Non-overshooting tracking controllers based on combinatorial polynomials

This paper presents a technique for designing twoparameter compensators that stabilize a plant and provide offset-free tracking of set-points without overshooting or undershooting. We first represent the impulse response of linear systems using combinatorial polynomials, based on which a new set of conditions is derived for the system to be externally positive. This result is then used in control synthesis to achieve monotonic tracking. In contrast to the methods available in the literature, the proposed technique always gives a solution whenever the problem is feasible, can yield as small a settling time as desired, and provides the freedom to choose the closedloop poles arbitrarily inside the unit circle, all obtained by low-degree controllers.