基于模型参考和内模原理的线性系统鲁棒控制设计

Robust control design of linear systems based on model reference and internal model principle

不确定性因素会使系统性能恶化,它包括系统不确定性参数和各种外部干扰等.本文针对这种不确定性线性系统,利用模型参考和内模原理,建立鲁棒控制系统结构,分析了其能控性条件,通过选择参考模型和内模实现系统能控,在此条件下,将鲁棒控制设计转换为控制系统的LQR问题进行研究,并运用最优控制理论,计算其反馈控制律.仿真结果表明该设计方法将"模型参考"与"内模原理"有机结合起来,提高了系统的鲁棒稳定性,有效抑制干扰,并实现系统性能的改善.

The uncertainties usually deteriorate the performance of the systems. It includes the uncertain parameters and the outside disturbances and so on. With model reference and internal model principle, a structure of robust control systems is built for this kind of linear uncertain systems, and its controllability condition is then analyzed. Its controllability condition can be satisfied by choice of reference model and internal model. On this condition, the robust control design can be converted into the linear quadratic regulator（LQR） problem, and the optimal control theory can also be utilized to compute its feedback control law. The simulation shows that model reference and internal model principle can be integrated into this approach, which can improve the robust stability of the systems, reduce disturbance efficiently and ameliorate its performance.