ИСТИНА

The paper is dedicated to the designing control for objects that may have desired working regimes unstable without additional guidance. The control signal is assumed limited in absolute value. The motion equations of a multi-link pendulum mounted on a moving base, on a wheel or a cart, are designed. Under some conditions, mathematical model allows separation of equations that describe only the pendulum motion. The task of stabilizing a single inverted pendulum mounted on a wheel is solved. So called «inertia wheel pendulum» is studied. A control algorithm is proposed and tested experimentally to translate this pendulum from any initial state into the top. Other modes of motion are realized by other proposed algorithms. The double pendulum with stationary suspension joint is considered. The control torque is applied in the inter-link or in the suspension joint. The control algorithms to ensure global stabilization of the inverted pendulum are designed. The problems of optimal swinging and damping are also discussed. A problem of stabilizing of a ball on a straight or curvilinear beam is studied. The goal is to control the voltage applied to the drive so that to stabilize the unstable equilibrium with maximal basin of attraction. The degree of instability of the above considered systems equal to one or two. For maximizing attraction basin of this kind systems, all control resources must be spent on the suppressing the unstable modes. The problem of gyroscopic stabilizing of the upright unstable position of a robot-bicycle is investigated theoretically and practically.