An iterative procedure is proposed to design decentralized PID controllers for multi loop
processes. Each SISO loop is designed at a time, the controller parameters are computed by
a convex optimization problem with constraints on stability margins. Despite the SISO
approach, loops interactions are taken into account by Gershgorin bands and Equivalent
Open-loop Process (EOP). Two simulation examples are presented to compare the
performance with related techniques.

In this paper, based on Effective Open-loop Process (EOP), an iterative procedure is
proposed to tune decentralized PID controllers for multivariable systems. The EOP is
obtained through the operation with matrices, regardless of the process order. From the
definition of the constraints, it is possible to guarantee minimum bounds of gain and phase
margins. The optimization problem subject to these constraints imposes stability restrictions
under the actual EOP loop-gain transfer function between the process input and output. The …