Active Vibration Control via Current Injection in Electric Motors

Abstract

This work presents a technique to actively reduce the vibrations generated by magnetic anisotropy in sinusoidal brushless motors through current injection. These vibrations are an unwanted phenomenon mainly generated by the interaction between the rotor magnets and the stator teeth. These produce vibrations which are then transmitted to the frame and other mechanical parts such as bearings, gearboxes, transmissions, and joints, thus reducing the life, performance, and reliability of these components. First, different design strategies and control algorithms to passively and actively attenuate the vibrations are reviewed. Then, a narrowband active method that attenuates a harmonic vibration through the injection of a harmonic current is presented. The effectiveness of the proposed method was demonstrated on a prototype of a Surface Permanent Magnet Synchronous Motor (SPMSM). For the motor under test, an attenuation of −13.5 dB at 650 rpm and −29 dB at 800 rpm was achieved on the main frequency component, caused by the magnetic anisotropy, which in turn corresponds to the 72nd harmonic of the rotor mechanical speed.

1. Introduction

The increasing usage of electric motors in industrial and household applications would benefit from a reduction in vibration and noise levels, improving end-user comfort and system performance. The Noise and Vibration Harshness (NVH) of electric motors may be categorized into electromagnetic, mechanical, and aerodynamic sources [1]. Aerodynamic NVH is typically generated by the presence of fans or by the turbulence in the air gaps of the motor. At high speeds, aerodynamic forces can induce vibrations in the stator and machine housing, resulting in high-frequency noise [2]. Mechanical NVH can be caused by shaft misalignment, dynamically unbalanced rotors, and mechanical components such as bearings, couplings, and gearboxes; the frequency ranges and intensities of mechanical NVH are related to each specific case, e.g., [3]. Among the electromagnetic NVH sources, those induced by torque ripples and cogging torque have been largely studied. These, in fact, can affect the general performance of the machine at low frequencies, causing mechanical and structural vibrations and producing particularly unpleasant noises for humans [4]. As a practical example, in a direct-drive system, the torque ripple produced by the motor is directly transferred to the load, decreasing the performance of the machine or even damaging its components [5]. Periodic disturbances due to magnetic anisotropy stem from the slotted nature of the stator. They cause torque and speed fluctuations, which can represent particularly negative factors during machine operation; therefore, methodologies to reduce these effects are highly desirable, and several techniques have been proposed in the literature [6].

Fluctuations of the motor-exciting torque are transmitted to mechanical components, causing unwanted vibrations and noise and reducing the life and reliability of these components, e.g., [7,8]. As an example, during operation, mechanical and structural parts can be affected by low-frequency vibration due to external conditions, medium-frequency vibrations caused by torque fluctuations of the motor, and high-frequency vibrations caused by nonlinear factors such as those occurring in gearboxes, i.e., stiffness in gear meshing, and clearances between gear teeth [9]. By reducing the harmonic components and power fluctuations transmitted from the motor to the mechanical transmission system and structures, the performance and life of the components can be significantly improved. Numerous studies in the field of mechanical engineering have been dedicated to knowledge and skills in implementing effective mitigation and isolation strategies to preserve mechanical and transmission systems from motor-borne vibrations. These may be classified into two main categories: passive mechanisms that attenuate the transmission of vibrations from the motor to the powertrain, and active control algorithms to mitigate the vibration produced by the motor itself. Examples are the optimization of the isolation of the coupling between the motor and the transmission device [10] and the active control of the hybrid powertrain in hybrid electric machines [11], but many others can be found in the literature, especially related to hybrid electric machines, e.g., [12]. The latter differ significantly in terms of power sources and powertrain systems from electric machines and traditional combustion engines, with new NVH issues and challenges [13].

The work presented here specifically concerns electric drives, where it is well known that unwanted frequency components on the supply current spectrum produce negative effects on motor behavior. High-frequency components, e.g., higher harmonics of the switching frequency, produce electromagnetic interference (EMI) [14], partial discharges [15], and bearing failures [16,17]. In fact, common-mode capacitive paths between the inverter and ground produce leakage currents and, therefore, unwanted effects. The most common topology of electric drive, the three-phase two-level inverter, is strongly affected by these problems. The common-mode voltage (CMV) can be reduced by using more complex drive topologies or specific modulations [18]. In [19], a spread spectrum technique has been employed to reduce unwanted harmonics, while in [20] the authors proposed a non-zero vector pulse width modulation to suppress CMV. In [21], a new modulation was presented, decreasing the amplitude of the 5th and 13th harmonics.

Permanent magnet electric motors (PMEMs) generate torque ripples when rotating, which causes the appearance of lower frequency components and, therefore, mechanical vibrations, which can be harmful to the powertrain and transmission. Such vibrations stem from the parasitic torque caused by the interaction between the permanent magnets of the rotor and the stator slots which house the windings. This torque depends on the mutual position between the stator and the rotor, and its periodicity per revolution depends on both the number of magnetic poles and the number of stator teeth. Torque ripple is present throughout the entire operating range of the motor, producing torque ripple and, especially at lower speeds, jerky motion. Conversely, at high speeds, the intrinsic inertia of the motor filters out the effects of the vibrating torque on the motor speed. However, torque ripple is always harmful to the transmission chain connected to the shaft and can generate vibrations and acoustic noise.

1.1. Literary Review of “Passive” Vibration Reduction Techniques

Torque ripple limitation is of particular interest for Interior Permanent Magnet Synchronous Motors (IPMSMs) and SPMSMs. Several “passive” techniques can be adopted to mitigate torque ripple generation in the motor design phase:

• Skewing stator or rotor magnets. This consists of a skew of the stator stack along its entire length with an angle equal to the slot pitch. It is very effective, but it has the disadvantage of increasing costs [22]. Similarly, rotor magnets can be skewed, which decreases the cogging torque, but at lower costs [23,24].
• Fractional-Slot Concentrated-Winding (FSCW). Fragmentation of the winding blocks of each pole into multiple stator caves. This solution provides high power-density, high slot-filling factor, and low cogging torque [25,26,27,28]. Conversely, Integral Slot Concentrated Windings (ISCW), characterized by a higher residual ripple, can also be adopted [29].
• Stator dummy slots, slot bridges/slot openings. Auxiliary slots can only be added to some teeth and for a part of the stator length [30,31]. To minimize the magnetic path differences seen by the magnets, the air gap of the cavities can be hidden by making magnetic bridge connections (shoes) between adjacent teeth, thus minimizing the cogging torque [32]. To minimize the cogging torque, the ratio between the magnetic pole arc and pole pitch must be optimized [33]. The negative effect of slot-bridging is flux leakage, which results in a reduction in average torque.
• Magnet pole geometry optimization. In [34,35], it was shown that by varying the offset and shape of the magnet in a Surface Permanent Magnet Synchronous Motor (SPMSM), the cogging torque decreases.
• Stator geometry optimization. In [36], the dependency between the stator slot depth and the cogging torque was analyzed, showing that increasing stator slot depth by 6.7% allows for a reduction in peak-to-peak cogging torque of 19.7%. Moreover, in [37], vibration noise was reduced by a mechanical modification on the stator teeth and stator yoke thickness to increase the resonant frequency and, thus, improve the overall stiffness and stability of the stator core. Also, in external rotor PMSMs, similar results can be achieved [38].
• External rotor. In [33], the external rotor of a PMSM was designed to achieve the minimum cogging torque.

All these techniques prevent the generation of cogging torque and vibrations using “passive” modes. However, they make the construction of the motor more complex and expensive, and for these reasons they often cannot be adopted, particularly when dealing with special motors or prototypes. Moreover, the adoption of these solutions leads to lowering the torque density and overall efficiency.

1.2. Literary Review of Active Vibration Control Systems

Active vibration reduction systems are gaining more and more importance, especially for existing systems, since they can be installed without the need to replace any components, thus minimizing installation costs. In [39,40], the torque ripple was reduced based on an analytical model. In [41], an iterative learning controller is used to minimize torque ripple, while in [42], an adaptive algorithm is used to self-tune the Fourier coefficients to minimize a periodic torque ripple. Many self-adaptive algorithms can be used with the aim of minimizing a cost function, be it noise, vibration, or torque ripple. In [43], the well-known Filtered-x Least Mean Square (FxLMS) [44] was used to dampen engine torque ripple, while in [45] the same algorithm was employed for the reduction of torque ripple in a PMSM. FxLMS adjusts the coefficients $w\left(n\right)$ of an adaptive filter to minimize the instantaneous squared error $\widehat{\xi }=e^2\left(n\right)$ using the steepest descent algorithm:

$$w\left(n+1\right)=w\left(n\right)+\mu x^{\prime }\left(n\right)e\left(n\right)$$

(1)

where n is the discrete time index, μ is the step size, $x^{\prime }\left(n\right)=\widehat{s}\left(n\right)\ast x\left(n\right)$, with $\widehat{s}\left(n\right)$ being the estimate of the secondary path $s\left(n\right)$, $x\left(n\right)$ the input signal, and $\ast$ the linear convolution. The error $e\left(n\right)$ is calculated as:

$$e\left(n\right)=d\left(n\right)-s\left(n\right)\ast \left[w\left(n\right)x\left(n\right)\right]$$

(2)

where $d\left(n\right)$ denotes the primary disturbance. Since disturbances in the reference signal can potentially lead to system instability, a common approach is to use the normalized FxLMS algorithm (FxNLMS), where the variable step size [46] is dynamically adjusted by weighting it proportionally to the power of the reference signal:

$$\mu ={\displaystyle \frac{\beta }{{x^{\prime }}^T\left(n\right)x\prime \left(n\right)}}$$

(3)

where β is a constant comprised between 0 and 2, but usually chosen in the range 0 < β < 1 [47]. The complexity of the FxLMS algorithm and other time-domain algorithms, e.g., the filtered-x affine projection (FxAP) [48], increases linearly with filter length, making them prohibitive for real-time systems. A solution is represented by the Partitioned Block Frequency Domain Adaptive Filter (PBFDAF) algorithms, which aim to reduce the computational effort while limiting the increase in latency. Among these, the partitioned block filtered-x LMS (FPBFxLMS) algorithm is well known [49]. The adaptive filter $w\left(n\right)$ is partitioned into P_w blocks of length L, and the frequency-domain weight vector of the p-th partition is:

$${\mathit{w}}_p\left(k\right)=\mathit{F}{\left[{\mathit{w}}_p^T\left(k\right),0_{1\times L}\right]}^T$$

(4)

where k denotes the frame index, 0_1×L is a 1 × L all-zero vector, and F is the Fourier transformation.

Many disturbances are periodic, such as those generated by engines, compressors, motors, fans, and propellers. In these cases, narrowband feedforward algorithms can also be used [50], using an appropriate electrical reference signal that contains the fundamental frequency and all the harmonics of the primary disturbance, as can be seen in [51], a recent study on PMSM. The commonly used reference signals are an impulse train, with a period equal to the inverse of the fundamental frequency of the periodic disturbance, or sinewaves with the same frequencies as the corresponding harmonic tones to be cancelled. In the first case, we talk about the “waveform synthesis algorithm” and the input signal $x\left(n\right)$ is given by [52]:

$$x\left(n\right)={\sum }_{-\infty }^{+\infty }\delta (n-kN)$$

(5)

where $\delta (·)$ is the discrete impulse train of period $N=T_0/T$, with $T_0=2\pi /{\omega }_0$, ${\omega }_0$ being the fundamental frequency of the disturbance. In the second case, we talk about “adaptive notch filter”, and the input signal $x\left(n\right)$ is given by the sum of M sinusoids:

$$x\left(n\right)={\sum }_{m=1}^M\left(A_m\cos \left({\omega }_{m}n\right)\right)$$

(6)

where $A_m$ and ${\omega }_m$ are, respectively, the amplitude and the frequency of the m-th sinusoid of the reference signal.

1.3. Authors’ Contribution

The presented active methods are particularly suitable for small-size motors driven by converters with a high switching frequency and, consequently, with a high cut-off frequency of the current loop. Under these assumptions, a relatively high-frequency separation between the frequency of the harmonics to be canceled and the cut-off frequency of the current loop can be guaranteed, and consequently, proportional-integral (PI) current regulators can compensate for the magnetic anisotropy acting on the current set-points. In case the current regulator bandwidth is insufficient for providing the needed spectral components, the compensating signal must be added directly to the d–q voltage axes. In [53], the authors propose a repetitive current control that eventually cancels the torque ripple by exploiting the repeating nature of the disturbance. The above methods can adapt to changing operating conditions and adjust the compensator’s operating parameters in real time.

In the proposed application, the motor has a nominal power of 3 kW with 72 stator teeth; therefore, the target frequency F_t to be canceled is the 72nd harmonic of the mechanical speed of the rotor F_r, i.e., F_t = 780 Hz for the 650 revolution-per-minute (rpm) case (F_r = 10.8 Hz) and F_t = 960 Hz for the 800 rpm case (F_r = 13.3 Hz). Since it is necessary to have a PWM frequency of at least one order of magnitude higher than the harmonic to be canceled to generate a sufficiently well-shaped sinusoid, and having a switching frequency of 10 kHz, the cut-off frequency of the current loop is limited to 700 Hz and the harmonic to be canceled is outside the bandwidth of the current controller. For this reason, unlike many works in the literature that perform the torque ripple compensation through an appropriate signal added to the current references, we explored a different method for attenuating the 72nd harmonic using a single-frequency; thus, M = 1 in (6), feed-forward active vibration control (AVC) that operates directly on the voltage value applied to the d-axis. This method is effective at frequencies higher than the current loop bandwidth and up to about one order of magnitude less than the switching frequency to generate a sufficiently well-shaped sinusoid; in our case, this translates to a maximum frequency that can be canceled of approximately 1 kHz. Given this consideration, the proposed method can find suitable applications in the reduction of parasitic vibrations of manually operated tools and machinery, for which the hand-arm regulation applies. The ISO 5349-1:2001 standard [54], named “Mechanical vibration—Measurement and evaluation of human exposure to hand-transmitted vibration”, specifically considers the negative effects of vibrations transmitted to the hands in the frequency range from 8 Hz to 1 kHz.

The motor under test, mounted on a motor test bench, was monitored with a piezoelectric accelerometer and three current sensors. Many combinations of amplitude and phase values of the injected current were tested, with the aim of maximizing the attenuation effect of the 72nd harmonic. Significant reductions of the measured acceleration were obtained: −13.5 dB at 780 Hz with the motor running at 650 revolutions-per-minute (rpm) and −29.0 dB at 960 Hz with the motor running at 800 rpm. The paper is arranged as follows: Section 2 provides all information related to the employed equipment and setup of the experimental measurements, Section 3 presents the results, and the conclusions are discussed in Section 4.

2. Materials and Methods

2.1. Model of the Motor under Test, Control Strategy and Current Injection Algorithm

The vibration reduction system was tested using a prototype of SPMSM, whose specifications are shown in

Table 1. Nameplate data of the motor under test.

Specification	Value
Nominal voltage	30 V
Nominal power	3000 W
Voltage constant	8.67 mV/rpm
Nominal speed	3500 rpm
Number of pole pairs	4
Nominal current	58 A
Nominal torque	8.1 Nm
Stator resistance	8.2 mΩ
Stator inductance	32 µH

, and an electric drive based on a field-oriented control (FOC) strategy based on the d–q model of the motor.

The general model of the motor on the d–q axes is derived from the following equations:

$$\left\{\begin{array}{l}{v}_d=R\cdot i_d+{\displaystyle \frac{d{\lambda }_d}{dt}}-{\omega }_e\cdot {\lambda }_q\\ {\lambda }_d=L_d\cdot i_d+{\lambda }_{m,d}\\ v_q=R\cdot i_q+{\displaystyle \frac{d{\lambda }_q}{dt}}+{\omega }_e\cdot {\lambda }_d\\ {\lambda }_q=L_q\cdot i_q+{\lambda }_{m,q}\end{array}\right.$$

(7)

where $v_d$ and $v_q$ are the voltages on the d–q axes; $i_d$ and $i_q$ are the currents on the d–q axes; R is the stator resistance; $L_d$ and $L_q$ are the stator inductance on the d–q axes, respectively; ${\lambda }_q$, ${\lambda }_q$ are the stator magnetic fluxes on the d–q axes produced by the d–q currents; ${\lambda }_{m,d}$, ${\lambda }_{m,q}$ are the fluxes produced by rotor magnets; and ${\omega }_e$ is the electrical speed. Using Laplace transformation, and under isotropic motor hypothesis, ($L_d=L_q=L_{eq}$):

$$\left\{\begin{array}{l}{v}_d=R\cdot i_d+s\cdot {\lambda }_d-{\omega }_e\cdot {\lambda }_q\\ {\lambda }_d=L_{eq}\cdot i_d+{\lambda }_{m,d}\\ v_q=R\cdot i_q+s\cdot {\lambda }_q+{\omega }_e\cdot {\lambda }_d\\ {\lambda }_q=L_{eq}\cdot i_q+{\lambda }_{m,q}\end{array}\right.$$

(8)

Assuming that ${\lambda }_{m,d}$ and ${\lambda }_{m,q}$ are not time-dependent, using $v_d$, ${\lambda }_d$, and ${\lambda }_q$ expressions, it results in:

$$v_d=R\cdot i_d+s\cdot L_{eq}\cdot i_d-{\omega }_e\cdot L_{eq}\cdot i_q$$

(9)

Similarly, using $v_q$, ${\lambda }_d$, and ${\lambda }_q$ expressions, it can be obtained that:

$$v_q=R\cdot i_q+s\cdot L_{eq}\cdot i_q+{\omega }_e\cdot \left(L_{eq}\cdot i_d+{\lambda }_{m,d}\right)$$

(10)

Under the previous assumptions, the torque can be expressed as:

$$T=p\cdot ({\lambda }_d\cdot i_q-{\lambda }_q\cdot i_d)$$

(11)

where p is the pole pairs of the motor. Using (2.b) and (2.d):

$$T=p\cdot \left[(L_{eq}\cdot i_d+{\lambda }_{m,d})i_q-(L_{eq}\cdot i_q+{\lambda }_{m,q})i_d\right]$$

(12)

and under the hypothesis of rotor magnet aligned on d-axis (${\lambda }_{m,q}=0$):

$$T=p\cdot {\lambda }_{m,d}\cdot i_q$$

(13)

As can be seen from (13), the ideal output torque is proportional to the current $i_q$, while $i_d$ has to be kept at zero, since it controls the magnetic flux of the motor that is already given by magnets. As previously mentioned, the control uses a FOC strategy based on the d–q model of the motor (Figure 1).

The currents on the d–q axes are controlled using two Proportional Integral (PI) regulators. Starting from $i_u$, $i_v$, and $i_w$ motor currents, using Clarke transformation (Equation (8)) two orthogonal currents $i_{\alpha }$, $i_{\beta }$ on fixed axes are obtained.

$$[B]={\displaystyle \frac{2}{3}}·\left(\begin{array}{lll}1& -{\displaystyle \frac{1}{2}}& -{\displaystyle \frac{1}{2}}\\ 0& {\displaystyle \frac{\sqrt{3}}{2}}& -{\displaystyle \frac{\sqrt{3}}{2}}\end{array}\right)$$

(14)

Then, the currents on the d–q axes are computed using the Park transformation (Equation (9)), which needs information about the rotor position $\theta$.

$$[A(\theta )]=\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right)$$

(15)

The currents on the d–q axes thus obtained are compared with the d–q current set-point, and their difference (the error) feeds PI regulators. Then, the output of the PI regulators are the voltages on the d–q axes, which can be transformed into the u-v-w voltages using the inverse Park transformation ${[A(\theta )]}^{-1}$ and inverse Clarke transformation ${[B]}^{-1}$.

As stated before, the transformation matrices require the rotor position, while the speed loop requires the instantaneous speed of the motor. To eliminate any physical speed sensor, and therefore increase the reliability of the entire system, a position/speed observer has been implemented. Since the position/speed observer relies on the back-electromotive force (BEMF), a start procedure must be implemented to accelerate the motor in open-loop mode until a minimum speed (400 rpm) is reached, allowing the observer to provide an accurate estimation of both position and speed. Therefore, every time the motor is started, an alignment procedure is carried out, feeding the stator windings with a current $i_d$ that aligns the magnetic axis of the rotor with the d-axis. Then, the motor is accelerated in an open loop, using an internally generated angle and keeping a constant current $i_q$, while $i_d$ is being held to zero. Once the motor speed rises above 400 rpm, the control mode changes from the internally generated angle to the observer-estimated angle.

A model reference adaptive system (MRAS) observer was adopted (Figure 2), consisting of an adjustable model containing the motor equations expressed on d–q axes [55]. It behaves like a digital twin of the physical motor with transformation matrices: all variables are estimated except for the phase currents and the voltages on d–q axes, and an adaptive law block adjusts the model’s behavior of the model to the real motor ($i_d^S$ and $i_q^S$ are the estimated currents). When a perfect match is achieved between the two blocks, the position $\tilde{\theta }$ and the speed ${\widehat{\omega }}_e$ estimated by the observer perfectly replicate the actual position and speed of the rotor.

For the harmonic attenuation algorithm (Figure 3), the cancellation signal is directly added to the voltage modulation index on the q-axis. The PI current regulator has been bypassed because, as previously discussed, the harmonic to be cancelled out is outside its bandwidth. The injected current $i_q^{\prime }$ is a function of:

$$v_q^{\prime }=v_q+v_o$$

(16)

where:

$$v_o=K_{INJ}\cdot \sin ({\theta }_{INJ}+{\phi }_{INJ})$$

(17)

is an oscillating voltage component for compensating the 72nd harmonic (torque ripple due to magnetic anisotropy), ${\theta }_{INJ}$ is the mechanical angle of the rotor position (estimated by the observer) multiplied by 72, ${\phi }_{INJ}$ and $K_{INJ}$ are the phase and the amplitude, respectively, determined to obtain the maximum harmonic cancellation. The injected current $i_q^{\prime }$ is responsible for the torque:

$$T^{\prime }=T+T_c$$

(18)

where T is the ideal torque (Equation (7)) and T_c is a compensating torque, due to the oscillating component $v_o$ of $v_q^{\prime }$. The values of ${\phi }_{INJ}$ and $K_{INJ}$ must be finely tuned so that $T_c$, caused by the injected current $i_q^{\prime }$, can generate a mechanical vibration having the same amplitude and opposite phase compared to the 72nd harmonic to be attenuated.

2.2. Simulations

Using the previously presented equations of the model of the SPMSM, of the d–q control algorithm and of the proposed injection method, a Matlab/Simulink simulation was carried out (Figure 4). With reference to Figure 4, the electrical model of the motor is included in the red block, and the current d–q control is built around it. As previously discussed, the $i_d$ setpoint is kept to zero, while the $i_q$ is given by the speed loop control. The compensation algorithm, both in simulation and experiment, is based on two look-up tables (the MAG LookUp Table and PHASE LookUp Table) that describe the magnitude and angle of the compensating voltage sinusoid as functions of the rotating frequency. The look-up table values were determined by linearization of the system around the operating point.

The effectiveness of the proposed algorithm has been proved with a plot of the motor torque that presents a comparison between compensated and uncompensated system (Figure 5).

As can be seen, using the compensation algorithm, the torque waveform presents dampened oscillations. After the encouraging simulation results, the compensation algorithm system was tested on an SPMSM on a motor test bench.

2.3. Measurement System

The vibration and current signals were measured on the motor mounted on a motor test bench, as shown in Figure 6.

The vibration signals were acquired using a triaxial piezoelectric accelerometer, a Dytran model 3233A, whose specifications are shown in

Table 2. Piezoelectric accelerometer Dytran 3233A.

Specification	Value
Type	IEPE
Sensitivity	1000 mV/g
Measurement range	±5 g peak
Frequency range	X, Y: 0.4 Hz–6 kHz Z: 0.4 Hz–3 kHz
Maximum Output Voltage	±5 V
Excitation	18–30 V DC

. At the same time, the three phase currents were measured with current sensors, type LF 210-S from the manufacturer LEM. See

Table 3. Current sensor LEM LF 210-S.

Specification	Value
Primary current	200 A
Secondary current	100 mA
Nominal sensitivity	0.5 mA/A
Sensitivity error	±0.1%
Frequency bandwidth (−3 dB)	100 kHz
Supply voltage (nominal)	±15 V
Closed loop (compensated)	Yes

for LEM sensor specifications. An image and a schematic representation of the complete acquisition system are shown in Figure 7.

All these signals were acquired with a digital Data Acquisition (DAQ) system composed of two parts: an Interface Board (IB), and a series of Acquisition Nodes (AN), connected to the IB via the Automotive Audio Bus (A²B). In this case, since there are only six signals to be acquired, a single AN was employed, as it can manage up to eight input signals. A²B technology exploits the concept of sensor network: a main IB manages the network, and a series of ANs (up to 11) connected in a daisy-chain topology acquire and transmit signals over it. Each network carries the power supply (2.7 W) and up to 32 signals, all synchronized by the bus with negligible jitter [56] and a deterministic latency of 50 µs, at the sampling frequency (fs) of 48 kHz (current standard in audio applications) over a single unshielded twisted pair (UTP) wire. Since it is a chain connection, the star topology usually employed by commercial analog systems is overcome, allowing the number, weight, and cost of the wiring to be significantly reduced, all desirable characteristics for any Condition Monitoring (CM) system [57,58,59]. The A²B nodes can be fully digital, e.g., equipped with micro electro-mechanical system (MEMS) transducers [60,61,62], or they can include on-board analog-to-digital conversion (ADC), as in the current work. The A²B acquisition node features a single chip to run the ADC, model AD1278 by Analog Devices (see

Table 4. Analog-to-Digital Converter AD1278.

Specification	Value
Architecture	24-bit delta-sigma
Number of channels	8, simultaneous sampling
Analog bandwidth	70 kHz
Maximum sampling rate	Up to 144 kS/s
DC accuracy—offset drift	0.8 µV/°C
DC accuracy—gain drift	1.3 ppm/°C
Serial interface	SPI or frame sync

for specifications). Up to 8 sensors can be acquired together, such as an Integrated Electronic Piezoelectric (IEPE) sensor, Integrated Circuit-Piezoelectric (ICP) sensor, or any other sensor with voltage output.

3. Results and Discussion

The experimental campaign was conducted at two different motor speeds, 650 rpm, a rotor frequency of F_r = 10.8 Hz, and 800 rpm, being F_r = 13.3 Hz. The motor was run at the target speed for 30 min to reach a stable temperature condition before starting the measurements. For each speed, a total of 25 measurements were performed by combining five values of amplitude and five values of phase of the injected current (see

Table 5. Attenuation values, expressed in decibel, for the 72nd harmonic component of the torque for different values of phase and amplitude of the injected current. Optimal performance is highlighted in bold. The rotor mechanical speed is 650 rpm (a) and 800 rpm (b).

(a) 650 rpm
Modulation index (KINJ)	$\mathrm{Phase}({\phi }_{INJ}$) [rad]
	−1.05	−0.79	0	0.79	1.05
0.05	−7.5 dB	−10.0 dB	−7.5 dB	−1.0 dB	0 dB
0.06	−5.0 dB	−8.5 dB	−11.5 dB	−1.0 dB	0.5 dB
0.07	−5.0 dB	−8.0 dB	−13.5 dB	−1.5 dB	0 dB
0.08	0 dB	−2.0 dB	−9.0 dB	−1.0 dB	0.5 dB
0.09	1.5 dB	0 dB	−5.0 dB	−1.0 dB	1.0 dB
(b) 800 rpm
Modulation index (KINJ)	$\mathrm{Phase}({\phi }_{INJ}$) [rad]
	−1.05	−0.79	0	0.79	1.05
0.05	−2.5 dB	−5.0 dB	−11.0 dB	−2.0 dB	0 dB
0.06	−1.5 dB	−4.0 dB	−17.5 dB	−2.5 dB	−0.5 dB
0.07	−0.5 dB	−3.0 dB	−29.0 dB	−2.0 dB	0 dB
0.08	1.5 dB	0 dB	−13.0 dB	−2.0 dB	0 dB
0.09	2.0 dB	0 dB	−8.0 dB	−2.0 dB	0 dB

) with the aim of maximizing the cancellation effect.

The vibration level was first measured for the nominal condition of the motor, i.e., in thermal equilibrium, without current injection, along the Y direction (the orientation of the accelerometer can be seen in Figure 6). This measurement was carried out to identify the target frequency (F_t) to be reduced in the interested operating frequency range. The spectra of acceleration levels were calculated by means of fast Fourier transform (FFT), averaging multiple blocks of 2¹⁶ samples each, overlapped by 75%, with Hann windowing. The frequency resolution is $d_f=f_s/2^{16}\cong 0.73\mathrm{H}\mathrm{z}$. The spectra are referred to the acceleration reference unit of the I.S. for dB conversion; that is, a_ref = 10⁻⁶ m/s².

The results are shown in Figure 8 (left) for the 650 rpm case ($F_r\cong 10.8\mathrm{Hz}$) and in Figure 9 (left) for the 800 rpm case ($F_r\cong 13.3\mathrm{Hz}$). The target frequency F_t, the one having the largest amplitude, resulted as the 72nd harmonic of the fundamental rotor frequency; that is, F_t = 780 Hz for the 650 rpm case and F_t = 960 Hz for the 800 rpm case. As can be seen in Figure 8 (right) for the 650 rpm case and in Figure 9 (right) for the 800 rpm case, the target frequencies F_t are also modulated by the rotor frequency F_r, which in turn causes the appearance of two further disturbance harmonics, i.e., the 71st and the 73rd. They correspond to the frequencies $F_t^{\prime }=769.2\mathrm{Hz}$ and $F_t^{\prime \prime }=790.8\mathrm{Hz}$ for the 650 rpm case and $F_t^{\prime }=946.7\mathrm{Hz}$ and $F_t^{\prime }=973.3\mathrm{Hz}$ for the 800 rpm case. However, only the 72nd harmonic was considered in this work, leaving a multi-tone cancellation algorithm for subsequent developments.

The effectiveness of the current injection technique was evaluated by calculating the amount of reduction in terms of acceleration level (dB) at the target frequency F_t, for each of the 25 conditions as a function of phase and amplitude of the injected current. The minimum points in the charts of Figure 10 correspond to the optimal combinations of phase and amplitude of the injected current, which provides the maximum cancellation performance. Remarkable results were obtained, with a reduction of the vibration level equal to −13.5 dB at F_t = 780 Hz for the 650 rpm case and to −29 dB at F_t = 960 Hz for the 800 rpm case. One can note that the optimal working point becomes narrower as the frequency increases, as usually happens in most of the Active Noise Cancelling (ANC) applications [63,64].

Then, the spectra of the acceleration level were also calculated for the AVC-on condition, running with the optimal parameters for the injected current. In Figure 11, they are shown in comparison with the nominal conditions, confirming the above analysis. One can note the target frequency F_t = 780 Hz for the 650 rpm case is reduced by 13.5 dB, and F_t = 960 Hz for the 800 rpm case by 29 dB.

Eventually, the time domain signals were analyzed by means of their Root Mean Square (RMS) value. For each tested speed, the optimal condition with AVC on and the nominal condition with AVC off were compared (

Table 6. Overall acceleration levels, with AVC system switched on and off.

Motor Speed [rpm]	AVC System Condition	Overall Acceleration Level [dB]
650	OFF	77.2
650	ON	75.5
800	OFF	76.3
800	ON	72.9

), with the aim of assessing the amount of overall vibration level reduction in the frequency range 8 Hz–1 kHz, considered by the hand-arm regulation for manually operated tools and machinery. The overall acceleration levels were reduced by 1.7 dB for the 650 rpm case and by 3.4 dB for the 800 rpm.

4. Conclusions

An effective application of an active vibration control system for electric motors was presented, with the aim of reducing a single torque harmonic caused by magnetic anisotropy. The developed technique makes use of the current injection, the amplitude, and phase, which are controlled to match the target frequency to be reduced. The effortlessness of the proposed solution allows the algorithm to be implemented on the same electronic board that performs the motor control, thus allowing the adoption of the active vibration control system with minimal additional costs. Multi-tone algorithms, such as Filtered-X Least Mean Square (FxLMS), can be used to control multiple harmonics simultaneously, thus further improving the effectiveness of the vibration control system, but their complexity requires the installation of a dedicated board equipped with high computational capabilities, such as a powerful micro-controller or a Field Programmable Gate Array (FPGA). Compared to “passive” vibration control, the active method has the advantage of being applicable to already existing systems, without the need to redesign or replace any electrical or mechanical part. Furthermore, it is less expensive than adopting more complex designs, such as rotor skewing, FSCW, or ISCW, at the cost of a slight increase in system power consumption.

A case study consisting of a SPMSM driven at two speeds, 650 rpm ($F_r\cong 10.8\mathrm{H}\mathrm{z}$) and 800 rpm ($F_r\cong 13.3\mathrm{H}\mathrm{z}$), was presented. Vibration measurements were acquired with an accelerometer, and the 72nd harmonic of the rotor mechanical speed F_r was identified as the target frequency F_t to be reduced, being the one with the largest amplitude in the frequency range considered by the ISO 5349-1:2001 standard [54] for the negative effects on humans of vibrations produced by manually operated tools and machinery, i.e., 8 Hz–1 kHz. Significant results were obtained, showing a reduction in acceleration levels of 13.5 dB at F_t = 780 Hz for the 650 rpm case and of 29 dB at F_t = 960 Hz for the 800 rpm case. Overall acceleration levels were also reduced in both cases, by 1.7 dB for the 650 rpm case and by 3.4 dB for the 800 rpm case. These results are of great importance for improving the comfort, performance, and reliability of electromechanical systems, by reducing noise and vibrations, which are particularly unpleasant for humans.