On the relation between equation formulation of constrained systems and implicit numerical integration and optimization

Koenders, P.A.J. (2002) On the relation between equation formulation of constrained systems and implicit numerical integration and optimization.

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Abstract:The aim of this study is to establish the relation between the implicit numerical integration process and control or optimization problems. The iteration process of the implicit numerical methods and minimization of an error can be seen as control problems. An inventory of different formulations of constrained nonlinear systems is made. Their dynamical properties are analyzed and applicable numerical techniques for their simulation are investigated. After studying the available nonlinear control strategies, we propose to use index reduction by means of feedback linearization as an alternative for implicit integration methods. Since a system controlled by means of feedback linearization is marginally stable the state vector will drift off the constraint manifold. Thus, we always have to use the projection algorithm to stabilize the system. Feedback linearization and the projection algorithm can be applied straightforwardly and the solution can be found by means of simple explicit solvers. The implementation of the feedback linearization and projection algorithm approach is relatively simple. The basic numerical techniques, the implementations and the performance are compared. The latter comparison is made by simulation of a model of the Flyball governor (James Watt¿s regulator for steam engines). The simulations are performed in the software package 20-Sim. The results of the study show that feedback linearization and projection algorithm are a suitable alternative for the implicit integration method.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:53 electrotechnology
Programme:Electrical Engineering MSc (60353)
Link to this item:http://purl.utwente.nl/essays/56899
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