ИСТИНА

The operation of many mechanisms of tools (metalworking machinery, robotic manipulators, walking robots) is characterized by undesirable vibrations. Such vibrations typically arise due to compliant elements in the design of the plant or in environment with which the plant is coupled. Such an element can be, for example, a compliant platform where the operated object (plant) is installed or an elastic gear that connects a motor with this movable object. Mechanical system containing compliant element is studied. The control parameter (force or torque) is bounded in magnitude. Only the first (lowest) resonance frequency is taken into account. Thus the system under consideration has two degrees of freedom and one control input. A double zero eigenvalue and two complex eigenvalues are in the linear mathematical model of this system. Control laws to steer the plant from the given initial state of rest to the given final state of rest in finite time are designed. These controls are divided into intervals on which it varies linearly depending on time or is constant. The time intervals where the control varies are equal to the period of the natural vibrations of the system. If there is no damping, this makes it possible to completely avoid vibrations on the time intervals where the control is constant including the time when the control signal becomes zero (identically). Another way to avoid the vibrations is to put the total time of the transient process equal to a multiple of the doubled period of the natural vibrations. There are many papers devoted to the problem of suppressing the undesirable vibrations. But in this article we try to avoid (to prevent) the generation of the undesirable vibrations.