Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

Proportional-Integral Controllers for Minimum-Phase Nonaffine-in-Control Systems

“…The extension to a (restricted) class of MIMO minimumphase nonaffine-in-control systems is presented in [4], [5]. The results of this note complement [1], [2] by 1) extending the applicability of PI controllers to unstable (minimum-phase) nonaffine-in-control systems, 2) showing that the constructed PI controller can be interpreted as an exact realization of an approximate feedback linearizing controller [6], and 3) showing that bounded tracking is achieved for reference signals not necessarily approaching a constant limit. Some practical examples of nonaffine-in-control systems include the continuous stirred tank reactor [7], switched reluctance motors [8], and some aircraft models [9].…”

“…In addition to its classical applications to linear time invariant (LTI) systems, justifications for the use of PI controllers on nonlinear systems have been furnished in [1]- [3], to name a few that are most relevant to the present note. In [2], single-input-single-output (SISO) affine-in-control nonlinear systems are considered.…”

“…It was shown that when the system is minimum-phase, an output-feedback PI controller with a high-gain observer (termed universal integral controller in [2]) can achieve asymptotic tracking of a sufficiently smooth reference signal that approaches a constant limit. For multiinput-multi-output (MIMO) nonaffine-in-control systems, [1] showed that if the open-loop system is exponentially stable, a stabilizing tracking PI controller can be constructed.…”

Robust control for a nonlinear servomechanism problem

“…The nonlinear servomechanism problem has been investigated by several researchers over the past decade; see, for example, Desoer and Lin (1985), Hepburn and Wonham (1984), Huang and Lin (1994), Huang and Rugh (1992), Isidori and Byrnes (1990), Isidori (1995), Khalil (1994), Mahmoud and Khalil (1996), and Priscoli (1993). The early studies have concentrated on the ideal case of a plant not a ected by uncertainties, but later, robust or structurally stable controllers were designed.…”

Stabilization on zero-error manifolds and the nonlinear servomechanism problem

“…Several authors have provided solutions for nonlinear servomechanism problems of various types, for example Desoer and Lin, [2], DiBenedetto, [3], and Francis and Wonham, [5]. In [SI Huang and Rugh consider a servomechanism problem for general nonlinear plants subject to constant disturbance and constant reference inputs via the stabilization of the manifold of constant operating points corresponding to zero error.…”