New framework of adaptive control theory and its application to motor driven systems

本项目的目标是建立一种新型的自适应控制理论，以克服经典自适应控制理论的不足。理论研究首先，我们建立了线性时变系统的ISS小增益定理，该定理保证了状态的指数收敛。在此基础上，建立了“自适应鲁棒控制理论”，该理论具有以下突出特点：(1)状态反馈、自适应观测器和自适应律设计的完全分离；(2)全局指数收敛和显式收敛速度的保证；(3)多输入多输出自适应控制理论；(4)不需要最小相位假设和与相对度无关的基于凸优化的数值设计工具。(1)通过大量的实验，验证了该系统在30次载荷变化和3次弹簧恒定变化情况下均能正常工作。(2)自适应鲁棒控制有效性的实验验证为越来越多的工业应用打开了大门。

The goal of this project is to establish a new type of adaptive control theory which can overcome the shortcomings of classic adaptive control theories. Through two years research effort, the followings achievements have been made.Theoretic StudyFirst, we founded an ISS small-gain theorem for linear time-varying systems which guarantees the exponential convergence of state. Then, based on this theorem "Adaptive Robust Control Theory" is established, which has the following outstanding properties: (1) complete separation in the designs of state feedback, adaptive observer and adaptation law (2) guarantee of global exponential convergence and explicit convergence rate (3) multi-input multi-output adaptive control theory (4) no need of minimum phase assumption and independent of relative degree The convex optimization based tool for numerical design has also been established.Application to motor-driven systems For the motor-driven systems that play an extremely important role in industrial applications, we have succeeded in developing a servo technology which does require on-site tuning. (1) Through numerous experiments, it has been validated that this system works well over 30 times of load variation and 3 times of spring constant variation. (2) The experimental validation of the efficacy of Adaptive Robust Control has opened the doors to more and more industrial applications.