Control of the Motion of an Inverted Spherical Pendulum on a Moving Base. Hybrid Impact Approach

A new hybrid method for the construction of control actions of a linear control system with constant coefficients is considered in this paper. It is assumed in this paper that a part of the discussed system meets some conditions. Some states of the main system are considered to be control actions for a subsystem for which and LQR stabilizer is acquired. Then, those control actions of the subsystem are used to construct the control actions for the main system. In the problem of controlling the motion of a complex linear system of an inverted spherical pendulum on a moving base, a new approach to the construction of control actions (hybrid action method) was used. It is assumed that a component of the complex system under discussion satisfies certain conditions. The inertial forces at the center of mass of the base of the composite system are considered to be the controlling influences on the inversion of the pendulum, for which the LQR stabilizer was purchased. The determined internal control actions on the inverted pendulum are then used to construct external control actions on the base of the composite system. In the end, a numerical analysis was carried out.