Active Control of Vibrations in a Rolling Process by Nonlinear Optimal Controller

Abstract

In this paper a method of suppressing vibrations in an industrial rolling process with varying rotational frequency is presented. The vibrations in a rolling process are problematic as they do not only cause structural fatigue on the machinery, but also deteriorate the quality of the end product. The traditional approach for this type of a problem would be to avoid the critical frequencies of the process by changing the rotation speed of the reel, thus decreasing the vibrations. However, in practice this is hard to achieve as the radial velocity of the reel should be constant, while rotation speed of the reel varies depending on the diameter of the reel. The changes in radial velocity are typically not allowed as the rolling process is usually part of a larger process, where change in rotation speed affects the whole process. This paper introduces a generic modified LQ-control law to tackle the problem. This control design was designed in a previous ACRVEM-project (Active Control of Radial Rotor Vibrations in Electric Machines) and has been successfully used in suppression of radial rotor vibrations in electric drives, resulting in 90% damping of the vibrations. The major drawback of the controller has been the limitations due to its linear nature; the control is applicable only at a certain predefined rotational frequency, and outside this frequency the controller becomes unstable. In order to resolve this problem, a nonlinear optimal state-feedback controller based on continuous gain scheduling is introduced. This modification of the original controller is capable of suppressing the vibrations over the whole operational frequency range. In this paper the modelling and identification of the rolling process is first discussed. After the model has been obtained the control design procedures for both linear and nonlinear controllers are presented in detail. The performances of both controllers are analyzed in extensive simulations. Finally the simulation results are validated by implementing the designed controllers in the actual rolling process. It will be shown that this control methodology is highly effective for this type of vibration damping problems resulting in over 90% decrease in the vibrations over the whole frequency range of rotation.

Comparison and performance analysis of some active vibration control algorithms

“…This method is proposed by the authors for the mitigation of multidimensional tonal output disturbances (Orivuori and Zenger, 2011a). The method shares some similarities with the FSCF and IDC methods, as it is essentially based on finding an optimal solution for the LQ problem related to a plant model containing the dynamics of the disturbance.…”

“…This is achieved by setting the design parameter in Equation ( 37) to a very small value, say " ¼ 10 À8 , corresponding to an addition of a very small damping factor to the disturbance signal. It can be readily shown that the addition of the damping has practically no impact on the resulting control signal, although it is a suboptimal solution from the theoretical point of view (Orivuori and Zenger, 2011a).…”

“…The resulting control approach, considered in this study, is known as the instantaneous harmonic control (IHC; Daley et al, 2008). The fifth control law proposed by the authors is a LQ-based approach to the stabilization of an augmented plant model through direct optimal feedback compensation (DOFC) of the disturbances (Orivuori and Zenger, 2011a).…”

Robust Attenuation of Frequency Varying Disturbances

“…An immediate solution to the problem involves the use of continuous gain scheduling, in which the controller coefficients are modified according to the current disturbance frequency. To this end the disturbance frequency (usually the rotating frequency) has to be measured of tracked (Orivuori & Zenger, 2010;. The state estimator can be written in the forṁ…”