二自由度云台非线性反步控制器设计

Nonlinear backstepping controller design for two-degree-of-freedom pan-tilt

针对二自由度云台的跟踪控制问题,依据反步法控制思想,提出一种基于增广李雅普诺夫函数的反步控制器设计方法。首先建立二自由度云台的非线性数学模型,并为模型的机械子系统设计了虚拟输入,根据实际控制目标求解虚拟输入的具体表达式。其次基于增广李雅普诺夫函数,引入跟踪误差将机械子系统改写为线性微分方程,利用其特征方程根的特点,推导系统实际的控制律,以及控制器参数需满足的条件。最后数值实例采用了电动云台拍摄系统远距离跟踪拍摄风电叶片表面图像,对水平和俯仰方向追踪风机叶片上某一目标点的期望轨迹进行仿真,系统经过4.05 s可达到预期跟踪性能,验证了所提方法的有效性。

For the tracking control problem of two-degree-of-freedom(2-DOF)pan-tilt,a backstepping controller design method based on augmented Lyapunov function is proposed by the backstepping control.Firstly,a nonlinear mathematical model was established for the 2-DOF pan-tilt,and was converted into a state-space form.The specific expression of a virtual input which is designed for the mechanical subsystem can be solved according to the actual control target.Secondly,the mechanical subsystem was rewritten into a linear differential equation by introducing tracking error based on an augmented Lyapunov function,while the roots of its characteristic equation was used to find the actual control law of the system and the controller parameters’conditions.Finally,in the numerical example,an electric pan-tilt camera system was used to track the wind turbine blade surface image from distance,and the desired trajectory of a target point on the wind turbine blade was tracked in the horizontal direction and the pitch direction together.The experiment results show that the system can achieve the desired tracking requirements after 4.05 s,which verifies the effectiveness of the proposed method.