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Reference governors for systems with polynomial constraints: theory and extensions
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Schieni, Rick. Reference governors for systems with polynomial constraints: theory and extensions. Retrieved from https://doi.org/doi:10.7282/t3-gd57-pm28

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TitleReference governors for systems with polynomial constraints: theory and extensions
NameSchieni, Rick (author); Burlion, Laurent (chair); Baruh, Haim (member); Yi, Jingang (member); Kolmanovsky, Ilya (member); Rutgers University; School of Graduate Studies
Date Created2023
Other Date2023-01 (degree)
SubjectMechanical engineering, Linear control systems
Extent163 pages : illustrations
DescriptionControls engineering focuses around the design of processes which ensure the system to be controlled is stable, can track some desired performance, and can reject disturbances. A great number of effective control techniques have been developed which focus on the transient response of the system however, many of these control schemes do not take system constraints, such as actuator saturation, into account. With techniques established which produce a satisfactory transient response of the system, it is desired to preserve the response of the original control technique while ensuring the constraints on the system are satisfied. This desire has led to the development of the reference governor add-on schemewhich modifies the reference signal to a pre-existing nominal controller to ensure system constraints are satisfied. In this work, a reference governor add-on scheme is designed for linear systems subject to polynomial constraints. The system state vector is first augmented with the reference governor signal to create the augmented state vector. Employing the Kronecker product allows one to derive an extended state vector which encapsulates the higher order powersof the original augmented state. With the higher order powers integrated into the extended state, the polynomial constraints can be written as linear constraints in terms of the new base vectors. It is shown that the Maximal Output Admissible Set (MOAS) for the extended system is finitely determined and the MOAS for the original system is a cross section of the MOAS computed for the extended system. The methodology presented to handle linear systems subject to polynomial constraints is then extended to handle systems subject to external disturbances and parametric uncertainties. Exploiting the convexity of the problem, it’s shown that the MOAS of a system subject to uncertainties can be calculated using the known bounds of the uncertain parameters and disturbances. Further extensions are made to handle the problem where the polynomial constraints acting on the system are piecewise and dependent upon the current value of the state. It’s shown that the regions of applicability of the piecewise constraints can be propagated into the future to determine feasible regions in which the state may exist. Each proposed method is supported by numerical examples which present the efficacy of the methods. It’s shown that the strategies developed in this work are applicable to real-world systems such as bistable structures, unmanned aerial vehicles, stall prevention of civil aircraft, and obstacle avoidance among others.
NotePh.D.
NoteIncludes bibliographical references
Genretheses
Persistent URLhttps://doi.org/doi:10.7282/t3-gd57-pm28
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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