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利用提取的系统高阶微分信息,提出了自适应高阶微分反馈控制器.某种程度上该控制器不依赖于单输入单输出(SISO)非线性仿射系统的模型.并且分析了闭环系统的稳定性和鲁棒性.通过将摆角方程的位移加速度看作是控制输入,将倒立摆系统转化成相互影响的两个SISO仿射系统,从而用两个串级高阶微分反馈控制器成功地实现了倒立摆系统的镇定与调节.数字仿真表明,控制器对摆的基准模型实现了较为满意的控制,而且该控制方法对非线性摩擦项,对摆长、摆质量、小车质量等参数变化以及外扰动具有强鲁棒性.
Based on the extracted high-order differential information of the system, an adaptive high-order differential feedback controller is proposed, which is not dependent on the model of a single-input-single-output (SISO) affine system to a certain extent. The stability and robustness of the system.According to the displacement acceleration of the swing angle equation as the control input, the inverted pendulum system is transformed into two SISO affine systems that affect each other, so that two cascaded higher-order differential feedback controllers The stabilization and adjustment of the inverted pendulum system are successfully achieved.The numerical simulation shows that the controller achieves more satisfactory control of the pendulum’s reference model and the control method has more control over the nonlinear friction term, swing length, pendulum mass, car quality and so on Parameter changes and external disturbances are robust.