Study on Model-Free Control of a Class of Nonlinear Discrete-Time Systems

A modified model-free adaptive control (MFAC) approach is proposed to address output fluctuation and overshoot problems existing in the prototype MFAC. Targeting a class of discrete-time nonlinear single-input single-output systems, historical input/output information is applied to construct explicit data model which is equivalent to the plant model in a real-time online manner. Control scheme is designed based on the data model such that model-free characteristic in control process is realized. A novel optimization index function is proposed by using the data model. An input compensation term is introduced on the basis of minimizing the tracking error in the prototype MFAC for restraining output response speed and softening control input. The input amplitude is reduced by the input compensation term for restraining output fluctuation and overshoot when the output change rate is too large. Adaptive matching between the output response and the control input is also realized. Numerical simulation results show that, compared with the prototype MFAC, the modified MFAC can significantly suppress the system output oscillation and overshoot under the same response time conditions. The output fluctuation of the closed-loop system is significantly reduced. The positive overshoot is reduced by about 10%, and the negative overshoot is effectively suppressed. The dynamic response of the closed-loop system is smoother and the operation is more stable. 本文提出一种改进型无模型自适应控制（model-free adaptive control, MFAC）方法，以解决原始MFAC方法易出现的输出振荡与超调问题。针对一类离散时间非线性单输入单输出系统，利用系统运行过程中采集得到的历史输入/输出信息实时在线构建与原系统等效的显式数据模型，基于此模型设计控制方案，实现控制过程的无模型特性。利用数据模型提出新型最优化指标函数，在原始MFAC方法最小化跟踪误差基础之上引入输入补偿项，用以约束输出响应速率，软化控制输入。当输出变化率过大时，输入补偿项降低系统输入幅值以抑制振荡与超调现象，实现输出响应与输入之间的自适应匹配。数值仿真结果表明：与原始MFAC方法相比，在响应时间相同的条件下，改进型MFAC可显著抑制系统的输出振荡与超调，闭环系统的输出波动明显减小，正向超调量降低约10%，反向超调得到有效抑制，闭环系统的动态响应更为平滑，运行更加平稳。