Independent design of multi-loop controllers considering multivariable interactions

A simple independent design method for multi-loop controllers was proposed that exploits process interactions for improving loop performance. The method channels the effect of interactions to individual loops for speeding up loop responses, which is realized by regarding each loop together with its corresponding interactions from all other loops as an equivalent single-input single-output (SISO) plant, and designing an independent SISO controller for it. Once an objective transfer function was specified for each of these equivalent processes, a set of simultaneous equations was formed and separated into independent ones, each of which contained only a controller element. They are solved to obtain accurate solutions, which can be well approximated by rational functions. The popular multi-loop PID controllers can be determined as a special case of rational approximation, and they give a rational trade-off between loop and docoupling performance. Simulation examples were presented to illustrate the effectiveness of the proposed method, such as the eight trays + reboiler distillation column separating methanol and water studied by Wood and Berry (1986). Comparisons were also made with the Biggest Log Modulus Tuning technique represented by Luyben (1986).