精确反馈线性化中虚拟输出函数的求解与应用

为使精确反馈线性化方法得到更广泛的应用，给出虚拟输出函数的简便求解方法．首先将虚拟输出函数的求解转化为偏微分方程组的求解，然后针对这类偏微分方程组的特点提出仿照求解齐次线性方程组的方法可以简便的求出虚拟输出函数．利用该方法为非线性舵鳍联合系统实现了状态反馈线性化，并基于闭环增益成形算法设计了非线性鲁棒控制器，仿真表明该控制器对原非线性系统能起到良好的控制作用．该方法简单、实用，对于状态反馈线性化的实现具有一定的指导意义．

Solution and Application of Imaginary Output Function in Exact Feedback Linearization

In order to make exact feedback linearization be more widely applied, the simple solution of imaginary output function was given in this paper. Firstly, the solution of imaginary output function was transformed into the solution of partial differential equations, whose solution could be got by imitating the solution of homogenous linear equations accordingly. With this method, a rudder/fin joint nonlinear system was exactly linearized, furthermore a nonlinear robust controller was designed based on closed-loop gain shaping algorithm. Simulation results showed that this controller had satisfactory performance on previous nonlinear system. This method was simple and practicable, which had some guiding significance for the realization of state feedback linearization.