具有H_(∞)性能的输入受限三级倒立摆控制器设计

Design of Input Constrained Triple Inverted Pendulum Controller with H_(∞) Performance

【目的】针对直线三级倒立摆控制输入受限下的稳摆控制问题,设计了具有H_(∞)性能的输入受限三级倒立摆控制器。【方法】利用线性矩阵不等式(LMI)方法,将控制输入约束问题转化为利用线性矩阵不等式求解优化值的优化问题,经Lyapunov稳定性推导出符合条件的LMI,利用MATLAB中的LMI工具箱求解得到有效的K。进一步在控制输入受限下引入H_(∞)性能指标,使所设计的控制输入受限下的算法具有H_(∞)性能。【结果】仿真结果表明,该控制器对于控制输入受限下的复杂高阶次不稳定系统具有很好的控制效果。【结论】控制输入信号在给定的受限范围内实现了三级倒立摆的稳摆要求,且引入H_(∞)性能指标后控制输入和摆杆波动更小。

[Purposes]To solve the stabilization control problem of triple inverted pendulum with control input constraint,an input constrained control strategy with H_(∞)performance is proposed.[Methods]By us-ing linear matrix inequalities(LMI),the control input constraint problem is transformed into an optimiza-tion problem using LMI to solve the optimization value.A suitable LMI is obtained by Lyapunov stability derivation,and an effective K is obtained by using the LMI toolbox in MATLAB.Furthermore,H_(∞)perfor-mance index is introduced to make the designed algorithm with control input constraint have H_(∞)perfor-mance.[Findings]The simulation results show that the control strategy has a good control effect on the complex high-order unstable system with control input constraint.[Conclusions]The control input sig-nal can achieve the stability requirement of the triple inverted pendulum within the given limited range,and the fluctuation of the control input and pendulum rod is less after the introduction of H_(∞)perfor-mance index.