WA1 Control Systems with Delay

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Observers for a class of Nonlinear Systems with Time-Varying Delay

Authors:

Aggoune W., CRPHT Technoport Schlassgoart, Luxembourg

Sallet G., INRIA Lorraine, France

ABSTRACT

In this paper, observers design for a class of nonlinear systems with time-varying delay is addressed. We use the Razumikhin approach to deduce general conditions for asymptotic convergence of the observer. These conditions are expressed in terms of the existence of a positive de nite matrix solution of a Riccati-type equation.

Key Words. Observers, nonlinear systems, time delay, Riccati-type equation.

wa1-1

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Functional Controllability and Right Invertibility for Systems over Rings

Authors:

Conte G., Universita' di Ancona, Italy

Perdon A. M., Universita' di Ancona, Italy

ABSTRACT

This paper is devoted to study the structure of linear systems with coeÆcients in a ring in connection with the so-called Functional Controllability Property and the Right Inversion Problem. A geometric characterization of Functional Controllability is given and a related notion of Relative Degree is introduced. Applications to delay-differential systyems are considered.

Keywords: Linear systems over ring, output reproducibility, delay-di erential systems

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Robust Analysis of Controllers for Linear Systems with Time Delay

Authors:

Hustak P., Technical University Brno, Czech Republic

Prokop R., Technical University Brno, Czech Republic

ABSTRACT

The contribution deals with the robust control design for linear systems with time delays. The proposed control synthesis is based on general solutions of Diophantine equations in the ring of Hurwitz stable and proper rational functions Rps. The methodology is suitable for stable and unstable transfer functions and covers both tracking and disturbance rejection problems. Several approximations of the time delay term is investigated and compared for stable and unstable processes. Perturbations and robustness are studied through the infinity (H.... ) norm and by open loop Nyquist plots. Resulting control laws for first order systems are of a general PID type and a scalar tuning parameter influencing robustness and properties of the closed loop system was introduced. Simulations were performed in Matlab and Simulink environment.

Key Words. Time-delay systems, linear approximations, robustness, PID controllers, Diophantine equations.

wa1-3

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A Simple Automatic Tuning Method for a Smith Predictor

Authors:

Kaya I., University of Sussex, United Kingdom

Tan N., University of Sussex, United Kingdom

ABSTRACT

In this paper a new approach is presented based on relay autotuning of a plant to find parameters for its control using a Smith predictor. A Smith predictor configuration is represented as its equivalent internal model controller, IMC, which provides the parameters of the PI or PID controller to be defined in terms of the desired closed-loop time constant, which can be adjusted by the operator, and the parameters of the process model. This means that only one parameter, namely the desired closed-loop time constant, is left for tuning. The ISE criterion was used to find the filter parameter, and simple equations were obtained to tune the Smith predictor. The method is very simple and has given improved results compared with some previous approaches.

Keywords: Relay autotuning, PID controller, Smith predictor, IMC Control

wa1-4

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Tuning Smith Predictors using Simple Formulae

Authors:

Kaya I., University of Sussex, United Kingdom

Tan N., University of Sussex, United Kingdom

ABSTRACT

Good control of processes with long dead time is often achieved using a Smith predictor configuration. However, not much work has been carried out on obtaining simple tuning rules for a Smith predictor scheme. This paper develops optimal analytical tuning formulae for PID controllers in a Smith predictor configu- ration assuming perfect matching. These formulae have been obtained by carrying out repeated optimizations on the error transfer function of a Smith predictor, assuming perfect matching, to find optimal relations between the normalized gain and the remaining parameters of the controller. Then the least square fitting method was used to find the constants in the assumed formulae to fit the graphical data obtained. Some examples are given to show thevalue of the approach presented. Keywords: Predictive control; Integral performance indices; Delay compensation; PID controllers

Keywords: Predictive control; Integral performance indices; Delay compensation; PID controllers

wa1-5

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