Compensation of friction and stick-slip uncertainties in trajectory tracking control of servo DC machines considering actuation constraints

Abstract

Nowadays, electric motors are common in many precision instrument industries that require high-precision control. If a suitable model of a servo system is available, accurate results can be obtained using a model-based control algorithm. The DC motor is one of the most widely used systems in precision industries, for which a high-precision controller can be designed using its mathematical model with feedback on position and velocity. In such systems and other rotating systems, it is necessary to consider friction in the control system design. Friction enters the system in the form of resistant force or torque in both static and kinetic states, which causes uncertainty in the dynamic modeling of the system, the stick-slip phenomenon, and creates a deadzone in the actuation system. In this article, considering a switching dynamic model for different states of a system subject to friction which has a saturation limit on the control input and an actuation system dependent on the angular velocity feedback, first, the stable reaching laws in two modes of position control and velocity control for different dynamic model switch modes are defined. Then, the control input that forces the tracking error to follow the corresponding reaching law for each control mode is calculated. In the next step, according to the limitations of the actuation system, such as saturation and deadzone, using the filtering mechanism and optimal search for each control mode, the desired values are filtered and it is guaranteed that the control input will be chosen within the allowed range. Finally, using the optimal switching mode selection mechanism, the optimal control mode is selected and the voltage is calculated as the next step input.