一种欠驱动两级柔性自平衡机器人的建模及其最优控制

An Under-actuated Two-stage Flexible Self-balancing Robot's Modeling and its Optimal Control

文章以一种欠驱动两级柔性自平衡机器人这一被控对象的控制问题作为出发点,详细阐述了其数学建模方法,讨论了其最优控制策略,并针对设计过程中出现的LQ加权矩阵Q的选取难题给出了一种解析解和证明,同时运用这一结论计算出了实际问题的加权矩阵Q,从而求得最优的状态反馈矩阵K;仿真结果表明,这样一种加权矩阵Q的求解方法是有效的,并能够在较为复杂的实际问题中获得应用。

The paper describes in detail its mathematical modeling method and optimal control tactics for solving an under- actuated two- stage flexible self-balancing robot＇ s control problem, which gives an analytical solution and its proof for a selection of the weighting matrix Q appearing in the LQ design process and uses the conclusion to calculate the weighting matrix Q in the practical problem and to obtain optimal state feedback matrix K. The simulation results shows that such a solving method of weighting matrix Q is effective and the method can he widely applied in more complex practical problem.