Huba M., Huba T. (2015) Constrained Pole Assignment Control for a 2nd Order Oscillatory System. In: Moreno-Díaz R., Pichler F., Quesada-Arencibia A. (eds) Computer Aided Systems Theory – EUROCAST 2015. Lecture Notes in Computer Science, vol 9520. Springer, Cham
The paper brings phase plane design of a constrained Proportional Derivative (PD) controller for undamped second order oscillatory plants. The approach is focused on achieving the possibly best tracking dynamics considering the control signal saturation. The linear pole assignment control and relay minimum time control are included as its limit solutions. The paper shows that such a task has infinitely many solutions. The existing degree of freedom follows from a free choice of a distance definition in evaluating deviation of the operating point from the considered invariant set specified by the required reference braking trajectory. It may be used to choose the simplest controller equations, or to modify the loop performance in the case of an unmodeled dynamics.