Design of Proportional Integral Controllers with Decouplers for Unstable Two Input Two Output Systems

Abstract

A method is proposed based on the equivalent transfer function (ETF) model to design multivariable proportional integral (PI) controllers for unstable multivariable systems with delay. The simplified decoupler decomposes the unstable multiloop systems into independent loops with ETFs as the resultant decoupled process model having unstable poles. PI controllers are designed for the diagonal elements of ETFs by the synthesis method meant for unstable first order plus time delay (FOPTD) systems. Since the overshoot is higher for the unstable systems, a double-loop control structure (inner-loop diagonal proportional (P) controllers with the decoupler and outer loop only with diagonal PI controllers) is proposed to get a reduced overshoot. Two examples of two input two output (TITO) unstable systems are considered to demonstrate the simplicity and effectiveness of the proposed method.