The topic of shaping and controlling transient responses of dynamic systems has important applications. Achieving a desired transient response is an essential design requirement for many control system. In this research, we discuss the impact on the transient response of linear systems when it is subjected to a set of integral constraints. The investigation is generalized in a theoretical framework. Formulation of three types of integral constraints is first discussed. The underlying goal of the problem is to shape the step response to generate a specific type of transient response which in turn satisfies the desired integral constraints. The problem is transformed to that of determining the specific structures of transfer functions that can satisfy these aforementioned constraints. Analytical results are established for a class of second-order systems with an additional zero. Subsequently, the results are extended to higher-order transfer functions and the desired characteristics that a general transfer function should have, to meet the three types of integral constraints, are derived. Next, the implementation requirements to ensure these dynamic characteristics with a given plant transfer function are addressed. In this regard, a control structure, employing combined feedforward and feedback actions, is proposed. Furthermore, necessary conditions to maintain the stability of the overall closed-loop system, generated by the proposed compensation, are established. Subsequent analysis that aims to satisfy the above-mentioned integral constraints in the presence of parametric uncertainties, is presented. In this regard, structured adaptive estimation strategies are proposed to deal with uncertainty. Implementation examples and simulation results are provided to validate the approaches developed in this work. Further examples to demonstrate the analysis using practical applications are also presented. Here, the utilization of the methods proposed in this work arises in the applications of designing decentralized control for power management of hybrid power systems.
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Doctor of Philosophy (Ph.D.)
College of Engineering and Computer Science
Mechanical and Aerospace Engineering
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Salih, Bilal, "Linear Systems with Integral Constraints on Transient Step-Response" (2019). Electronic Theses and Dissertations, 2004-2019. 6848.