基于弹性能量函数的非线性不确定系统控制方法

针对非线性不确定系统的控制问题,提出一种基于弹性能量函数的扰动观测方法和弹性跟踪控制方法.该方法以弹性能量函数为核心,将其分别应用于扰动观测器、虚拟跟踪指令以及弹性跟踪控制器的设计.该控制方法的突出优势是只根据误差来消除误差,不涉及误差的微分运算,控制器增益参数完全根据积分步长来整定.理论研究表明,所提出的弹性跟踪控制方法不仅可从理论上保证各级子控制器的稳定性,有效解决高阶SISO非线性不确定系统的控制问题,而且可有效避免反步控制方法出现的微分爆炸问题.此外,每个子控制器只有一个由积分步长即可整定的增益参数,因而控制器结构简单、计算量较小.仿真结果表明:所提出的控制方法不仅具有快的响应速度、高的控制精度以及强的抗扰动能力,而且不依赖于被控对象模型,在非线性不确定系统控制领域具有广泛的应用前景.

Nonlinear uncertain system control method based on elastic energy function

For the control problem of a nonlinear uncertain system, a disturbance observation method and an elastic tracking control method are proposed based on the elastic energy function. The elastic energy function is applied to design the disturbance observer, virtual tracking instruction and elastic tracking controller, respectively, as the core technology. The prominent advantage of the proposed control method is only according to the error to eliminate the error, does not involve the differential operators of the error, and the controller gain parameters are determined completely by the integral step. Theory research show that the proposed elastic tracking control method not only guarantees the stability of various sub-controller theoretically, and effectively solves the control problem of higher-order SISO nonlinear uncertain systems, but also effectively avoids the differential explosion problem of the back stepping control method. In addition, each sub-controller has only one gain parameter which can be tunned by the integral step, so the controller has simple structure and small calculation. Simulation results show that the proposed elastic tracking control method not only has fast response speed, high control precision and strong ability to resist disturbance, but also is not dependent on the controlled object model, therefore has wide application prospect in the field of nonlinear uncertain systems control.