用镜像映射方法求非稳定过程的鲁棒控制器

非稳定过程在开右半平面的零极点关于虚轴的对称值称为该零极点的镜像映射。通过镜像映射将非稳定过程转换成最小相位系统 ,然后用闭环增益成形算法求解鲁棒控制器。由于非稳定过程在镜像映射前后的奇异值曲线相同 ,而闭环增益成形方法直接根据鲁棒性能指标的奇异值曲线形状用闭环系统具有工程意义的参数构造出鲁棒控制器 ,故该控制器对非稳定过程同样具有鲁棒性。该方法求解过程异常简单 ,工程意义明确。

Solving Robust Controller of Unstable Process Using Mirror-Injection Method

The symmetric values about the imaginary axis of zero-poles which the unstable process lies in the open and closed right-half plane are defined as their mirror-injection. An unstable process is transformed into a minimum-phase system through mirror-injection, then solve the robust controller using closed loop gain shaping algorithm. Because its largest singular value curve is identical before or after the unstable process is mirror-injected, and the closed loop gain shaping algorithm constructs directly the robust controller using parameters having engineering sense according to the shape of the singular value curves of the robust performance index, the designed controller has equally robustness to the unstable process. The method has the advantages of simple design procedure and obvious physical sense.