期望极点/小静差周期跟踪系统的满意控制

Satisfactory Control of Periodically Tracking Systems Under Constraints of Desired Poles and Small Static Error

针对线性周期采样跟踪系统研究二个区域指标约束的满意控制问题 ,根据Lyapunov稳定性理论及稳态误差系数理论 ,利用提升法将N—周期跟踪系统满足区域极点、小静差输出的采样控制问题映射为矩阵不等式约束问题。再运用拆分法将提升系统满足上述矩阵不等式约束拆分为N个线性矩阵不等式组 (LMIs)约束问题 ,并通过Matlab工具箱对LMIs进行凸优化 ,给出一种有效的满意控制设计方法 ,并进行了算例验证。

Satisfactory control with two regional performance requirements is studied for a class of linear periodically sampled tracking systems. According to Lyapunov stability and theory of stable error coefficient, satisfactory control problem of linear periodically sampled tracking systems with desired regional poles and small static error indexes can be mapped into the problem with constraints of matrix inequalities through traditional lifting technique. These matrix inequalities can be divided into a set of N linear matrix inequalities (LMIs) by using Lyapunov theory. Satisfactory control of the associated systems is cast to a convex optimization problem subject to a set of LMIs by the LMI approach, and an effective designable approach to satisfactory control of the tracking system is presented. A numerical example confirms the results obtained.