Comparison of position controllers designed for an elastic system using its complete and deficient dynamic models

Abstract

This article is concerned with comparing the position controllers designed for an elastic system using its complete and deficient dynamic models. The system considered here as an application example consists of three rotors connected with two elastic shafts. Three kinds of controller are designed and compared. Controller-3 is designed using the complete dynamic model of the system. Therefore, it works perfectly, satisfying all the specified requirements. Controller-2 is designed based on a deficient model that consists of two rotors connected with a single elastic shaft. Therefore, it works with an acceptable performance only for limited magnitudes of its gains. If its gains are increased too much to improve the steady-state accuracy, the closed-loop system becomes unstable owing to the spillover effect induced by the unmodelled dynamic feature, which is the inertia at the midpoint of the shaft. Controller-1 is designed based on a more deficient model that consists of a single rotor mounted on a rigid shaft. Therefore, it also works with an acceptable performance only for limited magnitudes of its gains. With too large gains, it also suffers from the spillover effect induced by the unmodelled dynamic feature, which is the elasticity of the shaft. However, with the increasing gains, the spillover effect caused by controller-1 makes the closed-loop system increasingly oscillatory but never unstable. In other words, controller-1 is robust against the destabilizing tendency of the spillover effect. From this point of view, controller-1 is better than controller-2, even though the model used for controller-1 is more deficient than that used for controller-2. Another prominent feature of controller-1 is that it is highly sensitive to the location where the position and velocity sensors are placed to acquire the necessary feedback signals. If this location is different from the location where the controlling torque is applied, controller-1 destabilizes the closed-loop system.