Dynamic modeling and control of a bending combined roller system using Timoshenko beam theory and constrained model predictive control

Abstract

The roller system is an essential and very important part of a lot of fabric processing machines in the textile industry. This study proposes a new bending roller control system (BRCS) to control bending deformation and vibration of the roller system. First, a new mathematical model of a combined roller is obtained by using an eigenfunction expansion method and Timoshenko beam theory. The combined roller consists of inner steel and outer nylon layers to take full advantage and eliminate drawbacks of materials. Second, a hydraulic multi-cylinder system is put inside the roller at the suitable position. This solution not only increases significantly the power of the bending actuation system but also reduces the transient time of dynamic response and avoids damaging outside surfaces of the rollers. Finally, in order to improve dynamic response performance and open wide operating range of system, model predictive control (MPC) and constrained control are applied to the BRCS. Simulation results proved that the proposed control system is completely effective and reliable.

Feedback control of actuation‐constrained moving structure carrying Timoshenko beam

“…In Equation ( 10 If h[z, ̇z, 𝛉] mentioned in Equation (11), indicates the force that the elastic foundation exerts on the frame, then it can be said that 𝔉 = −h[z, ̇z, 𝛉] + F in which F is the applied control force. Consequently, the Equation ( 9) could be rewritten as Equation (12).…”

“…Distributed input control: In this approach, it is assumed that the information of all state variables of the continuous system can be measured across its whole domain and the required control input can be applied to the system throughout the whole domain as well. 12 It is clear that such a method is very difficult to implement due to the need for a large number of sensors and actuators. 13 2.…”

“…Wang and Yang proposed a transient vibration control using nonlinear convergence active vibration absorber for impulse excitation 11 . To control such continuous systems, one of the following overall approaches can be considered: Distributed input control: In this approach, it is assumed that the information of all state variables of the continuous system can be measured across its whole domain and the required control input can be applied to the system throughout the whole domain as well 12 . It is clear that such a method is very difficult to implement due to the need for a large number of sensors and actuators 13 …”

Active damping vibration and compensating deflection in the processing-roll system

“…From Equations ( 20), (26), and (35)-(37), the forcedmotion equations are described as follows: The state-space model of the control system with the multi-cylinder actuator is…”

“…This paper has proposed and developed a new control system for efficiently suppressing deflection and vibration. The dynamic structure of the system was analyzed using the separation variables method, Timoshenko beam theory, and Hamilton's principle [23][24][25][26][27] to derive new forced-response motion equations of the oil-roll control system. The accuracy of the state-space model based on the proposed equation of motion has a significant effect on the performance of the designed DMPC.…”