Dynamic Anti-Windup Controller Design for Linear Systems with Actuator Saturation

针对具有输入饱和的线性系统，基于Lyapunov理论，提出了一种抗环渐近镇定的控制策略。首先，提出了一种带观测器的输出反馈控制器，以实现对具有执行器饱和的线性系统的渐近跟踪。该控制器包括具有用于参考信号和干扰信号的抗绕组项的内部模型和状态观测器。证明了整个系统对于系统的任何初始条件都是渐近稳定的，只要参考信号和干扰信号的大小大小使得参考信号的渐近跟踪可以在不饱和执行器的情况下实现。其次，将传统的抗终结控制器中的恒定增益项扩展为具有由传递函数表示的动态。所提出的补偿器设计方法是对Kothare的静态抗绕组补偿器的线性条件的扩展。通过仿真和实验验证了该方法的有效性，并在此基础上提出了一种模型参考自适应控制的设计方法，以保证具有输入饱和的线性系统在考虑参数变化时的渐近跟踪。基于Lyapunov稳定性和Barbalat引理，针对渐近稳定和稳定的一阶、二阶系统，提出了一种反终结自适应律。通过实验和数值模拟验证了该方法的有效性。

Control strategies for anti-windup asymptotic stabilization are developed for linear systems with input saturation based on the Lyapunov theory.First, an output feedback controller with an observer is proposed in order to achieve asymptotic tracking for linear systems with actuator saturation. The controller includes an internal model with an anti-windup term for the reference and disturbance signals and a state observer. The overall system is shown to be asymptotically stable for any initial condition of the system, as long as the magnitudes of the reference and disturbance signals are sized such that asymptotic tracking of the reference signal can be achieved without saturating the actuator.Next, the constant gain term in the conventional anti-windup controller is extended to have dynamics that are represented by a transfer function. The proposed compensator design method is an extension of Kothare's linear conditioning for a static anti-windup compensator. The effectiveness of the proposed method is demonstrated using a one -link flexible arm through simulations and experiments.Furthermore, a design method of model reference adaptive control is proposed in order to guarantee asymptotic tracking for linear systems with input saturation, while taking parameter variation into account. An anti-windup adaptive law is proposed for asymptotically stable and stable first- and second-order systems based on Lyapunov stability and Barbalat's Lemma. The effectiveness of the proposed method is demonstrated experimentally and through numerical simulations.