一种基于J-无损分解的性能加权函数优化设计

Optimization design approach of performance weight function based on J-lossless factorization

为了提高伺服系统性能,提出一种基于J-无损分解的性能加权函数优化设计方法。首先,依据闭环系统H∞范数达到1的设计准则,给出了伺服系统性能加权函数优化设计算法的迭代步骤;其次,利用Bode积分关系以及H∞最优控制结果全通特性分析了算法的收敛性;最后,基于J-无损分解推导出性能加权函数优化设计的计算公式。所提出的优化设计算法易于迭代计算,能够在较少的迭代步骤内使得闭环系统H∞范数达到1。仿真实例验证了算法的有效性。

In order to get servo system＇ s best performance, an optimization design approach of performance weight function based on J-lossless factorization is proposed. Firstly, utilizing the criterion of closed loop system＇ s H∞ norm approaching 1, the servo system＇ s performance weight function design iteration steps were presented. Secondly, the algorithm＇ convergence was analyzed based on Bode＇s integral and allpass property of H∞ optimal control. Finally, the performance weight function calculating formula was deduced based on J-lossless factorization. The proposed optimization design method is easy to compute and closed loop system＇ s H∞ norm will approach 1 in a few steps. A simulation result is given to verify the proposed method＇s validation.