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STATE-FEEDBACK CONTROL

ECE4520/5520: Multivariable CONTROL Systems 1 STATE-FEEDBACK : STATE-FEEDBACK CONTROL We are given a particular system having : We know that open-loop system poles are given by eigenvaluesofA. Want to use change the dynamics. Will assume the form oflinearstatefeedback with gain ! ; K2R1"n: We assume known exactly: then, we ; B; C; DxK ! ! : For now we talk about regulation ( ) notes prepared by Dr. Gregory L. Plett. Copyrightc#2015, 2011, 2009, 2007, 2005, 2003, 2001, 2000, Gregory L. PlettECE4520/5520, STATE-FEEDBACK CONTROL6 2 For now we consider SISO systems, and generalize :DesignKso thatACLDA!BKhas some nice example, PerhapsAis unstable. DesignACLto be stable. Or, might want to put two poles at!2 j.(Poleplacement.)

OBJECTIVE: Design K so that A CL D A!BK has some nice properties. For example, Perhaps A is unstable. Design A CL to be stable. Or, might want to put two poles at!2˙j.(Poleplacement.) There are n parameters in the gain vector K and n eigenvalues of A. So, what can we achieve? EXAMPLE: Consider the (unstable) system x.t/P D " 11 12 # x.t/C " 1 ...

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