非线性系统近似最优PD动态补偿控制

Approximate optimal PD dynamic compensation control for nonlinear systems

本文研究了一类基于动态补偿的非线性系统的近似最优PD控制的问题.用微分方程的逐次逼近理论将非线性系统的最优控制问题转化为求解线性非齐次两点边值序列问题,并提供了从时域最优状态反馈到频域最优PD控制器参数的优化方法,从而获取系统最优的动态补偿网络,设计出最优PD整定参数,给出其实现算法.最后仿真示例将所提出的方法与传统的线性二次型调节器(LQR)逐次逼近方法相比较,表明该方法具有良好的动态性能和鲁棒性.

We consider the approximate optimal PD control for nonlinear systems based on the dynamic compensation. By using the successive approximation theory of differential equations, the original optimal control problem of nonlinear systems is transformed into a sequence of non-homogeneous linear two-point-boundary-value（TPBV） problems, which converts the optimization of the state variables feedback in the time domain into the optimization of PD controller parameters in the frequency domain. According to this method, the system optimal dynamic compensation network is obtained; the optimally tuned parameters of PD controller are designed and the realization algorithm is developed. Simulations show that the result is more robust and with better dynamic performance than that obtained by successively approximating the traditional linear quadratic regulator（LQR）.