Karl Johan Åström

A new model for control of systems with friction

In this paper we propose a new dynamic model for friction. The model captures most of the friction behavior that has been observed experimentally. This includes the Stribeck effect, hysteresis, spring-like characteristics for stiction, and varying break-away force. Properties of the model that are relevant to control design are investigated by analysis and simulation. New control strategies, including a friction observer, are explored, and stability results are presented. >

Paper: Automatic tuning of simple regulators with specifications on phase and amplitude margins

The paper describes procedures for automatic tuning of regulators of the PID type to specifications on phase and amplitude margins. The key idea is a simple method for estimating the critical gain and the critical frequency. The procedure will automatically generate the appropriate test signal. The method is not sensitive to modelling errors and disturbances. It may be used for automatic tuning of simple regulators as well as initialization of more complicated adaptive regulators.

System identification-A survey

The field of identification and process-parameter estimation has developed rapidly during the past decade. In this survey paper the state-of-the-art/science is presented in a systematic way. Attention is paid to general properties and to classification of identification problems. Model structures are discussed; their choice hinges on the purpose of the identification and on the available a priori knowledge. For the identification of models that are linear in the parameters, the survey explains the least squares method and several of its variants which may solve the problem of correlated residuals, viz. repeated and generalized least squares, maximum likelihood method, instrumental variable method, tally principle. Recently the non-linear situation, the on-line and the real-time identification have witnessed extensive developments. These are also reported. There are 230 references listed, mostly to recent contributions. In appendices a resume is given of parameter estimation principles and a more detailed exposition of an example of least squares estimation.

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.

Friction Models and Friction Compensation

This paper reviews friction phenomena and friction models of interest for automatic control. Particular emphasis is given to two recently developed dynamic friction models: the Bliman-Sorine model and the LuGre model. These models capture many frictional phenomena observed in laboratory experiments. The behaviours of the models in different situations are discussed in detail. Methods for friction compensation are presented and illustrated with results from practical experiments.

The future of PID control

Abstract This paper presents the state of the art of PID control and reflects on its future. Particular issues discussed include specifications, stability, design, applications, and performance of PID control. The paper ends with a discussion of alternatives to PID and its future.

Paper: Zeros of sampled systems

The zeros of the discrete time system obtained when sampling a continuous time system are explored. Theorems for the limiting zeros for large and small sampling periods are given. A condition which guarantees that the sampled system only has stable zeros is also presented.

Theory and applications of adaptive control-A survey

Progress in theory and applications of adaptive control is reviewed. Different approaches are discussed with particular emphasis on model reference adaptive systems and self-tuning regulators. Techniques for analysing adaptive systems are discussed. This includes stability and convergence analysis. It is shown that adaptive control laws can also be obtained from stochastic control theory. Issues of importance for applications are covered. This includes parameterization, tuning, and tracking, as well as different ways of using adaptive control. An overview of applications is given. This includes feasibility studies as well as products based on adaptive techniques.

Comparison of Riemann and Lebesgue sampling for first order stochastic systems

The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

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.