Parametric Synthesis of Fractional Order Controllers for a Two-Mass Electromechanical Fire Lifts Basket Turning System

Abstract

In practice, the fire lifts arrow is a complex and not completely rigid object. Imperfect manufacturing of mechanical elements and their connections, elastic deformations of the arrow during operation, reactive action of fire-extinguishing substances cause elastic oscillations when the basket is moved. A promising method of damping elastic vibrations of the arrow is the use of an automatic control system. The synthesized ACS driven by the movement of the arrow should provide the following requirements: static and dynamic accuracy of reproduction of given trajectories, high speed, smooth acceleration and braking of the motor, the necessary margin of stability, absence of significant over-regulation in transition modes, low sensitivity to coordinate and parametric disturbances, etc. To meet these requirements, a number of fundamentally different ACSs and methods of their synthesis were analyzed. As a result of the analysis by the method of the generalized characteristic polynomial, a positional three-loop system of subordinate control by the rotation of the basket was synthesized, taking into account the elastic properties of the basket with the arrow. The synthesized system of subordinate control allows damping of elastic oscillations, providing optimal transitional processes of basket rotation and low sensitivity, in steady state, to the action of disturbances. The transition functions of the angular speed controllers of the motor and basket, which were obtained in the process of synthesis, are of a high order and turned out to be quite complex from the point of view of practical implementation. It is proposed to replace these controllers with more compact PI λ D μ controllers or fractional order controllers. Conducted research through mathematical modelling confirmed the effectiveness of replacing high-order angular speed controllers of the motor and basket with fractional-order controllers or PIλDμ -controllers, the transfer functions of which are determined by approximating the transition functions of the controllers using the genetic algorithm method.