Michel Gevers

Iterative feedback tuning: theory and applications

We have examined an optimization approach to iterative control design. The important ingredient is that the gradient of the design criterion is computed from measured closed loop data. The approach is thus not model-based. The scheme converges to a stationary point of the design criterion under the assumption of boundedness of the signals in the loop. From a practical viewpoint, the scheme offers several advantages. It is straightforward to apply. It is possible to control the rate of change of the controller in each iteration. The objective can be manipulated between iterations in order to tighten or loosen performance requirements. Certain frequency regions can be emphasized if desired. This direct optimal tuning algorithm is particularly well suited for the tuning of the basic control loops in the process industry, which are typically PID loops. These primary loops are often very badly tuned, making the application of more advanced (for example, multivariable) techniques rather useless. A first requirement in the successful application of advanced control techniques is that the primary loops be tuned properly. This new technique appears to be a very practical way of doing this, with an almost automatic procedure.

Stable adaptive observers for nonlinear time-varying systems

An adaptive observer/identifier for single input/single output observable nonlinear systems that can be transformed to a certain observable canonical form is described. Sufficient conditions for stability of this observer are provided. These conditions are in terms of the structure of the system and canonical form, the boundedness of the parameter variations, and the sufficient richness of some signals. The scope of the canonical form and the use of the observer/identifier is motivated by the presentation of applications to time-invariant bilinear systems, nonlinear systems in phase-variable form a biotechnological process, and a robot manipulator. In each case, the specific stability conditions are presented. >

Quantifying the error in estimated transfer functions with application to model order selection

Previous results on estimating errors or error bounds on identified transfer functions have relied upon prior assumptions about the noise and the unmodeled dynamics. This prior information took the form of parameterized bounding functions or parameterized probability density functions, in the time or frequency domain with known parameters. Here we show that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique. This significantly reduces the prior infor- mation required to estimate transfer function error bounds. We illustrate the usefulness of the method with a number of simula- tion examples. The paper concludes by showing how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under-model- ing. Another simulation study compares our method to Akaikes well-known FPE and AIC criteria.

A convergent iterative restricted complexity control design scheme

In this contribution we propose an optimization approach to the design of a restricted complexity controller. The design criterion is of LQG type containing two terms. The first term is the quadratic norm of the error between the output of the true closed loop and a desired response. The second term is the quadratic norm of the input signal. It is shown that the minimization of this criterion does not require a model of the system. Closed loop experimental data can be used instead. The result is an iterative scheme of closed loop experiments and controller updates which converges to a local minimum of the design criterion under the condition of bounded signals.<<ETX>>

Towards a Joint Design of Identification and Control

This paper aims at introducing the reader to the various issues that arise in the development of a coherent methodology for the development of robust control design on the basis of models identified from data. When a reduced complexity model is identified with the purpose of designing a robust controller, the model is just a vehicle for the computation of a controller. The design of the identification and of the controller must be seen as two parts of a joint design problem. The central message of this paper is to show that the global control performance criterion must determine the identification criterion. This leads to non standard identification criteria, which can be minimized by appropriate experimental set-ups.

Identification for control: From the early achievements to the revival of experiment design

This paper presents the authors views on the development of identification for control. The paper reviews the emergence of this subject as a specific topic over the last 15 years, at the boundary between system identification and robust control. It shows how the early focus on identification of control-oriented nominal models has progressively shifted towards the design of control-oriented uncertainty sets. This recent trend has given rise to an important revival of interest in experiment design issues in system identification. Some recent results on experiment design are presented.

Iterative weighted least-squares identification and weighted LQG control design

Many practical applications of control system design based on input-output measurements permit the repeated application of a system identification procedure operating on closed-loop data together with successive refinements of the designed controller. Here we develop a paradigm for such an iterative design. The key to the procedure is to account for evaluated modelling error in the control design and, equally, to let the closed-loop controller requirements determine the identification criterion. With an H-2 control problem, this is achieved by frequency weighting the linear-quadratic Gaussian (LQG) control criterion with filters that reflect the closed-loop plant/model mismatch, and by filtering the identifier signals used in a least-squares identification scheme in a logical and mutually supportive fashion.

Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices

Until recently, it was believed that a necessary and sufficient condition for convergence of the Riccati difference equation of optimal filtering was that the system be both delectable and stabilizable. Recently, it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular. The present paper generalizes these results in several directions. First, properties of the algebraic Riccati equation are established for the case of singular state transition matrix. Second, several assumptions previously imposed in establishing convergence of the Riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability, weakening the conditions on the initial covariance, and allowing the state transition matrix to be singular. Third, results on the convergence and properties of the Riccati equations are expressed as both necessary and sufficient conditions, whereas previous results were only sufficient. These extensions mean that the results have wider applicability, including fixed-lag smoothing problems and filtering for systems with time delays. The implications of the results in the dual problem of optimal control are also studied.

Iterative feedback tuning of PID parameters: comparison with classical tuning rules

We apply the Iterative Feedback Tuning (IFT) method to the tuning of PID parameters in applications where the objective is to achieve a fast response to set point changes. We compare the performance of these IFT-tuned PID controllers with the performance achieved by four classical PID tuning schemes that are widely used in industry. Our simulations show that IFT always achieves a performance that is at least as good as that of the classical PID tuning schemes, and often dramatically better: faster settling time and less overshoot. In addition, IFT is also optimal with respect to the presence of noise, whereas the other schemes are designed for noise-free conditions. The IFT method used here is a variant of the initial IFT scheme, in which no weighting is applied to the control error during a time window that corresponds to the transient response, and where the length of this window is progressively reduced. This method was initially proposed in Lequin (CD-ROM of European Control Conference, Paper TH-A-H6, Brussels, Belgium, 1997) and elaborated on in Lequin et al. (Proceedings of the 14th IFAC World Congress, Paper I-3b-08-3, Beijing, Peoples Republic of China, 1999, pp. 433-437)

Identification For Control: Optimal Input Design With Respect To A Worst-Case

Parameter identification experiments deliver an identified model together with an ellipsoidal uncertainty region in parameter space. The objective of robust controller design is thus to stabilize all plants in the identified uncertainty region. The subject of the present contribution is to design an identification experiment such that the worst-case