Multi-loop PI Controller Design for Multivariable Non-square Systems

Based on the theory of equivalent transfer function（ETF), we propose a multi-loop PI（proportional integral) controller design method for high dimensional multivariable non-square systems with time-delays. Firstly, by exploiting the relationship between the ETF and the generalized inverse of transfer function of the non-square systems, an analytical expression of ETF is derived. Then, based on the obtained ETF, the multi-loop PI controler parameters are calculated by exploiting IMC-PID（internal model control-proportional integral derivation) theory with the help of the Maclaurin expansion. The proposed ETF design approach not only has higher accuracy, but is also applicable to high dimensional non-square systems. Finally, several examples are given to demonstrate the simplicity and the effectiveness of the designed method.