Dynamic proportional-integral-derivative (PID) method for plate straightening based on changes in yield strength

A dynamic proportional-integral-derivative (PID) method for plate straightening based on changes in yield strength, comprising the steps of:

• determining yield strength of a plate to be straightened at a temperature currently detected;
• calculating a predicted straightening force of each of a plurality of straightening rolls based on the yield strength at the temperature;
• obtaining a measured straightening force of each of the plurality of straightening rolls;
• determining a yield strength error Δσfront using a numerical approximation method based on an error between a predicted straightening force and a measured straightening force of a previous straightening roll;
• determining a yield strength error Δσmiddle using the numerical approximation method based on an error between a predicted straightening force and a measured straightening force of a current straightening roll;
• determining a yield strength error Δσrear using the numerical approximation method based on an error between a predicted straightening force and a measured straightening force of a next straightening roll;
• determining parameters of a PID controller based on the yield strength errors Δσfront, Δσmiddle, and Δσrear;
• calculating a target reduction of a corresponding straightening roll based on the yield strength error Δσmiddle and the yield strength at the temperature;
• inputting the target reduction into the PID controller with the parameters determined, to output a measured reduction of the current straightening roll to a roll straightening machine comprising the plurality of straightening rolls;
• and
• moving the current straightening roll by the roll straightening machine according to the measured reduction of the current straightening roll, for straightening the plate to be straightened;
• wherein the step of calculating a predicted straightening force of each of the plurality of straightening rolls based on the yield strength at the temperature comprises:
• calculating a reduction of each of the plurality of straightening rolls based on the yield strength at the temperature;
• calculating a variation of a ratio of curvature of each of the plurality of straightening rolls based on the reduction;
• calculating an elastic bending moment of each of the plurality of straightening rolls based on the variation of the ratio of curvature;
• and
• calculating the predicted straightening force of each of the plurality of straightening rolls based on the elastic bending moment.