2011/10/12 by Valery N. Pilipchuk, Pilipchuk, V. N.
Engineering · #93C10 #93C55 #Control Systems in Engineering #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Mechanisms and Dynamics
paper · pdf · doi:10.48550/arxiv.1110.2811
openalex publication_date 2011/10/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the damping constant of least squares and sampling time step of the controller must be inversely related to insure that vanishing the time step has little effect on the results. The algorithm is illustrated on two linearly coupled Duffing oscillators near the 1:1 internal resonance. In particular, it is shown that varying the dissipation ratio of one of the two oscillators can significantly suppress the nonlinear beat phenomenon.