Optimal structure for the trajectory controller

When designing a trajectory tracking controller for a moving vehicle, there are usually two approaches: first, strictly theoretical and not very easily implementable; second, using a trial and error method. Using a trial and error method, designer usually starts with one of the well-known PID structures of the controller and then parameters are tuned. Our attention was attracted to the fact that all possible structures, i.e. P, PI, PD and PID controllers, seems to be an appropriate. The aim of this paper is to suggest possible theoretical solutions of the follower algorithm. Considering that a tracking process can be simplified as an integrating system, we know that a P-controller can track only a step changes of the trajectory with zero system deviation and PI controller can track linearly increasing path also with the zero system deviation. To follow a harmonic trajectory with zero deviation it is necessary to use a non-linear controller working in a sliding mode. In this paper we show how to design such a controller and actuator with respect to the parameters of the tracked trajectory.