Predictive Position Control of Planar Motors Using Trajectory Gradient Soft Constraint With Attenuation Coefficients in the Weighting Matrix

Abstract

This article proposes a predictive position control method of planar motors using trajectory gradient soft constraint with attenuation coefficients in the weighting matrix to achieve high-precision, time-varying, and long-stroke positioning. Based on a built dynamics model of a planar motor developed in the laboratory, a predictive model is established to predict the future positions of the motor. To improve the positioning precision, a soft constraint defined by a trajectory gradient difference between the gradients of the reference position and predictive position sequences is introduced to the cost function. Then, an explicitly analytical solution of the optimal control is obtained by minimizing the cost function. To highlight the stronger effects of the trajectory gradients closer to the current time, the attenuation coefficients are applied to the weighting matrix of the added soft constraint. The stability of the control system is proved employing the linear quadratic optimal control method and the Lyapunov stability theory. Moreover, the time complexity is discussed based on the analytical control action to show low computational burden of the proposed method. Finally, the given simulation and experimental results demonstrate the effectiveness of the proposed method to achieve high-precision time-varying positioning for planar motors.