Robust control system synthesis for constrained systems and its experimental validation

真实的控制系统有诸如输入和输出信号的限制。考虑系统约束是很重要的，因为如果在控制系统设计中忽略系统约束，控制系统可能会不稳定或失去预期性能。本文主要研究了约束系统的鲁棒控制系统设计，特别是1)带干扰抑制的模型预测控制，2)约束系统的补偿律，得到了以下结果。1)针对具有加性扰动的系统，我们首先引入了极小-极大型目标函数，并刻画了极大值扰动序列。在此基础上，得到了一种具有干扰抑制特性的输入约束线性系统的降阶模型预测控制。通过假设扰动有界，进一步推导出同时具有输入约束和状态约束的系统的预测控制。2)研究了闭环系统连续时间输入信号对与控制器状态及相应输出之间的关系。然后，明确了对系统投入产出关系有主导作用的对。基于这一结果，得到了满足系统约束的补偿律。

Real control systems have constraints such as limitations on input and output signals. It is important to take into account system constraints since a control system may be destabilized or expected performance would be lost if system constraints are neglected in control system design. This research focused on robust control system design for constrained systems, in particular, 1) model predictive control with disturbance attenuation, 2) compensation law for constrained systems, and we have the following results. 1) We first introduce a min-max type objective function for systems with additive disturbance and characterize the maximizing disturbance sequence. Based on this result, we have obtained a reduced order model predictive control with disturbance attenuation property for input constrained linear systems. We further derived an MPC for systems with both input and state constraints by assuming the bounded disturbance. 2) We have investigated the relationship between the pair of a continuous-time input signal and controller state and corresponding output for a closed-loop system. We then clarified the pairs which have dominant effect on input-output relationship of the system. A compensation law that satisfies systems constraints is obtained based on this result.