Discrete-time implementation of Smith’s predictor on the state space

Authors

DOI:

https://doi.org/10.17979/ja-cea.2025.46.12140

Keywords:

Systems with time-delays, Linear systems, Process control, Disturbance rejection, Regulation, Digital implementation, Predictive control

Abstract

In this paper it is considered how to apply the Smith’s predictor only with state variables, focusing on its discrete-time implementation in order to obtain the same behavior of the conventional predictor based on the external representation of the process. Its performance is analyzed through simulations on a single input-single output system with transport delay and proportional integral control against disturbances. In addition, it is compared with the alternative of directly modeling the time-delay with a chain of state variables.

References

Åström, K. J., Wittenmark, B., 1997. Computer-controlled systems. Theory and design. Prentice Hall, Tercera edición.

Guzmán, J. L., García, P., Hägglund, T., Dormido, S., Albertos, P., Berenguel, M., 2008. Interactive tool for analysis of time-delay systems with dead-time compensators. Control Engineering Practice 16 (7), 824–835. DOI: https://doi.org/10.1016/j.conengprac.2007.09.002

Martínez, J. L., Morales, J., 2016. Control aplicado con variables de estado. Paraninfo, Segunda edición.

Molnar, T. G., Hajdu, D., Insperger, T., 2019. The Smith predictor, the modified Smith predictor, and the finite spectrum assignment: A comparative study. In: Gao, Q., Karimi, H. R. (Eds.), Stability, Control and Application of Time delay Systems. Butterworth-Heinemann, Ch. 10, pp. 209–226. DOI: https://doi.org/10.1016/B978-0-12-814928-7.00010-X

Normey-Rico, J. E., Camacho, E. F., 2009. Unified approach for robust deadtime compensator design. Journal of Process Control 19 (1), 38–47. DOI: https://doi.org/10.1016/j.jprocont.2008.02.003

Ollero, A., 1991. Control por Computador. Descripción interna y diseño óptimo. Marcombo Boixareu.

Ono, M., Shibasaki, H., Matsumoto, K., Sasaki, K., Ishida, Y., 2010. Discrete modified smith predictor based on optimal control method for a plant with an integrator. In: IEEE International Conference on Systems, Man and Cybernetics.

Istanbul, Turkey, pp. 630–635. DOI: 10.1109/ICSMC.2010.5641821

Pereira, R. D., Torrico, B. C., do Nascimento, J. N., Alves Lima, T., de Almeida Filho, M. P., Nogueira, F. G., 2023. Smith predictor-based feedforward controller for measurable disturbances. Control Engineering Practice 133,

DOI: https://doi.org/10.1016/j.conengprac.2023.105439

Salcedo, J., Feliu, V., , Rivas, R., 2021. State feedback temperature control based on a Smith predictor in a precalciner of a cement kiln. IEEE Latin America Transactions 19 (01), 138–146. DOI: 10.1109/TLA.2021.9423857

Sanz, R., García, P., Albertos, P., 2018. A generalized Smith predictor for unstable time-delay SISO systems. ISA Transactions 72, 197–204. DOI: https://doi.org/10.1016/j.isatra.2017.09.020

Smith, O. J. M., 1957. Closed control of loops with dead-time. Chemical Engineering Progress 53, 217–219.

Zhang, B., Tan, W., Li, J., 2020. Tuning of Smith predictor based generalized ADRC for time-delayed processes via IMC. ISA Transactions 99, 159–166. DOI: https://doi.org/10.1016/j.isatra.2019.11.002

Downloads

Published

2025-09-01

Issue

Section

Ingeniería de Control