鲁棒稳定性对最优二次型控制设计的约束

Robust stability constraints on linear quadratic optimal control

中文关键词  伺服系统  内模原理  LQR最优控制  鲁棒稳定性  卡尔曼等式

英文关键词  servo systems  internal model  LQR optimal control  robust stability  Kalman’s equality

中文摘要

      高品质反馈系统中, 对象的模型不确定性给最优控制设计带来许多困难. 本文针对车载“动中通”天线伺 服系统, 研究了一种内模扩展的线性二次调节器(LQR)最优控制设计方法. 根据卡尔曼等式和小增益定理, 给出了 系统的鲁棒稳定性对控制器设计参数的约束条件, 以及鲁棒稳定裕量与二次最优性能指标参数的定量关系. 最后通 过MATLAB仿真和实际系统实验, 验证了控制器的有效性.

英文摘要

      Plant uncertainties make it difficult to design optimal linear quadratic regulator (LQR) feedback controllers. The key issue is that for LQR optimal control design problem, there is no effective way to select proper weighting parameters in the cost function to guarantee the robust stability of the systems. This work investigates the internal model extended LQR optimal control design for the servo system in a communications on the move (COTM) system. Based on the Kalman’s equality and the small gain theorem, the robust stability constraints on the weighting parameters in the cost function are elaborated and the quantitative relationship between the robust stability margin and the weighting parameters in the cost function are derived. Finally, the effectiveness of the results in this work is validated by MATLAB simulations and experimental results.