Liesbeth Luyckx

STABILIZATION OF A CLASS OF NONLINEAR PROCESSES BY LINEAR FEEDBACK

Abstract We discuss the stabilization of a class of nonlinear systems describing the dynamics of a stirred tank chemical reactor. The stabilization is achieved using linear dynamic feedback. Several types of controllers are defined for which closed loop global asymptotic stability of the set point can be proved. We also discuss the case where the closed loop possesses several equilibrium states and the controller is designed to ensure global convergence of the set of the equilibria. The approach relies on the direct method of Lyapunov and uses concepts from dissipativity and passivity theory.

Bounded Nonlinear Control of a Rotating Pendulum System

We are interested in the output feedback control of mechanical systems governed by the Euler‐Lagrange formalism. The systems are collocated actuator‐sensor controlled and underactuated. We present a design method by means of a specific example : the set point control of a rotating pendulum. We use constrained output feedback, whereby the control inputs satisfy a priori imposed upper bounds. The closed loop stability analysis relies on the direct method of Liapunov. This results in a frequency criterion on the controller’s linear dynamic component and some restrictions on its nonlinearities. The control parameters are tuned for maximizing closed loop damping.

A Two‐point Boundary Value Problem in Nonlinear Stability Analysis

Computational methods combining simulation and geometrical analysis are presented to estimate a set point’s basin of attraction in the state space of autonomous nonlinear systems. Dynamical systems are considered which possess global Lyapunov functions. The Lyapunov function is used to analyse the geometrical structure of the stability boundary, which determines the numerical procedure to be followed. Moreover the problem is studied of visualizing the estimated stability boundary in a higher dimensional state space.

VIBRATION CONTROL OF A CLASS OF GENERALIZED GRADIENT SYSTEMS

The suppression of oscillations in a class of generalized gradient systems using nonlinear dynamic output feedback is investigated. A class of controllers is considered which, in addition to a linear dynamic component, possess several types of nondynamic nonlinearities. Frequency domain conditions on the transfer matrix of the controllers linear component are presented that ensure the convergence of all closed-loop solutions to an equilibrium point in state space, thus eliminating the occurrence of sustained oscillations. Practically important technical applications include a.o. the set point control of mechanical systems described by the Euler–Lagrange equations and their equivalent Hamiltonian formulation. The obtained results constitute a systems theoretical basis for a new method of nonlinear vibration controller design.