SDRE-based Control Method Research For Permanent Magnet Synchronous Motors (PMSM)

Permanent Magnet Synchronous Motors (PMSMs) have been widely applied inmodern high-precision servo systems for their excellent low-speed performance, gooddynamic behavior and wide-speed operations.Design and implementation of optimal controller which based on State-dependentRiccati Equation (SDRE) is researched in this paper. The main works are as follows:1. PMSM’s model building. PMSM’s mathematical model in ABC coordinate isbuilt according to its physical model, and definition of three coordinates is given. Withprinciple of equal magnetomotive force and power invariance, transformation formulasof currents, voltages and flux between coordinates is got. With the study above,PMSM’s mathematical models in dq and αβ coordinates is got. For the furtherresearch, PMSM’s mathematical model is given as an affine nonlinear dynamicequation. The designed control law which is given in the following study can be usedfor practical system’s control.2. The design problem of optimal controllers with non-quadratic performanceindex for a class of affine nonlinear systems is considered, which is based on SDREmethod. With extended linearization which contained in SDRE method, affinenonlinear systems’ dynamics can be transformed into State-dependent Coefficient(SDC) form equations. The optimal control problem for nonlinear systems generallyleads to Hamilton-Jacobi-Bellman (HJB) equation or nonlinear two-point boundaryvalue (TPBV) problem and its solution is difficult to obtain. In order to avoid HJBequation and TPBV problem, SDRE method is adopted which can transform theproblem into solving SDRE. Coefficient matrix A(x)of SDC form usually is not uniquefor multi-variable systems, an extended linearization method is proposed in this sectionto get unique A(x). Besides, freedom factor is introduced to make A(x)get extra freedom. Weighting matrices in performance index are allowed to be state-dependent,consequently, a method to choose weighting matrices of state-dependent is proposed,which is beneficial to performance’s improvement.3. Taking a PMSM as control object, the optimal controller’s design problem withnon-quadratic performance index is considered. According to PMSM’s affine nonlinearmathematical model given above, SDRE method is used for PMSM’s optimalcontroller design, and concrete design steps are given. Simulation is carried out toevidence the effectiveness of the method proposed in the paper.4. The implementation problem of SDRE-based controllers for PMSMs isconsidered. The main demands for engineering applied controllers are capacity ofreal-time online controlling and high control accuracy. The θ-Dtheory’s approximatesolution to SDRE controller is studied, and the control law in which coefficients can begot offline is obtained. With-Dmethod, SDRE-based controllers have propertiesof real-time online controlling. Meanwhile, Improved Newton method’s iterativeprinciple of solution of SDRE is researched, and Improved Newton method is adoptedfor high precision solution of SDRE. With Improved Newton method, SDRE-basedcontrollers have properties of high control accuracy. The research results affordchoices to different engineering demands. Simulations are carried out by a PMSMmodel to evidence the effectiveness and practicability of the methods proposed in thepaper.