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基于T-S模糊模型,讨论了一类非线性离散时间系统的控制问题。采用T-S模糊模型来描述非线性系统的动态模型,再将非线性系统的全局T-S模糊模型转化为线性不确定系统的模型。这样复杂的非线性系统的稳定问题就转化为线性不确定系统的鲁棒镇定问题。采用离散时间滑模控制方法实现线性不确定系统的鲁棒镇定。利用用线性矩阵不等式技术设计稳定的滑动模面,以降低非匹配不确定对系统的影响。给出了线性矩阵不等式形式的稳定滑动模面存在的充分条件。此外还给出了滑模控制律的设计方法。所给设计方法可保证系统鲁棒镇定,并且在滑动模面附近的抖振可明显减弱。最后,给出了truck-trailer的仿真算例,证明了所给方法的可行性和有效性。
Based on the T-S fuzzy model, the control of a class of nonlinear discrete-time systems is discussed. The T-S fuzzy model is used to describe the dynamic model of nonlinear system, and then the global T-S fuzzy model of nonlinear system is transformed into the model of linear uncertain system. The stability of such a complex nonlinear system transforms into a robust stabilization problem for linear uncertain systems. Robust stabilization of linear systems with uncertainties by discrete time sliding mode control. The use of linear matrix inequalities to design a stable sliding surface to reduce the impact of non-matching uncertainty on the system. The sufficient conditions for the existence of stable sliding modes in the form of linear matrix inequalities are given. In addition, the design method of sliding mode control law is given. The given design method can ensure robust stabilization of the system, and the chattering around the sliding mode surface can be significantly reduced. Finally, a simulation example of truck-trailer is given, which proves the feasibility and effectiveness of the proposed method.