A new calculation method of feedback controller gain for bilinear paper-making process with disturbance

• A new method to calculate the feedback control gain for a class of multivariable bilinear system.
• A robust H∞ state feedback controller has been designed for multivariable bilinear paper making process.
• The stabilization conditions for multivariable bilinear systems in terms of Lyapunov via LMI have been studied.
• The control law is robustified in H∞ sense to attenuate external disturbance.
• Two sections of paper making processes with disturbance are used to illustrate the applicability of the proposed method.

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.