Dynamic loop interactions and multi-loop PID controller design

In a multi-loop PID control system, a nominal model for the effective open-loop dynamics that include interactions through other loops is formulated. A standard representation for complementary sensitivity function of single loops with a global parameter is used to exempt the needs for controllers of the other loops. By making uses of such nominal models, the design of controllers can be performed straightforward as for single loop systems. An inverse-based method for designing SISO and PID controllers is thus presented.