Obtaining the Worst Case RGA and RDGA for Uncertain Systems via Optimization

An optimization based method for calculating the worst case lower and upper bounds of relative gain array (RGA) and relative disturbance gain array (RDGA) for uncertain process models is presented. Its superiority over the previous methods reported in the literature is discussed. Simulation examples are used to illustrate the proposed method. Both RGA and RDGA ranges are useful for control structure determination and the related robustness as they provide information regarding the sensitivity to gain uncertainties. It is shown that for a particular degree of uncertainties, the range of process gain determinant should not include 0 to ensure the successfulness of the calculation.