1. CONSTRAINED NON-STATIONARY STATE FEEDBACK SPEED CONTROL OF PMSM
TOMASZ TARCZEWSKI1, MICHAŁ SKIWSKI1, LECH M. GRZESIAK2
1 Nicolaus Copernicus University, Institute of Physics, Toruń, Poland
2 Warsaw University of Technology, Institute of Control and Industrial Electronics, Warsaw, Poland
14 September, 2017

2. Real-time experiments
Outline
Introduction
Model of PMSM drive
Proposed controller
Non-stationary state feedback controller
Automatic selection of penalty matrices
Introducing constraints into control system
Real-time experiments
Laboratory setup
Experimental responses
Conclusion
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

3. Introduction
Examples of permanent magnet synchronous motors applications in a field of variable speed drive:
automotive: hybrid and electrical cars, electric power steering devices
heating, ventilating, air conditioning (HVAC) applications
Quiet and efficient operation of the PMSM drive is desirable
Mathematical model of the drive (i.e., PMSM fed by VSI) is non-linear and cross- coupled
Cascade control structure with PID controllers responsible for speed and current regulation is most often used
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

4. Introduction (cont’d)
State Feedback Controller (SFC) can also be applied to speed control of PMSM
all state-space variables are controlled by single controller
superior disturbance compensation
direct design for non-linear and non-stationary model of the plant
coefficients of controller have to be determined
constraints of state and control variables should be taken into account to achieve fast dynamic response
An artificial bee colony optimization procedure will be employed to automatic selection of non-stationary SFC coefficients
An a posteriori constraints introduction into control system with SFC will be shown
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

5. State-space model of the plant
Model of PMSM drive
State-space model of the plant
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

6. Non-stationary state feedback controller
Discrete control law
Discrete performance index
Weighting matrices
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

7. Automatic selection of penalty matrices
Properties of artificial bee colony optimization algorithm
ABC is based on the foraging behavior of honey bees:
employed bees  responsible for visiting food sources
onlookers  make the decision to choose a food source
scouts  responsible for random search of a new food sources
The position of a food source is a potential solution of the optimization problem
The quality of a food source is described by the nectar amount
The main parameters associated with ABC algorithm:
the number of colony size  NP
the number of food sources  NP/2
the number of optimized parameters  D
the lower  lb and the upper  ub bounds of D
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

8. Automatic selection of penalty matrices (cont’d)
An application of ABC to automatic selection of penalty matrices for LQR
Control objectives to be meet:
satisfactory dynamical behavior of angular speed for step changes of reference signal
zero d-axis current
smooth shape of q-axis control signal
Proposed performance index:
Constraints handling method (Deb’s rules) :
for two feasible solutions, the one having better objective function is chosen
any feasible solution is preferred to any infeasible solution
for two infeasible solutions, the one having smaller constraint violation is chosen
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

9. Automatic selection of penalty matrices (cont’d)
Auto-tuning procedure
Evolution of performance index
Evolution of angular speed
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

10. Automatic selection of penalty matrices (cont’d)
Non-stationary gain coefficients of SFC
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

11. Automatic selection of penalty matrices (cont’d)
Simulation response
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

12. Automatic selection of penalty matrices (cont’d)
Simulation response
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

13. Introducing constraints into control system
Formula for calculation of the q-axis constraint:
The boundary values of q-axis voltage:
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

14. Constrained non-stationary state feedback controller
Block scheme
Flowchart
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

15. Laboratory stand Parameter Value Unit Rated power PN 1.73 kW
Rated current IN 4 A
Moment of inertia Jm
8.3810-3
kgm2
Viscous friction Bm
1.410-3
Nms/rad
Parameter
Value
Unit
Stator resistance Rs
1.05 
Stator inductance Ls
12.68 mH
Torque constant Kt
0.94
Nm/A
Converter gain Kp
100
Parameter
Value
Unit
Switching frequency fPWM
33.(3)
kHz
Sampling period Ts 30 s
No of pole pairs p 3
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

16. Real-time experiments
Experimental response
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

17. Conclusion
Constrained non-stationary state feedback controller has been successfully applied to speed control of PMSM
Controller was designed directly from non-linear and cross-coupled model of the plant
An artificial bee colony optimization algorithm has been applied to determine penalty matrices for controller
Model predictive approach was employed to a posteriori introduce constraints into control system with state feedback controller
Proposed control scheme has been implemented in modern, SiC based drive with high switching frequency
Simulation and experimental results prove proper operation of the drive
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM

18. Thank you for your attention
T. Tarczewski, M. Skiwski, L.M. Grzesiak, Constrained non-stationary state feedback speed control of PMSM