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Licensed Unlicensed Requires Authentication Published by De Gruyter November 24, 2017

Analysis of Control Degrees of Freedom in Batch and Cyclic Processes

  • Ayoub Safari and Reza Eslamloueyan EMAIL logo


Recently, we have proposed a new formulation approach for control degree of freedom (CDOF) analysis of process systems. This formula interrelates the CDOF and elements of a process flow diagram (PFD). The formulation is accurate, easily applicable by process engineers, and needs little prior knowledge of the process under study. This paper describes further about this new formulation and its advantages by applying it to batch and cyclic processes. The results demonstrate the correctness of the method in  determining CDOF for all case studies at both steady state and dynamic conditions. The CDOF for “reheat regenerative Rankine” and “vapor absorption refrigeration” cycles have been determined to be 9 and 8, respectively. The steady state CDOF values for the Rankine and refrigeration cycles have been calculated as 8 and 4, respectivley. Also the CDOF for the process of  “heat pump integrated with batch distillation column”  is 4 that verifies the suggested formula of CDOF. The method also gives beneficial insights about the manipulated variables (MVs) in a control system.


[1] Seider WD, Seader JD, Lewin DR. Product and process design principles: synthesis analysis and evaluation. New York: Wiley, 2003.Search in Google Scholar

[2] Dixon DC. Degrees of freedom in dynamic and static systems. Ind Eng Chem Funda. 1972;11(2):198–205.10.1021/i160042a009Search in Google Scholar

[3] Rodriguez M, Gayoso JA. 2006. Degrees of freedom analysis for process control. 16th European symposium on computer Aided Process Engineering and 9th International symposium on Process Systems Engineering. Garmisch-Partenkirchen, Germany.10.1016/S1570-7946(06)80258-0Search in Google Scholar

[4] Pham QT. Degrees of freedom of equipment and processes. Chem Eng Sci. 1994;49:2507–12.10.1016/0009-2509(94)E0056-VSearch in Google Scholar

[5] Ponton JW. Degrees of freedom analysis in process control. Chem Eng Sci. 1994;49:2089–95.10.1016/0009-2509(94)E0033-MSearch in Google Scholar

[6] Konda NV, Rangaiah GP, Krishnaswamy PR. A simple and effective procedure for control degrees of freedom. Chem Eng Sci. 2006;61:1184–94.10.1016/j.ces.2005.08.026Search in Google Scholar

[7] Safari A, Eslamloueyan R. A new plant-wide approach for control degrees of freedom of process systems. Chem Eng Res Des. 2017;120:259–70.10.1016/j.cherd.2017.02.016Search in Google Scholar

[8] Skogestad S. Control structure design for complete chemical plants. Comput Chem Eng. 2004;28:219–34.10.1016/j.compchemeng.2003.08.002Search in Google Scholar

[9] Konda NV, Rangaiah GP. Control degrees of freedom analysis for plant-wide control of industrial processes. In: Rangaiah GP, Kariwala V, editors. Plant-wide control: recent developments and applications. New Delhi: John Wiley and Sons, 2012:73–96.Search in Google Scholar

[10] Luyben WL. Design and control degrees of freedom. Ind Eng Chem Res. 1996;35:2204–14.10.1021/ie960038dSearch in Google Scholar

[11] Luyben WL, Tyreus BD, Luyben ML. Plant-wide process control. New York: McGraw-Hill, 1998.Search in Google Scholar

[12] Sharifzadeh M. Integration of process design and control: A review. Chem Eng Res Des. 2013;91:2515–49.10.1016/j.cherd.2013.05.007Search in Google Scholar

[13] Bejan A. Advanced engineering thermodynamics. New York: John Wiley & Sons, 2016.10.1002/9781119245964Search in Google Scholar

[14] Jensen JB, Skogestad S. Steady-state operational degrees of freedom with application to refrigeration cycles. Ind Eng Chem Res. 2009;48:6652–59.10.1021/ie800565zSearch in Google Scholar

[15] Dincer I, Ratlamwala TA. Integrated absorption refrigeration systems comparative energy and exergy analyses. Switzerland: Springer, 2016.10.1007/978-3-319-33658-9Search in Google Scholar

Received: 2017-08-16
Revised: 2017-11-10
Accepted: 2017-11-11
Published Online: 2017-11-24

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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