1. Student: Po-Jui Hsiao Adviser: Ming-Shyan Wang Date : 4/12/2011
Design and Implementation of a Robust Current-Control Scheme for a PMSM Vector Drive With a Simple Adaptive Disturbance Observer
Yasser Abdel-Rady Ibrahim Mohamed, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 4, AUGUST 2007
Student: Po-Jui Hsiao
Adviser: Ming-Shyan Wang
Date : 4/12/2011
製作：100%

2. Outline Abstract Introduction
Modeling of PMSM(permanent-magnet synchronous motor) with uncertainties
Adaptive disturbance observer
Observer design
Stability Analysis and observer tuning
Evaluation results
Experimental setup
Experimental 1
Experimental 2
Experimental3
Experimental4
Conclusions
References

3. Abstract
The robust controller is realized by including an adaptive element in the reference-voltage generation stage using the feedforward control.
The time-varying nature and the high-bandwidth property of the uncertainties in a practical PMSM drive system, the adaptive element is simply chosen as the estimated uncertainty function, which adaptively varies with different operating conditions.
The frequency modes of the uncertainty function are embedded in the control effort, and a robust current-control performance is yielded.
To provide a high-bandwidth estimate of the uncertainty function, a simple adaptation law is derived using the nominal current dynamics and the steepest descent method.

4. Introduction
For high-performance control of a PMSM, a widely used approach is to employ the field-orientation mechanism [2], using synchronous frame proportional–integral (PI) current controllers with an active state-decoupling scheme.
In [9], a back-EMF compensation method has been proposed to obtain a current-control scheme that is independent of back-EMF variation. The back EMF has been estimated by using the feedback of the delayed input voltages and currents in a discrete-time domain.
A simple and effective robust control scheme can be achieved by estimating the voltage disturbance, which is caused by the uncertainties, and using the estimate in feedforward control.

5. Modeling of PMSM with uncertainties
In Park’s d-q frame, which rotates synchronously with an electrical angular velocity , the stator voltage and electromagnetic torque equations of a PMSM are expressed as
where and are the d- and q-axes stator voltages, respectively; and are the d- and q- axes stator currents, respectively; and are the d- and q- axes stator inductances, respectively; R is the stator per-phase resistance; is the magnet’s flux linkage; P is the number of the pole pairs; is the electromagnetic torque; subscript “o” denotes the nominal value.

6. Modeling of PMSM with uncertainties
, , and represent the lump of uncertainties that are caused by parameter variations, flux harmonics, and other unstructured uncertainties, respectively, and they are given by
where ; ; ; ; and , , and represent unstructured uncertainties due to unmodeled dynamics.

7. Adaptive disturbance observer
Fig. 1. Overall block diagram for the proposed current controller

8. Adaptive disturbance observer
A. Observer design
Since the harmonic components that are included in the inverter output voltage are not correlated with the sampled reference currents, the pulse-width-modulated (PWM) voltage source inverter(VSI) can be assumed as a zero-order hold circuit with transfer function given by
where T is the discrete-time control sampling period and s is the Laplace operator.

9. Adaptive disturbance observer
For digital implementation of the control algorithm, the PMSM current dynamics in (1) can be represented in a discrete-time domain with the conversion in (6), as follows:
where
k is the iteration integer and T is the sampling period.

10. Adaptive disturbance observer
To estimate the uncertainty function , an adaptive natural observer is constructed with the following input/output relation:
where the symbol “ˆ” denotes the estimated quantities.
The estimation error vector can be defined as
Due to the properties of guaranteed convergence and optimizing the performance, a quadratic error function is defined as follows:

11. Adaptive disturbance observer
To minimize the objective function, one can evaluate the following Jacobian as:
For the steepest descent algorithm [14], the change in the estimate is calculated as
where is the adaptation gain matrix.

12. Adaptive disturbance observer
B. Stability Analysis and observer tuning
The Lyapunov function is selected as
where is the error due to the adaptation process.
The Lyapunov’s convergence criterion must be satisfied such that
where is the change in the Lyapunov function.
Equation (14) is satisfied when as , as shown in (13). The term is given by

13. Adaptive disturbance observer
Using (7) and (8) with the adaptation law in (12), the change in can be given by
By substituting (16) into (15), can be given as
To satisfy (14), the adaptation gains and are chosen as

14. Fig. 2. Experimental setup.
Evaluation results
A. Experimental setup
Fig. 2. Experimental setup.

15. Evaluation results motor1 motor2 property
Two test motors with the following specifications are used for better evaluation of the proposed method:
motor1
motor2
property
a high-speed surface-mounted PMSM
a low-speed direct-drive surface-mounted PMSM
Load
1.5N*m
10N*m
rpm
3000r/min
120r/min
0.825Ω
15Ω
9.5mH
21.3mH
0.079Wb
0.345Wb

16. Evaluation results B. Experimental 1
Fig. 3. Measured control performance with the conventional PI decoupling controller starting with for motor 1. (a) q-axis current component. (b) Phase-a current.

17. Evaluation results
Measured control performance with the proposed controller starting
with for motor 1. (a) q-axis current component. (b) Phase-a current. (c) Estimated q-axis disturbance

18. Evaluation results C. Experimental 2
Fig. 5. Measured q-axis current performance with the conventional PI decoupling controller starting with for motor 1.

19. Evaluation results
Fig. 6. Measured control performance with the proposed controller starting with for motor 1. (a) q-axis current component. (b) Estimated q-axis disturbance.

20. Evaluation results D. Experimental 3
Fig. 7. Measured q-axis current tracking error with the conventional PI decoupling controller starting with for motor 1.

21. Evaluation results
Fig. 8. Measured control performance with the proposed controller starting with for motor (a) q-axis current tracking error. (b) Estimated q-axis disturbance.

22. Evaluation results E. Experimental 4
Fig. 9. Measured control performance with the conventional PI decoupling controller for motor 2.
(a) Torque response: Time domain and steady-state harmonics spectrum.
(b) Phase-a current response: Time domain and steady-state harmonics spectrum.

23. Evaluation results
Fig. 9. Measured control performance with the conventional PI decoupling
controller for motor 2. (c) Speed response.

24. Evaluation results
Fig. 10. Measured control performance with the proposed controller for motor 2.
(a) Torque response: time-domain and steady-state harmonics spectrum.
(b) Phase-a current response: time-domain and steady-state harmonics spectrum.

25. (c) Speed response. (d) Estimated q-axis disturbance.
Evaluation results
Fig. 10. Measured control performance with the proposed controller for motor 2.
(c) Speed response. (d) Estimated q-axis disturbance.

26. Conclusions
This paper has introduced a robust current-control scheme for a PMSM with a simple adaptive disturbance observer.
To guarantee the system’s convergence and to properly tune the proposed observer, a stability analysis based on a discrete-time Lyapunov function has been used.
Comparative evaluation experiments were carried to test the effectiveness of the proposed control scheme under different operating conditions.

27. References
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28. References
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30. Thanks for your attention!