基于LMI的约束Hammerstein系统最优控制器设计

Design of optimal controller of constrained Hammerstein systems based on LMI

针对具有输入约束的Hammerstein系统,提出了一种基于线性矩阵不等式(LMI)的最优控制器设计方法.运用非线性分离两步法控制策略,首先通过线性矩阵不等式(LMI)技术给出Ham-merstein模型线性子系统的状态反馈最优控制;其次,通过求解非线性方程组计算实际控制量.两步法策略充分利用了Hammerstein模型的特殊结构,把控制器设计问题仍归结在线性控制系统范围内.进一步,利用Lyapunov稳定性理论建立了闭环稳定的充分条件.最后通过聚丙烯牌号切换的仿真验证笔者算法的有效性.

For Hammerstein system with input constraints,the design method for optimal controllers is proposed based on LMI.Two-step method control strategy of nonlinear separation is adopted.Firstly,a state feedback optimal control of the linear subsystem of Hammerstein models is presented by using the LMI technique;secondly,the actual control actions are calculated by solving nonlinear algebraic equations.The two-step strategy makes a full use of the special structure in Hammerstein model and it comes down the controller design problem within the linear control system.Moreover,the Lyapunov＇s method is used to derive sufficient conditions for the closed-loop stability.Finally,a simulation of polypropylene grade transitions verifies the effectiveness of the method proposed here.