时变不确定性系统的二自由度最优鲁棒稳态跟踪控制器设计

TWO DEGREE OPTIMAL ROBUST STEADY-STATE TRACKING CONTROLLER DESIGN FOR PLANT WITH TIME-VARYING UNCERTAINTY

研究了被控系统存在范数有界的时变模型摄动和未知外部干扰时鲁棒稳态跟踪问题 .利用二自由度控制结构和 Youla参数化方法 .提出了一个最坏情况稳态绝对误差的精确计算公式 ,利用该公式最优稳态跟踪控制器设计问题可化为一个有限维 l1 优化问题 .因此控制器设计只需解一个标准线性规划问题 .此外 ,还证明了所提出的控制器可同时保证系统的鲁棒稳定性和最优跟踪性能 .仿真结果表明了该方法的有效性和可行性 .

This paper addresses the robust steady-state tracking problem when the system under consideration is subject to norm bounded time-varying uncertainty as well as unknown external bounded disturbances. With the help of two-degree control scheme and Youla parametrization, we propose an exact formula for computing the worst-possible steady-state absolute value of the control error. Using this formula, we show that the problem of designing a controller that minimizes the worst case steady-state controller error is reduced to a finite dimensional l1 optimization problem. Hence, the proposed controller can be obtained by solving a standard linear programming problem. We also demonstrate that the proposed controller ensures both optimal robust stability and optimal steady-state tracking performance. The experimental results manifest the approach's effectiveness.