Controlling oscillation amplitudes via feedback (Q2710007)

The authors propose a feedback control strategy which reduces the amplitude of a limit cycle of a nonlinear system near a Hopf bifurcation point, while maintaining the equilibrium points as well as the Hopf bifurcation points. The parameters in the control law are determined using frequency domain techniques, where higher-order harmonic balance approximations are used in order to obtain information about the nonlinear system under consideration near the bifurcation point. NEWLINENEWLINENEWLINEWhile this control law explicitly depends on the derivatives of the state variables, an alternative feedback control derived from the first avoids this dependence replacing the derivatives by suitable approximations. NEWLINENEWLINENEWLINEThe performance of both feedback laws is finally illustrated by simulation results, where for both control laws, the amplitude of the controlled limit cycles turn out to have approximately half the amplitude of the uncontrolled limit cycle.