active control system; hot dip galvanizing line; steel strip; flexion vibration modes; torsion modes
Abstract :
[en] This paper concerns the design of an active control system for a hot dip galvanizing line. The control system aims at reducing the vibrations of the steel strip in order to improve the quality of the product. The mechanical structure is quite flexible and many vibration modes need to be controlled. The actuators and the sensors are collocated and the control law is a direct velocity feedback, which doesn't require any model of the plant. This control law adds damping on all the vibration modes and it guarantees the stability of the system. The position of the actuators is chosen to maximize the controllability and the observability. The relevance of this strategy is discussed. The natural frequencies of the mechanical system are evaluated using the Finite Element Method. In this particular example, it was found that the frequencies of the flexion vibration modes almost match the frequencies of the torsion modes. The corresponding pole/zero pattern leads to very small root loci where the damping increment is strongly limited.
A simulation of the closed loop system is required to evaluate the performance of the active control and to choose the feedback gain. The time-domain evolution of the mechanical structure is computed using the Finite Element Method and an implicit integration scheme. Assuming that the control system is digital and neglecting the dynamics of the actuators, the control system is introduced into the mechanical simulation as a users' routine called at each sampling time of the digital controller. This quite general approach allows to deal with nonlinear eff ects either in the mechanical structure or in the control system, what opens new perspectives in integrated simulation of controlled flexible mechanisms. The simulation shows that a single actuator is not able to control the whole steel strip. Even if the gain increases, the controlled point becomes quickly a fixed point, and the vibration of the rest of the structure is not significantly attenuated. At least three actuators are necessary to get the expected performance.