First order plus frequency dependent delay modeling : new perspective or mathematical curiosity?

The first-order-plus-dead-time model (FOPDT) is a popular simplified representation of higher order dynamics. However, a well known drawback is the rapid decrease of the frequency response accuracy with increasing process order. This especially applies to the higher frequency range. Literature offers solutions by extending this three parameter model with more parameters. Here, a fractional dead time is proposed. As such, a Frequency-Dependent Delay (FDD) is introduced, which offers a better approximation. As the fractional-order term introduces nonlinear coupling between the phase and the magnitude of the process, the fitting of the function becomes an iterative process, so a constrained multi-objective optimization is needed. This novel model, first-order-plus-frequency-dependent-delay or FOPFDD is fitted on a real electrical ladder network of resistors and capacitors of four and eight parts. The classic model, which is clearly a special case of the new model, is outperformed in the entire bandwidth

Identification of first and second order systems by reset control

[EN] The article presents a method for the identification of first and second order processes with time delay using reset controllers in the absence of disturbances. The method is based on compliance with the method of harmonic balance, which implies the use of an approximation of the control reset by its describing function. The FORE controller (First Order Reset Element) with fixed bandwidth has been chosen because it is the easiest reset driver that possesses all the inherent characteristics in this type of drivers and its descriptive function depends on the amplitude and frequency of its sinusoidal signal input. On the other hand, the fact that the behavior of this reset driver depends on of its reset band allows studying the impact of this parameter in the identification process and in its accuracy.[ES] El artículo presenta un método para la identificación de plantas de primer y segundo orden con retardo usando controladores reseteados en ausencia de perturbaciones. El método se basa en el cumplimiento del principio de equilibrio armónico, lo que implica el uso de una aproximación del controlador reseteado mediante su función descriptiva. Para la realización de este trabajo se ha elegido el controlador FORE (First Order Reset Element) con banda de reset porque es el controlador reseteado que posee todas las características intrínsecas de este tipo de controladores y presenta una función descriptiva que depende de la amplitud y frecuencia de la señal sinusoidal de su entrada. Por otro lado, el que el comportamiento de este controlador dependa de la anchura de la banda de reset que se haya fijado permite estudiar el impacto de este parámetro en el proceso de identificación y en su precisión.Este trabajo ha sido realizado parcialmente gracias al apoyo del Ministerio de Economía y Competitividad de España a través de los fondos asignados a los proyectos DPI2017-84259-C2-2-R y DPI2016-79278-C2-1-R.Zaragoza, S.; Sanchez, J.; Baños, A. (2020). Identificación de sistemas de primer y segundo orden mediante control basado en reset. Revista Iberoamericana de Automática e Informática industrial. 17(2):116-129. https://doi.org/10.4995/riai.2020.11598OJS116129172Bajarangbali, R., Majhi, S., Pandey, S., 2014. Identification of FOPDT and SOPDT Process Dynamics Using Closed Loop Test. ISA Trans. 53, 1223-1231. https://doi.org/10.1016/j.isatra.2014.05.014Bajarangbali, R., Majhi, S., 2017. Estimation of First and Second Order Systems. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. https://doi.org/10.1007/s40010-017-0357-6Baños, A., Dormido, S., Barreiro, A., 2011. Limit Cycles Analysis of reset control systems with reset band. Nonlinear Analysis: Hybrid Systems, 5, 163-173. https://doi.org/10.1016/j.nahs.2010.07.004Baños, A., Barreiro, A., 2012a, Reset Control Systems, Springer, London, 2012. https://doi.org/10.1007/978-1-4471-2250-0Barreiro A., Baños, A., 2012b. Sistemas de Control Basados en Reset. RIAI 9, 329-346. https://doi.org/10.1016/j.riai.2012.09.007Baños, A., Vidal, A. , 2012. Design of Reset Control Systems: the PI+CI Compensator. Journal of Dynamic Systems, Measurement, and Control, 134. https://doi.org/10.1115/1.4004773Beschi, M., Dormido, S., Sánchez, J., Visioli, A., Yebra, L. J., 2014. Event-based PI plus Feedforward Control Strategies for a Distributed Solar Collector Field. IEEE Trans. Control Syst. Technol. 22, 1615-1622. https://doi.org/10.1109/TCST.2013.2279216Beschi, M., Dormido, S., Sánchez, J., Visioli, A., 2015a. Closed-Loop Automatic Tuning Technique for an Event-Based PI Controller. Ind. Eng. Chem. Res. 54, 6362-6370. https://doi.org/10.1021/acs.iecr.5b01024Beschi, M., Dormido, S., Sánchez, J., Visioli, A., 2015b. An Event-based PI Controller Autotuning Technique for Integral Processes. Proceedings of the 1st IEEE International Conference on Event-Based Control, Communication, and Signal Processing; Krakow, Poland. https://doi.org/10.1109/EBCCSP.2015.7300684Chang, R.C., Shen, S.H., Yu, C.C., 1992. Derivation of Transfer Function from Relay Feedback Systems. Ind. Eng. Chem. Res. 31, 855-860. https://doi.org/10.1021/ie00003a030Clegg, J.C., 1958. A Nonlinear Integrator for Servomechanisms. Trans A.I.E.E. 77, 41-42. https://doi.org/10.1109/TAI.1958.6367399Davo, M.A., 2015. Análisis y Diseño de Sistemas de Control Reseteados. Tesis Doctoral. Universidad de Murcia. http://hdl.handle.net/10201/46666Friman, M., Waller, K.V., 1997. A Two-Channel Relay for Autotunning. Ind. Eng. Chem. Res. 36, 2662-2671. https://doi.org/10.1021/ie970013uGelb, A., Van der Velde, W. E., 1968. Multiple-Input Describing Functions and Nonlinear System Design. McGraw-Hill, New York, NY.Gu, D., Ou, L., Wang, P., Zhang, W., 2006. Relay Feedback Autotuning Method for Integrating Processes with Inverse Response and Time Delay. Ind. Eng. Chem. Res. 45, 3119-3132. https://doi.org/10.1021/ie050739nHo, W.K., Feng, E.B., Gan, O.P., 1996. A Novel Relay Auto-Tuning Technique for Processes with Integration. Control Eng. Prac. 4, 923-928. https://doi.org/10.1016/0967-0661(96)00090-1Horowitz, I.M., Rosenbaum, P., 1975. Nonlinear Design for Cost of Feedback Reduction in Systems with Large Parameter Uncertainty. Int. J. Control 24, 977-1001. https://doi.org/10.1080/00207177508922051Kaya, I., 2006. Parameter Estimation for Integrating Processes Using Relay Feedback Control under Static Load Disturbances. Ind. Eng. Chem. Res. 45, 4726-4731. https://doi.org/10.1021/ie060270bKhalil, H. K., 2002. Nonlinear Systems, Prentice Hall, NJ.Li, W., Eskinat, E., Luyben, W.L., 1991. An Improved Autotune Identification Method. Ind. Eng. Chem. Res. 30, 1530-41. https://doi.org/10.1021/ie00055a019Liu, T., Wang, Q.G., Huang, H.P., 2013. A Tutorial Review on Process Identification from Step to Relay Feedback Test, J. Process Control, 23, 1597-1623. https://doi.org/10.1016/j.jprocont.2013.08.003Liu T, Gao F., 2012. Industrial Process Identification and Control: Design Step-Test and Relay-Experiment-based Methods. Springer-Verlag. London, UK.Luyben, W. L., 1987. Derivation of Transfer Functions for Highly Nonlinear Distillation Columns. Ind. Eng. Chem. Res. 26, 2490-2495. https://doi.org/10.1021/ie00072a017Sánchez, J., Guinaldo, M., Visioli, A., Dormido, S., 2018a. Identification of Process Transfer Function Parameters in Event-based PI Control Loops. ISA Trans. 75, 157-171. https://doi.org/10.1016/j.isatra.2018.01.033Sánchez, J., Guinaldo, M., Visioli, A., Dormido, S., 2018b. Enhanced Event-based Identification Procedure for Process Control. Ind. Eng. Chem. Res. 57, 7218-7231. https://doi.org/10.1021/acs.iecr.7b05239Scali, C., Marchetti, G., Semino, D, 1999. Relay with Additional Delay for Identification and Autotuning of Completely Unknown Processes. Ind. Eng. Chem. Res. 38, 1987-1997. https://doi.org/10.1021/ie980616lShen, S.H., Wu, J.S., Yu, C.C., 1996. Use of Biased-Relay Feedback for System Identification. AIChE J. 42, 1174-1180. https://doi.org/10.1002/aic.690420431Slotine, J.J., Li, W., 1991. Applied Nonlinear Control. Prentice Hall, Englewood Cliffs, NJ.Srinivasan, K., Chidambaram, M., 2003. Modified Relay Feedback Method for Improved System Identification. Comput. Chem. Eng. 27, 727-732. https://doi.org/10.1016/S0098-1354(02)00257-0Wang, P., Gu, D., Zhang, W., 2007. Modified Relay Feedback Identification Based on Describing Function Analysis. Ind. Eng. Chem. Res. 46, 1538-1546. https://doi.org/10.1021/ie061141yZaragoza, N., 2018. Identificación de Plantas Estables en Lazo Cerrado mediante Controladores Reseteados de Banda Fija. Trabajo Fin de Máster Ingeniería de Sistemas y Control. UNED, Madrid

PID control system analysis, design, and technology

Designing and tuning a proportional-integral-derivative (PID) controller appears to be conceptually intuitive, but can be hard in practice, if multiple (and often conflicting) objectives such as short transient and high stability are to be achieved. Usually, initial designs obtained by all means need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired. This stimulates the development of "intelligent" tools that can assist engineers to achieve the best overall PID control for the entire operating envelope. This development has further led to the incorporation of some advanced tuning algorithms into PID hardware modules. Corresponding to these developments, this paper presents a modern overview of functionalities and tuning methods in patents, software packages and commercial hardware modules. It is seen that many PID variants have been developed in order to improve transient performance, but standardising and modularising PID control are desired, although challenging. The inclusion of system identification and "intelligent" techniques in software based PID systems helps automate the entire design and tuning process to a useful degree. This should also assist future development of "plug-and-play" PID controllers that are widely applicable and can be set up easily and operate optimally for enhanced productivity, improved quality and reduced maintenance requirements

PI/PID Controller Relay Experiment Auto-Tuning with Extended Kalman Filter and Second-Order Generalized Integrator as Parameter Estimators

This paper presents a method for the estimation of key parameters of limit cycle oscillations (amplitude and frequency) during a relay experiment used for automatic tuning of proportional-integral (PI) and proportional-integral-derivative (PID) feedback controllers. The limit cycle parameter estimator is based on the first-order extended Kalman filter (EKF) for resonance frequency estimation, to which a second-order generalized integrator (SOGI) is cascaded for the purpose of limit cycle amplitude estimation. Based on thus-obtained parameters of the limit cycle oscillations, the ultimate gain and the ultimate period of the limit cycle oscillations are estimated. These are subsequently used for the tuning of PI and PID controller according to Takahashi modifications of Ziegler-Nichols tuning rules. The proposed PI and PID controller auto-tuning method is verified by means of simulations and experimentally on the heat and air-flow experimental setup for the case of air temperature feedback control. The results have shown that the proposed auto-tuning system based on relay control experiment for the heat and air-flow process PI/PID temperature control can capture the ultimate gain and period parameters fairly quickly in simulations and in experiments. Subsequent controller tuning according to Takahashi modifications of Ziegler-Nichols rules using thus-obtained ultimate point parameters can provide favourable closed-loop load disturbance rejection, particularly in the case of PID controller

PI/PID Controller Relay Experiment Auto-Tuning with Extended Kalman Filter and Second-Order Generalized Integrator as Parameter Estimators

This paper presents a method for the estimation of key parameters of limit cycle oscillations (amplitude and frequency) during a relay experiment used for automatic tuning of proportional-integral (PI) and proportional-integral-derivative (PID) feedback controllers. The limit cycle parameter estimator is based on the first-order extended Kalman filter (EKF) for resonance frequency estimation, to which a second-order generalized integrator (SOGI) is cascaded for the purpose of limit cycle amplitude estimation. Based on thus-obtained parameters of the limit cycle oscillations, the ultimate gain and the ultimate period of the limit cycle oscillations are estimated. These are subsequently used for the tuning of PI and PID controller according to Takahashi modifications of Ziegler-Nichols tuning rules. The proposed PI and PID controller auto-tuning method is verified by means of simulations and experimentally on the heat and air-flow experimental setup for the case of air temperature feedback control. The results have shown that the proposed auto-tuning system based on relay control experiment for the heat and air-flow process PI/PID temperature control can capture the ultimate gain and period parameters fairly quickly in simulations and in experiments. Subsequent controller tuning according to Takahashi modifications of Ziegler-Nichols rules using thus-obtained ultimate point parameters can provide favourable closed-loop load disturbance rejection, particularly in the case of PID controller

An estimation approach for process control based on asymmetric oscillations

[Abstract] An estimation procedure for process control has been developed based on the information obtained from the oscillations that a non-linear element as a simple relay introduces in the feedback loop. Features of the method are: (1) the procedure does not demand a priori process information, (b) non-iterative algorithms are needed to derive the process parameters, (c) only one test is needed, and (d) it allows identifying the process at a user-specified phase lag in the third quadrant. The method is presented for estimation of most common transfer functions found in chemical and process industry: integrators, first-, second- as well as processes with non-minimum-phase dynamics.Ministerio de Economía y Competitividad; PI2012-31303Ministerio de Economía y Competitividad; DPI2014-55932-C2-2-

Field test of quantum key distribution in the Tokyo QKD Network

A novel secure communication network with quantum key distribution in a metropolitan area is reported. Different QKD schemes are integrated to demonstrate secure TV conferencing over a distance of 45km, stable long-term operation, and application to secure mobile phones.Comment: 21 pages, 19 figure

Autotuning of an In-Line pH Control System

A novel autotuning procedure is presented through application to an industrial in-line pH control system. The procedure has three advantages over classical relay auto-tuners: experiment duration is very short (no need for limit-cycle convergence); all data is used for identification (instead of only peaks and switch instances); a parameter uncertainty model is identified and utilized for robust controller synthesis