A Fractional Order Sliding-mode Controller with Predefined Tracking Time for Trajectory Tracking Control in Motor Servo Systems

In this paper, a fractional order sliding-mode controller with predefined tracking time is proposed for servo motor to achieve trajectory tracking. The proposed controller enables the angular position of servo motor to track a given trajectory at a tracking time t
f
in spite of disturbances/uncertainties, and the tracking time can be set in advance. The proposed controller is composed of two parts: the first one, named nominal control, is based on optimal control theory to assure the states of disturbances free system converge to zero at the predefined time. The second part, named robust control, is based on the super-twisting control algorithm (STA) modified with the fractional-order integration, allowing the integral of the discontinuous function to assume a fractional order to compensate the disturbances which are not necessarily integer-order differentiable, such as those generated from dynamic friction, input noise and mechanical vibrations. The effectiveness of the proposed controller is demonstrated on a DC servo system via simulation and experiments.