基于LMI方法的网络化保性能PID控制

Networked guaranteed cost PID control via LMI approach

针对具有双边时变时延和数据丢包的网络控制系统(NCSs),研究了基于线性矩阵不等式(LMI)方法的二阶过程网络化保性能比例积分微分(PID)控制。通过采用状态反馈的增广状态空间模型重新描述了具有典型二阶传递函数形式的控制对象和PID控制增益,同时结合时滞系统的分析方法,将PID跟踪控制器参数选择归结为LMI求解问题。进一步地,采用自由权矩阵、互逆凸组合以及锥补线性化方法,给出了满足性能的控制器参数的求解方法,实现了采用传统的PID控制方法实现网络化轨迹跟踪控制。最后通过示例仿真和实验,验证了本文所提方法的有效性。

Aiming at the networked control systems(NCSs) with bilateral time-varying delay and packet dropouts, this work investigates networked guaranteed cost proportional integral derivative(PID) control via linear matrix inequality(LMI) approach for second-order processes. By using the augmented state space form to rewrite a controller with typical second-order process transfer function and the time-delay system approach, the selection of PID tracking controller parameters is reduced to the solution of linear matrix inequalities. Based on the free weight matrix, the reciprocal convex combination and the cone complementarity linearization method, the controller parameters which satisfy the tracking performance are obtained, and the traditional PID control method is adopted to realize networked trajectory tracking control. Finally, the examples of numerical simulation and experiment are given to illustrate the effectiveness of the proposed method.