Heuristic-based multi-scale control procedure of simultaneous multi-loop PID tuning for multivariable processes

• New simultaneous multi-loop PID tuning using 4 parameters for an n × n MIMO process.
• Heuristic and optimization procedures are proposed to tune the 4 parameters.
• Difficult multi-loop PID tuning is reduced to a simple task by using the method.
• Numerical examples show the effectiveness of the method.

A multi-loop PID control system is widely used in process industry where finding good values for the controller parameters is very challenging without systematic procedures. In this paper, based on the multi-scale control scheme a simultaneous multi-loop tuning method for an arbitrary n × n MIMO processes is proposed. The salient feature of the method is that it reduces the multi-loop PID tuning parameters from 4n to only 4 common multi-scale control parameters. Both heuristic- and optimization-based procedures are proposed in order to apply the simultaneous tuning method, which should substantially simplify difficult multi-loop tuning involving numerous controller parameters. To ensure adequate robustness of the multi-loop control system, the balanced sensitivity function is used with the tuning method. Numerical studies based on 2 × 2, 3 × 3, 4 × 4 and 5 × 5 MIMO processes demonstrate the effectiveness of the tuning method.