An analytic expression for closed-loop output behavior under multiloop PID control

An analytic expression is derived for closed-loop output behavior under a multiloop PID control. Based on the analytic expression obtained, optimization problems are formulated to assess 1) best achievable quadratic performance using multiloop PID control, 2) best achievable quadratic performance on key process variables while maintaining reasonable performance on other less critical process variables, 3) achievable performance improvement with decouplers, and 4) effects of loop pairing on achievable performance. It is shown through a simulated example that individual loop performance as well as the overall multiloop PID control performance can be assessed by using the proposed method.