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

基于李雅普诺夫理论，针对具有输入饱和的线性系统，提出了一种抗饱和渐近镇定的控制策略。首先，针对具有执行器饱和的线性系统，提出了一种带观测器的输出反馈控制器，实现了系统的渐近跟踪。该控制器包括一个内部模型与抗windup长期的参考和干扰信号和状态观测器。整个系统被证明是渐近稳定的系统的任何初始条件下，只要参考和干扰信号的大小，使渐近跟踪的参考信号可以实现不饱和的actuator.Next，在传统的抗windup控制器的恒定增益项扩展到具有动态的传递函数所表示的。所提出的补偿器设计方法是Kothare的静态抗饱和补偿器的线性条件的扩展。以单连杆柔性臂为例，通过仿真和实验验证了所提方法的有效性，并进一步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的情况下的渐近跟踪。基于李雅普诺夫稳定性和Barbalat引理，针对渐近稳定和稳定的一阶和二阶系统，提出了一种抗饱和自适应律。实验和数值仿真结果表明了该方法的有效性。

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.