Vol 16, No 2 (2012) > Articles >

Worst Case of Relative Disturbance Gain Array for Uncertain Distillation System

Rudy Agustriyanto 1 , Jie Zhang 2


  1. Chemical Engineering, Surabaya University, Surabaya 60292, Indonesia
  2. School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK



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.

Keywords: distillation control, relative disturbance gain array, relative gain array
Published at: Vol 16, No 2 (2012) pages: 135-143

Access Counter: 3274 views, 661 PDF downloads, .

Full PDF Download


S. Skogestad, Comput. Chem. Eng. 28 (2004) 219.

E. Bristol, IEEE Trans. Autom. Control 11/1 (1996) 133.

A. Niederlinski, Automatica 7/6 (1971) 691.

G. Stanley, M. Marino-Galarraga, T.J. McAvoy, Ind. Eng. Chem. Process Des. Dev. 24/4 (1985) 1181.

M.J. He, W.J. Cai, W. Ni, L.H. Xie, J. Process Control 19 (2009) 1036.

Z.X. Zhu, Ind. Eng. Chem. Res.35/11 (1996) 4091.

J.W. Chang, C.C. Yu, AICHE J. 38/4 (1992) 521.

D. Chen, D.E. Seborg, AICHE J. 48/2 (2002) 302.

V. Kariwala, S. Skogestad, J.F. Forbes, Ind. Eng. Chem. Res. 45/5 (2006) 1751.

R. Agustriyanto, J. Zhang, Proc. of the 2007 American Control Conference, New York, USA, 2007, p.5360.

P. Grosdidier, M. Morari, B.R. Holt, Ind. Eng. Chem. Fundam. 24/2 (1985) 221.

S.S. Rao, Engineering Optimization–Theory & Practice, 4th ed., John Wiley & Sons, Inc, 2009,


T.F. Edgar, D.M. Himmelblau, L.S. Lasdon, Optimization of Chemical Processes, McGraw-Hill,

, p.672.

S.S. Ding, W. Luyben, Ind. Eng. Chem. Res. 29/7 (1990) 1240.