Cascaded Robust Fault-Tolerant Predictive Control for PMSM Drives
Round 1
Reviewer 1 Report
The paper is well written and presents a new structure of control in the context of the PMSM.
In particular, a valid combination between the Model Predictive Control and Sliding Mode Control is presented.
In my opinion just a few chages can be considered
I would like to propose to write something about the d-q transform after the presentation of equation (1). The d-q transform is indicated in Figure 5, but please clarify the notation (Park, Clarke, d-q, etc).
The most important aspect to be clarified is the importance of SMC as robust tool which allowed to apply two cascaded MPC strategies effectively.
Moreover, the two MPC structures must be explained in Detail.
Concerning the cited literature, I think that the list of the papers can be expanded considering recent litterature. The following papers could be taken into conideration. The papers are related to the topic and they enphasize different important aspects which the authors could take into account to reformulate the introduction in terms of a more expanded review part.
Here below an adaptive PID Controller is used to control a permanent magnet actuator.
In fact, the authors correctly said in the introduczion that "
"This makes it difficult for PI control algorithms to obtain a satisfying dynamic performance in the entire operating range for PMSM [9]. "
Nevertheless in the litterature this problem was addressed. In the following paper and in the litterature therein you can find anoverview of thes aspects.
Mercorelli, P., Lehmann, K., Liu, S.
Robust Flatness Based Control of an Electromagnetic Linear Actuator Using Adaptive PID Controller
(2003) Proceedings of the IEEE Conference on Decision and Control, 4, pp. 3790-3795.
The following paper presents an efficient two-step reduction strategy for parametric transient electromagnetic simulations. The first step involves the conversion of a large system of parametrised differential algebraic equations (PDAEs), obtained after finite element (FE) discretisation into a significantly smaller system of ordinary differential equations, while symbolically preserving the parameters.
Bazaz, M.A., Nabi, M.U., Janardhanan, S.
Modelling and simulation strategy for parametric transient electromagnetic simulations
(2013) International Journal of Modelling, Identification and Control, 18 (3), pp. 251-260.
The following contribution considers a brief design review of the Permanent Magnet Synchronous Motors has been presented. A procedure has been developed to predict the steady state and dynamic performances of a brushless permanent magnet synchronous motor.
In your contribution, which i based on sliding mode control, the model plays an important role with respect to the robustness of the whole control strategy. In fact, if the equivalent control law cancels better the nonlinearity, the switching phenomenon can be reduced.
Azizur Rahman, M., Zhou, P.
Analysis of brushless permanent magnet synchronous motors
(1996) IEEE Transactions on Industrial Electronics, 43 (2), pp. 256-267.
The following contribution gives an impulse in the same context of the paper mentioned above. As explained, eve though Sliding Mode Control represents a structural robust control technique, the following paper proposes an identification technique of the parameters can help to minimize the effort of the corrective part of the law and thus to reduce the chattering phenomenon.
Mercorelli, P.
Parameters identification in a permanent magnet three-phase synchronous motor of a city-bus for an intelligent drive assistant
(2014) International Journal of Modelling, Identification and Control, 21 (4), pp. 352-361.
Author Response
Response to Reviewer 1 Comments
We thank the respected reviewers for their interest in our manuscript and for their helpful comments that will definitely improve our manuscript and we have tried to do our best to respond to the points raised. The referees have brought up some good points and we appreciate the opportunity to clarify our research objectives and results. As indicated below, we have checked all the comments provided by the reviewers and have made necessary changes accordingly to their indications. For your convenience, the comments/questions are in black and our responses are in blue. The changes in the main text are also highlighted in blue. We hope that the new version of the paper passes your qualification criteria. However, we are open to further modifications if you think it is necessary. Thank you very much for your wonderful services.
Reviewer: 1
The paper is well written and presents a new structure of control in the context of the PMSM. In particular, a valid combination between the Model Predictive Control and Sliding Mode Control is presented. In my opinion just a few changes can be considered
Question 1. I would like to propose to write something about the d-q transform after the presentation of equation (1). The d-q transform is indicated in Figure 5, but please clarify the notation (Park, Clarke, d-q, etc).
Response:
In the revision manuscript, the Park and Clarke transformation are expressed in the mathematical model derivation process of PMSM. The dq-axis mathematical model of the PMSM can be given as the dq-axis set of the three-phase motor. Thus, the Park and Clarke transformation of dq-axis voltage can be expressed as
（1）
whereandare the d-and q-axis stator voltages, respectively;,anddenote the three phase stator voltage;is the electrical rotor angle.
(Page 2, line 20)
Question 2. The most important aspect to be clarified is the importance of SMO as robust tool which allowed to apply two cascaded MPC strategies effectively. Moreover, the two MPC structures must be explained in Detail.
Response:
Thank you for your comments! In order to improve the robustness of predictive control system, the IT-SMO is designed to observe the external disturbances. The predictive speed controller is used to realize the speed control in this paper. The IT-SMO is designed to observe the external disturbance, so as to improve the robustness against the load perturbation and permanent magnet demagnetization. The main objective of the current control is to control motor currents with high accuracy that is as fast as possible. Parameter perturbation and permanent magnet demagnetization deteriorate the current control performance if these factors is not considered in the design of the controller. Compared with the conventional speed PI controller, the proposed scheme shows its superiority in control precision and disturbance rejection. In addition, the proposed scheme presents strong robustness and excellent dynamic response in the case of parameter perturbation and permanent magnet demagnetization, where the weakness the conventional PCC is successfully overcome.
The disturbance observe value is used as the feedback input of the predictive control system. According to (14), the optimal control law can be can be expressed as
（15）
According to (15), the predictive speed controller can be designed as follows:
（19）
whereis the observed value of.is the q-axis current reference output by predictive speed controller.
According to (15), the predictive speed controller can be designed as follows:
（20）
where,are the observed values of,.，are the d- and q-axis voltage reference output by predictive current controller. In order to give a more detailed description of the two MPC structures, the block diagram of the two MPC implementation is shown in Fig.5.
Fig. 2 The block diagram of CRFTPC method
Question 3. Concerning the cited literature, I think that the list of the papers can be expanded considering recent litterature. The following papers could be taken into conideration. The papers are related to the topic and they emphasize different important aspects which the authors could take into account to reformulate the introduction in terms of a more expanded review part.
Response:
Authors agree with the reviewer that the references in this article have been supplemented with recent references. In particular, the references added by the reviewer are supplemented. Supplementary references are as follows:
[10] Mercorelli P, Lehmann K, Liu S. Robust flatness based control of an electromagnetic linear actuator using adaptive PID controller[C]//42nd IEEE Conference on Decision and Control. 2003, 4: 3790-3795.
[7] Bazaz M A, Nabi M, Janardhanan S. Modelling and simulation strategy for parametric transientelectromagnetic simulations[J]. International Journal of Modelling, Identification and Control, 2013, 18(3): 251-260.
[24] Rahman M A, Zhou P. Analysis of brushless permanent magnet synchronous motors[J]. IEEE Transactions on Industrial Electronics, 1996, 43(2): 256-267.
[25] Mercorelli P. Parameters identification in a permanent magnet three-phase synchronous motor of a city-bus for an intelligent drive assistant[J]. International Journal of Modelling, Identification and Control 5, 2014, 21(4): 352-361.
Thanks very much for your attention and we greatly appreciate your time in handling our revised paper.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This paper presents cascaded robust fault-tolerant predictive controller, trying to achieve high performance speed loop and current loop for permanent magnet synchronous motor (PMSM) drives. However, there are some questions to be tackled below.
a. “d” and “q” should be in italic in the expression of “d-axis and q-axis”.
b. Why aren’t the formulas about δd andδq between (2) and (3) numbered? And how can they be derived?
c. Why is it possible to ignore the influence of the current loop control in the servo control system when PI controller is used?
d. Is the formula (20) a current controller or speed controller? I think it is a current controller while you present it is a speed controller.
e. Why do you believe a hyperbolic tangent function is effective to avoid chattering effects?
f. A predictive controller is discrete, so the comparative study about PI controller should also be discrete, but in simulation, the PI parameters are 2000 and 0.5, respectively. Apparently, they are gotten in continuous analysis.
g. The article is based on a servo system in the introduction and the analysis parts. But for simulation, the load torque can be 300Nm (max to 700Nm), representing the system is with thick rotor. Therefore, is it possible that the machine is used in a servo system?
h. The unit for toque should be Nm rather than N.
i. The rotational inertia is 100kgm2? Really? What kind of motor is it? Reconfirm it please.
Author Response
Response to Reviewer 2 Comments We thank the respected reviewers for their interest in our manuscript and for their helpful comments that will definitely improve our manuscript and we have tried to do our best to respond to the points raised. The referees have brought up some good points and we appreciate the opportunity to clarify our research objectives and results. As indicated below, we have checked all the comments provided by the reviewers and have made necessary changes accordingly to their indications. For your convenience, the comments/questions are in black and our responses are in blue. The changes in the main text are also highlighted in blue. We hope that the new version of the paper passes your qualification criteria. However, we are open to further modifications if you think it is necessary. Thank you very much for your wonderful services. Reviewer: 2 This paper presents cascaded robust fault-tolerant predictive controller, trying to achieve high performance speed loop and current loop for permanent magnet synchronous motor (PMSM) drives. However, there are some questions to be tackled below. Question 1. “d” and “q” should be in italic in the expression of “d-axis and q-axis”. Response: We are glad to report that in the revised version of the paper, the expression of “d-axis and q-axis” has been corrected. Question 2. Why aren’t the formulas about δd andδq between (2) and (3) numbered? And how can they be derived? Response: We have numbered the equation. The detailed derivation steps are as follows: The voltage equations of PMSM in synchronous rotating frame are usually described as[22], （1） Under control, the electromagnetic torque is, （4） The mechanical dynamic model can be described as follows, （5） where and are the d-and q-axis currents, respectively; , , and are the nominal value of stator resistance, the d-axis inductance, the q-axis inductance and the moment of inertia, respectively. is the friction coefficient, and is the electrical rotor speed. is the flux linkage established by the permanent magnets. is the number of pole pairs, is the electromagnetic torque, and is the load torque. Introducing , , and , where , and are nominal values and , , and are perturbation values of the corresponding model parameter. The flux linkage amplitude varies from initial to when demagnetization fault occurs, and defining as the new flux linkage components of d-axis. Therefore, according to (1), the voltage equations is expressed as follows when parameter perturbation and permanent magnet demagnetization are considered: （2） where and represent the unknown disturbances caused by parameter perturbation and permanent magnet demagnetization, they can be defined as （3） Question 3. Why is it possible to ignore the influence of the current loop control in the servo control system when PI controller is used? Response: Thank you for your comments! The purpose of this paper is to analyze the effect of parameter changes on the controller when the PI controller is used in the speed loop. In this case, the influence of the current control loop is neglected. However, in the next section, the control performance of the current control loop is analyzed. Question 4. Is the formula (20) a current controller or speed controller? I think it is a current controller while you present it is a speed controller. Response: Thank you for your comments! The cascaded predictive control structure is described in detail. According to (14), the optimal control law can be can be expressed as （15） According to (15), the predictive speed controller can be designed as follows: （19） where is the observed value of . is the q-axis current reference output by predictive speed controller. According to (15), the predictive speed controller can be designed as follows: （20） where , are the observed values of , . ， are the d- and q-axis voltage reference output by predictive current controller. In order to give a more detailed description of the two MPC structures, the block diagram of the two MPC implementation is shown in Fig.5. Fig. 2 The block diagram of CRFTPC method Question 5.Why do you believe a hyperbolic tangent function is effective to avoid chattering effects? Response: The curve of hyperbolic tangent function and sign function is shown in Fig. 1. From Fig. 1, it can be observed that the traditional symbol function is a right angle when switching, so it will cause chattering in the system. However, the hyperbolic tangent function has a smooth surface when switching, which can avoid the chattering caused by the function switching. Fig. 2 Curve of hyperbolic tangent function and sign function Question 6. A predictive controller is discrete, so the comparative study about PI controller should also be discrete, but in simulation, the PI parameters are 2000 and 0.5, respectively. Apparently, they are gotten in continuous analysis. Response: Thank you for your comments! The speed control performance comparison of conventional PI and proposed CRFTPC is verified. Authors agree with the reviewer that the PI controller should also be discrete. In this simulation case, the predictive controller is used in the current loop of both methods, but the PI controller and the predictive controller are used in the speed loop, respectively. The purpose is to compare the control performance of the PI controller and proposed predictive controller. Considering the dynamic response and overshoot of the PI controller, when the PI controller is in the optimal control state, the proportional gain and the integral coefficient are respectively selected as 2000 and 0.5 by actual debugging. Question 7. The article is based on a servo system in the introduction and the analysis parts. But for simulation, the load torque can be 300Nm (max to 700Nm), representing the system is with thick rotor. Therefore, is it possible that the machine is used in a servo system? Response: Thank you for pointing out this! From table. I, it is known that the simulation parameters has a particularly large moment of inertia and a large torque. The simulation parameters of the motor are provided by the Electric Locomotive Research Institute and are the parameter of a high-speed traction motor. This machine can be used in special occasions such as high-speed traction motors and tanks. Question 8. The unit for toque should be Nm rather than N. Response: We are glad to report that in the revised version of the paper, the expression error has been corrected. Question 9. The rotational inertia is 100kgm2? Really? What kind of motor is it? Reconfirm it please. Response: Thank you for your comments! The simulation parameters of the motor are provided by the Electric Locomotive Research Institute and are the parameter of a high-speed traction motor. We have confirmed that the motor's moment of inertia is 100kgm2. This motor can be used in special occasions such as high-speed traction motors and tanks. Thanks very much for your attention and we greatly appreciate your time in handling our revised paper.
Author Response File: Author Response.docx
Reviewer 3 Report
The paper is well presented and organized.
The topic is also interesting.
The proposed control is verified both with numerical results and experimental results.
The authors must respone/improve only the following points:
1) set the format in lines 81-93;
2) Line 78: "Under id=0 control". Probably the authors means that the used control is a Maximum Torque per Ampere
control, which determines the id=0. Otherwise in (1), the id disappears.
Author Response
Response to Reviewer 3 Comments
We thank the respected reviewers for their interest in our manuscript and for their helpful comments that will definitely improve our manuscript and we have tried to do our best to respond to the points raised. The referees have brought up some good points and we appreciate the opportunity to clarify our research objectives and results. As indicated below, we have checked all the comments provided by the reviewers and have made necessary changes accordingly to their indications. For your convenience, the comments/questions are in black and our responses are in blue. The changes in the main text are also highlighted in blue. We hope that the new version of the paper passes your qualification criteria. However, we are open to further modifications if you think it is necessary. Thank you very much for your wonderful services.
Reviewer: 3
The paper is well presented and organized. The topic is also interesting. The proposed control is verified both with numerical results and experimental results. The authors must response /improve only the following points:
Question 1. set the format in lines 81-93;
Response:
We are glad to report that in the revised version of the paper, the article format has been corrected in lines 81-93.
Question 2. Line 78: "Under id=0 control". Probably the authors means that the used control is a Maximum Torque per Ampere control, which determines the id=0. Otherwise in (1), the id disappears.
Response:
Authors agree with the reviewer that the id current in equation (1) will disappear under id=0 control. However, the proposed algorithm can be used for both maximum torque per ampere control and id=0 control. Therefore, the id current is included in equation (1).
Thanks very much for your attention and we greatly appreciate your time in handling our revised paper.
