State Feedback Controllers

Abstract

• 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. • Want to use the input u(t) to modify the eigenvalues of A to change the system dynamics. K Assume a full-state feedback of the form: • u(t) = r − Kx(t) where r is some reference input and the gain K is R 1×n • If r = 0, we call this controller a regulator • Find the closed-loop dynamics: x ˙ (t) = Ax(t) + B(r − Kx(t)) = (A − BK)x(t) + Br = A cl x(t) + Br y(t) = Cx(t) A, B, C x(t) y(t) r u(t) −