Hexadic tank system represents an extension of quadruple tank system for controlling non-growth-associated product dynamics in bioprocess industries, including two stage continuous fermentations, multiple distillation columns, pharmaceutical, and food processing applications. This study presents a comprehensive analysis encompassing theoretical foundations, simulation frameworks, hardware implementation, and experimental validation of three control algorithms: LQR, Linear MPC, and Robust MPC, evaluated under disturbance and non-disturbance conditions. Among the three control algorithms, Linear MPC with disturbances ($\hbox {LMPC}_{\text {D}}$) achieves superior performance with the lowest mean error (1.67), maximum error (2.00), control variance (3.47), and overall sensitivity (2.52), with high settling times. $\hbox {RMPC}_{\text {D}}$ shows the fastest minimum response (1.93 s) but exhibits higher mean error (2.5) and maximum error (5.0), and overall sensitivity (3.94). LQR controllers exhibit poor performance, with high sensitivity (94.08–226.47), large errors, and longer settling times (especially for $\hbox {LQR}_{\text {D}}$), rendering them unsuitable for practical implementation. All controllers maintain zero steady-state error with stable eigenvalues ($-6.76\times 10^{-3}$ to $-4.34\times 10^{-19}$). This confirms that the model predictive control strategies are optimal for tracking precision, disturbance rejection, and parameter insensitivity in bioprocess applications.
| [1] |
Åström KJ, Kumar PR. Control: a perspective. Automatica, 2014, 50(1): 3-43.
|
| [2] |
de Matas M, De Beer T, Folestad S, Ketolainen J, Lindén H, Lopes JA, Oostra W, Weimer M, Öhrngren P, Rantanen J. Strategic framework for education and training in Quality by Design (QbD) and process analytical technology (PAT). Eur J Pharm Sci, 2016, 90: 2-7.
|
| [3] |
Ferreira AP, Tobyn M. Multivariate analysis in the pharmaceutical industry: enabling process understanding and improvement in the PAT and QbD era. Pharm Dev Technol, 2015, 20(5): 513-527.
|
| [4] |
Grebeck M. A comparison of controllers for the quadruple tank process. Department of Automatic Control, Lund Institute of Technology: Technical Report; 1998.
|
| [5] |
Ho M-T, Lin C-Y. PID controller design for robust performance. IEEE Trans Autom Control, 2003, 48(8): 1404-1409.
|
| [6] |
Jayaprakash J, Davidson D, Subhahencyjose P. Comparison of controller performance for MIMO process. Int J Emerg Technol Adv Eng. 2013;3(8).
|
| [7] |
Johansson KH. The quadruple-tank process: a multivariable laboratory process with an adjustable zero. IEEE Trans Control Syst Technol, 2000, 8(3): 456-465.
|
| [8] |
Lan J, Zhao D. Finding the LQR weights to ensure the associated Riccati equations admit a common solution. IEEE Trans Autom Control, 2023, 68(10): 6393-6400.
|
| [9] |
Mhaskar P, Kennedy AB. Robust model predictive control of nonlinear process systems: handling rate constraints. Chem Eng Sci, 2008, 63(2): 366-375.
|
| [10] |
Mohammed RN, Abu-Alhail S, Xi-Wu L. Long-term operation of a novel pilot-scale six tanks alternately operating activated sludge process in treating domestic wastewater. Environ Technol, 2014, 35(15): 1874-1885.
|
| [11] |
Nagrath D, Prasad V, Bequette BW. A model predictive formulation for control of open-loop unstable cascade systems. Chem Eng Sci, 2002, 57(3): 365-378.
|
| [12] |
Orike S, Odeyemi FM, Obasi ME. Design and simulation of a multi tank water level controller. Glob Sci J. 2020;8(3).
|
| [13] |
Rathore AS. QbD/PAT for bioprocessing: moving from theory to implementation. Curr Opin Chem Eng, 2014, 6: 1-8.
|
| [14] |
Rawlings JB, Mayne DQ, Diehl M, et al.. Model Predictive Control: Theory, Computation, and Design, 2017. Madison, WI, Nob Hill Publishing. 2
|
| [15] |
Short M. A simplified approach to multivariable model predictive control. Int J Eng Technol Innov, 2015, 5(1): 19-32
|
| [16] |
Sistu PB, Bequette BW. Nonlinear predictive control of uncertain processes: application to a CSTR. AIChE J, 1991, 37(11): 1711-1723.
|
| [17] |
Sun Z, Dai L, Liu K, Dimarogonas DV, Xia Y. Robust self-triggered MPC with adaptive prediction horizon for perturbed nonlinear systems. IEEE Trans Autom Control, 2019, 64(11): 4780-4787.
|
| [18] |
Vada J, Slupphaug O, Johansen TA. Efficient infeasibility handling in linear MPC subject to prioritized constraints. In: European Control Conference (ECC). IEEE; 1999. p. 1166–71.
|
| [19] |
Zobel-Roos S, Schmidt A, Mestmäcker F, Mouellef M, Huter M, Uhlenbrock L, Kornecki M, Lohmann L, Ditz R, Strube J. Accelerating biologics manufacturing by modeling or: Is approval under the QbD and PAT approaches demanded by authorities acceptable without a digital-twin?. Processes, 2019, 7(2): 94.
|
Funding
Indian Institute of Technology Indore
RIGHTS & PERMISSIONS
Jiangnan University
PDF
