Real-time tracking control of a position servo employing fractional order controllers

摘要

This work studies the tracking control performance of a DC position servo driving a load, a metal rod attached to the DC servo shaft, acting as a robot link. Such a servo is controlled by three IO (Integer Order) and three FO (Fractional Order) controllers. The IO controllers are: the LQR (Linear Quadratic Regulator) controller, the PC (Predictive Controller) controller, and the BC (Backstepping Controller) controller. The FO controllers are counterparts of IO controllers. That is, FO LQR, FO PC, and FO BC controllers, which can be obtained substituting in each IO controller s by s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> and 1/s by 1/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , where s is the Laplace operator, and m and n are fractional numbers between 0 and 1. The modified Oustaloup filter is used to approximate the FO operators s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> and 1/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . The trajectory signal used for all experiments is a ramp added to a sinusoid. Experimental results demonstrate that both, IO and FO controllers perform well with little differences.