Nonovershooting and nonundershooting exact output regulation

Abstract

We consider the classic problem of exact output regulation for a linear time invariant plant. Under the assumption that either a state feedback or measurement feedback output regulator exists, we give design methods to obtain a regulator that avoids overshoot and undershoot in the transient response.

Nonovershooting multivariable tracking control for time-varying references

“…The output regulation framework can also be used for the asymptotic rejection of known time-varying disturbances; further details are provided in [16]. Examples were given to show that the design method can offer superior transient performance to the CNF method of [8].…”

“…In [15] it was shown that the design method of [1] for tracking a constant step reference could be successfully implemented in conjunction with full and reduced order observers. This was extended to the tracking of time-varying references with dynamic measurement feedback in [16]. Provided the initial observer error is sufficiently small, the nonovershooting properties of full state feedback control are preserved.…”

Nonovershooting output regulation for feedback linearisable MIMO systems

“…The early works [2]- [4] considered the step response of linear single-input single output (SISO) systems. The problem of avoiding overshoot in the step response of a multiple-input multiple output (MIMO) linear system was first considered in [5], and this was extended to the nonovershooting tracking of time-varying signals in [6]. Recently [7] gave necessary and sufficient conditions for the existence of static state feedback controller to achieve a monotonic step response, for MIMO linear systems.…”

“…However, unlike [9], we do not employ an additional coordinate change to the chainof-integrators system. Instead we adapt the nonovershooting control methods of [5] and [6] to linear chain-of-integrator systems. These methods involve selecting candidate sets of closedloop eigenvalues and applying simple analytic tests to determine the shape of the closed-loop system response arising from the specified initial condition.…”

Initial-value compensation of a proportional–integral–derivative controller for non-overshooting motion

“…At the mode-switching instant, the plant’s initial state is often nonzero, and the plant cannot be assumed to be initially at rest. In the literature, 8,9 controller designs were proposed for plants with nonzero initial states to achieve non-overshooting step responses. However, these designs were presented for systems subject to step references only.…”