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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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