MA3 Nonlinear Systems

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Stable Inversion of Discrete-Time Nonlinear Maximum Phase Systems

Authors:

Li S., Georgia Institute of Technology, USA

Taylor D., Georgia Institute of Technology, USA

ABSTRACT

This paper formulates and solves the problem of stable inversion for a class of discrete-time nonlinear systems possessing either completely stable or completely unstable zero dynamics. Given a desired output trajectory, the new stable inversion method determines bounded desired trajectories for the input and state variables that satisfy the plant state and output equations. The desired input and state trajectories may be used as feedforward signals for tracking control purposes, and/or they may be used to study the influence of plant parameters on control requirements. The stable inversion process involves numerical calculations with Newton iterations and is causal for minimum-phase systems and noncausal for maximum-phase systems. An appli-cation to an electronic power conversion circuit illustrates the significant benefits of computing the feedforward input using stable inversion instead of the more traditional dc-gain method, including large reductions in peak transient error, settling time and overshoot.

Keywords: digital control, feedforward control, nonlinear systems, nonminimum-phase systems, power converters.

ma3-1

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Nonlinear Controllers for Nonlinear Passive Systems with Arbitrary Input Nonlinearities

Authors:

Haddad W., Georgia Institute of Technology, USA

Chellaboina V., University of Missouri-Columbia, USA

ABSTRACT

A nonlinear dynamic compensator framework for nonlinear passive systems with arbitrary input nonlinearities is proposed. For this class of systems we prove global closed-loop stability by modifying the dynamic compensator to include a suitable input nonlinearity. The proof of this result is based on dissipativity theory and shows that the nonlinear controller modification counteracts the effects of the input nonlinearity by recovering the passivity of the plant and the compensator.

Key Words. Nonlinear control, passive systems, actuator nonlinearities, dissipativity theory

ma3-2

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A Small-Gain Theorem for Locally Input-to-Output Stable Interconnected Systems

Authors:

Tzamtzi M., Institute of Accelerating Systems and Applications, Greece

ABSTRACT

The results of the present paper extend the nonlinear small-gain theorem to the case of “local input-to-output practical stability”. The criterion which must be satisfied by the gain functions can give results for a wide class of systems, since it can be applied to gain functions that cannot be overbounded by any linear function in a neighborhood of zero.

Key Words: nonlinear systems, small-gain theorem, input-to-output practical stability (IOpS)

ma3-3

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A stabilization methodology for invariant systems on Lie groups

Authors:

Apostolou N., University of Patras, Greece

Kazakos D., University of Patras, Greece

ABSTRACT

This paper deals with the stabilizability of invariant control systems defined on Lie groups. A stabilization technique is presented which under certain hypotheses can lead to a criterion assuring the existence of a feedback controller which steers every initial condition to a specified target point of the state space of these systems.

Key words: Invariant systems, stabilization, Lie groups.

ma3-4

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Self-Modulation in Nonlinear Feedback Systems with Jump Resonance

Authors:

Nemescu M., Technical University "Gh. Asachi", Romania

Temneanu M., Technical University "Gh. Asachi", Romania

ABSTRACT

The paper proposes to present in a compact form, the phenomenon of self-modulation that is likely to appear in nonlinear feedback systems presenting jump resonance. The system contains a time slow variable parameter depending on the modification by jump of the output signal. Due to this, the output signal undergoes a process of self-modulation in amplitude and phase through resonance jumps.

Key Words. Nonlinear feedback system, jump resonance, self-modulation.

ma3-5

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