两轮自平衡小车建模及LQR控制算法设计

Modeling and LQR Control Algorithm Design of Two-wheeled Self-balancing Vehicle

为了提高两轮自平衡机器小车建模的准确性,提出了一种加入拉格朗日乘子函数精确建立两轮自平衡小车动力学模型的方法,利用拉格朗日方程推导出是否引入拉格朗日乘子函数的两轮自平衡小车系统的动力学方程。将动力学方程求解的结果数据与ADAMS模型中的仿真数据进行对比。基于LQR算法设计两轮自平衡小车的控制器,将该算法分别在ADAMS与Simulink中设计实现并对比实验数据。仿真数据比较结果表明,两个独立仿真环境下的数据结果几乎一致,验证了该建模方法的准确性以及控制算法的有效性。

In order to improve the modeling accuracy of two-wheel self-balancing vehicle,a method of adding Lagrange multiplier function to accurately establish the dynamic model of two-wheel self-balancing vehicle was proposed.The dynamic equations of two-wheel self-balancing vehicle system whether introducing Lagrange multiplier function were derived by using Lagrange equation.The results of solving the dynamic equation were compared with the simulation data in Adams model.The controller of two-wheeled self-balancing vehicle was designed based on LQR algorithm.The algorithm was implemented in ADAMS and Simulink respectively,and the experimental data were compared.The simulation results show that the results of the two independent simulation environments are almost unanimously,which verifies the accuracy of the modeling method and the effectiveness of the control algorithm.