A Classical Design Approach of Cascaded Controllers for a Traction Elevator

Abstract

A traction elevator is a control system that can be driven by Direct Current (DC) motors. Premised on the reviewed literature, operations of control systems incorporated with DC motors are restrained by nonlinearities that deviate the controlled variables (position, speed, and torque) from the reference input. Controllers designed with appropriate gains annul the nonlinearities inhibiting the operation of a traction elevator. However, the literature did not account for detailed mathematical designs for the controller gains. Also, the modeled elevators had complex architectures. Hence, this research is aimed at modeling a simplified traction elevator and using the dynamics of its subsumes to mathematically design the gains of three controllers arranged in a cascaded topology to mitigate errors in the three control loops of the elevator. The Position of the elevator's car was controlled using a Proportional (P) controller while the Proportional-Integral (PI) controller controlled individually the speed and torque of the elevator’s cabin. A novel objective function which was based on Integral Time Absolute Error (ITAE) was incorporated into the elevator’s model to measure the deviation of the control variables from the input reference. The MATLAB Simulink environment was used in the modeling and simulation of the elevator system. The result obtained for the gain of the P controller for the elevator position, speed, and torque were 0.3652, 25.8, and 2.19, respectively. The gains of the integral controllers for the elevator speed and torque were 1372.3 and 219 respectively. A position reference of 100 m was used to verify the utilization of the controller gains. The result of the study improved existing literature because of the clarified elevator model and the output responses of the three controlled loops which were intuitive with lesser errors at steady state. For instance, steady-state errors of 3.54, 10.45, and 5% were obtained respectively in the position, speed, and current responses of the modeled elevator.