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Technical Brief

Three-Stage Feedback Controller Design With Applications to Three Time-Scale Linear Control Systems

[+] Author and Article Information
Verica Radisavljevic-Gajic

Department of Mechanical Engineering,
Villanova University,
800 East Lancaster Avenue,
Villanova, PA 19085
e-mail: verica.gajic@villanova.edu

Milos Milanovic

Department of Mechanical Engineering,
Villanova University,
800 East Lancaster Avenue,
Villanova, PA 19085
e-mail: mmilano5@villanova.edu

Garrett Clayton

Department of Mechanical Engineering,
Villanova University,
800 East Lancaster Avenue,
Villanova, PA 19085
e-mail: garett.clayton@villanova.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 17, 2016; final manuscript received March 10, 2017; published online June 28, 2017. Assoc. Editor: Soo Jeon.

J. Dyn. Sys., Meas., Control 139(10), 104502 (Jun 28, 2017) (10 pages) Paper No: DS-16-1252; doi: 10.1115/1.4036408 History: Received May 17, 2016; Revised March 10, 2017

This paper presents a new technique for design of full-state feedback controllers for linear dynamic systems in three stages. The new technique is based on appropriate partitioning of the linear dynamic system into linear dynamic subsystems. Every controller design stage is done at the subsystem level using only information about the subsystem (reduced-order) matrices. Due to independent design in each stage, different subsystem controllers can be designed to control different subsystems. Partial subsystem level optimality and partial eigenvalue subsystem assignment can be achieved. Using different feedback controllers to control different subsystems of a system has not been present in any other known linear full-state feedback controller design technique. The new technique requires only solutions of reduced-order subsystem level algebraic equations. No additional assumptions were imposed except what is common in linear feedback control theory (the system is controllable (stabilizable)) and theory of three time-scale linear systems (the fastest subsystem state matrix is invertible)). The local full-state feedback controllers are combined to form a global full-state controller for the system under consideration. The presented results are specialized to the three time-scale linear control systems that have natural decomposition into slow, fast, and very fast subsystems, for which numerical ill conditioning is removed and solutions of the design algebraic equations are easily obtained. The proposed three-stage three time-scale feedback controller technique is demonstrated on the eighth-order model of a fuel cell model.

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