离散直接自适应模糊滑模控制一步设计

One-Step Design of Direct Adaptive Fuzzy Sliding Mode Control for Discrete Nonlinear Systems

滑模控制设计方法一般需要分两步进行,即设计稳定的滑模面和能使滑模到达的滑模控制器。对于离散非线性系统的模糊滑模控制,两步设计变得较为复杂。针对离散非线性系统轨迹跟踪控制问题,提出了一种采取一步直接进行自适应模糊滑模控制的方法。首先给出问题描述及动态模糊逻辑系统(Dynamic Fuzzy Logical System,DFLS);然后针对线性滑模面,基于在线参数自调整的DFLS逼近控制器中的非线性动态函数,一步构造设计了滑模控制律。通过Lyapunov分析方法,证明了所采取的自适应律能够保证滑模可达的同时,也能保证闭环系统误差也是渐近稳定的,并具有一定的鲁棒稳定性、抖振削弱和自适应性等优点。最后,在一阶倒立摆系统中应用所提出的控制设计方法,进行了仿真研究。仿真结果验证了该方法的正确性和优越性能。

Generally sliding mode control design consists of two steps, stable sliding mode design and sliding mode controller design that guarantees the reachability of the sliding mode. However, for fuzzy sliding mode control design of discrete nonlinear systems, the two steps become more complex. In this paper, a new direct adaptive fuzzy sliding mode control design for discrete nonlinear systems is presented to solve the problem of trajectory tracking. Firstly, problem formula and dynamic fuzzy logical system （DFLS） are proposed and then sliding mode control design is constructed in one step based on DFLS with parameters self-tuning online. The Lyapunov analysis theory shows that the adaptive law can not only guarantee the reachability of the sliding mode, but also the stability of the tracking error. The over-all system is asymptotically stable with robustness, chattering free and adaptive. Finally the performance of the design is verified by simulations of an inverted pendulum system.