Quasi-optimal control of rotation of a rigid body about a fixed axis taking friction into account

A mechanical system is considered that consists of a rotating base and a rigid body which can rotate with respect to the base around the axis coinciding with the axis of the base rotation. The control of the body’s motion with respect to the base is performed using a direct (high-torque) electric drive. The voltage applied across armature circuit terminals of the motor serves as a control variable. A dynamical model of the system is proposed that takes into account the friction moment in the rolling bearings with respect to the rotation axis. The rolling-friction moment is represented by an odd function of the angular velocity of body rotation that has a jump discontinuity at zero, as is the case for the dry-friction characteristic. An optimal control problem for bringing the body to the specified angular position in the absence of friction is solved. The time integral of a quadratic function of the control and phase variables is the functional to be minimized. For the system with friction, quasi-optimal feedback control laws are constructed, and sticking zones are estimated which are caused by sliding and rolling dry friction. Control modes are proposed with compensation for nonidealities and perturbation factors. Mathematical simulation is conducted and the dynamical characteristics of the process under control are determined.