2.14AnalysisandDesignofFeedbackControlSystems （2.14 analysisanddesignoffeedbackcontrolsystems）.pdfVIP

2.14 Analysis and Design of Feedback Control Systems State-Space Representation of LTI Systems Derek Rowell October 2002 1 Introduction The classical control theory and methods (suc has root locus) that we have been using in class to date are based on a simple input-output description of the plant, usually expressed as a transfer function. These methods do not use any knowledge of the interior structure of the plant, and limit us to single-input single-output (SISO) systems, and as we have seen allows only limited control of the closed-loop behavior when feedback control is used. Modern control theory solves many of the limitations by using a muc h“richer” description of the plant dynamics. The so-called state-space description provide the dynamics as a set of coupled first-order differential equations in a set of internal variables known as state variables, together wit ha set of algebraic equations that combine the state variables into physical output variables. 1.1 Definition of System State The concept of the state of a dynamic system refers to a minimum set of variables, known as state variables, that fully describe the system and its response to any given set of inputs [1-3]. In particular a state-determined system model has the characteristic that: A mathematical description of the system in terms of a minimum set of variables xi (t), i = 1, . . . , n, together wit hknowledge of those variables at an initial time t0 and the system inputs for time t ≥ t , are sufficient to predict the future system 0 state and outputs for all time t t0 . Th