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Title: Time - and frequency - domain approximation techniques for optimal control
Author: Chuang, Shaw Choon
Awarding Body: University of London
Current Institution: Imperial College London
Date of Award: 1972
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Approximation techniques for optimising control functions using both time and frequency domain methods are interest. The use of models of high-order systems with a low-order state-space subsystem in parallel with a convolution-described subsystem is considered. An optimisation algorithm for the parallel model, using the Dynamic Programming approach, is developed and computed results are given for an example. Algorithms for obtaining feedback gains for the parallel model with a quadratic cost is developed, using a variational approach. Similar algorithms are also presented for the same model when the quadratic cost includes a sensitivity function term. The convergence of these algorithms is proved. A continued fraction expansion (CFE) technique is proposed for modelling multivariable transfer functions to give good approximations to the initial transient response while yielding the correct steady-state response for a class of in puts. Another approximation technique, called Modified Pads Approximation (MPA) which differs from the well-known Pads approximation, is also presented, for modelling multivariable transfer functions. It is shown that, under certain conditions, the CFB and MPA techniques yield the same model. A technique is developed for obtaining approximations to the transfer function of a system such that the steady-state responses of the system and its low-order model are the same for a class of inputs. The technique is based on modelling the system's impulse response by a linear combination of orthonormal functions. For multivariable systems, low-order models of the transfer function matrices can be obtained by applying the technique to each element of the system's weighting function matrix. A minimal realisation of the resulting low-order model of the transfer function matrix can then be simply obtained. New lower bounds for the minimum cost for convolution-described linear dynamical systems with quadratic cost functions are presented. Besides its application as Stopping conditions for iterative optimisation algorithms to decide when a control sufficiently close to the optimal control has been achieved, it can also be used to check the accuracy of a simplified model to a system. The CPE and MPA approximation techniques developed before are used to approximate the optimal control for regulator problems formulated in the frequency domain. It is done by performing a sequence of simple spectral factorisations which each require considerably less effort than the complete spectral factorisation which is necessary for the determination of the optimal control in the frequency domain. It should be particularly useful for high-order linear multivariable systems. A frequency domain algorithm is proposed which iterates to give a suboptimal control with increasingly detailed structure.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available