Motion control of the inverted pendulum: development of the installation, identification of the system and synthesis of the optimal motion controller

Abstract

In the work, an approach has been developed that allows of synthesizing optimal controllers of dynamic systems. It consists in the identification of a physical model of a dynamical system (in the case under consideration of the "inverted pendulum" type). This provides the ground for the controller synthesis problem statement. This approach does not require a mathematical model of the system in the form of a system of differential equations, which is its advantage. However, in order to use the advantage, it is necessary to estimate the quality of the system identification. Such calculations showed the validity of the developed approach. The synthesis of the optimal controller was carried out on the basis of the well-known methodology, which presupposes the reduction of the original problem to the problem of unconstrained optimization of a function with a complex topology. For this, a modified particle swarm optimization method has been used. Experimental validation of the control results has shown in practice the complete achievement of the control goal – stabilization of the system with the presence of minor residual oscillations of the phase coordinates of the system.