P.M.J. Van den Hof

Bio: P.M.J. Van den Hof is an academic researcher from Delft University of Technology. The author has contributed to research in topics: System identification & Robust control. The author has an hindex of 27, co-authored 104 publications receiving 2440 citations.

A generalized orthonormal basis for linear dynamical systems

Abstract: In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l/sub 2sup n/. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients. >

System identification with generalized orthonormal basis functions

Abstract: A least squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of generalized basis functions. The basis functions are orthogonal in H/sub 2/ and generalize the pulse, Laguerre and Kautz (1954) bases. The construction of the basis is considered and bias and variance expressions of the identification algorithm are discussed. The basis induces a new transformation (Hambo transform) of signals and systems, for which state space expressions are derived. >

A generalized orthonormal basis for linear dynamical systems

Abstract: In many areas of signal, system and control theory orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems, and that compose an orthonormal basis for the signal space l/sub 2//sup n/. To this end use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, e.g., the Laguerre functions and the pulse functions, related to the use of the delay operator, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e. to obtain a good approximation by retaining only a finite number of expansion coefficients. >

Suboptimal feedback control by a scheme of iterative identification and control design

Abstract: In this paper a framework for an iterative procedure of identification and robust control design is introduced wherein the robust performance is monitored during the subsequent steps of the iterative scheme. By monitoring the performance via a model-based approach, the possibility to guarantee performance improvement in the iterative scheme is being employed. In order to monitor achieved performance (for a present controller) and to guarantee robust performance (for a future controller), an uncertainty set is used where the uncertainty structure is chosen in terms of model perturbations in the dual Youla parametrization. This uncertainty structure is shown to be particularly suitable for the control performance measure that is considered. The model uncertainty set can be identified by an uncertainty estimation procedure on the basis of closed-loop experimental data. To obtain performance robustness, robust control design tools are used to synthesise controllers on the basis of the identified uncertainty set.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Iterative feedback tuning: theory and applications

Abstract: 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.