For n-by-n multivariable processes, multiloop controllers have n degrees of freedom and hence the n diagonal elements of closed-loop transfer functions can be designed to have desired closed-loop responses. Multiloop controllers having desired closed-loop responses can be considered as an extension of the single-input single-output internal model control and they can be used as reference controllers. However, computations of such multiloop controllers have not been well developed. The Newton-Raphson method and the iterative sequential loop closing method can be used, but they can suffer from a divergence problem for some processes. Here, the continuation method is applied to obtain multiloop control systems with desired closed-loop responses for a robust computation. The multiloop controllers with desired closed-loop responses can be used to obtain dynamic interaction measures and design multiloop PID controllers.

Desired Closed-loop Response Multiloop Control System Continuation Method Dynamic Interaction Measure Multiloop PI/PID Controller

Seborg DE, Edgar TF, Mellichamp DA, Process dynamics and control, 2nd Ed., Wiley, New Jersey (2004)
Morari M, Zafiriou E, Robust process control, Prentice Hall, New Jersey (1989)
Lee Y, Park S, Lee M, Brosilow C, AIChE J., 44(1), 106 (1998)
Jung JH, Choi JY, Lee JT, Ind. Eng. Chem. Res., 38(4), 1580 (1999)
Mayne DQ, Automatica, 9, 201 (1973)
Hovd M, Skogestad S, Automatica, 30(10), 1601 (1994)
Seydel R, Hlavacek V, Chem. Eng. Sci., 42, 1281 (1987)
Horn RA, Johnson CR, Topics in matrix analysis, Cambridge Univ. Press, N.Y. (1991)
Lee JT, Edgar TF, Comput. Chem. Eng., 28(4), 479 (2004)
Lee J, Edgar TF, Ind. Eng. Chem. Res., 43(2), 283 (2004)
Luyben WL, Ind. Eng. Chem. Process Des. Dev., 25, 654 (1986)
Ogunnaike BA, Ray WH, AIChE J., 25, 1043 (1979)
Wood RK, Berry MW, Chem. Eng. Sci., 28, 1707 (1973)
Lee M, Lee K, Kim C, Lee J, AIChE J., 50(7), 1631 (2004)
Shen SH, Yu CC, AIChE J., 40(4), 627 (1994)