Theoretical and experimental study of PI control, adaptive control and variable structure control for converted traditional milling machines

Abstract

In this paper, the control plant is a traditional lead screw with a hand wheel-actuated milling machine that has been converted to a d.c. servo-motor control type. This old-fashioned machininingi table is a non-linear, time-varying system due to the effects of obvious backlash and irregular Coulomb friction between sliding surfaces. Three different control methods are employed for this plant to investigate the operating performance. The theoretical derivations of these control methods are described briefly. Since the control parameters have significant change, the traditional PI with relay control has to adjust the suitable gain values for each case. It is not a convenient application. The variable structure model-following control methods needs to select appropriate logical gain values and a suitable relay offset. Additionally, these two approaches cannot guarantee a stable closed-loop system. The third method for this non-linear system is a stable convergent one-step-ahead adaptive control algorithm. The experimental results show that these control methods give reasonable performance of transient response, tracking and robustness under the influence of the delay of the motor driver and 1 mm backlash of each axis. For a low speed trajectory tracking control ( V s < 3 mm/s), the traditional PI with relay control and the variable structure model-following control give better performance.