This paper presents an extension of the inverted decoupling approach that allows for more flexibility in choosing the transfer functions of the decoupled apparent process. In addition, the expressions of the inverted decoupling are presented for general n × n processes, highlighting that the complexity of the decoupler elements is independent of the system size. The realizability conditions are stated in order to select a proper configuration, and the different possible cases for each configuration are shown. Comparisons with other works demonstrate the effectiveness of this methodology, through the use of several simulation examples and an experimental lab process. Keywords Decoupling control Inverted decoupling Simplified decoupling PID control

This paper presents a new methodology to design multivariable proportional-integral-derivative (PID) controllers based on decoupling control. The method is presented for general n × n processes. In the design procedure, an ideal decoupling control with integral action is designed to minimise interactions. It depends on the desired open-loop processes that are specified according to realisability conditions and desired closed-loop performance specifications. These realisability conditions are stated and three common cases to define the open-loop processes are studied and proposed. Then, controller elements are approximated to PID structure. From a practical point of view, the wind-up problem is also considered and a new anti-wind-up scheme for multivariable PID controller is proposed. Comparisons with other works demonstrate the effectiveness of the methodology through the use of several simulation examples and an experimental lab process.