Youla-Kucera Parametrization Research Articles

A self-tuning control scheme for disk file servos

The authors present a self-tuning control scheme for disk file track-following servos. The scheme augments an existing fixed controller to recover a specified nominal performance in the presence of unmodeled dynamics. The compensator used in each disk file is individually tuned by inserting an add-on adjustable compensator to the nominal compensator, utilizing a linear fractional transformation (LFT) known as the Youla-Kucera parametrization. Similarly, the difference between the actual disk drive dynamics and the nominal model is characterized by an unknown transfer function, using the Youla-Kucera parametrization applied to the plant rather than the compensator. The algorithm consists of two steps: identification of the unmodeled dynamics transfer function, followed by the synthesis of the add-on compensator, utilizing the linear quadratic Gaussian (LQG) compensator methodology.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the Youla-Kucera parametrization for nonlinear systems

We consider the problem of stabilizing a nonlinear plant through the use of a, possibly unstable, pre-compensator and a stable feedback-compensator, and parameterizing a class of such stabilizers in terms of a BIBO stable map Q. In the linear case, by means of superposition the pre-and feedback-compensator can be combined in such a way that the BIBO map Q occurs in just one feedback loop within the controller, feeding back output residuals (prediction errors) to the control inputs. The main contribution of this paper is to develop a nonlinear generalization of this property. Building on earlier work in forming the Youla-Kucera parametrization for nonlinear systems, we show the equivalence of the class of all (bounded-input) stabilizing nonlinear pre- and feedback-compensators to a class of possibly unstable feedback controllers in which a map Q s is present in only the one feedback loop. We then show that necessary and sufficient condition to achieve stability of the system is that Q s be BIBO stable. One advantage of the new formulation is that differential boundedness assumptions do not involve the parametrization Q s in any way. Just as the linear versions of our results have applications in the areas of optimal control and adaptive control of linear systems, it is conjectured that the present results will underlie more general results for adaptive control and nonlinear systems.

Left coprime factorizations and a class of stabilizing controllers for non-linear systems

Abstract The problem of representing a class of non-linear systems by both left and right bounded-input-bounded-output (BIBO) coprime factors is studied. Based on the coprime factorizations, the class of all stabilizing controllers of a particular structure for the set of plants under consideration is then characterized in term of a BIBO stable map, Q. The results specialize to the Youla-Kucera parametrization in the linear case. Results giving the various conditions for a non-linear feedback system to be well posed are also presented.