UNSTABLE STATES STABILIZATION OF THE REVERSE PENDULUM WITH SCREW ACTUATORS

Abstract

The subject of study in the article is the technological process for the analytical synthesis of stabilization algorithms for unstable states of a reverse pendulum with screw actuators. The purpose is to develop the technology of optimal analytical synthesis of stabilization algorithms for unstable states of a reverse pendulum with screw actuators. Tasks: to form the physical model of a reverse pendulum with screw actuators. To develop using the Lagrangian formalism nonlinear mathematical model of the reverse pendulum with screw electric actuators as the automatic stabilization object. Build the linearized mathematical model of the automatic stabilization object in the state space. To analyze the functional properties of the automatic stabilization object. To form the structural schemes of the states’ stabilization automatic system for the reverse pendulum with screw actuators. To obtain analytical relations for calculating the optimal parameters values of the stabilization algorithms for unstable states of the reverse pendulum with screw actuators. To synthesize the optimal stabilization algorithm of the angular position for the specific reverse pendulum with screw electric actuators. The methods used are: Lagrange’s method, analytic linearization, state space, Laplace’s transformation. The following results were obtained. A technological process of optimal analytical synthesis of stabilization algorithms for unstable states of the reverse pendulum with screw actuators has been formed. The specific numerical example illustrates the productivity of the proposed process of analytical design and tools for the parametric synthesis of the stabilization algorithms for the reverse pendulum with screw actuators. Conclusions. The scientific novelty of the results is as follows: various models of the reverse pendulum with screw actuators are obtained as the automatic stabilization object, differing from those known for taking into account the dynamic properties of screw actuators that create control stabilization moments. The conditions for choosing the parameters of the proportional-differential structure of stabilization algorithms are formed to ensure the stability and optimality of the transition process of the close-loop stabilization system that differ from those known by the formation specifics of the stabilization control moments by the integral criterion of a weighted error modulus.