Chemical processes are usually multivariable systems

which non-square system with more outputs than inputs is known as thin system. Till now

the most common method of designing control configuration for thin systems is to form square systems by increasing or decreasing variables such that only fully decentralized PID control could be achieved with one input pairing to one output. Some critical process variables cannot be used as controlled variables or non-critical variables cannot be included in feedback loops

so the control system often does not meet requirements. With introduction of a non-square gain array relative to average frequency

a method for designing cascade control configuration was proposed through analyzing variable pairing in thin systems. This method fully utilized feedbacks of all output variables without addition of new input variables

so system feedback was more complete and a cascade control was developed for both critical and non-critical variables. Two case study showed that this method achieved not only proper variable pairing but also good control performance especially in speed and efficiency of interference reduction.