Navneet Kapoor

An anti-windup design for linear systems with input saturation

Abstract An anti-windup design problem is posed and it is shown that all “observer-based” anti-windup modifications solve this problem at least locally. Sufficient conditions for an observer-based anti-windup modification to solve the global version of this problem are presented. A novel observer-based anti-windup design is then proposed such that the anti-windup problem can be interpreted in terms of a reduced-order system. In particular, the proposed anti-windup design induces an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed-loops. The dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin, stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function. The second part of the paper shows how the original dynamic compensator can be modified, while retaining those dynamic features that produce a desirable closed-loop steady-state response, to ensure that the requisite invariant subspace exists and it is reasonably tuned for input saturation. Two case studies are carried out on systems that have been investigated in the literature.

Stabilization of nonlinear processes with input constraints

Abstract This work deals with nonlinear processes which, in the absence of input constraints, can be locally stabilized by a linearizing static state feedback law. Such systems, under unconstrained linearizing control laws, possess a cascaded structure between a (asymptotically or exponentially) stable nonlinear subsystem and an exponentially stable linear subsystem, which allows for a straightforward stability analysis. In the presence of input constraints, however, this cascaded structure breaks down to an interconnection between two nonlinear subsystems; analyzing the stability of such interconnections is a rather cumbersome task, that typically results in conservative estimates of regions of stability. In this article, we present an analysis framework for the local stabilization of such processes and the estimation of regions of closed-loop stability in the presence of input constraints. The proposed approach entails: (i) specifying a region in state–space where the closed-loop system behaves effectively as a cascade and asymptotic stability can be guaranteed in the presence of constraints, provided that the states of the system remain in this region for all times; and (ii) constructing invariant sets within this region that qualify as regions of closed-loop stability. A detailed case study is carried out on a polymerization reactor example and the desirable features of the proposed methodology are aptly illustrated.

Stabilization of systems with input constraints

This article deals with the stabilization of constrained linear systems and statespace linearizable nonlinear systems and the estimation of regions of closed-loop stability. To this end, linear and linearizing static state feedback control laws are considered and a methodology to design their gains is presented. The resulting closed-loop system is such that it can be transformed, via a change of variables, into a form that facilitates the estimation of regions of stability without having to resort to a Lyapunov stability analysis. The desirable features of this approach are its ease of implementation and its relative non-conservativeness over a Lyapunovbased approach; these are illustrated by applying the theory to various examples.

Stabilization of unstable systems with input constraints

This article deals with the synthesis of stabilizing controllers for unstable linear systems and feedback linearizable unstable nonlinear systems, and the estimation of closed-loop regions of stability, in the presence of input constraints. The proposed methodology involves reducing the problem of stabilizing a system of arbitrary dimension into one of stabilizing a subsystem of dimension one, such that the stability of the overall system is ensured by guaranteeing the stability of the latter. The desirable features of the proposed methodology are its ease of implementation and its relative nonconservativeness over existing approaches; these are demonstrated by applying the proposed methodology to a chemical reactor example and comparing it with a Lyapunov-based approach.

An invariant subspace technique for anti-windup synthesis

We discuss anti-windup synthesis for linear systems with input saturation. In particular, we discuss algorithms that induce an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed-loops. The dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin, stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function. In the static case, the state feedback gains are determined from a finite (perhaps empty) set of gains that are completely determined by the nominal controller. In the dynamic case, the state feedback gains are free design parameters.

On the dynamics of nonlinear systems with input constraints

In this work we deal with the dynamical analysis of nonlinear systems with input constraints. A characterization of the domain of attraction of the region of controllability of an equilibrium point under bounded control is provided and the concept of regions of invariance within such domains of attraction is introduced and characterized. The concepts and results are illustrated through case studies on chemical reactor models. (c) 1999 American Institute of Physics.

On the Dynamics of Nonlinear Process Systems with Input Constraints

Abstract This work deals with the dynamical analysis of nonlinear process systems with input constraints. In particular, a characterization of the “domain of attraction” of an equilibrium point under bounded control is provided and the notion of regions of invariance within these domains of attraction is introduced and characterized. A case study on a two-dimensional Gray and Scott model of an isothermal, auto-catalytic reaction occurring in a CSTR is also carried out.