1. Disturbance rejection control method
For permanent magnet synchronous motor
speed-regulation system
Shihua Li , Cunjian Xia, Xuan Zhou
Elsevier, Mechatronics 22 (2012) 706–714
Advanced Servo Control 12/24/2014 Student: T A R Y U D I / 林運昇 Advisor: Prof. Ming-Shyan Wang

2. Outline Introduction The mathematical model of PMSM Controller design
Speed controller design
Current controller design
Simulation and experiment results
Experimental results
Conclusion
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3. Introduction
For the speed loop, regarding parameter variations and load torque as the
lumped disturbances, an ESO based disturbance rejection control law is
developed.
Considering the dynamics of q-axis current, the coupling between rotor speed
and d-axis current as well as the back electromotive force are regarded as
lumped disturbances for the q-axis current loop, lumped disturbances are
estimated by introducing an ESO.
Thus a composite control law consisting of proportional feedback and
disturbance feedback compensation simplified model is developed to control the
q-axis current.
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4. Introduction The general structure of the PMSM servo system
Fig.  The principle block diagram of PMSM system based on vector control.
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5. The Mathematical Model of PMSM
Where:
  Rs  : Stator resistance, 
ud, uq  : d- and q-axes stator voltages, 
id, iq  : d- and q-axes stator currents, 
Ld, Lq : d- and q-axes stator inductances, and Ld = Lq = L
  np  : Number of pole pairs of the PMSM, 
ω  : Rotor angular velocity of the motor, 
ψf  : Flux linkage, 
TL  : Load torque, 
B  : Viscous friction coefficient and 
J  : Rotor inertia.
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6. Controller Design
ESO is the main disturbance estimation technique. It regards the lumped disturbances of system, which consists of internal dynamics and external disturbances, as a new state of system
The control scheme includes a speed loop and two current loops
Fig. The principle diagram of PMSM system under ESO based composite control methods.
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7. The principle of ESO-based control method
Example , how to construct linear ESO will be shown below
Where
  f ( x, t) : the unknown nonlinear function
 d(t) : the external disturbance 
u : the control signal
x : the output of system
  b   : the control gain
a  (t  ) = f  (x  , t  ) + d  (t  )
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8. Speed controller design
Define  x 1 = x  , x 2 = a (t).
And a linear ESO can be constructed as follows [1]:
Where
where −p(p > 0) is the desired double pole of ESO. z1 is the estimate of x1 and z2 is the estimate of a(t). Here, according to the analysis in [1], z1(t) is an estimate of the output x(t) while z2(t) is an estimate of the lumped disturbance a(t), i.e., z1(t) → y(t) and z2(t) → a(t).
A composite control law is designed as follows:
where x∗ is the reference input of x.
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9. Speed controller design
The torque equation of PMSM system is
where
Control gain
The lumped disturbances consisting of the friction, the external load disturbances, and the tracking error of current-loop of iq
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10. Speed controller design
Then an ESO can be designed as
where z1 is the estimate of angular velocity ω, z2 is the estimate of the lumped disturbances.
A composite control law of speed loop can be designed as
where k   is the proportional gain, ω∗ is the reference speed
is the output of speed loop controller
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11. ESO-based speed controller
Fig. 2. The block diagram of ESO-based speed controller
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12. Current controller design
An ESO-based controller is designed for the q-axis current loop. For the d-axis current loop, a standard PI control algorithm is employed.
The equation of q  -axis current loop is written as follows:
where the lumped disturbances of q  -axis current loop are
consisting of the coupling between rotor speed and d-axis current, the dynamics of q-axis current, the back electromotive force
The ESO of q-axis current loop can be designed as follows:
where −pq(pq > 0) is the desired double pole, z11 is the estimate of iq, and z12 is the estimate of aq(t).
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13. Current controller design
A composite control law of q  -axis current loop can be designed as
where k  q is the proportional gain of q  -axis current loop controller
 is the q-axis reference current
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14. PMSM system under ESO based composite control methods
A control scheme which employs disturbance rejection control laws for not
only speed loop but also the q-axis current loop
Fig. 3. The principle diagram of PMSM system under ESO based composite control methods.
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15. Simulation and experiment results
The parameters of the PMSM are taken the same as follows:  
Rs = 1.74 Ω,
Ld = Lq = 4 mH,
ψf = 0.402 Wb,
 J = 1.78 × 10−4 kg m2,
 B = 7.4 × 10−5 N ms,
 np = 4
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16. Simulation setup Parameter setup
The saturation limit of q-axis reference current is 11.78 A.
The proportional and integral gains of d-axis current controllers of the two control schemes are kp = 50, ki = 2500.
The parameters of q-axis current loop of the speed ESOC scheme are the same as that of the d-axis current loop.
The proportional gain and the desired double-pole of ESO of the speed loop of the speed ESOC scheme are k = 1.5, p = 5000.
For the current ESOC scheme, the proportional gain and the desired double-pole of the current and speed loops are takes as kq = 50, pq = 2000, and k = 1.5, p = 5000, respectively.
The load torque TL = 2.5 Nm is added at t = 0.1 s.
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17. Simulation results
The tracking responses for the q  -axis current loop under speed ESOC and current ESOC methods
Fig. 4. Curves of        under speed ESOC and current ESOC methods: (a) the whole curves under speed ESOC method, (b) the whole curves under current ESOC method,
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18. Simulation results
Fig. 4. Curves of        under speed ESOC and current ESOC methods: (c) the local curves of (a) in time domain [0, 0.01] s, (d) the local curves of (b) in time domain [0, 0.004] s,
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19. Simulation results
Fig. 4. Curves of        under speed ESOC and current ESOC methods: (e) the local curves of (a) in time domain [0.099, 0.103] s, and (f) the local curves of (b) in time domain [0.099, 0.103] s
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20. Simulation results The speed responses of the PMSM system
Fig. 5. Response of speed under speed ESOC and current ESOC methods: (a) the whole curves, (b) the local curves in time domain [0, 0.06] s, and (c) the local curves in time domain [0.098, 0.105] s.
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21. Simulation results
Estimation effects of ESO for speed and current loops
Fig. 6. The actual and estimate value of disturbances under current ESOC method: (a) a, z2 of speed loop, (b) aq, z12 of q-axis current loop
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22. Simulation results
Estimation effects of ESO for speed and current loops
Fig. 6. The actual and estimate value of disturbances under current ESOC method: (c) the local curves of (a) in time domain [0, 0.003] s, (d) the local curves of (b) in time domain [0, 0.008] s,
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23. Simulation results
Estimation effects of ESO for speed and current loops
Fig. 6. The actual and estimate value of disturbances under current ESOC method: (e) the local curves of (a) in time domain [0.099, 0.103] s, and (f) the local curves of (b) in time domain [0.099, 0.106] s.
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24. Experiment setup DSP TMS320F2808 with a clock frequency of 100 MHz
An intelligent power module (IPM) with a switching frequency of 10 kHz
The Hall-effect devices and are converted through two 12-bit A/D converters
An incremental position encoder of 2500 lines
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25. Experiment setup
The saturation limit of q-axis reference current is 11.78 A.
The proportional and integral gains of d-axis current controllers of the two control schemes are kp = 42, ki = 2600.
The parameters of q-axis current loop of the speed ESOC scheme are the same as that of the d-axis current loop.
The proportional gain and the desired double-pole of ESO of the speed loop of the speed ESOC scheme are k = 1.2, p = 330.
For the current ESOC scheme, the proportional gain and the desired double-pole of the current and speed loops are takes as kq = 25, pq = 870, and k = 1.2, p = 330, respectively.
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26. Fig. 8. Response curves of system when the reference speed is 1000 rpm: (a) iq,iq* (b) speed in the absence of load, and (c) speed in the presence of load.
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27. Fig. 9. Speed response curves when the reference speed is 500 rpm: (a) in the absence of load and (b) in the presence of load.
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28. Fig. 10. Speed response curves when the reference speed is 1500 rpm: (a) in the absence of load and (b) in the presence of load.
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29. The performance comparisons
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30. Conclusion
To improve the disturbance rejection ability, a control scheme which employs disturbance
rejection control laws for not only speed loop but also the q-axis current loop, has been
proposed.
Considering the dynamics of q-axis current, the coupling between rotor speed and d-axis
current as well as the back electromotive force have been regarded as lumped disturbances
for the q-axis current loop.
The lumped disturbances have been estimated by using an extended state observer.
Thus a composite control law consisting of proportional feedback and feed forward
compensation based on disturbance estimation has been developed to control the q-axis
current.
Simulation and experiment comparisons have been presented to verify the effectiveness of
the proposed method.
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31. References
1. Miklosovic R, Gao ZQ. A robust two-degree-of-freedom control design technique and its practical application. In: 39th IAS annual meeting on industry application conference; p. 1495– Li, Shihua, Cunjian Xia, and Xuan Zhou. "Disturbance rejection control method for permanent magnet synchronous motor speed-regulation system."Mechatronics 22.6 (2012):
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32. Thank you for your attention
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