Linear Quadratic Regulator and Model Predictive Control Applied to a Four-Tank System: A Performance Comparison

Authors

  • William Oswaldo Chamorro Hernández Universidad Tecnológica Equinoccial
  • Pablo Velarde Rueda Universidad Tecnológica Equinoccial

DOI:

https://doi.org/10.29019/enfoqueute.v9n1.257

Keywords:

MPC, LQR, Optimal control, Least Square Method, Process Control, 4-Tank System

Abstract

This paper shows a comparison between two linear controllers, a PI-LQR and a Soft-Constrained MPC applied to a Four-Tank process, which main characteristics are the nonlinearities, multiple inputs and outputs coupled together and slow behavior. The model was linearized around an operating point by using an optimization method, named least square. Also, a general mathematic formulation for both controllers is presented that can be extended to any process control. All the procedure was described in detail as well as the simulation results for both controllers. To achieve a real performance comparison the experimental data were obtained under the same conditions and all the response parameters were analyzed.

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References

Alvarado, I.; Limon, D.; Muñoz de la Peña, D.; Maestre, J.M. & Ridao, M.A., 2011. A comparative analysis of distributed mpc techniques applied to the hd-mpc four-tank benchmark. Journal of Process Control, p. 800–8015.
Askari, M., Moghavvemi, M., Almurib, H. & Muttaqi, K., 2016. Multivariable offset-free model predictive control for quadruple tanks system. Transactions on Industry Applications, p. 1882–1890.
Camacho, E. & Bordons, C., 2004. Model Predictive Control in the Process Industry. Springer-Verlag.
Chamorro, W., Velarde, P. & Mosquera, G., 2017. On the Performance Comparison between PI-LQR and Soft-Constrained MPC Applied to a 4-Tanks System. INCISCOS 2017 (Por publicarse).
Cheng, J. y otros, 2016. Robust finite-time sampled-data control of linear systems subject to random occurring delays and its application to four-tank system. Volumen 281:55–76.
Engules, D., Hot, M. & B., A., 2015. Level control of a coupled-tank system via eigenvalue assignment and lqg control.. In Proceedings of the 23th Mediterranean Conference on Control and Automation (MED), p. 1198–1203.
Cheng, J.1; Chen, S.; Liu, Z.; Wang, H. & Li, J. 2016. Stochastic model predictive control approaches applied to drinking water networks. Optimal Control Applications and Methods In Press,.
Guillod, O., Sarria, V., Kenfack, S. & Pulgarin, C., 2003. An innovative coupled solar-biological system at field pilot scale for the treatment of biorecalcitrant pollutants. Issue 159(1):89–99.
H. Gouta, S.H. Said, N. Barhoumi & F. MSahli 2017. Generalized predictive control for a coupled four tank MIMO system using a continuous discrete time observer. ISA transactions, p. 280–292.
Herrera, M., Chamorro, W., Gomez, P. & Camacho, O., 2015. Two-wheeled inverted pendulum robot nxt lego mindstorms Mathematical modelling and real robot comparisons. Revista Polit´ecnica.
Jimenez, A., Al-Hadithi, B. M., Alonso, L. & Perez-Oria, J., 2013. Linear quadratic regulator based takagi-sugeno model for multivariable nonlinear processes. In System Theory, Control and Computing (ICSTCC), p. 285–290.
Johansson, K., 2000. The quadruple-tank process: a multivariable laboratory process with an adjustable zero. Volumen 8(3):456–465.
Mavrias, G., Fuchs, W. & Binder, H. a. R. B., 2003. Anaerobic treatment of wastewater with high organic content using a stirred tank reactor coupled with a membrane filtration unit. Volumen 37(4):902–908.
Najarro, R., López, R., Racines, R. E. & Puris, A., 2017. Un Algoritmo Genético Híbrido para la Optimización del Flow Shop Scheduling bajo Restricciones de Entornos Reales. Enfoque UTE, 8(5), pp. 14-25.
Sugeno, M. & Takagi, T., 1985. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on systems man, and cybernetics, p. 116–132.
Velarde, P., Valverde, L., Maestre, J. M. & Ocampo-Martinez, C., 2017. On the comparison of stochastic model predictive contro strategies applied to a hydrogen-based microgrid. Journal of Power Sources, p. 161–173.
Vikram, K., Haizhou, P., Wong, M. & de Queiroz, M., 2005. Experimental validation of a nonlinear backstepping liquid level controller for a state coupled two tank system. Issue 13(1):27–40,.

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Published

2018-03-30

How to Cite

Chamorro Hernández, W. O., & Velarde Rueda, P. (2018). Linear Quadratic Regulator and Model Predictive Control Applied to a Four-Tank System: A Performance Comparison. Enfoque UTE, 9(1), pp. 204 – 216. https://doi.org/10.29019/enfoqueute.v9n1.257

Issue

Vol. 9 No. 1 (2018)

Section

Automation and Control, Mechatronics, Electromechanics, Automotive

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