Modeling and adaptive vibration control for variable-length strip rolling systems with actuator faults and output constraints

In this study, a vibration suppression control strategy for flexible variable-length strip rolling systems is explored under time-varying actuator failures and output constraints. First, a new partial differential equation and ordinary differential equations of variable-length strip rolling systems are established by considering the variable tension difference, variable speed, and unknown nonlinear rolling force in the rolling process. Then, in order to achieve the displacement constraints of the strip and avoid the initial value requirement of the system, an adaptive barrier Lyapunov function is put forward by introducing a shifting function. Additionally, the effect of the nonlinear rolling force of the system is eliminated by adopting the radial basis function neural network, and the adaptive technique is employed to approximate the unknown parameters. Next, a boundary vibration control law for the variable-length strip rolling system is proposed based on the backstepping approach to maintain the strip vibration displacement in a small neighborhood around zero. Finally, the applicability of the control algorithm is verified using numerical simulations, and the influence rule for the tension difference change in vibration displacement is implemented to confirm the correctness of the theoretical analysis.