Sensorless Control of PMSM Based on Backstepping-PSO-Type Controller and ESO-Type Observer Using Real-Time Hardware

Round 1

Reviewer 1 Report

Here are my comments:

- Is backstepping-type control law suitable for any non-linearities of the control system?

- In line 186, the 1% stationary error is generated from parameter mismatching or other?

- A clear block set for SIL and HIL are missing, please indicating clear the real and virtual path in the experimental setup.

- A proofreading is required.

 

Author Response

Dear reviewer, thanks for your recommendations.

1. The mathematical model of the PMSM is nonlinear. The nonlinearity is due to the fact that products of the state vector components (terms such as ωi_q and ω·i_d ) occur in the mathematical model. These nonlinearities can be considered as “soft” in the sense that the description functions concerned are of continuous type and even derivable due to the physical characteristics of the state vector components. It can be noted that the procedure for obtaining the controller presented starts from the FOC-type structure which exploits the cascade structure, i.e. the fact that the outer speed control loop provides the control quantity i_qref, which will supply the control quantities u_d and u_q through the current control loops. It can be noted that this structure can be used to follow the steps in designing a backstepping control control law. The recursive control design for the backstepping law requires a system consisting of subsystems which radiate out from an inner system to the outer subsystems, and the stabilization is achieved in several stages, each based on a Lyapunov function.

In addition, the functions that describe the nonlinearities of the system must be at least of Lipschitz type, a condition which is fulfilled, given that these functions are continuous due to the physical nature of the state vector components.

2. The PI controller is a relatively simple controller that can generate satisfactory performance of the control system around a static operating point characterized by the steady-state values of the system parameters. If these parameters vary quite a lot, the performance of the control system decreases, therefore a steady-state error can occur. In the specific case presented, the nominal value of the load torque is of 1Nm, and in the presented simulation there is a change to 4Nm, showing the limits of the PI-type controller, even if the tuning parameters K_p and K_i  of the PI controller have been optimized using a PSO - Particle Swarm Optimization method. After synthesizing the backstepping control law, the performances of the control system and its robustness in case of large variations of the system parameters are demonstrated through numerical simulations.
3. In the stages of development of a real-time control application, we note the conceptualization and formalization of the problem by phenomenological description using the differential equations, the continuation of the study by following a particular formalism of the control theory, the synthesis of the controller in the form of equations, followed by several series of numerical simulations performed using specialized simulation environments to test the entire system without resorting to hardware elements (except the PC which runs the numeric simulations). These steps fall within the SIL paradigm and have been summarized in Sections 2-5.
4. A proofreading has been done.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is focused on design of sensorless control of PMSM. The introduction of the paper and theoretical part is well written and design steps are easy to follow. There is typo after integral in eq. 30 that does not correspond with Fig. 8.

The experimental part is not proving/showing much from designed controllers. I would assume more comparisons with simulation results. The part dealing with configuration of simulink is too long and is too simplified for reader that does not have any experience with code generation from simulink.

Questions

1) How will deal your backsteping controntroler eq. 21 and 30. with voltage limitation of the source i mean ratio between ud^2 + uq^2 = uDC^2. 

2) In simulations was motor loaded to 4Nm why are experimets done for noload. How does it test load torque observer?

3)Time axis of Fig. 36 does not correspond to other figures what is then meaning of the figure

4) Simulate and show iq same as in fig. 38 that we can compare simulation with reality.

Author Response

Dear reviewer, thanks for your recommendations.

            We corrected Equation (30) and Figure 8.

            Several explanations regarding code generation from Simulink have been added to the text (Section 6). In terms of the implementation of the control algorithm in F280379D MCU, in addition to the explanations added to the text (Section 6), the main specification consists in the fact that the program used for the numerical simulations is rebuilt with blocks from the Motor Control Blockset (MCB) and the Embedded Coder Support Package for TI C2000 Processors toolboxes, and the continuous integral block “1/s” is replaced with a discrete integral block “(k·Ts)/(z-1)”.

• The voltage signal (u_d^ 2 + u_q^ 2) ^ 1/2 is presented in the following figure. The speed reference is of 1600rpm. The motor is supplied by the inverter whose power source is provided by the DC intermediate circuit with u_DC The term in equation (21) di_qref/dt is the one that can add a sudden increase of the term uq. In this sense, both in the numerical simulation and in the control software application implemented in the microcontroller, this term is passed through a “rate limiter” type function. In this way, control saturation is prevented and the equation (u_d^ 2 + u_q^ 2)^1/2 = u_DC is kept.
• In order to demonstrate the robustness of the inferred control law, in the simulation, although the nominal torque of the motor is 1Nm, we present numerical simulations for 4Nm or 8Nm of the load torque with good results of the control system, both in stationary and in dynamic regime. The load torque observer has been tested by numerical simulation (accurately retrieves an imposed variation of the load torque) and was implemented in the microcontroller. This is a low cost variant to the alternative that involves the use of a dynamometer (consisting of a DC motor connected to the PMSM axle and a dedicated control unit to obtain a load torque within the desired limits).
• We redid Figure 36.

We made the proposed comparison.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Authors have answered most of my concerns. There is only one follow-up. The needs of the recursive control design for backstepping that mentioned in the last reply should be highlighted in the content.

Author Response

Dear reviewer, thanks for your recommendations.

We have inserted text regarding the backstepping control law design.

A proofreading has been done. 

Author Response File: Author Response.pdf