Björn Wittenmark

On self tuning regulators

The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time single-input single-output systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analysed. The main results are two theorems which characterize the closed loop system obtained under the assumption that the parameter estimates converge. The first theorem states that certain covariances of the output and certain cross-covariances of the control variable and the output will vanish under weak assumptions on the system to be controlled. In the second theorem it is assumed that the system to be controlled is a general linear stochastic nth order system. It is shown that if the parameter estimates converge the control law obtained is in fact the minimum variance control law that could be computed if the parameters of the system were known. This is somewhat surprising since the least squares estimate is biased. Some practical implications of the results are discussed. In particular it is shown that the algorithm can be feasibly implemented on a small process computer.

Stochastic analysis and control of real-time systems with random time delays

The paper discusses modeling and analysis of real-time systems subject to random time delays in the communication network. A new method for analysis of different control schemes is presented. The method is used to evaluate different suggested schemes from the literature. A new scheme, using so called timestamps, for handling the random time delays is then developed and successfully compared with previous schemes. The new scheme is based on stochastic control theory and a separation property is shown to hold for the optimal controller.

Paper: Theory and applications of self-tuning regulators

This paper reviews work on self-tuning regulators. The regulator algorithms, their theory and industrial applications are reviewed. The paper is expository-the major ideas are covered but detailed analysis is given elsewhere.

Timing problems in real-time control systems

The paper formulates and discusses timing problems in real-time systems from the sampled data point of view. Different ways to eliminate the effects of communication delays are considered.

Paper: Practical issues in the implementation of self-tuning control

Implementation aspects of self-tuning regulators are discussed in the paper. There is a large discrepancy between simulation or academic algorithms and practical algorithms. In the idealized environment of simulations it is easy to get different types of adaptive algorithms to perform well. In practice the situation is quite opposite. The adaptive or self-tuning controller must be able to handle nonlinearities, unmodelled dynamics and unmodelled disturbances over a wide range of operating conditions. Some aspects of how to implement self-tuning controllers are discussed in the paper. This includes robustness, signal conditioning, parameter tracking, estimator wind-up, reset action and start-up. Different ways to use the prior knowledge about the process are also discussed.

Stochastic Adaptive Control Methods: A Survey

There is a vast literature about adaptive (self-organizing, self-optimizing) control systems. The aim of this paper is to point out some of the main ideas. Since there exists good survey papers about several of the classes of adaptive controllers the main part of this paper will concentrate on recent developments. The paper will cover stochastic adaptive controllers. The problem of dual control is given particular attention.

Adaptive Dual Control Methods: An Overview

This paper gives an overview of different techniques for solving the dual control problem. The optimal solution can quite straightforwardly be characterized. The solution is, however, numerically demanding. A large number of suboptimal dual controllers have been developed over the years and the paper gives an overview and discussion of different approaches.

Dynamic pictures and interactive learning

We present interactive learning tools used in courses in automatic control at Lund Institute of Technology. The learning tools are aimed at improving the understanding of and intuition for the abstract parts of the control courses. The tools, mainly dynamic interactive modules for a course in sampled-data systems, are implemented in Matlab and can be used over the Internet.

An approach to adaptive control using real time identification

An adaptive controller consisting of a real time identifier and a minimum variance regulator is discussed. The identification is done by augmenting the state with the unknown parameters of the process. This usually leads to a non-linear filtering problem. By choosing a model of special structure the problem can, however, be reduced to a linear problem. The control law is derived using stochastic optimal control theory. By choosing a special criterion, the stochastic control problem can be solved analytically. The behaviour of the adaptive controller is illustrated in two examples.

Hankel-norm based interaction measure for input-output pairing

In this paper a new interaction measure for stable multivariablesystems is introduced.The interaction measure, the Hankel Interaction Index,is a dynamic extension of the underlying idea in the classicRelative Gain Array (RGA) and its various extensions. The new index isbased upon the Hankel normof the SISO elementary subsystems built from the original MIMOsystem. The main advantage of the Hankel Interaction Index is itsability to quantify frequency dependent interactions and that it canbe used for input-output pairing.