Performance comparison of state observers in linear systems through the application to a continuous current engine
DOI:
https://doi.org/10.33131/24222208.310Keywords:
System, model, state vector, observability, dynamics, estimation, measurementAbstract
In many industrial processes, there are essential variables which need constant monitoring for process control tasks. However, often such measurement is complicated, or there is just no adequate sensor to perform this goal; this creates a significant challenge for engineers, who must somehow have measurement and control over system variables. An alternative for cases in which the access to the state vector is unfeasible is to obtain an estimate of the non-measurable states of the system through a state observer. The observer is a dynamic system whose states converge to those of the observed system, based on the system model and the observation of the input and output of the system. This information is used to estimate variables that are difficult to measure to make possible the full description of the behavior of the dynamic system. In this work, a set of state observers is designed and implemented to estimate the speed of a DC motor by measuring its stator current. Using different types of state estimators such as Luenberger Estimator, Kalman Filter for Linear Systems and the Sliding Mode Observer, we intend to estimate the DC motor speed correctly based on its mathematical model and stator current measurement. In both the simulations and the implementation of the observers, the response of these to unexpected perturbations that could alter the standard conditions of the system is analyzed and compared. The results suggest that each observer has specific conditions where their performance is enhanced.
Downloads
References
[2] J. D. Sánchez-Torres, A. G. Loukianov, J. A. P. Murillo, B. Giraldo, and H. Botero, “A high order sliding mode observer for systems in triangular input observer form,” in Robotics Symposium, 2011 IEEE IX Latin American and IEEE Colombian Conference on Automatic Control and Industry Applications (LARC), 2011, pp. 1–6.
[3] J. D. Sanchez-Torres, A. G. Loukianov, J. A. Murillo, B. Giraldo, and H. Botero, “An equivalent control based second order sliding mode observer using robust differentiators,” in Robotics Symposium, 2011 IEEE IX Latin American and IEEE Colombian Conference on Automatic Control and Industry Applications (LARC), Bogotá, Colombia, 2011, pp. 1–6.
[4] J. E. Castano, J. A. Patino, and J. J. Espinosa, “Model identification for control of a distillation column,” in Robotics Symposium, 2011 IEEE IX Latin American and IEEE Colombian Conference on Automatic Control and Industry Applications (LARC), 2011, pp. 1–5.
[5] M. Giraldo and J. Patiño, “Controladores prealimentados y realimentados para sistemas de primer orden con tiempo muerto y ganacia variable,” Rev. CINTEX, vol. 16, pp. 103–108, 2011.
[6] P. Deossa, J. Patino, J. Espinosa, and F. Valencia, “A comparison of Extended Kalman Filter and Levenberg-Marquardt methods for neural network training,” in Robotics Symposium, 2011 IEEE IX Latin American and IEEE Colombian Conference on Automatic Control and Industry Applications (LARC), Bogotá, Colombia, 2011, pp. 1–5.
[7] F. Valencia, J. López, J. Patiño, and J. Espinosa, “Bargaining Game Based Distributed MPC,” in Distributed Model Predictive Control Made Easy, Springer Netherlands, 2014, pp. 41–56.
[8] P. Deossa, A. Marquez, and J. Espinosa, “Integration of economic MPC, energy load and price estimation with Holt Winters models,” in 2014 IEEE PES Transmission & Distribution Conference and Exposition - Latin America (PES T&D-LA), Medellin, Colombia, 2014, pp. 1–5.
[9] A. E. Florián Villa, “Metodología de análisis de observabilidad para estimadores de estado en sistemas de energía eléctrica,” Master thesis, Universidad Nacional de Colombia, Colombia, 2015.
[10] R. Horta, J. Espinosa, and J. Patino, “Frequency and voltage control of a power system with information about grid topology,” in Automatic Control (CCAC), 2015 IEEE 2nd Colombian Conference on, 2015, pp. 1–6.
[11] V. Srdanovic, O. B. Henao, and S. H. Ruiz, “Modelado e Identificación de un Sistema Electromecánico y Diseño del Control PID para Gobernar Inalámbricamente el Desplazamiento de un Objeto Móvil,” Rev. CINTEX, vol. 22, no. 1, pp. 25–46, 2017.
[12] Julian Alberto Patino, J. J. Espinosa, and R. E. Correa, “A comparison of Kalman-based schemes for localization and tracking in sensor systems,” in Communications (LATINCOM), 2010 IEEE Latin-American Conference on, 2010, pp. 1–5.
[13] J. A. Patiño Murillo, “Kalman-based schemes for mobile nodes localization in ad-hoc networks,” Universidad Nacional de Colombia - Sede Manizales, 2011.
[14] A. Navarro, J. D. Sanchez-Torres, O. Begovich, G. Besancon, and J. . Patino-Murillo, “An algebraic observer for Leak Detection and Isolation in plastic pipelines,” in Control Conference (ECC), 2013 European, Zurich, Switzerland, 2013, pp. 926–931.
[15] H. A. Botero Castro and H. D. Alvarez Zapata, “Una revisión de los métodos más frecuentes para la estimación del estado en procesos químicos,” Dyna, no. 158, pp. 135–146, 2009.
[16] R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems,” Trans. ASME–Journal Basic Eng., vol. 82, no. Series D, pp. 35–45, 1960.
[17] B. Osorio, J. Osorio, L. Mejía, G. E. Campillo, and R. Covaleda, “La conceptualización del campo eléctrico y magnético. Análisis de las concepciones de los estudiantes,” Rev. CINTEX, vol. 20, no. 1, pp. 123–137, 2015.
[18] G. Rubio-Astorga, J. D. Sánchez-Torres, J. Cañedo, and A. G. Loukianov, “High-Order Sliding Mode Block Control of Single-Phase Induction Motor,” IEEE Trans. Control Syst. Technol., vol. 22, no. 5, pp. 1828–1836, Sep. 2014.
[19] D. G. Luenberger, “Observing the State of a Linear System,” IEEE Trans. Mil. Electron., vol. 8, no. 2, pp. 74–80, Apr. 1964.
[20] S. V. Drakunov and V. I. Utkin, “Sliding mode control in dynamic systems,” Int. J. Control, vol. 55, no. 4, pp. 1029–1037, Apr. 1992.
[21] J. Barrientos and H. Botero, “Diseño de un observador de estado en un bioproceso para la producción de etanol,” Rev. CINTEX, vol. 15, pp. 27–35, 2010.
[22] J. Patino, F. Valencia, and J. Espinosa, “Sensitivity analysis for frequency regulation in a two-area power system,” Int. J. Renew. Energy Res., vol. 7, no. 2, pp. 700–706, 2017.
[23] J. Patiño, J. D. López, and J. Espinosa, “Analysis of Control Sensitivity Functions for Power System Frequency Regulation,” in Applied Computer Sciences in Engineering, vol. 915, J. C. Figueroa-García, E. R. López-Santana, and J. I. Rodriguez-Molano, Eds. Cham: Springer International Publishing, 2018, pp. 606–617.
[24] Z. Yin, C. Zhao, Y.-R. Zhong, and J. Liu, “Research on Robust Performance of Speed-Sensorless Vector Control for the Induction Motor Using an Interfacing Multiple-Model Extended Kalman Filter,” IEEE Trans. Power Electron., vol. 29, no. 6, pp. 3011–3019, Jun. 2014.
