Optimization of Oscillations of Mechanical Systems

Abstract—The problem of controlling oscillations near the equilibrium position of a scleronomic mechanical system with several degrees of freedom is solved. One degree of freedom is not controllable directly, while the others are controlled by servos. An original method for finding an optimal control of the oscillation amplitude for the uncontrolled degree of freedom by choosing a control law for the other degrees of freedom is proposed. The set of controlled coordinates can include both positional and cyclic coordinates. Compared to Pont-ryagin’s maximum principle, the proposed method does not contain adjoint variables and significantly reduces the dimension of the analyzed system of differential equations. The effectiveness of the method is demonstrated as applied to a specific pendulum system.