基于Backstepping方法的一类非线性系统控制器优化设计

Controller Optimization Design for a Class of Nonlinear System Based on the Backstepping Approach

目的研究一类非线性系统设计的稳定控制器对参数的调节性能.方法运用Backstepping方法和线性矩阵不等式技术,将子系统所得非线性控制器和系统线性化后部分状态控制器相结合,可得到使整个非线性系统稳定的控制器.结果设计出使系统稳定的控制器,进一步对控制器参数进行调节,使系统性能满足指标要求,并给出了可调参数优化设计的算法.通过对直线型一级倒立摆系统仿真,绘制系统超调值随可调参数变化的三维曲面图、系统超调值随可调参数变化的三维曲面图、超调值和调节时间的等高线图、不同参数值对应的状态响应曲线图,验证了所提算法的可行性和有效性.结论针对一类非线性系统,设计出部分线性化控制器,不仅能镇定系统,而且参数值选取具有多样性,进而保证系统达到不同的期望性能指标.

A controller was designed to stabilize a class of nonlinear system that can satisfy the expected performance via parameter modulations. By utilizing the Backstepping approach and the linear matrix inequality technique,combining nonlinear controllers of subsystems with part of state controllers after linearization,a stable controller was obtained to make the system satisfy index requirements by modulating parameters. An optimization design algorithm for adjustable parameters was presented. Three- dimensional surface curves of overshoot and adjust time with variation of parameters,contour lines of overshoot and adjust time,response curves from three groups with different parameters were draw n by simulations on a linear inverted pendulum system,which verifies the feasibility and the effectiveness of the algorithm. Conclusion is that the class of nonlinear system can be stabilized by the partial linearization controller with diverse parameters. It indicates thesystem can realize different expected performance indexes with adjustable parameters.