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针对一类未知时变时滞非线性系统,提出一种基于观测器的重复控制方案.采用线性矩阵不等式设计非线性观测器,所设计的控制律含有PID反馈项,常值参数自适应律是微分-差分型的,时变参数学习律是差分型的.在假设未知时变时滞、时变参数和参考输出的周期有已知的最小公倍数下,通过构造一个Lyapunov-Krasovskii型复合能量函数,证明了所有闭环信号有界且输出跟踪误差收敛.仿真实例表明了算法的有效性.
For a class of nonlinear systems with unknown time-varying delay, an observer-based repetitive control scheme is proposed. The nonlinear observer is designed by using the linear matrix inequality. The designed control law contains PID feedback term and the constant value parameter adaptive law is Differential-differential type, time-varying parameter learning law is differential type. Under the assumption that the unknown time-varying delay, the time-varying parameters and the reference output have the least common multiple of the known cycles, by constructing a Lyapunov-Krasovskii complex energy function It is proved that all the closed-loop signals are bounded and the output tracking error converges. The simulation shows the effectiveness of the algorithm.