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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.) There arenparameters in the gain vectorKandneigenvalues , what can we achieve?EXAMPLE:Consider the (unstable) "1112# "10# ! !1/.s!2/!1Ds2!3sC1: ! ! !BKD"1112#!"10#hk1k2iD"1!k11!k212#: So, ! !3 !

ECE4520/5520: Multivariable Control Systems I. 6–1 STATE-FEEDBACK CONTROL 6.1: State-feedback control We are given a particular system having dynamics x.t/P D Ax.t/CBu.t/ y.t/D Cx.t/CDu.t/: We know that open-loop system poles are given by eigenvalues of A. Want to use input u.t/ to change the dynamics.

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