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16.30 Topic 11: Full-state feedback control

Topic #11 feedback control Systems State-Space Systems Full-state feedback control How do we change the poles of the state-space system ? Or, even if we can change the pole locations. Where do we change the pole locations to? How well does this approach work? Reading: FPE Fall 2010 11 1 Full-state feedback Controller Assume that the single-input system dynamics are given by x (t) = Ax(t)+ Bu(t) y(t) = Cx(t) so that D = 0. The multi-actuator case is quite a bit more complicated as we would have many extra degrees of freedom. Recall that the system poles are given by the eigenvalues of A.

Oct 17, 2010 · Fall 2010 16.30/31 11–5 Ackermann’s Formula • The previous outlined a design procedure and showed how to do it by hand for second-order systems. • Extends to higher order (controllable) systems, but tedious. • Ackermann’s Formula gives us a method of doing this entire design process is one easy step. K = 0 ... 0 1 M−1Φ d(A) c •M

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