Independent design of multi-loop controllers considering multivariable interactions

In this paper, a simple independent design method for multi-loop controllers is proposed which exploits process interactions for the improvement of loop performance. Unlike many other methods that emphasize suppression of interactions for decoupling purposes, our method is developed to channel the effect of interactions to individual loops for speeding up loop responses. This is achieved 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 is specified for each of these equivalent processes, a set of simultaneous equations is formed and separated into independent ones, each of which contains one controller element only. They are then solved to obtain exact solutions, which are usually irrational. The exact solutions can be well approximated by rational functions. The popular multi-loop PID controllers can naturally be obtained as a special case of rational approximation, and they give a reasonable trade-off between loop and decoupling performance. Simulation examples are provided to show the effectiveness of the proposed method, and comparisons are made with the BLT method.