一种非线性鲁棒PID控制器设计方法

Robust PID control for a class of nonlinear systems

针对一类非线性不确定系统,提出了一种基于PID(比例-积分-微分)控制的鲁棒控制方法.整个控制器由PID控制器和一个鲁棒补偿器构成.首先,基于系统的标称模型设计PID控制器;然后在PID控制的基础上,设计一个辅助鲁棒补偿器,用于补偿系统非线性、参数摄动和外界扰动等对系统控制性能的影响.补偿器的设计基于李雅普诺夫(Lyapunov)稳定性理论进行,从而保证了闭环系统的鲁棒稳定.采用该方法对倒立摆跟踪问题进行了仿真控制,仿真结果验证了设计方案的有效性.

A robust control design method was proposed for a class of nonlinear systems with uncertainty. The controller was composed of a proportional integral differential （PID）controller and a robust compensator. The whole design was divided into two steps. A PID controller was developed based on the linear nominal model of the plant. On the basis of the developed PID controller, a robust compensator was given to compensate for the bad influence resulted from the system parameter perturbation, the unknown external disturbance , the model error because of linearization and so on. The compensating control law was derived by Lyapunov stability theory, as a result, the stability of the closed loop system was guaranteed despite the uncertainty, the robustness of the system was improved accordingly. Applying the proposed control method to the tracking control of an inverted pendulum, the results of numerical simulations show the validity of this scheme.