Analysis Of Lateral Movement System In Rolling Process With Actuator Saturation And L2-disturbances

Abstract:

Lateral movement of a strip is typical problem in rolling mill process which results in quality deterioration of products and in worst case, a fatal accident that may harm workers. It is a cause of instability of rolling process and as a result, trouble related with decrease of productivity is more likely happen. In this paper, according to the linear mathematical model of lateral movement, a feedback law considering stability and disturbance tolerance of the closed loop system with actuator saturation is proposed.For a linear system, one of the suitable measurements of disturbance rejection is using L2 gain, the ratio of the L2 norm between disturbance and system output. However, sufficiently large disturbance may cause the state and output of the system unbounded. In this paper, degree of disturbance is represented as the bounded energy concept. The first step of the proposed control method is getting maximum disturbance energy such that the state will be bounded for. The second step is getting disturbance rejection capability which is measured by the restricted L2 gain over a given bounded disturbance energy. These approaches are based on constrained optimization problems with two nested ellipsoid. Optimization problem which makes state trajectories starting from the point inside of an ellipsoid to stay in the outer ellipsoid with bounded disturbance energy is formulated to the LMI optimization problem. Solving LMI problem where the feedback gain is free parameter, feedback gain of the lateral movement system with actuator saturation is presented. Numerical examples are shown to confirm the efficiency of proposed control algorithm in lateral movement problem.

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