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为了实现对具有时变摄动死区非线性系统的跟踪控制,本文提出了一种基于自适应模糊逼近器的Backstepping控制方法。该方法通过将死区特性合理分解,并将自适应模糊逼近器嵌入到Backstepping设计步骤中,逐步递推得到控制律。所提出的控制方法适用于高阶非线性系统,并且不要求被控系统满足匹配条件;所采用的模糊逼近器是非线性参数化的,亦即不要求其模糊基函数是完全确定已知的,从而降低了对先验知识的依赖性。为了得到未知参数的自适应律,本文先应用Taylor级数展开式将具有非线性关系的未知参数相互分离,使其呈现线性关系,然后根据Lyapunov稳定性定理给出在线可调参数的自适应律。此外,所设计的自适应律是对与未知参数向量的范数相关的变量进行在线调节,这样可以有效减少需要在线调节的参数数量,从而降低了控制器的在线计算负担,提高了系统的响应速度和控制精度。本文给出的控制设计能够有效地克服死区特性对系统性能的影响,使得闭环系统所有信号均指数收敛到原点的指定邻域内,系统输出可以按给定的精度跟踪参考信号。最后,本文用一个仿真实例验证了所给控制方法的有效性。
In order to realize the tracking control of the nonlinear system with time-varying perturbation dead zone, this paper presents a Backstepping control method based on adaptive fuzzy approximator. The method decomposes dead-zone characteristics reasonably and embeds the adaptive fuzzy approximator into Backstepping design steps to recursively obtain the control law. The proposed control method is suitable for higher-order nonlinear systems and does not require the controlled system to satisfy the matching conditions. The fuzzy approximators used are nonlinearly parameterized, that is, the fuzzy basis functions are not required to be completely determined and known. Thus reducing the dependence on prior knowledge. In order to get the adaptive law of unknown parameters, we first apply Taylor series expansion to separate the unknown parameters with non-linear relationship from each other and make them appear linear relationship. Then according to the Lyapunov stability theorem, the adaptive law of online adjustable parameters . In addition, the designed adaptive law adjusts the variables related to the norm of the unknown parameter vector online, which can effectively reduce the number of parameters that need to be adjusted online, thus reducing the on-line computing burden of the controller and improving the system response Speed and control accuracy. The control design presented in this paper can effectively overcome the impact of dead-band characteristics on the system performance, so that all the signals in the closed-loop system converge exponentially to the designated neighborhood of the origin, and the system output can track the reference signal with the given accuracy. Finally, a simulation example is used to verify the effectiveness of the proposed control method.