同时含状态和输入时滞系统的最优滑模控制

研究了一类线性时滞系统的变结构控制器的设计问题。为了简化变结构控制器的设计,首先通过非奇异线性变换将含状态时滞和输入时滞的线性系统化为无时滞系统。其次,在新坐标下,设计变结构控制器。结合二次型性能指标最优控制方法,给出了线性无时滞系统最优滑模的综合设计方法。引入趋近律方法设计控制律,有效的削弱了抖振并能保证系统在有限的时间内到达滑模面。最后,提出并证明了原系统渐近稳定的充分条件。仿真例证了该方法的有效性。

Optimal Sliding Mode Control for Linear Systems with Input and State Delays

The problem of designing sliding mode controllers for a class of linear systems with time delays was concerned. The original system with both input and state time delays was first rewritten into a form without any time delays by a nonsingular linear transformation. Then the sliding mode controller was designed based on the transformed system. The quadratic performance index optimal control technique was introduced to design the optimal sliding mode. By applying reaching law approach, the selected control law ensures that all trajectories starting off the manifold reach it in finite time and have low chattering in the sliding motion. Finally, a sufficient asymptotic stability condition of the original system was proposed. The efficiency and superiority of the proposed method were demonstrated by simulation study.