Analytical Design of PI/PID Controllers for Double-Loop Control Systems

For chemical and industrial two-input-two-output processes with time delays,an analytical method for designing the PI/PID controllers was proposed based on a double-loop control structure that is often used in practice.According to the robust control H_2 optimal performance specification,the practically desired diagonal elements of the system transfer matrix are suggested,and in view of the coupling action existing between the two closed loops,dynamic detuning factors are introduced to design the optimal double-loop controllers,and their executable PI/PID forms are derived using a mathematical rational approximation approach.At the same time,the sufficient and necessary conditions for holding the control system robust stability are analyzed,and the stability criterion in terms of the spectral radius is presented.A simulation example was included to demonstrate the superiority of the proposed method over recently developed design methods based on numerical calculation.