基于Nevanlinna-Pick插值的跟踪系统H_∞鲁棒控制器设计

H_∞ Robust Controller Design for Tracking System Via Nevanlinna-Pick Interpolation

传统的H∞鲁棒控制器通常都是基于线性矩阵不等式求解的,因此阶次较高,不利于实现,而基于Nevanlinna-Pick插值的H∞鲁棒控制器设计方法能够有效的解决这一问题。本文提出一种改进的同伦算法用于求解控制器设计过程中出现的非线性方程,避免了经典同伦法中逆矩阵的求解。针对某一跟踪系统设计基于Nevanlinna-Pick插值的H∞鲁棒控制器,通过阶跃响应和正弦信号的跟踪响应可以看出,与高阶超前滞后校正环节相比,前者构成闭环系统的跟踪精度要比后者的控制精度高,且具有较强的鲁棒稳定性。

The traditional H∞ robust controllers were designed by solving linear matrix inequalities,which have higher degree and are difficult to be realized.A new design method of H∞ robust controller was proposed based on NevanlinnaPick interpolation,where a modified homotopy method was introduced to solve the nonlinear algebraic equations induced in the design process,which can avoid calculating the matrix inverse.The robust controller was designed for tracking system.From both step response and sinusoidal response,the proposed H∞robust controller has higher accuracy and robustness,compared with lead-lag compensator.