基于T-S模型的非线性系统离散时间滑模控制

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。

Discrete-time Sliding Mode Control of Nonlinear Systems Based on T-S Fuzzy Model

The control issue of nonlinear discrete-time systems was addressed based on the Takagi-Sugeno (T-S) fuzzy model. A nonlinear system dynamic model is represented by a T-S fuzzy model. The global T-S fuzzy model of nonlinear system was transformed into linear uncertain system model. So the stability problem of nonlinear systems becomes the robust stabilization problem of linear uncertain systems. Discrete-time sliding mode control approach was employed, which can ensure that linear uncertain system is robust stabilization. The stable sliding surface was designed by using linear matrix inequality (LMI) technique to reduce the influence of mismatched uncertainties. The sufficient condition for the existence of stable sliding surface was derived in terms of LMIs. Moreover the design of sliding mode control law was proposed. The system robust stability can be guaranteed and the chattering around the sliding surface was obviously reduced by the proposed design approach. Finally, an illustrative example of truck-trailer shows the feasibility and effectiveness of the proposed method.