基于LMI的随机系统PID相容性研究

Consistency analysis of desired indices based on LMI for PID regulator

针对具有随机白噪声输入的随机系统,分析了PID控制下期望指标的相容性问题。以状态空间和线性矩阵不等式(linear matrix inequality,LMI)为工具,首先把PID控制问题转化为局部状态反馈问题,得到了PID可稳定的LMI判据,进而当判定系统可稳时,给出了求取闭环系统最大衰减度指标、与衰减度指标相容的稳态输出方差相容区间的算法以及PID参数的求解方法,且文中算法都可以通过MATLAB软件的LMI工具箱自动求解。最后通过实例说明该方法的有效性。

For the stochastic system with white noise input, the consistency problem of desired indices for PID controller is investigated. Based on the tool of state space method and the linear matrix inequality（LMI）, the problem is transformed to the partial state feedback problem first, and the LMI criterion to judge is found and then if the given plant can meet the stabilization criterion, the algorithm to calculate the maximal attenuation degree of the closed-loop system and the lower bound for the steady-state output covariance indices consistent with the given attenuation is given, also the parameters of PID regulator can be found simultaneously. The proposed algorithm can be solved by the LMI toolbox of MATLAB software automatically and conveniently. Finally the method is illustrated by the application example.