“On the Computation of Disturbance Rejection Measures”

Authors: Morten Hovd, David L. Ma and Richard D. Braatz,
Affiliation: NTNU, Department of Engineering Cybernetics and University of Illinois at Urbana-Champaign
Reference: 2004, Vol 25, No 1, pp. 45-56.

Keywords: controllability analysis; disturbance rejection

Abstract: In any process plant design, a central question is whether it is possible to achieve acceptable control with the available manipulated variables, while taking into account the disturbances that can be expected. Some little known controllability measures have been proposed to address such issues (Wolff, 1994; Skogestad and Wolff, 1992). The main reason these controllability measures have received little attention is probably that, while, their mathematical formulation was defined, no algorithms were provided to solve the mathematical problems. This paper shows how to calculate these controllability measures, and applies the algorithms to some process examples.

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[1] BERGH, L.G. MACGREGOR, J. F. (1987). Spatial control of sheet and film forming processes, Canadian J. of Chemical Engineering, 65: 148-155 doi:10.1002/cjce.5450650124
[2] BRAATZ, R.D., LEE, J.H. MORARI, M. (1996). Screening plant designs and control structures for uncertain systems, Computers and Chemical Engineering, 20: 463-468 doi:10.1016/0098-1354(95)00036-4
[3] BRAATZ, R. D. MORARI, M. (1994). Minimizing the Euclidian condition number, SIAM Journal on Control and Optimization, 32: 1763-1768 doi:10.1137/S0363012992238680
[4] BRAATZ, R.D., TYLER, M.L., MORARI, M., PRANCKH, F.R. SARTOR, L. (1992). Identification and cross-directional control of coating processes, AIChE 38: 1329-1339 doi:10.1002/aic.690380903
[5] CAO, Y., OWENS, D.H. ROSSITER, D. (1998). Output effectiveness and scaling sensitivity for secondary measurement selection, Chem. Eng. Res. Des., pp. 849 854 doi:10.1205/026387698525469
[6] CAO, Y., ROSSITER, D. OWENS, D. (1997). Input selection for disturbance rejection under manipulated variable constraints, Computers and Chemical Engineering, pp. S403-S408 doi:10.1016/S0098-1354(97)87535-7
[7] FALK, J. E. (1973). A linear max-min problem, Mathematical Programming, 5: 169-188 doi:10.1007/BF01580119
[8] FEATHERSTONE, A. P. BRAATZ, R. D. (1997). Control-oriented modeling of sheet and film processes, AlChE J., 43: 1989-2001.
[9] FEATHERSTONE, A.P. BRAATZ, R.D. (1998). Integrated robust identification and control of large scale processes, Ind Eng. Chem. Res., 37: 97-106 doi:10.1021/ie970356s
[10] FEATHERSTONE, A.P., VANANTWERP, J.G. BRAATZ, R.D. (2000). Identification and Control of Sheet and Film Processes, Springer Verlag, London, UK.
[11] FISHER, W.R., DOHERTY, M.F. DOUGLAS, J.M. (1988). The interface between design and control, Parts 1,2, and 3, Ind. and& Eng. Chem. Res., 27: 597-615 doi:10.1021/ie00076a012
[12] GARCIA, C.E., PRETT, D.M. MORARI, M. (1989). Model predictive control: Theory and practice - A survey, Automatica, 25: 335-348 doi:10.1016/0005-1098(89)90002-2
[13] GROSSMANN, I.E. FLOUDAS, C.A. (1987). Active constraint strategy for flexibility analysis in chemical processes, Computers and Chemical Engineering, 11: 675-693 doi:10.1016/0098-1354(87)87011-4
[14] HALEMANE, K.P. GROSSMAN, L.E. (1983). Optimal process design under uncertainty, AlChE J, 29: 425-433.
[15] HOVD, M., BRAATZ, R.D. SKOGESTAD, S. (1996). SVD controllers for H2-, H-Infinity,-, and mu-optimal control, Automatica, 33: 433-439 doi:10.1016/S0005-1098(96)00167-7
[16] HOVD, M. SKOGESTAD, S. (1992). Simple frequency-dependent tools for control system analysis, structure selection and design, Automatica, 28: 989-996 doi:10.1016/0005-1098(92)90152-6
[17] LEE, J.H., BRAATZ, R.D., MORARI M. PACKARD, A. (1995). Screening tools for robust control structure selection, Automatica, 31: 229-235 doi:10.1016/0005-1098(94)00062-N
[18] LEWIN, D.R. (1996). Multivariable feedforward control design using disturbance cost maps and a genetic algorithm, Computers and Chemical Engineering, 20: 1477-1489 doi:10.1016/0098-1354(95)00233-2
[19] LEWIN, D. R. (1996). A simple tool for disturbance resiliency diagnosis and feedforward control design, Computers and Chemical Engineering, 20: 13-25 doi:10.1016/0098-1354(95)00006-N
[20] LUENBERGER, D. G. (1984). Linear and Nonlinear Programming, Addison-Wesley Publishing Co, Reading, Massachusetts, 2nd edn.
[21] PIETTE, R., HARRIS, T.J. MCLELLAN, P.J. (1995). Graphical interpretations of steady-state interaction measures, Ind. Eng. Chem. Res., 34: 4436-4450 doi:10.1021/ie00039a035
[22] RAWLINGS, J. B. CHIEN, I.-L,. (1996). Gage control of film and sheet-forming process, AlChE J, 42: 753-766.
[23] RAWLINGS, J.B. (1999). Tutorial: Model predictive control technology, In Proc. of the American Control cont., pp. 662-676, Piscataway, New Jersey IEEE Press.
[24] SAHINIDIS, N.V. (1996). BARON: A general purpose global optimization software package, Journal of GlohalOptimization, 8: 201-205 doi:10.1007/BF00138693
[25] SKOGESTAD, S. WOLFF, E.A. (1992). Controllability measures for disturbance rejection, In J. D. PERKINS, ed., Preprints of the IFAC Workshop on Interactions Between Process Design and Process Control, pp. 23-29, September.
[26] SWANEY, R.E. GROSSMANN, I.E. (1985). An index for operational flexibility chemical process design, Part II: computational algorithms. AIChE el, 31: 631-641 doi:10.1002/aic.690310413
[27] TYLER, M.L. MORARI M. (1995). Estimation of cross directional properties: Scanning versus stationary sensors, AIChEJ., 41: 846-854 doi:10.1002/aic.690410412
[28] VANANTWERP, J.G. BRAATZ, R.D. (2000). Fast model predictive control of sheet and film processes, IEEE Trans. on Control Systems Technology, 8: 408-417 doi:10.1109/87.845872
[29] VANANTWERP, J.G. BRAATZ, R. D. (2000). Model predictive control of large scale processes, of Process Control, 10: 1-8.
[30] VANANTWERP, J. G., FEATHERSTONE, A. P. BRAATZ, R. D. (2001). Robust cross-directional control of large scale sheet and film processes, J. of Process Control, 11: 149-178 doi:10.1016/S0959-1524(00)00045-7
[31] VAN DE WAL, M. DE JAGER, B.A. (1995). Control structure design: A survey, In Proc of the American Control Conf, pp. 225-229, Piscataway, New Jersey, June 21-23. IEEE Press.
[32] WOLFF, E. A. (1994). Studies on Control of Integrated Plants, PhD thesis, Department of Chemical Engineering, University of Trondheim, Norway.

  title={{On the Computation of Disturbance Rejection Measures}},
  author={Hovd, Morten and Ma, David L. and Braatz, Richard D.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}