Non-recursive robust/adaptive integrated control design framework for nonlinear systems with mismatched disturbances

DOI编号  10.7641/CTA.2022.10858
2022,39(9):1641-1650

 作者 单位 E-mail 董鑫 上海电力大学 自动化工程学院 dongxin@mail.shiep.edu.cn 张传林 上海电力大学 自动化工程学院 clzhang@shiep.edu.cn

针对一类含不匹配干扰的非线性系统的控制问题, 基于递归化方案得到鲁棒或自适应控制律是常见的设计思路, 如反步法及其衍生控制策略等. 然而, 递归设计的控制律通常由含多偏微分项的多个虚拟控制器组成, 形式复杂的同时, 控制参数选取也较为困难, 易出现“复杂性爆炸”的问题, 因此较难得到广泛的工程应用. 同时, 因递归设计处理系统的非线性与不确定性的差异较大, 难以实现鲁棒/自适应控制的本质性融合. 本文从一个新颖的非递归控制角度出发, 提出了一个能够融合鲁棒/自适应控制策略的设计框架, 实现系统在不匹配受扰情形下的无静差跟踪. 仅通过一步坐标变换, 在等价的可镇定系统框架下, 根据实际工况来灵活切换合适的控制增益, 为工程师同时提供了两个可供选择的控制方案. 相较于已有算法, 本文所提控制器形式简洁易实现, 参数易调节, 适用范围广. 案例分析与实例仿真验证阐明了所提方法的简洁性及有效性, 并给出了一体化控制器工作模式的选取原则.

For a class of nonlinear systems with mismatched disturbances, it is a common design approach to develop robust/adaptive control laws based on recursive schemes, such as back stepping method and its derivatives. However, recursive control laws are usually composed of multiple virtual controllers with multiple partial differential terms, which are complex in form and difficult to select control parameters, they are prone to “complexity explosion”. Therefore, it is hard to be applied to practical engineering. Additionally, due to the handling variations between nonlinear terms with uncertainties via recursive designs, it is in trouble to achieve an intrinsic blend of robust/adaptive control. In this paper, a novel non-recursive control manner is proposed to integrate robust/adaptive control design framework to achieve an offset-free tracking result for the systems with mismatched disturbances. With a one-step coordinate transformation, the system can flexibly switch to the appropriate bandwidth property according to the practical operating conditions in the framework of an equivalent stabilizable system, providing engineers with two alternative control laws at the same time. Compared with existing algorithms, the proposed control strategy has the following features: the controller form is simple to be implemented, easy to adjust parameters, and has a wide range of applications. Case studies and simulations illustrate the simplicity and effectiveness of the proposed approach. Meanwhile, the selection principles of the integrated controller operating modes are provided.