基于SDRE的永磁同步电动机的近似最优控制

针对具有仿射非线性模型的永磁同步电动机,研究其非二次型性能指标的最优控制问题。非线性非二次型最优控制问题导致难以求解的HJB(Hamilton Jacobi Bellman)方程,为避免这一难题,首先采用SDRE(State-Depend-ent Riccati Equation)法将其转化成状态相关的Riccati方程求解问题。SDRE法需要在每一次采样时刻实时地求解一个代数Riccati方程,在高阶系统中巨大的运算耗时使得SDRE控制器难以实现,为此进一步采用一种有效求解SDRE控制器的方法 -θ-d法,它只需求解一次与初始状态相关的代数Riccati方程,控制器的其余参数均可离线通过矩阵的相关运算获得,从而大大地减少了在线计算量。另外,SDRE方法可以通过适当选取状态相关的加权矩阵,以较小的控制作用获得与常量权矩阵相近甚至更好的控制效果。最后,以永磁同步电动机为实例进行的仿真验证了本文方法的有效性与可行性。

Approximate Optimal Control for PMSM Based on SDRE Method

Optimal control problem with non-quadratic performance index is considered for Permanent Magnet Synchronous Motor(PMSM) with affine nonlinear model.Nonlinear non-quadratic optimal control problem leads to the difficulty of solving nonlinear HJB(Hamilton Jacobi Bellman) equation,in order to avoid the HJB problem,state-dependent Riccati equation(SDRE) method was adopted firstly to change the problem into the issue of solving state-dependent Riccati equation.However,algebraic Riccati equations are required to solve in real time at each step,so the SDRE controller is hard to achieve on line for high order systems for its huge computational burden,so that θ-d method which can solve SDRE controller effectively was further adopted.Only one algebraic Riccati equation related with the initial states is required to solve,while other parameters of the controller can be obtained by off-line computing of matrixes.So that the on line computation can be lessened obviously.Besides,better performance with less effort can be obtained by choosing weight matrixes of state-dependent appropriately.Simulation verified the effectiveness and feasibility of the method proposed in this paper for PMSM system.