基于约束输入变速吸引律的离散重复控制器设计

Rare-variant attracting law based design of discrete-time repetitive controllers with constrained input

针对离散时间线性系统的周期跟踪问题,提出一种能够约束控制输入变化速度的变速吸引律,结合干扰抑制措施构造了理想误差动态,并由此导出离散重复控制器.分析表明,该变速吸引律能使跟踪误差在有限时间内单调收敛至零,且误差收敛速度可控.为刻画误差动态行为,推导了有界扰动下的误差单调收敛域、绝对值收敛域和稳态误差带,并给出了收敛步数.针对伺服电机系统的仿真与实验结果验证了所提出控制方案的有效性.

The problem of periodic tracking is addressed for discrete-time linear systems. A rare-variant attracting law for the repetitive controller design is presented, and the ideal error dynamic is formed based on the proposed attracting law, by which the discrete-time repetitive controller is designed. It is shown that the control input is constrained within the pre- specified region, and the monotonic convergence of the tracking error is ensured in finite time. Consequently, the undesirable high-frequency switching between different values of the control signal is avoided. To characterize the error dynamics, the monotone convergence region, the absolute convergence boundary and the steady state error band are derived, respectively, in the presence of the bounded disturbances. The expression for the convergence steps is also given. Both numerical simulation and experiment results demonstrate the effectiveness of the nrot）osed renetitive control scheme.