自平衡控制系统稳定性分析与验证

Stability analysis and verification of self-balancing control system

针对目前自平衡系统稳定性控制方法的复杂性,对控制器运算速度要求高的问题,提出一种依据自平衡系统重心运动方程来分析系统的稳定性以及维持系统稳定的控制方法。该方法通过刚体动力学推导系统重心运动方程,应用控制理论分析系统的稳定性。在失稳的情况下,采用卡尔曼滤波与误差比较的方法消除陀螺仪的积分误差并获取精确的倾角数据,运用角度、角速度及对应的参数构成的合成加速度组成反馈支路配置系统极点,将当前倾角和角速度配以适当的参数组成比例微分(proportion differential,PD)控制器,完成对系统稳定性的控制。测试表明,该方法能降低系统运算的复杂度,维持系统的稳定。

In view that the control method of present self-balancing system stability is so complex, and the controller requires high operation speed of the control system, this paper presents a control method by using the centre of gravity equations of motion to analyze the system stability and maintain the system stability. This method derives the system center of gravity equation of motion by rigid body dynamics, and uses the control theory to analyze the system stability. In the case of instability, it applies the method of Kalman filter and error compares to eliminate the integral error of gyroscope and to ac- quire an accurate angle , at the same time , using the angle, the angular velocity and the resultant acceleration made by the corresponding parameters to make up the feedback branch configuration system poles, what＇ s more, configuring the angle and angular velocity with appropriate parameters to make up the PD controller, at last completing the control of the system stability . Tests show that this method can reduce the complexity of the system operator and maintain the system stability.