This paper considers the problems of designing multivariable proportional-integral-derivative (PID) controllers for discrete-time systems with D-stability and/or performance constraints. First, the PID control problem is cast into a static output feedback (SOF) control problem, and linear matrix inequality (LMI) conditions are presented. Then, a cone complementarity linearisation (CCL) method is used to solve the SOF-stabilisation problem, and a coordinate transformation matrix (CTM) optimisation approach is extended to solve the optimal SOF control problem. Finally, a numerical example is provided to show the effectiveness and advantage of the CTM optimisation approach, and application to the anti-sway and positioning control of an overhead crane demonstrates the validity of the approach.

中文翻译：

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应用于桥式起重机的离散时间多变量PID控制器设计

本文考虑了为具有 D 稳定性和/或性能约束的离散时间系统设计多变量比例积分微分 (PID) 控制器的问题。首先，将 PID 控制问题转化为静态输出反馈 (SOF) 控制问题，并提出线性矩阵不等式 (LMI) 条件。然后，使用锥互补线性化（CCL）方法解决 SOF 稳定问题，并扩展坐标变换矩阵（CTM）优化方法来解决最优 SOF 控制问题。最后，通过数值算例展示了CTM优化方法的有效性和优势，并将其应用于桥式起重机的防摇和定位控制，证明了该方法的有效性。