基于线性二次调节器算法的两轮自平衡机器人最优控制方法

两轮自平衡机器人作为一种多输入多输出系统,虽然已在许多日常使用中得到应用,但大多数研究只关注通过试验实验或使用简易的数学模型来达到平衡.为了研究两轮自平衡机器人完整数学模型建模和运动平衡控制器设计,首先,根据机器人的电机模型、车轮模型和摆体模型,推导机器人运动的状态空间模型;其次,分析系统的可控性和可观性,并结合状态估计和反馈控制设计具有状态估计的反馈控制器,同时引入线性二次调节器(linear quadratic regulator,LQR)控制方法以完善控制器在机器人运动中的控制效果.仿真实验结果表明:具有状态估计的反馈控制器和LQR控制方法对于这类自平衡机器人运动平衡控制具有良好的稳定性和鲁棒性.

Research on Optimal Control Method of Two-wheel Self-balancing Robot Based on LQR Algorithm

As a multi input and multi output system, two wheeled self balancing robot has been used in many daily applications, but most of the researches only focus on achieving balance through experiments or using simple mathematical models. Therefore, in order to study the complete mathematical model modeling and motion balance controller design of the two wheeled self balancing robot, the state space model of the robot motion is deduced based on the motor model, wheel model and pendulum model of the robot; the controllability and observability of the system are analyzed, and the feedback controller with state estimation is designed by combining state estimation and feedback control, At the same time, LQR control method is introduced to improve the control effect of the controller in robot motion. The simulation results show that the feedback controller with state estimation and LQR control method have good stability and robustness for this kind of self balancing robot.