基于参数优化和补偿信号的非线性广义预测控制方法

Nonlinear generalized predictive control method based on parameter optimization and compensation signal

针对一类存在干扰和未知不确定性的复杂非线性被控过程的跟踪控制问题,将广义预测控制和信号补偿法相结合,提出了补偿信号驱动的非线性广义预测控制方法.采用低阶线性模型和未知非线性项来表示被控对象,未知非线性项表示系统建模误差及干扰等不确定性.采用低阶线性模型设计广义预测控制器,根据广义预测控制闭环系统可获得未知非线性项对系统影响的跟踪误差,引入最小化跟踪误差和控制量波动的一步最优控制设计补偿信号,抵消未知非线性项对被控对象的影响,改善系统动态性能.所提方法将以往要求未知非线性项全局有界的条件放宽为Lipschitz条件,证明了闭环系统的稳定性和收敛性.为了进一步提升系统动态性能,提出了基于梯度下降法的控制器加权参数的优化方法.仿真对比实验验证了所提算法的有效性.

For the tracking control problem of a class of complex nonlinear controlled processes with disturbances and unknown uncertainties,a compensation signal-driven nonlinear generalized predictive control method is proposed by combining the generalized predictive control and signal compensation techniques.The controlled object is represented by a low-order linear model and an unknown nonlinear term,which represents uncertainties such as system modeling errors and disturbances.A low-order linear model is used to design the generalized predictive controller.The tracking error affected by the unknown nonlinear term can be obtained from the generalized predictive control closed-loop system.A compensation signal is designed by introducing the one-step ahead optimal control to minimize the tracking error and the fluctuation of the control input,thereby eliminating the effect of the unknown nonlinear term on the controlled object and improving the dynamic performance of the system.The proposed method relaxes the previous condition that the unknown nonlinear term is globally bounded to the Lipschitz condition,which proves the stability and convergence of the closed-loop system.To further improve the dynamic performance of the system,an optimization method based on gradient descent for the weighting parameters of the controller is proposed.The effectiveness of the proposed method is verified by simulation comparison experiments.