf{r}}^2\_{ds} + \frac{L\_m R\_r}{\sigma L\_s L^2{}\_r} \boldsymbol{\Psi}^s\_{dr} + \frac{L\_m \omega\_r}{\sigma L\_s L\_r} \boldsymbol{\Psi}^s\_{qr} + \frac{1}{\sigma L\_s} \boldsymbol{V}^s\_{ds} \tag{42}$$

$$\frac{d}{dt}(\mathbf{i}^{\rm s}{}\_{\rm qs}) = \frac{(L^2{}\_{\rm m}R\_r + L^2{}\_rR\_s)}{\sigma L\_\text{s}L^2{}\_r}\mathbf{i}^2{}\_{\rm qs} + \frac{L\_mR\_r}{\sigma L\_\text{s}L^2{}\_r}\boldsymbol{\psi}^{\rm s}{}\_{\rm qr} - \frac{L\_m\omega\_r}{\sigma L\_\text{s}L\_r}\boldsymbol{\psi}^{\rm s}{}\_{\rm dr} + \frac{1}{\sigma L\_\text{s}}\boldsymbol{V}^{\rm s}{}\_{\rm qs} \tag{43}$$

The change in d-q axis stator current is calculated from the estimated flux and voltages. Therefore, the desired state equations are given by

$$\frac{d}{dt}(X) = AX + BV\_s \tag{44}$$

where,

$$dX = \begin{bmatrix} \ i\_{ds} & i\_{qs} & \Psi\_{dr} & \Psi\_{qr} \end{bmatrix}^T \tag{45}$$

$$V = \begin{bmatrix} \ V\_{ds} & V\_{qs} & 0 & 0 \ \end{bmatrix}^T \tag{46}$$

$$A = \begin{bmatrix} -\frac{\frac{L\_m^2 R\_r + L\_r^2 R\_s}{\sigma L\_s L\_r^2}}{\sigma L\_s L\_r^2} & 0 & \frac{\frac{L\_m R\_r}{\sigma L\_s L\_r}}{\sigma L\_s L\_r} & \frac{L\_m \omega\_r}{\sigma L\_s L\_r^2} \\ 0 & -\frac{\frac{L\_m^2 R\_r}{\sigma L\_s L\_r^2}}{\sigma L\_s L\_r^2} & -\frac{L\_m \omega\_r}{\sigma L\_s L\_r^2} & \frac{L\_m R\_r}{\sigma L\_s L\_r} \\ \frac{\frac{L\_m R\_r}{\sigma L\_r}}{L\_r} & 0 & -\frac{\frac{R\_r}{\sigma L\_r}}{L\_r} & -\omega\_r \\ 0 & \frac{\frac{L\_m R\_r}{\sigma L\_r}}{L\_r} & \omega\_r & \frac{R\_r}{L\_r} \end{bmatrix} \tag{47}$$

$$B = \begin{bmatrix} \frac{1}{\sigma L\_s} & 0\\ 0 & \frac{1}{\sigma L\_s} \\ 0 & 0 \\ 0 & 0 \end{bmatrix} \tag{48}$$

$$\mathbf{C} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \tag{49}$$

The dynamic equation is modified by altering the hyper plane, and the filter equation is given by

$$\frac{d\pounds}{dt} = \left[\not{A}\right]\pounds + \left[\not{B}\right]u + k\_{\text{sw}}sat(\not{t\_{\text{s}}} - \not{t\_{\text{s}}} - \not{d})\tag{50}$$

$$S = \hat{\mathbf{r}}\_s - \ \mathbf{i}\_s - \hat{d} \tag{51}$$

$$
\hat{d} = k \overleftarrow{T\_{\text{dus}}} \, \text{and } \mathfrak{Y} = [\mathbb{C}] \mathfrak{X} \tag{52}
$$

$$
\widehat{T\_{dis}}^- = T^\*\_{\mathfrak{e}} - \mathfrak{j}\frac{d\mathfrak{i}\mathfrak{j}}{dt} - B\_{\mathfrak{v}}\,\,\widehat{\mathfrak{v}}\tag{53}
$$

The speed adaptation is given by Equations (54) and (55)

$$
\omega\_r = K\_p \left( \varepsilon\_{\rm ids} \left. \boldsymbol{\psi}^s \right|\_{\rm qr} - \varepsilon\_{\rm iqs} \left. \boldsymbol{\psi}^s \right|\_{\rm dr} \right) + K\_1 \int \left( \varepsilon\_{\rm ids} \left. \boldsymbol{\psi}^s \right|\_{\rm qr} - \varepsilon\_{\rm iqs} \left. \boldsymbol{\psi}^s \right|\_{\rm dr} \right) dt \tag{54}$$

$$\frac{dv}{dt} = \epsilon^T \left[ (A + \mathbf{GC})^T + (A + \mathbf{GC}) \right] \mathbf{e} - \frac{2\Delta\nu\_r \left( \varepsilon\_{\rm dis} \widehat{\boldsymbol{\phi}^{s-}}\_{qr} - \varepsilon\_{\rm ips} \boldsymbol{\phi}^s\_{qr} \right)}{c} + \frac{2\Delta\omega\_r}{\lambda} \frac{d\boldsymbol{\phi}\_r}{dt} \tag{55}$$

The rotor speed is estimated from the estimated flux using a hyper plane-based state equation.

#### *2.4. Neural Network Based Modified Model Reference Adaptive System Model*

The model reference adaptive system (MRAS) estimators are the peak conservative method because of their modest structure and they have less associated calculation obligations than the other approaches. The elementary diagram of the MRAS contains an adjustable model, reference model, and an adaption mechanism. After the speed tuning, the error signal is given to the adaptation mechanism that is a neural network-based controller block. Here the output of both models is processed up to the errors linking the two models which depart to zero. The prototype accepts the voltage and current of the stator and determines the flux vector of the rotor. An adaptation mechanism with a neural network-based controller block is used to adapt the speed, so that the speed error is zero. The reference model equations are given by Equations (56) and (57).

$$
\hat{\Psi}\_{dr}^{s} = \int \frac{-1}{T\_r} \left. \Psi^{s}\_{\,\,dr} - \omega\_r \left. \Psi^{s}\_{\,\,qr} + \frac{L\_{\text{II}}}{T\_I} \right. \right|\_{\,\,k} \tag{56}
$$

$$
\hat{\Psi}\_{qr}^{s} = \int \omega\_r \, \Psi\_{dr}^{s} - \frac{1}{T\_r} \, \Psi\_{qr}^{s} + \frac{L\_{\text{ll}}}{T\_r} \, i\_{qs}^{s} \tag{57}
$$

The neural network-based Adaptive model equations are given by the following equations.

$$O\_k = \sum\_{j=1}^j \omega\_{kj} \oslash\_j(\mathbf{x}) \tag{58}$$

$$
\omega\_{kj}(t+1) = \omega\_{kj}(t) + \eta e(t)\mathcal{Q}\_j \tag{59}
$$

$$c\_{\dot{\jmath}}(t+1) = c\_{\dot{\jmath}}(t) + \frac{\eta c(t) \mathcal{Q}\_{\dot{\jmath}} \omega\_{\dot{\jmath}}(\mathbf{x} - \mathbf{c}\_{\dot{\jmath}})}{\sigma^2} \tag{60}$$

$$\mathcal{Q}\_{\dot{j}}(\mathbf{x}) = \exp\left[\frac{-||\mathbf{x} - \mathbf{c}\_{\dot{j}}||^{2}}{\sigma^{2}\_{\dot{j}}}\right] \tag{61}$$

$$
\sigma\_{\dot{\jmath}}(t+1) = \sigma\_{\dot{\jmath}}(t) + \eta e(t) \mathcal{Q}\_{\dot{\jmath}} \omega\_{\dot{\jmath}} || \mathbf{x} - \mathbf{c}\_{\dot{\jmath}} || \frac{1}{\sigma^3} \tag{62}
$$

$$
\Psi\_{dr}^{s} = \int \frac{-1}{T\_r} \left. \Psi\_{dr}^{s} - \omega\_r \psi\_{qr}^{s} + \frac{L\_m}{T\_r} \dot{r}\_{ds}^{s} \tag{63}
$$

$$
\hat{\psi}\_{qr}^{s} = \int \omega\_r \,\psi\_{dr}^{s} - \frac{1}{T\_r} \,\psi\_{qr}^{s} + \frac{L\_m}{T\_r} \, i\_{qs}^{s} \tag{64}
$$

The error signal is given by Equation (65). It is being fed to the P-I regulator to obtain the speed signal (66).

$$
\xi = \hat{\psi}\_{dr}^{s} \,\,\hat{\psi}\_{qr}^{s} - \hat{\psi}\_{dr}^{s} \,\,\hat{\psi}\_{qr}^{s} \tag{65}
$$

$$
\omega\_r = \zeta^\mathbf{r} \left( K\_p + \frac{K\_1}{\mathbf{s}} \right) \tag{66}
$$

The rotor speed is estimated from the estimated flux of the neural network-based model reference adaptive system.

#### *2.5. Modified Extended Kalman Filter Method*

R.E. Kalman proposed the method of an Extended Kalman filter (EKF) method in the year 1960. He put out his exalted paper describing an iterative answer to the digital-data linear trickling issues. An iterative estimator is a Kalman filter. This implies that only the evaluated state from the precedent time step and the measurement of current are required to tally the evaluation for the present state. In contradiction to bundle guesstimation methods, no background of observations and evaluation is compulsory. It is bizarre in being solely a time domain filter. The Kalman filter has two incisive phases: predict and update. The forecast phase manipulates the state evaluation from the preceding time step to outgrow an evaluation of the state at the current time step. In the upgraded phase, calculated data at the prevailing time step is utilized to clarify this prophecy to appear at a recent, (hopefully) more authentic state estimate, again for the current time step. In the collected works, a trendy technique for the data guesstimation of IM is the EKF. Typical ambiguity and nonlinearities innate to the induction motor are highly beneficial for the speculative identity of EKF. Using this technique, it is likely to develop the networked approximation of states while acting on the concurrent interconnection of data in a reasonably smaller time gap, also captivating the structure and measurement noises exactly into annals. This is the logic behind the EKF, which has developed an ample utilization spectrum in the sensor-less regulation of IMs, even if it is estimated intricacy. In this proposed method, the filter equation is altered by including a sliding hyper plane, and this will improve the performance of the system. The rotor voltage equations are given by (67).

$$
\dot{\Psi}^{s}{}\_{qr}R\_r + \frac{d}{dt}\left(\psi^{s}{}\_{qr}\right) - \omega\_r \left.\psi^{s}{}\_{dr} = 0\tag{67}
$$

From the voltage model of flux guesstimation, the rotor axis flux is given by

$$
\Psi\_{\;\;qr}^{\;\!\!s} = \;L\_{\;m}\dot{\imath}\_{\;\;qs}^{\;\!\!s} + \;L\_{\;r}\dot{\imath}\_{\;\;qr}^{\;\!\!s} \tag{68}
$$

$$
\dot{M}\_{dr}^{s} \, R\_{l} + \frac{d}{dt} (\psi\_{\, dr}^{s}) + \omega\_{r} \psi\_{\, qr}^{s} = 0 \tag{69}
$$

*Energies* **2019**, *12*, 920

$$
\psi^s\_{\;\;dr} = L\_m \mathfrak{i}^s\_{\;\;ds} + L\_r \mathfrak{i}^s\_{\;\;dr} \tag{70}
$$

After eliminating *i s dr* and *i s qr*

$$\frac{d}{dt}(\boldsymbol{\psi}^{s}{}\_{dr}) = -\frac{R\_{r}}{L\_{r}}\boldsymbol{\psi}^{s}{}\_{dr} - \omega\_{r}\boldsymbol{\psi}^{s}{}\_{qr} + \frac{L\_{m}R\_{r}}{L\_{r}}\,\dot{\mathbf{r}}^{s}{}\_{ds} \tag{71}$$

$$\frac{d}{dt} \left( \boldsymbol{\psi}^{s}{}\_{qr} \right) = -\frac{R\_r}{L\_r} \boldsymbol{\psi}^{s}{}\_{qr} + \omega\_r \boldsymbol{\psi}^{s}{}\_{dr} + \frac{L\_m R\_r}{L\_r} \boldsymbol{\psi}^{s}{}\_{qs} \tag{72}$$

$$\frac{d}{dt}(\psi^s\_{\,\,dr}) = \frac{L\_r}{L\_m} \, V^s\_{\,\,ds} - \frac{L\_r}{L\_m} \, (R\_s + \sigma L\_s S) \dot{r}^s\_{\,\,ds} + N(k) \tag{73}$$

$$\frac{d}{dt}\left(\boldsymbol{\psi}^{\boldsymbol{s}}{}\_{\boldsymbol{q}\boldsymbol{r}}\right) = \frac{L\_{\boldsymbol{r}}}{L\_{m}}\,\boldsymbol{V}^{\boldsymbol{s}}{}\_{\boldsymbol{q}\boldsymbol{s}} - \frac{L\_{\boldsymbol{r}}}{L\_{m}}\,(\boldsymbol{R}\_{\boldsymbol{s}} + \sigma L\_{\boldsymbol{s}}\mathcal{S})\boldsymbol{i}^{\boldsymbol{s}}{}\_{\boldsymbol{q}\boldsymbol{s}} + \boldsymbol{N}(\boldsymbol{k})\tag{74}$$

$$\frac{d}{dt}(\dot{\mathbf{r}}^{\rm s}\_{\rm ds}) = -\frac{\left(L^{2}\_{\rm m}R\_{\rm r} + L^{2}\_{\rm r}R\_{\rm s}\right)}{\sigma L\_{\rm s}L^{2}\_{\rm r}}\dot{\mathbf{r}}^{2}\_{\rm ds} + \frac{L\_{\rm m}R\_{\rm r}}{\sigma L\_{\rm s}L^{2}\_{\rm r}}\boldsymbol{\Psi}^{\rm s}{}\_{\rm dr} + \frac{L\_{\rm m}\omega\_{\rm r}}{\sigma L\_{\rm s}L\_{\rm r}}\boldsymbol{\Psi}^{\rm s}{}\_{\rm qr} + \frac{1}{\sigma L\_{\rm s}}\boldsymbol{V}^{\rm s}{}\_{\rm ds} + \mathcal{N}(\boldsymbol{k})\tag{75}$$

$$\frac{d}{dt}(\dot{\mathbf{f}}^{s}{}\_{qs}) = -\frac{\left(L^{2}{}\_{m}\mathbf{R}\_{r} + L^{2}{}\_{r}\mathbf{R}\_{s}\right)}{\sigma\mathbf{L}\_{s}L^{2}{}\_{r}}\,\dot{\mathbf{f}}^{2}{}\_{qs} + \frac{L\_{m}\mathbf{R}\_{r}}{\sigma\mathbf{L}\_{s}L^{2}{}\_{r}}\,\boldsymbol{\Psi}^{s}{}\_{qr} - \frac{L\_{m}\omega\_{r}}{\sigma\mathbf{L}\_{s}L\_{r}}\,\boldsymbol{\Psi}^{s}{}\_{dr} + \frac{1}{\sigma\mathbf{L}\_{s}}\,\boldsymbol{V}^{s}{}\_{qs} + \mathcal{N}(\boldsymbol{k})\tag{76}$$

Therefore, the desired state equation is given by

$$\frac{d}{dt}\left(X\right) = AX + BV\_s + N(k)\tag{77}$$

$$X = \begin{bmatrix} i\_{ds} & i\_{qs} & \Psi\_{dr} & \Psi\_{qr} \end{bmatrix}^T \tag{78}$$

$$V = \begin{bmatrix} V\_{ds} & V\_{qs} & 0 & 0 \end{bmatrix}^T \tag{79}$$

$$A = \begin{bmatrix} -\frac{L\_m^2 R\_r + L\_r^2 R\_s}{\sigma L\_s L\_r^2} & 0 & \frac{L\_m R\_r}{\sigma L\_s L\_r} & \frac{L\_m \omega\_r}{\sigma L\_s L\_r^2} \\ 0 & -\frac{L\_m^2 R\_r + L\_r^2 R\_s}{\sigma L\_s L\_r^2} & -\frac{L\_m \omega\_r}{\sigma L\_s L\_r^2} & \frac{L\_m R\_r}{\sigma L\_s L\_r} \\ \frac{L\_m R\_r}{L\_r} & 0 & -\frac{R\_r}{L\_r} & -\omega\_r \\ 0 & \frac{L\_m R\_r}{L\_r} & \omega\_r & \frac{R\_r}{L\_r} \end{bmatrix} \tag{80}$$

$$B = \begin{bmatrix} \frac{1}{\sigma L\_s} & 0\\ 0 & \frac{1}{\sigma L\_s} \\ 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{bmatrix} \tag{81}$$

$$\mathbf{C} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \tag{82}$$

The dynamic equation is modified by altering the hyper plane, and the Filter equation is given by (83)

$$\frac{d\hat{\mathcal{K}}}{dt} = \left[\hat{A}\right]\hat{\mathcal{K}} + \left[B\right]u + k\_{\text{sw}}sat\left(i\_{\text{s}} - i\_{\text{s}} - \hat{d}\right) \tag{83}$$

$$S = i\_s - i\_s - \hat{d} \tag{84}$$

$$d = k \overbrace{T\_{dis}}^{-} \text{ and } \mathfrak{Y} = [\mathbb{C}] \mathfrak{X} \tag{85}$$

$$
\widehat{T\_{\rm dis}}^{-} = T^\* \, \_c - j \frac{d\widehat{v}\widehat{v}}{dt} - B\_v \, \widehat{\omega} \tag{86}
$$

The speed adaptation algorithm is given by

$$
\omega\_r = \mathcal{K}\_p \left( \varepsilon\_{\rm ids} \,\psi\_{\rm qr}^s - \varepsilon\_{\rm iqs} \,\psi\_{\rm dr}^s \right) + \mathcal{K}\_1 \int \left( \varepsilon\_{\rm ids} \,\psi\_{\rm qr}^s - \varepsilon\_{\rm iqs} \,\psi\_{\rm dr}^s \right) \,\mathrm{d}t \tag{87}
$$

The parameters of the induction motor illustrated in Table 1 are estimated for the 2.2 kW of the induction motor by a conventional direct current Resistance test, no load, blocked rotor test, and retardation test.


**Table 1.** Machine parameters.

#### **3. Simulation Results and Discussions**

In sensor-less method regulation of an induction motor drive process the vector regulation without a speed sensor. For closed loop operations, the speed encoder is mandatory in both decoupling and scalar regulation drive. In the vector regulation with indirect form, a signal of speed is mandatory for the entire operation. A speed encoder is objectionable in the drive as it adds rate and consistency snags beyond the requirement for shaft enlargement and the mounting arrangements. It is important to evaluate the wave of speed from the currents and voltages of a machine terminal with the Digital signal processor (DSP). However, the guesstimation is commonly intricate and profoundly reliant on the parameters of the machine. While the regulation of without-sensor drives are free at this time, the change in parameter, predominantly closer to zero speed, enacts a provocation in the exactness of speed guesstimation [21].

For large routine, changeable speed solicitations, the poly-phase asynchronous motors are used broadly because of having less rate, powerfulness, and less maintenance, and thus, they substitute the direct current motor drives. To achieve better torque and efficiency, the speed regulation of the induction motor is important. The dynamic modelling of a quinary phase induction motor is simulated in Matlab software. The phase voltages are converted into d-q axis voltages in three phases to a two phase lock. The speed and torque of the quinary phase induction motor have been estimated. The dynamically modelled induction motor in the quinary phase has 66% reduced torque pulsations and better linearity in the speed of the rotor, and also speed has been increased by 50% when compared to the induction motor in three phases as illustrated in Figures 1 and 2 and Table 2.

**Figure 1.** Speed response of dynamically modelled induction motor: (**a**) proposed five phase motor and (**b**) conventional three phase motor.

**Figure 2.** Torque response of dynamically modelled induction motor: (**a**) proposed five-phase motor and (**b**) conventional three-phase motor.


**Table 2.** Performance comparison of three- and poly-phase induction motor.

#### *3.1. Conventional Direct Synthesis Method*

The speed guesstimation of the quinary phase induction motor using the direct synthesis method has been executed. The direct axis and quadrature axis fluxes are obtained using a current model block. The speed of the quinary phase motor has been approximated using the direct synthesis method. It can be seen that there is some difference between the estimated value and the reference value, so the accuracy of this method is low. Some speed pulsations of high magnitude are also present in the estimated speed. The estimated speed obtained using the direct synthesis method and reference speed has been demonstrated in Figure 3.

**Figure 3.** Estimated speed of a quinary phase induction motor obtained using Direct Synthesis Method.

#### *3.2. Neural Network Based Model Reference Adaptive System*

The speed guesstimation using MRAS is executed in MATLAB software. The d and q axis voltages and currents obtained from dynamic model block [22] are fed to MRAS regulation, and the estimated speed is feedback to the adjustable model as shown in Figure 4.

**Figure 4.** Model Reference Adaptive System.

The estimated speed of the quinary phase induction motor obtained using the MRAS method and the reference speed of the motor is demonstrated in Figure 5. The speed of the quinary phase motor has been approximated using the Model Reference Adaptive System method. It is observed that the estimated value and reference values are almost the same, thus offering good accuracy in guesstimation.

**Figure 5.** Estimated speed of the quinary phase induction motor obtained using Model Reference Adaptive Method.

#### *3.3. Modified Luenberger Observer Technique*

The speed guesstimation using the Luenberger observer method is executed in MATLAB software. This is illustrated in Figure 6. The speed response from the speed estimation using a Luenberger observer results in a small steady state error of 9 rpm, and the settling time took more than 2 s, which is high compared to all other methods.

**Figure 6.** Estimated speed of the quinary phase induction motor obtained using a Luenberger observer method.

#### *3.4. Modified Extended Kalman Filter*

The speed guesstimation using the Kalman Filter method is being executed in MATLAB software. It can be observed from Figure 7 that the steady state error becomes zero and the settling time is also reduced drastically.

**Figure 7.** Estimated speed of the quinary phase induction motor obtained using Kalman Filter Method.

Speed pulsations of high magnitude are being observed in the estimated speed obtained by the direct synthesis method, which is not desirable. The rotor speed has been estimated using the direct synthesis method, model reference adaptive system, Luenberger observer method, and Kalman filter method. From the transient analysis, for the estimated speed obtained using these methods, the accuracy is better for the Kalman filter method because a steady-state error is zero and also the settling time is minimum compared to the other methods, so the speed reaches a stable state quickly. The Kalman filter enjoys very low settling time compared to all the above-mentioned guesstimation techniques that are depicted in Table 3.

The extended Kalman filter is the most popularly used observer in induction motor drive due to its nonlinearities and robustness of parameter variations. Conventionally, the covariance matrix and the parameters are tuned by a trial and error method. Due to the trial and error method, complexity and computational time is high. Based on the obtained model of a modified, extended Kalman filter, the computational time has been reduced.


**Table 3.** Comparison of the guesstimation techniques by time domain analysis.

#### **4. Speed Deviation and Torque Ripple Reduction of Induction Motor Drive in Parallel Using Extended Kalman Filter**

It is observed in both the simulation and hardware that the speed control of the induction motor is a challenging problem in the absence of a power electronics component [23,24]. In the proposed method, the induction motor with estimated parameters for sensor-less drive is analysed and compared with a conventional space vector modulation-based induction motor drive with a speed sensor. As no sensors are used, it makes the system more rugged, stable, less costly, and reduce in size. The two bogies setup where considered in this proposed method for electric traction locomotive application.

The speed of the five phase induction motor is estimated by the direct synthesis method, modified model reference adaptive system, Luenberger observer, and extended Kalman filter. From the above-mentioned speed estimation techniques, the extended Kalman filter has better performance than the other three methods. The speed and torque performance of the proposed method were analysed under the change in stator resistance, rotor resistance, low speed, and low inertia and compared with the conventional method. Here the proposed method is considered for electric traction locomotive application.

The speed response of the proposed method under normal conditions and parameter variations is shown in Figures 8 and 9 respectively. In the rotor speed curve, the reference speed represented in yellow colour is matched to the estimated speed represented in red colour, and the actual speed is displayed in blue colour. The speed response of the conventional method under normal condition and parameter variations is as shown in Figures 10 and 11 respectively. The speed error is far less in the proposed method, and it is robust to parameter variation compared to the conventional method. The speed error has been reduced by 70% in the proposed method compared to the conventional method.

**Figure 8.** Speed response of proposed sensorless induction motor drive under normal running conditions using Extended Kalman filter: (**a**) induction motor 1 and (**b**) induction motor 2.

**Figure 9.** *Cont.*

**Figure 9.** Speed response of proposed sensorless induction motor drive under parameter variations using Extended Kalman filter: (**a**) change in stator resistance, (**b**) change in rotor resistance, (**c**) low speed, and (**d**) low inertia.

**Figure 10.** *Cont.*

**Figure 10.** Speed response of inverter-fed induction under normal running conditions using a conventional space vector modulation-based induction motor drive with a speed sensor: (**a**) induction motor 1 and (**b**) induction motor 2.

**Figure 11.** *Cont.*

**Figure 11.** Speed response of inverter-fed induction motor under parameter variations using a conventional space vector modulation-based induction motor drive with a speed sensor: (**a**) change in stator resistance, (**b**) change in rotor resistance, (**c**) low speed, and (**d**) low inertia.

For the rotor speed, curve deviation is large compared to the proposed method. In the electromagnetic torque curve, the torque ripple is less in the proposed method compared to the conventional method as demonstrated in Figures 12–15 respectively. The torque ripple is reduced by 85% in the proposed method compared to the conventional method.

**Figure 12.** Torque response of induction motor drive under normal conditions for proposed method: (**a**) induction motor 1 and (**b**) induction motor 2.

**Figure 13.** *Cont.*

**Figure 13.** Torque response of induction motor drive under normal condition for conventional method: (**a**) induction motor 1 and (**b**) induction motor 2.

(**c**)

**Figure 14.** Torque response of induction motor drive under parameter variations for proposed method: (**a**) change in stator resistance, (**b**) low speed, and (**c**) low inertia.

**Figure 15.** Torque response of induction motor drive under normal conditions for conventional method: (**a**) change in stator resistance, (**b**) change in rotor resistance, (**c**) low speed, and (**d**) low inertia.

The robustness of the proposed extended Kalman filter-based sensorless induction motor drive is compared with the conventional method. The robustness of the proposed method is proved by varying the stator resistance, rotor resistances, inertia, and step change in speed; also, under the low-speed region, it is proved that even though parameters varied, the performances are not affected compared to the conventional method.

#### *Inference of Result*

In the proposed method, the torque ripple is reduced by 85% and speed deviation reduced by 70% more than the conventional one. The performance is robust for parameter variations like a change in stator resistance, rotor resistance, low frequency, low inertia, the step change in speed, and low speed. The five phase induction motor has better performance than three phase induction motor in terms of torque ripple and speed error.

Speed pulsations of high magnitude are observed in the estimated speed obtained by the conventional direct synthesis method presented in B.K. Bose, which is not desirable in terms of response time compared to the proposed methods presented in the article. The conventional space vector modulated induction motor drive with a speed sensor has a high amplitude of torque ripple, ultra-low resolution rotary encoder, and it is difficult to realize proper control not robust for faulty environmental situations. The above-mentioned difficulties have been corrected in the proposed method of a sensor-less drive presented in this article.

#### **5. Hardware Results and Discussion**

The performance acquired in the simulation is analysed experimentally in hardware setup also. The hardware setup for the sensor-based induction motor drive shown in Figure 16. The no-load test is performed on two motors connected in parallel. It is observed that the size and cost of the device are high. Thus, variable speed control becomes very difficult for this condition. The above-mentioned difficulties have been rectified in this proposed sensorless drive. The hardware setup for the sensorless drive is illustrated in Figure 17. Twenty-five percent of the size and cost of the system has been reduced in the proposed method.

The difference between set speed and actual speed becomes nearly zero, and the speed deviation between the two motors is less in the proposed method compared to the conventional method as depicted in Figures 18 and 19 and in Tables 4–7.

**Figure 16.** Hardware setup for conventional method.

**Figure 17.** Hardware setup for proposed method.

**Table 4.** Speed response of conventional method under normal conditions.


**Table 5.** Speed response of conventional method under parameter variations.


**Table 6.** Speed response of proposed method under normal conditions.



**Table 7.** Speed response of proposed method under parameter variations.

**Figure 18.** Speed response of proposed method: (**a**) normal conditions and (**b**) parameter variations.

(**a**)

**Figure 19.** *Cont.*

**Figure 19.** Speed response of conventional method: (**a**) normal conditions and (**b**) parameter variation.

#### **6. Conclusions**

The dynamically modelled quinary phase induction motor has reduced torque pulsations and better linearity in the rotor speed when compared to those of a three-phase induction motor. The rotor speed has been estimated using the conventional direct synthesis method, neural network-based model reference adaptive system, modified Luenberger observer, and extended Kalman filter methods. Comparing the estimated speed obtained using these methods, the accuracy is best for the Kalman filter method. Speed pulsations of high magnitude are observed in the estimated speed obtained by the direct synthesis method, which is not desirable. The Kalman filter employs very low settling time compared to all the above-mentioned guesstimation techniques. The minimization of speed error and torque ripple for the sensorless induction motor drive has been achieved. The hardware setup was implemented for the above-mentioned sensorless drive.

The current limiting factor of this proposed sensorless induction motor drive based on field-oriented control with proportional integral controller has ideal integration problems due to direct current offset, and, in addition, performance is not adequate at zero speed and low frequency. In future, the author will implement the modified model predictive control-based sensor-less induction motor drive for traction applications to improve the performance under zero speed and low-frequency conditions because of the speed characteristics of traction drive including the zero speed stat-up.

**Author Contributions:** Investigation, Software, Validation, Writing—original draft, Methodology, S.U.; Project administration, Supervision, Writing—review & editing, C.S.; Resources, S.P.

**Funding:** The research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Torque Distribution Algorithm for an Independently Driven Electric Vehicle Using a Fuzzy Control Method: Driving Stability and Efficiency**

#### **Jinhyun Park 1,2, In Gyu Jang <sup>3</sup> and Sung-Ho Hwang 1,\***


Received: 30 October 2018; Accepted: 11 December 2018; Published: 13 December 2018

**Abstract:** In this paper, an integrated torque distribution strategy was developed to improve the stability and efficiency of the vehicle. To improve the stability of the low friction road surface, the vertical and lateral forces of the vehicle were estimated and the estimated forces were used to determine the driving torque limit. A turning stability index comprised of vehicle velocity and desired yaw rate was proposed to examine the driving stability of the vehicle while turning. The proposed index was used to subdivide turning situations and propose a torque distribution strategy, which can minimize deceleration of the vehicle while securing turning stability. The torque distribution strategy for increased driving stability and efficiency was used to create an integrated torque distribution (ITD) strategy. A vehicle stability index based on the slip rate and turning stability index was proposed to determine the overall driving stability of the vehicle, and the proposed index was used as a weight factor that determines the intervention of the control strategy for increased efficiency and driving stability. The simulation and actual vehicle test were carried out to verify the performance of the developed ITD. From these results, it can be verified that the proposed torque distribution strategy helps solve the poor handling performance problems of in-wheel electric vehicles.

**Keywords:** in-wheel electric vehicle; independent 4-wheel drive; torque distribution; fuzzy control; traction control; active yawrate control

#### **1. Introduction**

Eco-friendly vehicles have become a primary research issue due to problems like environmental pollution and energy resources. Hybrid electric vehicles have already gone beyond the commercialization stage and taken a large portion of the automobile market, and purely electric vehicles are expected to gradually appear in the automobile market after commercialization [1–5].

The biggest reasons for reluctance in purchasing electric vehicles are the expensive price and short driving distance on a single charge. However, these two factors are in a trade-off relationship with each other. Although battery capacity is the most important factor that determines driving distance on a single charge, increase of battery volume is the biggest factor that increases the price of vehicles. Therefore, important research topics for commercialization of electric vehicles would be to select a battery with appropriate capacity and maximize driving distance through efficient use of the selected battery [6–11].

Electric vehicles with in-wheel motors have advantages like fast response and easy embodiment of active driving safety systems like TCS (Traction Control System), ABS (Anti Brake-lock System) and VDC (Vehicle Dynamic System) without adding additional actuators due to independent driving control of each wheel. Therefore, existing studies on the in-wheel system were mainly focused on improving linear driving performance, improving driving stability during turns, improving turn performance through torque vectoring, and controlling the slip on low-friction roads and asymmetric roads. However, such a vehicle dynamic control system has a problem that it influences the driving efficiency badly only considering the stability of the driving [1–11].

Gu proposed a method of optimizing efficiency of in-wheel electric vehicles through two-wheel/four-wheel conversion by considering the loss of motor and inverter [12]. However, there are many difficulties in maximizing the efficiency of a motor simply based on a two-wheel/four-wheel conversion. Lin proposed a driving strategy that uses DOE (Design of experiments) to derive the optimal driving torque ratio of a motor according to the velocity and accelerator pedaling [13], but failed to account for energy optimization while braking. Chen proposed a driving force distribution strategy to optimize the efficiency of a motor by predicting geographical conditions using GPS and GIS signal [14,15]. Such a control strategy has to be preceded by accurate positioning of vehicles, and it requires a high-precision GPS sensor. It is difficult to use a high-precision GPS sensor in mass-produced vehicles because of the high price. Xu proposed a regenerative braking control strategy to optimize the efficiency and braking performance of electric vehicles using a fuzzy control technique [16]. As such, several studies attempted to increase the efficiency of in-wheel electric vehicles, but most of these studies only focus on braking or driving and lack the consideration of reduced driving stability.

In this study, a torque distribution strategy considering driving stability and efficiency was proposed. In order to improve the stability of the low friction road surface, the vertical force and the lateral force of the vehicle were estimated and the limit driving torque was determined using the estimated force. A fuzzy-based cornering stability index was suggested, and a torque distribution strategy based on turning conditions was proposed. The vehicle stability index using the slip ratio and cornering stability index is proposed. An integrated torque distribution strategy was created using the proposed driving stability index and the torque distribution strategy for increased efficiency. A simulation and an actual vehicle test were conducted to verify the proposed algorithm

#### **2. Vehicle Stability Control**

The target vehicle is driven through four in-wheel motors. At this time, the driving/braking torque is determined by the driver's accelerator pedal or brake pedal. However, if the torque is controlled by merely reflecting the will of the driver, the vehicle may fall into an unstable state. Therefore, in this study, the stability of the vehicle is secured through slip control, yaw rate control.

#### *2.1. Slip Control*

Figure 1 shows Coulomb's friction circle [17]. The friction circle indicates that the vector sum of the longitudinal force and lateral force of the tire is less than or equal to the product of the normal force and the friction coefficient of the road surface [18–20].

$$
\mu F\_z \ge \sqrt{F\_x^2 + F\_y^2} \tag{1}
$$

where *μ* is the coefficient of friction, *Fz* is the normal force of the tire, *Fx* is the longitudinal force of the tire, and *Fy* is the lateral force of the tire. In order for the vehicle to perform stable driving, the driving and braking forces should be kept not to exceed the friction circle, which is expressed as follows:

$$F\_{\text{Tx\\_max}} = \sqrt{\left(\mu F\_z\right)^2 - F\_y^2} \tag{2}$$

*Fx\_max* denotes the maximum drive and braking force determined by the friction circle. In other words, the driving force limit can be obtained when the road friction coefficient, the normal force and the

lateral force are known. However, the normal force cannot be measured from the sensor during the driving in real time, so Equation (3) is needed to get normal force values.

$$\begin{cases} F\_{zfl} = \frac{1}{2} \frac{L\_r}{L} mg - \rho\_f a\_y m \frac{h\_x}{l\_f} - a\_X m \frac{h\_y}{L} \\ F\_{zfr} = \frac{1}{2} \frac{L\_r}{L} mg + \rho\_f a\_y m \frac{h\_y}{l\_f} - a\_X m \frac{h\_x}{L} \\ F\_{zrl} = \frac{1}{2} \frac{L\_f}{L} mg - \rho\_f a\_y m \frac{h\_y}{l\_f} + a\_x m \frac{h\_x}{L} \\ F\_{zrr} = \frac{1}{2} \frac{L\_f}{L} mg + \rho\_f a\_y m \frac{h\_y}{l\_f} + a\_x m \frac{h\_y}{L} \end{cases} \tag{3}$$

where *Fzfl*, *Fzfr*, *Fzrl* and *Fzrr* are the normal force of each tire. g is the gravitational acceleration. Front and rear roll stiffness distributions are defined as *ρ<sup>f</sup>* and *ρr*. *hg* means the height of the center of gravity, and the accelerations of longitudinal direction and lateral direction are *ax* and *ay*. *tf* and *tr* are the front and rear tread lengths of the vehicle. *L* is the wheelbase, *Lf* and *Lr* are the distance from the center of gravity to the front wheel and rear wheel.

**Figure 1.** Concept of friction circle.

Lateral acceleration is generated in the vehicle when turning, and the lateral force is generated in the tire in order to cope with lateral acceleration. In this paper, the Dugoff tire model is used to formulate the nonlinear characteristics of the lateral forces in the tire [20,21].

The Dugoff tire model expresses the lateral force of a nonlinear tire as a function of the slip angle (*α*), the longitudinal slip rate (*λx*), the cornering stiffness (*Cα*) and the tire longitudinal stiffness (*Cλ*) that occur in each tire. Since the cornering stiffness and longitudinal stiffness of an actual tire are very different, the Dugoff tire model enables more precise tire behavior analysis compared with a linearly-expressed formula proportional to the cornering stiffness. In addition, in the actual Dugoff tire model, it is assumed that the vertical force of the tire is constant, but in this paper, the change is reflected including the previously estimated vertical force. However, the cornering stiffness is assumed to be a constant.

$$\begin{cases} \alpha\_f = \delta\_f - \frac{V\_y + L\_f \gamma}{V\_x} \\ \alpha\_r = -\frac{V\_y - L\_r \gamma}{V\_x} \end{cases} \tag{4}$$

$$\begin{array}{l} \lambda\_x = \frac{V\_x - r\omega\_w}{V\_y} \text{ (during breaking)}\\ \lambda\_x = \frac{r\omega\_w - V\_x}{r\omega\_w} \text{ (during acceleration)} \end{array} \tag{5}$$

where *δ<sup>f</sup>* is the front wheel steering angle, *γ* is the yawrate of the vehicle, *r* and *ω<sup>w</sup>* are the effective radius of rotation and angular velocity of the tire respectively. Cornering stiffness and tire longitudinal stiffness are *C<sup>α</sup>* and *Cλ*. The tire lateral force using the Dugoff tire model is expressed as follows:

$$F\_y = \mathbb{C}\_a \frac{\tan(\alpha)}{1 + \lambda\_x} f(\kappa) \tag{6}$$

where *f*(*κ*) and the variable κ are obtained as follows:

$$f(\kappa) = \begin{cases} (2-\kappa)\kappa & (\kappa < 1) \\ 1 & (\kappa \ge 1) \\ \frac{\mu F\_z(1+\lambda\_x)}{2\left[\left(\mathbb{C}\lambda\lambda\_x\right)^2 + \left(\mathbb{C}\_\hbar\tan(a)\right)^2\right]^{1/2}} & \end{cases} \tag{7}$$

Finally, the lateral forces generated on each tire using the Dugoff tire model are defined as follows:

$$\begin{aligned} F\_{yfl} &= \mathbb{C}\_{af} \frac{\tan(a\_{fl})}{1 + \lambda\_{xfl}} f(\kappa\_{fl}) \\ F\_{yfr} &= \mathbb{C}\_{af} \frac{\tan(a\_{fr})}{1 + \lambda\_{xfl}} f(\kappa\_{fr}) \\ F\_{yrl} &= \mathbb{C}\_{ar} \frac{\tan(a\_{rl})}{1 + \lambda\_{xl}} f(\kappa\_{rl}) \\ F\_{yrr} &= \mathbb{C}\_{ar} \frac{\tan(a\_{rr})}{1 + \lambda\_{xrr}} f(\kappa\_{rr}) \end{aligned} \tag{8}$$

A simulation was performed to verify the lateral forces estimated in this way. The simulation was performed using CarSim 8.0 and MATLAB/Simulink 2012a. Simulation parameters such as vehicle weight, wheelbase and tread lengths used for simulation were attached as an appendix, and parameters of vehicle velocity and acceleration were used assuming CarSim's data as sensor signals. Conditions of the simulation were set to a cruise driving situation after acceleration to 50 km/h with the steering angle fixed at 100◦. Figure 2 shows the simulation results. FL, FR, RL and RR mean front left wheel, front right wheel, rear left wheel and rear right wheel respectively. The simulation on the left side is the result of assuming the normal force of the Dugoff tire model as the normal force on each wheel when the vehicle is at a stop. The simulation on the right side is the result of using normal force predicted by Equation (3). A moving average filter was applied to secure the reliability of the predicted normal force value. Despite the fact that the vehicle reached normal turning status with an estimator based on fixed normal force, the error of maximum lateral force was about 800 N, showing an accuracy of about 79%. On the contrary, when the vehicle reached normal turning state with an estimator based on the predicted normal force, the error of maximum lateral force was about 140 N, showing an accuracy of about 95.3%. Especially, outer wheels that can a have direct effect on the driving stability of the vehicle while turning were found to have high accuracy in an excessive turning situation.

Using the normal force and the lateral force obtained above, the limit driving torque can be obtained as follows:

$$\begin{cases} T\_{\text{Slip\\_limit\\_fl}} = rF\_{\text{X\\_max\\_fl}} = r\sqrt{\left(\mu F\_{zfl}\right)^2 - F\_{yfl}^2} \\ T\_{\text{Slip\\_limit\\_fr}} = rF\_{\text{X\\_max\\_fr}} = r\sqrt{\left(\mu F\_{zfr}\right)^2 - F\_{yfr}^2} \\ T\_{\text{Slip\\_limit\\_rl}} = rF\_{\text{X\\_max\\_rl}} = r\sqrt{\left(\mu F\_{zrl}\right)^2 - F\_{yrl}^2} \\ T\_{\text{Slip\\_limit\\_rr}} = rF\_{\text{X\\_max\\_rr}} = r\sqrt{\left(\mu F\_{zrr}\right)^2 - F\_{yrr}^2} \end{cases} \tag{9}$$

**Figure 2.** Simulation results of estimated lateral force.

#### *2.2. Active Yawrate Control Considering Driving Efficiency*

The bicycle model has been used for the design of direct yaw moment control (DYC) in many previous researches. The desired yaw rate can be easily and exactly calculated to guarantee yaw stability based on the bicycle model through the driver's steering intention. As shown in Figure 3, the bicycle model indicates vehicle lateral dynamics in an assumption that wheels are located at the vehicle center line.

The dynamic equations of the bicycle model in terms of force balance and moment balance are expressed as follows [22]:

$$\begin{split} mV\_{x}(\dot{\beta} + \gamma) &= \mathbb{C}\_{f} \left( \delta\_{f} - \beta - \frac{L\_{f}\gamma}{\upsilon} \right) + \mathbb{C}\_{r} \left( -\beta + \frac{L\_{r}\gamma}{\upsilon} \right) \\ &\quad \ast \dot{\gamma} = L\_{f}\mathbb{C}\_{f} \left( \delta\_{f} - \beta - \frac{L\_{f}\gamma}{V\_{x}} \right) - L\_{r}\mathbb{C}\_{r} \left( -\beta + \frac{L\_{r}\gamma}{V\_{x}} \right) + M\_{\tilde{z}} \end{split} \tag{10}$$

where *β* is the body side slip angle, *γ* is the yaw rate, *m* is the vehicle mass, *Iz* is the vehicle yaw moment of inertia, *Vx* is the vehicle longitudinal velocity, and *Mz* is the correction yaw moment. *Lf* and *Lr* are the CG-front and CG-rear axle distances, *Fyf* and *Fyr* are the lateral tire forces of the front and

rear axle, respectively. *Cf* and *Cr* are the front and rear wheel cornering stiffness and *δ<sup>f</sup>* is the steering angle. State-space expression of the bicycle model is given as follows:

$$
\begin{bmatrix}
\dot{\mathcal{B}} \\
\dot{\gamma}
\end{bmatrix} = \begin{bmatrix}
\frac{-\mathbb{C}\_{f} - \mathbb{C}\_{r}}{mV\_{x}} & \frac{-mV\_{x}^{2} - L\_{f}\mathbb{C}\_{f} + L\_{r}\mathbb{C}\_{r}}{mV\_{x}^{2}} \\
\frac{-L\_{f}\mathbb{C}\_{f} + L\_{r}\mathbb{C}\_{r}}{I\_{z}} & \frac{-L\_{f}^{2}\mathbb{C}\_{f} - L\_{r}\mathbb{C}\_{r}}{V\_{x}I\_{z}}
\end{bmatrix} \begin{bmatrix}
\dot{\mathcal{B}} \\
\gamma
\end{bmatrix} + \begin{bmatrix}
\frac{\mathbb{C}\_{f}}{mV\_{x}} & 0 \\
\frac{L\_{f}\mathbb{C}\_{f}}{I\_{z}} & \frac{1}{I\_{z}}
\end{bmatrix} \begin{bmatrix}
\delta\_{f} \\
M\_{z}
\end{bmatrix} \tag{11}
$$

where *L* is the wheelbase. The desired yawrate can be expressed as a function of the steering angle *δ<sup>f</sup>* and the vehicle longitudinal velocity *Vx*. It is represented as follows:

$$\gamma\_d = \frac{V\_x}{L + \frac{mV\_x^2 \left(L\_r C\_r - L\_f C\_f\right)}{2C\_f C\_r L}} \delta\_f \tag{12}$$

(**a**) Full vehicle model (**b**) Bicycle model

**Figure 3.** Schematic diagram of full vehicle and bicycle lateral dynamics model.

The desired yaw moment to follow the desired yaw rate is defined as follows:

$$M\_z = I\_z \dot{\gamma}\_d + (\mathbb{C}\_f L\_f - \mathbb{C}\_r L\_r)\beta + \frac{\mathbb{C}\_f L\_f^2 + \mathbb{C}\_r L\_r^2}{V\_\chi} \gamma - \mathbb{C}\_f L\_f \delta - \eta I\_z (\gamma - \gamma\_d) \tag{13}$$

where *η* is a positive constant. In the lower controller, the control input in (13) consists of the individual tire forces generated by the in-wheel motor system. The correction yaw moment is obtained as follows:

$$M\_{\overline{z}} = t\_f \cos(\delta\_f)(F\_{\mathbf{x}fr} - F\_{\mathbf{x}fl}) + L\_f \sin(\delta\_f)(F\_{\mathbf{x}fr} + F\_{\mathbf{x}fl}) + t\_f \sin(\delta\_f)(F\_{\mathbf{y}fl} - F\_{\mathbf{y}fr}) + t\_l(F\_{\mathbf{x}rl} - F\_{\mathbf{x}rl}) \tag{14}$$

Assuming that the steering angle is small, sin(δ) is assumed to be zero. Equation (14) is rewritten as follows:

$$M\_z = t\_f \cos(\delta\_f) (F\_{xfr} - F\_{xfl}) + t\_r (F\_{xrr} - F\_{xrl}) \tag{15}$$

Since the VDC of an internal combustion engine vehicle or ordinary electric vehicle is difficult to control the driving force independently, the correction moment for over steering or under steering during a left turn is generated as shown in Figure 4. Such a correction moment can improve the driving stability of a vehicle, but it can decrease the velocity of the vehicle as well. Velocity decrease not only makes the driver feel odd while driving but also causes additional driving force, which leads to the low driving efficiency of the vehicle.

**Figure 4.** Correction yaw moment during left turn using brake.

To solve this problem, cornering situations were classified and a driving force distribution strategy was proposed as shown in Figure 5. Cornering situations are largely divided into three types, namely stable cornering, transient cornering and unstable cornering. Stable cornering is a driving situation in which the velocity of the vehicle is relatively slow and the desired yaw rate is low, so the driving torque of the motor is not expected to have a critical impact on driving stability. Thus, the correction yaw moment is generated through driving torque. Excessive cornering is a domain in which vehicle velocity and desired yaw rate have intermediate values. Since excessive driving torque can make the vehicle unstable, correction yaw moment is generated using both the driving force and braking force. Lastly, unstable cornering is a situation of high velocity or high desired yaw rate where the driving torque can greatly affect the driving stability. Correction yaw moment is generated only using braking force. To satisfy such rules, a controller needs to be comprised so that three yaw moment distribution strategies intervene according to the situation. However, there is a problem that excessive mode conversion occurs when the vehicle is operated around the mode conversion point. A Fuzzy controller was used to prevent excessive switching errors while fulfilling such a purpose. The fuzzy logic has been proposed to solve the problems of various logic which judged only the existing true and false, and it can output various values between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false [23]. Composition of the fuzzy controller is as presented in Table 1. The input membership function of the fuzzy controller includes the velocity of the vehicle and desired yaw rate. Output membership function outputs the cornering stability index (σ) with a value of 0~2. Cornering stability index indicates a stable cornering situation as it gets closer to 0 and an unstable cornering situation as it gets closer to 2. Final AYC (Active Yawrate Control) torque output is defined as Equation (16). The operating region of AYC is shown in Figure 6.

$$\begin{array}{llll}T\_{f\bot\bot Y\mathsf{C}} = & T\_{fl}(\mathit{ABS},\mathit{BPS}) \pm T\_{fl\text{-}stable}(1-\sigma) \pm T\_{fl\text{-}trans}(\sigma) & (\sigma \le 1) \\ & T\_{fl}(\mathit{ABS},\mathit{BPS}) \pm T\_{fl\text{-}trans}(2-\sigma) \pm T\_{fl\text{-}unstable}(\sigma-1) & (1<\sigma \le 2) \\ & T\_{fr\text{-}AYC} = & T\_{fr}(\mathit{ABS},\mathit{BPS}) \pm T\_{fr\text{-}stable}(1-\sigma) \pm T\_{fr\text{-}trans}(\sigma) & (\sigma \le 1) \\ & T\_{fr}(\mathit{ABS},\mathit{BPS}) \pm T\_{fr\text{-}trans}(2-\sigma) \pm T\_{fr\text{-}unstable}(\sigma-1) & (1<\sigma \le 2) \\ & T\_{rl}(\mathit{ABS},\mathit{BPS}) \pm T\_{rl\text{-}stable}(1-\sigma) \pm T\_{rl\text{-}trans}(\sigma) & (\sigma \le 1) \\ & T\_{rl}(\mathit{ABS},\mathit{BPS}) \pm T\_{rl\text{-}trans}(2-\sigma) \pm T\_{rl\text{-}unstable}(\sigma-1) & (1<\sigma \le 2) \\ & T\_{rr}\mathit{AVC} = & T\_{rr}(\mathit{ABS},\mathit{BPS}) \pm T\_{rr\text{-}stable}(1-\sigma) \pm T\_{rr\text{-}trans}(\sigma) & (\sigma \le 1) \\ & T\_{rr}(\mathit{ABS},\mathit{BPS}) \pm T\_{rr\text{-}trans}(2-\sigma) \pm T\_{rr\text{-}unstable}(\sigma-1) & (1<\sigma \le 2) \\ \end{array} \tag{16}$$

**Figure 5.** Correction yaw moment during left turn using in-wheel motor.

**Table 1.** Cornering stability Index.

**Figure 6.** Operating region of acitve yaw rate control.

#### *2.3. Integrated Driving Torque Distribution Strategy Considering Driving Efficiency and Stability*

When a vehicle accelerates or climbs a hill while driving, it requires a large amount of driving force. However, the desire of the driver can be followed without using the maximum torque of the motor in case of cruise drive or downhill drive. Generating same driving torque on four wheels makes it difficult to drive the motor in the efficient region. As a solution to this problem, a driving torque distribution strategy that appropriately distributes the driving force and regenerative braking force of the front and rear wheels according to the situation to improve the efficiency of the vehicle was proposed as described in previous paper [24]. However, since the developed distribution strategy is a strategy that considers driving efficiency in a stable situation, there is a problem of reducing driving stability of the vehicle in a rapid cornering situation or low-friction road situation. The following driving stability index (*ψ*) was proposed to solve this problem.

$$\psi = \frac{1}{\hat{\lambda}}(\lambda)(\lambda > 0.1) + \frac{1}{\hat{\lambda}}(\dot{\lambda})(\lambda > 0.1) + \frac{1}{\hat{\sigma}}(\sigma) + \frac{1}{\hat{\sigma}}(\dot{\sigma})\tag{17}$$

where *λ* is the slip rate, # *<sup>λ</sup>* is the slip rate limit, . *λ* is the differential value of slip rate, # . *λ* is the differential value limit of slip rate, *<sup>σ</sup>* is the cornering stability index, #*<sup>σ</sup>* is the cornering stability index limit, . *σ* is the differential value of cornering stability index, and # . *σ* is the differential value limit of the slip rate. Each term represents the ratio of the current value to the limit value that determines driving stability. For instance, if the slip rate limit is 0.2 and the current slip rate is 0.15, the stability index for slip rate of the vehicle is 0.75. The stability index is calculated for four variables, and the sum becomes the driving stability index of the vehicle. The inequality equation that constitutes the term that determines the stability of the slip rate was added to decide the stability of the slip rate only in the area where the slip rate becomes larger than 0.1 by considering the area with a slip rate smaller than 0.1 as a stable area. If one of four variables that constitute Equation (17) has a value larger than 1, the vehicle is considered to be in an unstable state and is controlled only using the torque for improving driving stability. However, if the value is between 0 and 1, the driving stability evaluation index is used as a weight factor to determine the intervention rate of the efficiency controller and driving stability controller. The final torque values determined are expressed by the equations as follows:

$$\begin{array}{l} T\_{fl\\_final} = T\_{fl\\_ST\mathcal{C}}(\psi) \pm T\_{fl\\_Eff}(1-\psi) \\ T\_{fr\\_final} = T\_{fr\\_ST\mathcal{C}}(\psi) \pm T\_{fr\\_Eff}(1-\psi) \\ T\_{rl\\_final} = T\_{rl\\_ST\mathcal{C}}(\psi) \pm T\_{rl\\_Eff}(1-\psi) \\ T\_{rr\\_final} = T\_{rr\\_ST\mathcal{C}}(\psi) \pm T\_{rr\\_Eff}(1-\psi) \end{array} \tag{18}$$

where *TSTC* is torque determined to improve the driving stability of the vehicle, and *TEff* is the torque value determined to increase the efficiency of the vehicle. The vehicle stability index has values from 0 to 1, and the values close to 1 equate to unstable values. If the vehicle stability index is 1, only the *TSTC* is determined to be the output torque by (1 − *ψ*) term, and if the evaluation index is 0, only the *Teff* is configured to be an output. Sometimes the final torque may exceed the *Tstc*, but the simulation found that the stability of the driving was less affected. It seems that when the final torque affects the driving stability of the vehicle, only the *Tstc* is output as the vehicle stability index becomes 1. The final torque, thus determined, controls the driving stability and efficiency of the vehicle through four in-wheel motors.

The block diagram of the integrated torque distribution strategy is shown in Figure 7. The torque distribution strategy for increased efficiency proposed in previous papers is located at the bottom of the block diagram. The slip controller and AYC proposed in this paper are located at the top of the block diagram. Driving efficiency and driving stability of the vehicle were secured in the end by determining the intervention rate of these two torque distribution strategies using the driving stability evaluation index.

The operating region of ITD is shown in Figure 8. In the area where the vehicle is determined to be stable, the distribution strategy for increased efficiency primarily intervenes. In the area where the instability of the vehicle increases, driving stability and driving efficiency are secured using the slip controller and AYC.

**Figure 7.** Integrated driving torque distribution strategy considering driving efficiency and stability.

**Figure 8.** Operating region of integrated driving torque distribution strategy.

#### **3. Simulation and Experimental Results**

#### *3.1. Double Lane Change Simulation*

A double-lane change simulation was performed to identify the effect of the proposed torque distribution strategy on the driving stability of the vehicle. The ISO double lane change test consists of an entry and an exit lane and has a length of 12 m and a side lane with a length of 11 m. The width of the entry and side lane are dependent on the width of the vehicle; the width of the exit lane is constantly 3 m wide. The lateral offset between the entry and side lane is 1 m and the longitudinal offset is 13.5 m. For the same lateral offset, the side and exit lane have a slightly shorter longitudinal displacement of 12.5 m. The simulation was performed at a target speed of 50 km/h to verify the performance of the AYC. Driving trajectory is shown in Figure 9. The road friction condition was 0.5 of a wet road. According to the simulation results, vehicles without a torque distribution strategy showed a large over shoot of about 0.46 m, whereas vehicles applied with the torque distribution strategy showed a small over shoot of about 0.18~0.19 m. Vehicles applied with AYC have similar behavior as vehicles applied with integrated torque distribution (ITD). Since this is a low velocity situation with a high desired yaw rate, the final driving torque determined by the vehicle stability index (*ψ*) places a greater priority on the driving stability control than the efficiency control.

Detailed simulation results are shown in Figures 10 and 11. The x-axis of each graph represents the time, and the y-axis represents the data and units of each graph title. FL, FR, RL and RR mean front left wheel, front right wheel, rear left wheel and rear right wheel respectively. The trend line for comparison was based on vehicles without a torque distribution strategy. Based on the comparison of motor torque, vehicles applied with AYC and ITD showed relatively similar tendencies, but torque output differs between 0~1 seconds section and 5~6 seconds section. As this section is a section in which the vehicle drives straight, the torque distribution strategy intervenes to improve driving efficiency. The steering wheel input is largest in vehicles without a torque distribution strategy, and cases applied with AYC and ITD show similar values. Based on the yaw rate of 1~4 seconds section, vehicles without a torque distribution strategy have a low yaw rate despite having larger steering input compared to other vehicles. This is probably caused by correction yaw moment according to the application of the torque distribution strategy. However, vehicles without a torque distribution strategy have the highest yaw rate in 4~5 seconds section. This section is the 55~65 m region of driving trajectory shown in Figure 9. Excessive steering value results from increasing the deviation from the driving path. Vehicles applied with AYC and vehicles applied with ITD have similarly small values of side slip angle, which is used to determine the driving stability of a vehicle while cornering. This is probably because if the vehicle without ITD is not able to follow the driver's desired path, the driver enters a larger steering angle. On the other hand, if the vehicle to which the ITD is applied does not follow the driver's desired path, ITD will assist with the motor driving torque, so the driver will maintain the small steering input. Thus, if the driver maintains a small steering input, the probability that the vehicle will go into an unstable state is reduced.

**Figure 9.** Target path and driving path of short double lane change (Target velocity: 50 km/h).

**Figure 10.** Simulation results of short double-lane change (No control, Fixed distribution).

(**a**) Active yawrate control (**b**) Integrated torque distribution

**Figure 11.** Simulation results of short double-lane change (AYC, ITD).

#### *3.2. Complex Driving Road Simulation*

A simulation was carried out to verify the overall performance of the proposed torque distribution strategy. Target driving path for the simulation and the result of driving according to the distribution strategy are shown in Figure 12. Road condition was configured as 0.5 of a wet road for driving stability assessment.

The simulation was performed on a case without a torque distribution strategy, a case with left and right fixing torque distribution, a case applied with active yaw rate control, and a case applied with integrated torque distribution. Comparing the results of driving trajectory, vehicles without a torque distribution strategy cannot follow the target driving path in the expanded region and roll over occurs. On the contrary, vehicles applied with the three torque distribution strategies show similar path following.

Figures 13 and 14 show detailed simulation results according to the application of each distribution strategy. The x-axis of each graph represents time, and the y-axis represents the data and units of each graph title. FL, FR, RL and RR mean front left wheel, front right wheel, rear left wheel and rear right wheel respectively. The results for points A, B and C were analyzed to compare the driving performance according to the distribution strategy. First, vehicles without the distribution strategy generate mostly identical torque in all motors despite a large amount of cornering at point A. Vehicles were found to deviate from the driving path due to a rapid increase of the yaw rate, side slip angle and slip ratio. The case applied with the left and right fixing torque distribution strategy and the case applied with AYC were found to maintain similar driving stability. However, the case applied with integrated torque distribution shows the reduced driving torque of the motor and maintains the slip ratio in a stable region compared to other distribution strategies because the slip controller intervenes at point A. However, it has a larger yaw rate and side slip angle compared to the other distribution strategies in section B-C. This is probably because the final driving torque determined by the vehicle stability index (*ψ*) places a greater priority on efficiency control. SOC (State of Charge) based on repeated driving of the driving path in Figure 12, intended to quantitatively compare driving efficiency according to the application of each distribution strategy, is shown in Figure 15. Driving distance based on SOC is shown in Table 2. The range of SOC is 0.8~0.7, and the driving distance from the use of 0.1 SOC was compared. The results for vehicles without a torque distribution strategy are not included because they could not be driven due to overturn. Looking at Table 2, the case applied with AYC showed total driving distance increased by about 3.87% compared to the case applied with the left and right fixing torque distribution strategy. Total driving distance was increased by about 10.93% in the case applied with integrated torque distribution. The proposed torque distribution strategy was found to increase driving efficiency while securing the driving stability of vehicles.

**Figure 12.** Target path and driving path for complex road.

**Figure 13.** Simulation results for complex driving road (No control, Fixed distribution).

**Figure 14.** Simulation results for complex driving road (AYC, ITD).

**Figure 15.** Simulation results of battery SOC for complex driving road.

**Table 2.** Simulation results of efficiency.


#### *3.3. Vehicle Test*

The actual vehicle experiment was conducted to determine the effect of the developed torque distribution strategy on the driving stability of the actual vehicle. Based on KIA automotive's gasoline ray model, the target vehicle was equipped with an in-wheel motor for independent driving. The experimental conditions were selected as follows.


The velocity of the vehicle must be found accurately to apply the proposed control algorithm to the vehicle and to perform performance verification. In this paper, an experiment was conducted using the velocity signal of RT 3000 mentioned earlier. RT 3000 has an inertial navigation system that has position accuracy of about 40 cm and a velocity accuracy of 0.1 km/h. Data output rate is 100 Hz, which secures data in real time. Figure 16 shows the Slalom test course. Figure 17 shows the actual experimental scene and the sensor used during the experiment. The photograph on the top right side is the sensor attached to the vehicle.

Figure 18 shows the driving test results according to the application of ITD. The x-axis of each graph represents time, and the y-axis represents the data and units of each graph title. FL, FR, RL and RR mean front left wheel, front right wheel, rear left wheel and rear right wheel respectively. Comparing the velocity results, the two vehicles were driven while maintaining similar velocity. However, whereas the vehicle not applied with ITD maintained constant motor-driving torque, the vehicle applied with ITD showed left and right driving torques change to follow the desired yaw

rate of the driver. Looking at the steering angle results, the vehicle applied with ITD showed a smaller steering angle compared to the vehicle not applied with ITD. This is probably because if the vehicle without ITD is not able to follow the driver's desired path, the driver enters a larger steering angle. On the other hand, if the vehicle to which the ITD is applied does not follow the driver's desired path, ITD will assist with the motor-driving torque, so the driver will maintain the small steering input.

To quantitatively compare the test results, the peak values of steering angle, yaw rate and lateral acceleration are presented in Table 3. The R.M.S value of the peak value of steering angle is 80.4 for the vehicle not applied with ITD and 55.8 for the vehicle applied with ITD, which is about 30.6% smaller. Also, since the vehicle applied with ITD was able to drive with a small radius of turning, the R.M.S value of the peak value of yaw rate was also decreased by about 6.5%. On the contrary, since the vehicle applied with ITD showed a sudden change of direction compared to the vehicle not applied with ITD, the R.M.S value of the peak value of lateral acceleration was increased by about 16.7%. The vehicle was confirmed to be driven in the path wanted by the driver with relatively small steering input through the application of ITD, contributing to improved driving stability of the vehicle.

**Figure 17.** Slalom test and measuring sensor.

**Figure 18.** Slalom test results (Target velocity: 40 km/h).


**Table 3.** Peak values of slalom test results.

#### **4. Conclusions**

An integrated torque distribution strategy was developed to improve the stability and efficiency of the vehicle. In order to improve the stability of the low friction road surface, the vertical force and the lateral force of the vehicle were estimated and the limit driving torque was determined using the estimated force. A turning stability index comprised of vehicle velocity and desired yaw rate of the driver was proposed to examine the driving stability of the vehicle while turning. The proposed index was used to subdivide the turning situations and to propose a torque distribution strategy which can minimize deceleration of the vehicle while securing turning stability. The torque distribution strategy for increased driving stability and the torque distribution strategy for increased efficiency proposed were used to create an integrated torque distribution strategy. A vehicle stability index based on the slip rate and turning stability index was proposed to determine the overall driving stability of the vehicle, and the proposed index was used as a weight factor that determines the intervention of the control strategy for increased efficiency and the control strategy for improved driving stability.

The simulation and actual vehicle test were carried out to verify the performance of the developed ITD. Based on the short double-lane change simulation on low-friction roads, the vehicle applied with ITD showed best path tracking and the smallest reduction of velocity. Based on the results of complex road simulation, the vehicles without torque distribution strategy were overturned around sharp corners, whereas the vehicles applied with the torque distribution strategy were driven stably. In addition, the vehicle applied with ITD showed the most desirable results for driving efficiency. An actual vehicle test was performed to evaluate the performance of ITD on an actual vehicle. The test conditions were selected for slalom driving at 40 km/h. As a result of the actual vehicle test, the vehicle applied with ITD was found to be driven in the path wanted by the driver with relatively small steering input compared to the vehicle not applied with ITD. From these results, it can be confirmed that the proposed driving torque distribution strategy improves the efficiency and driving stability of the independent driving electric vehicle. This is an improvement over the various studies mentioned in the introduction, focusing only on improving the driving efficiency of the vehicle.

**Author Contributions:** Conceptualization, J.P., S.-H.H. and I.G.J.; Methodology, J.P.; Software, J.P.; Validation, S.-H.H. and I.G.J.; Writing-Original Draft Preparation, J.P.; Writing-Review & Editing, S.-H.H.; Project Administration, S.-H.H.

**Funding:** Please add: This research was funded by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2018-0-01426) supervised by the IITP (Institute for Information & communications Technology Promotion)

**Acknowledgments:** This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2018-0-01426) supervised by the IITP (Institute for Information & communications Technology Promotion)

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**


**Table A1.** Parameters of the target in-wheel electric vehicle.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*
