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针对多变量离散控制系统的控制设计问题,提出了一种设计数字PID(proportional-integral-derivative)控制器的新方法.通过Kalman-Yakubovic-Popov(KYP)引理,对离散系统z域按系统频率和采样周期的乘积范围进行划分;然后基于模型匹配原则将PID控制器设计转化为求相应区域内H_∞范数构成的不等式最优解问题.同时将此不等式用系统状态空间中各系数矩阵表示,利用解线性矩阵不等式的方法进行求解;最后,通过数值例子验证,该方法可提高系统对频率和采样周期取值的鲁棒性,从而使所设计的控制器有更大的适用范围.
Aiming at the problem of control design of multivariable discrete control system, a new method for designing a PID controller is proposed. By using Kalman-Yakubovic-Popov (KYP) lemma, Frequency and sampling period, and then based on the principle of model matching, the PID controller design is transformed into the optimal solution of the inequality formed by H_∞norm in the corresponding region.At the same time, this inequality is modeled by the coefficient matrix in system state space Which is solved by solving the linear matrix inequality. Finally, the numerical example shows that this method can improve the robustness of the system to the values of the sampling frequency and the sampling period, so that the designed controller has more applicability.