Abstract: There are many flatness regulating means in modern mills and these means have coupling relations with each other reciprocally. In order to analyse the effective rules of various flatness regulating means on various order flatness components, taking HC mill for example and using the tilting roll, the bending work roll, asymmetry the bending work roll and the axial shifting intermediate roll as flatness regulating means, the effective coefficients of various regulating means on the linear, quadratic, cubic and biquadratic flatness components are calculated by theory model built by the partition model effective function method and the strip element variation method. It is indicated that the effective rules of the tilting roll and the asymmetry bending work roll on flatness are similar and they mainly affect the linear and cubic flatness components, where the effect extent on the linear flatness component is bigger than that on the cubic flatness component and The bending work roll and the axial shifting intermediate roll mainly affect the quadratic and biquadratic flatness components where the effect extent on the quadratic flatness component is bigger than that on the biquadratic flatness component. The result opens out the effective rules of various regulating means on various order components and provides the theory foundation for building on-line flatness control model.

Key words: Effective coefficient, Effective matrix, Flatness, HC mill, Bouc-Wen hysteresis model, Feedforward and adaptive PID composite controller, Hammerstein model, Neural net, Post-buckling pre-compression actuator, Rate-dependent hysteresis