Analytical multiloop PI/PID controller design for two-by-two processes with time delays

In this paper, an analytical multiloop controller design method is proposed for industrial and chemical two-by-two processes with time delays. By proposing the practically desired closedloop diagonal transfer functions and the dynamic detuning factors to reduce the interactions between individual loops, the ideally desired multiloop controllers are inversely derived, which, however, are unavoidably involved with time delays in a complex manner and therefore difficult to realize. Hence, the mathematical Maclaurin series expansion is utilized to reproduce them in the form of a conventional PI/PID controller for implementation. Then a corollary derived from the generalized Nyquist stability theorem is provided to ascertain the nominal system stability. Meanwhile, the sufficient and necessary constraints for tuning the proposed multiloop PI/PID controllers to hold the control system robust stability are analyzed in the presence of the process multiplicative uncertainties. Finally, several commonly used simulation examples are included to demonstrate the effectiveness of the proposed method.