基于μ-合成的直流电机鲁棒控制器研究

Robust controller research on DC motor based on μ-synthesis

针对电机负载参数变化引起的模型不确定性,该文基于μ-合成控制理论,尝试设计具有较强鲁棒性的直流电机速度控制系统。首先依据干扰抑制原理,通过引入虚拟不确定块等将系统鲁棒性能问题转化为鲁棒稳定性问题,然后通过求解合适的权重矩阵使控制系统的性能满足设计要求;最后分别运用复数及混合μ-合成控制算法求得两种鲁棒控制器,并运用Hankel奇异值及动态性能空间方法予以简化。鲁棒性能分析及扰动抑制结果表明:所设计的两种控制器对电机负载的摄动均具有较强的鲁棒性,且对于标称值仅为实数的不确定闭环系统,采用D-G-K迭代混合μ-合成控制算法设计的鲁棒控制器对扰动具有明显更强的抑制效果。

Aiming at the problem of model uncertainty caused by the DC motor load variations,robust DC motor speed control system was designed usingμ-synthesis control theory in this article.Firstly,by introducing fictive uncertainty,the robust performance problem was transformed into robust stability problem according to the principle of interference suppression.Secondly,the weighting functions were selected properly to have the control system to meet the design requirements.Lastly,the complex and mixedμ-synthesis D-K iteration algorithm were used to solve the controllers,and these two controllers were simplified using the Hankel singular values and dynamic performance space procedures.Robustness analysis and disturbance rejection results showed that:there are relatively strong robustness of the two controllers on the motor load perturbation,and for the closed-loop system with only real number nominal value,the controller designed by D-G-K Iteration mixedμ-synthesis algorithm has obviously stronger robust to the disturbance suppress.