Malekpoor, Somayeh (2016). Optimization methods for deadbeat control design: a state space approach. (Unpublished Doctoral thesis, City University London)
Abstract
This thesis addresses the synthesis problem of state deadbeat regulator using state space techniques. Deadbeat control is a linear control strategy in discrete time systems and consists of driving the system from any arbitrary initial state to a desired final state infinite number of time steps.
Having described the framework for development of the thesis which is in the form of a lower linearfractional transformation (LFT), the conditions for internal stability based on the notion of coprime factorization over the set of proper and stable transfer matrices, namely RH, is discussed. This leads to the derivation of the class of all stabilizing linear controllers, which are parameterized affinely in terms of a stable but otherwise free parameter Q, usually known as the Qparameterization. In this work, the classical Q parameterization is generalized to deliver a parameterization for the family of deadbeat regulators.
Time response characteristics of the deadbeat system are investigated. In particular, the deadbeat regulator design problem in which the system must satisfy time domain specifications and minimize a quadratic (LQGtype) performance criterion is examined. It is shown that the attained parameterization for deadbeat controllers leads to the formulation of the synthesis problem in a quadratic programming framework with Q regarded as the design variable. The equivalent formulation of this objective as a quadratic integral in the frequency domain provides the means for shaping the frequency response characteristics of the system. Using the LMI characterization of the standard H problem, a new scheme for shaping the system frequency response characteristics by minimizing the infinity norm of an appropriate closedloop transfer function is introduced. As shown, the derived parameterization of deadbeat compensators simplifies considerably the formulation and solution of this problem.
The last part of the work described in this thesis is devoted to addressing the synthesis problem of deadbeat regulators in a robust way, when the plant is subject to structured normbounded parametric uncertainties. A novel approach which is expressed as an LMI feasibility condition has been proposed and analysed.
Publication Type:  Thesis (Doctoral) 

Subjects:  Q Science > QA Mathematics 
Departments:  Doctoral Theses School of Mathematics, Computer Science & Engineering Doctoral Theses > School of Mathematics, Computer Science and Engineering 
URI:  http://openaccess.city.ac.uk/id/eprint/14396 

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