Research articleDesign of multiloop PI controllers based on quadratic optimal approach

•LQR methodology was extended to obtain multiloop PI controllers.•The multiloop PI controllers are obtained in a two-steps procedure.•Different balances of error and control quadratic indeces were explored.•A distillation column and a nonlinear CSTR were used as study cases.•Diagonal controllers have a similar operations to the original decentralized ones.

The LQR methodology is extended to produce multiloop PI controllers in this study. With this method, a multivariable P controller is first obtained and then diagonalized using an iterative procedure. The resulting controller is further complemented with the integral action in a similar process. The proposed tuning process explores different values of the control weight matrix to balance the output error and control signal in both stages, and is refined through additional indices related with the error to reference tracking, disturbance rejection and the associated control use. In addition, the diagonalization procedure is generalized to obtain multiloop versions of existing multivariable PI controllers. The developed theory was applied to the design of multiloop controllers for a distillation column as well as the diagonalization of existing controllers for a nonlinear CSTR. The tuning procedure allowed the synthesis of multiloop PI controllers with performance indices comparable to those reported by other authors. Furthermore, diagonalized controllers exhibited a similar operation as the original multivariable ones.