WORST CASE OF RELATIVE DISTURBANCE GAIN ARRAY FOR UNCERTAIN DISTILLATION SYSTEM

This article discusses the constrained nonlinear optimization formulation for calculating the worst case of lower and upper bounds of relative disturbance gain array (RDGA) for uncertain process models. The proposed approach seeks the minimum and maximum values of the relative disturbance gains subject to the constraints in which the process and disturbance gains are within their uncertainty ranges. RDGA ranges are useful for control structure determination and the related robustness, as they provide information regarding the sensitivity to gain uncertainties. The proposed method is demonstrated by ternary distillation column case study. Closed loop simulation results support the analysis based on the proposed method. It is shown that for a particular degree of uncertainties, the range of process gain determinant should not include zero to ensure the successfulness of the calculation. For the distillation system being studied, the maximum allowable α is 0.339 to avoid the singularity of matrix K.