不确定线性动态控制系统的鲁棒性设计方法

ROBUST DESIGN OF LINEAR DYNAMIC SYSTEM WITH UNCERTAINTY

鲁棒线性控制器设计的主要问题是针对对象模型不确定性 ,寻找线性反馈控制器 ,使得不确定控制系统稳定 .针对具有线性、非线性或时变结构的模型不确定性多变量动态系统 ,采用动态补偿器结构与原系统进行增广 ,构成闭环动态近似系统 .根据 Gronwall引理 ,推导出了基于不确定性范数上界的动态线性系统鲁棒稳定的充分条件 .根据该鲁棒稳定条件 ,给出了具体的动态不确定系统的鲁棒性设计算法 .通过选择适当的变换阵 ,利用特征值配置技术求出动态补偿器的参数 ,来满足鲁棒稳定条件 ,使得闭环不确定动态系统稳定 ,从而提出了一种时域内鲁棒线性控制器设计方法——动态补偿器法 .该方法同样适用于控制器为输出反馈的情形 .给出了具体设计实例 。

The main problem of designing a robust linear controller is to look for a suitable controller that can stabilize the control system with uncertainty. For the multi-variable dynamic system with linear, nonlinear and time-variant model uncertainties, we adopted dynamical compensator and augmented the system so that a closed approximate system was obtained. Based on Gronwall lemma, we derived the sufficient condition for robust stabilization. By selecting suitable transform matrix and utilizing the technique of eigenvalue assignment, we yielded the parameters of dynamical compensator to meet the need of robust stabilization condition and to stabilize the closed uncertainty system, thus formed a new design method of robust linear control system in time domain--dynamical compensator method. A design procedure was given. The method is also suitable for the situation of output feedback. A design example is given to check the simple and effective technique.