一类非线性系统的加速度规划输出跟踪动态控制

Output tracking control with acceleration assignment for a class of nonlinear systems

针对一类严格反馈形式的非线性二阶多输入多输出系统,提出一种带有加速度规划的输出跟踪动态控制策略.引入一个代替时间变量的路径参数用以规划路径跟踪时的加速度,回避了设计内环加速度控制回路的常规方法,简化了控制器的设计过程.对二阶系统的控制项求导进行系统扩维,基于新的增广系统,设计了使系统输出收敛于期望路径的反馈线性化动态控制律.再对加速度跟踪误差基于梯度法设计更新律使其渐近收敛于零,最后通过调节期望加速度实现定常速度控制.理论分析表明,误差闭环系统一致渐近稳定,速度误差有界.动力定位船舶循迹控制仿真结果表明了所提出控制器的有效性.

For a class of second order nonlinear multi input multi output（MIMO） systems with strict feedback,an output path-following controller with acceleration assignment is proposed.A path variable,instead of the time variable,is used to program the acceleration in path-following task to eliminate the extra inner acceleration control loop for simplifying the controller design procedure.The derivative of the control term is employed to form an augmented system,the output of which is driven to follow the desired path according to a feedback linearizing dynamic control law.The update law obtained by the gradient method is used to achieve the asymptotic convergence of the acceleration error.The constant speed control is realized by adjusting the desired acceleration.The stability analysis indicates that the closed-loop error system is asymptotically stable and the speed error is bounded.Simulation of the tracking control for a dynamically positioning vessel is presented to illustrate the feasibility and effectiveness of the proposed controller.