A shifting pole placement approach for the design of performance-varying multivariable PID controllers via BMIs

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, the design of a performance-varying multivariable Proportional-Integral-Derivative (PID) controllers is presented. The main objective is to provide a framework for changing online the closed-loop behavior of the controlled system using the shifting pole placement approach. In order to carry out this target, the PID design problem is transformed into a static output feedback design problem which is analyzed through the linear parameter-varying (LPV) paradigm. An academic example is used to demonstrate the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization - A Guide for Parameters Computation Based on Robustness

[EN] A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and are intended as a tool for designers who seek to implement LADRC by considering the load disturbance response of processes whose behavior is approximated by a general first-order system with delay. The validation of the proposed tuning rules is done through illustrative examples and the control of a nonlinear thermal process. Compared to classical PID (Proportional-Integral-Derivative) and other LADRC tuning methods, the derived functions offer an improvement in either disturbance rejection, robustness or both design objectives.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades, Spain, under Grant RTI2018-096904-B-I00.Martínez, BV.; Sanchís Saez, J.; Garcia-Nieto, S.; Martínez Iranzo, MA. (2021). Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization - A Guide for Parameters Computation Based on Robustness. Mathematics. 9(5):1-34. https://doi.org/10.3390/math90505171349

A fast design technique for robust industrial controllers

This paper provides a new fast design method for robust industrial controllers via majorant systems in the frequency domain. The proposed methodology allows to establish several fast design techniques for a broad class of industrial controllers of plants with internal and/or external delays, parametric and/or structural uncertainties, and subject to disturbances, when an analytical model of the plant or data acquired from simple experimental tests are available. The provided design and control techniques are more general with respect to the Ziegler-Nichols ones and their numerous variants, which, in some cases, do not guarantee the control system stability. The used key idea consists in increasing the frequency response of the process to be controlled with the frequency response of a simpler system, also of order greater than one, with external delay, which allows designing, using simple formulas, controllers of PI, PID, PIDR, PI2, PI2D, PI2DR, PI2D2, and PI2D2R types. The designed controllers always guarantee stability margins larger than those of appropriate reference systems. Therefore, good performance of robustness of the stability and tracking precision of smooth references, with respect to parametric and/or structural uncertainties and/or smooth disturbances, are always guaranteed. The stated general methodology and various performance comparisons, also about the tracking precision of references with bounded first or second derivative, are illustrated and validated in several case studies, experimentally too

Articles indexats publicats per investigadors del Campus de Terrassa: 2017

Aquest informe recull els 241 treballs publicats per 222 investigadors/es del Campus de Terrassa en revistes indexades al Journal Citation Report durant el 2017Postprint (published version

Optimal Nash tuning rules for robust PID controllers

In this paper, we propose tuning rules for one degree-of-freedom proportional-integral-derivative controllers, by considering important aspects such as the trade-off in the performance in the servo and regulation operation modes and the control system robustness by constraining the maximum sensitivity peak. The different conflicting objectives are dealt with by using a multi-objective optimization algorithm to generate the trade-off optimal solutions. In this context, a simple tuning rule is determined by using the Nash solutions as a multi-criteria decision making technique. The Nash criteria is shown to provide convenient trade-off solutions for the controller tuning problem. Illustrative simulation examples show the effectiveness of the method

PID Tuning: Analytical approach based on the weighted Sensitivity problem

[EN] The PID controller is the most common option in the realm of control applications and is dominant in the process control industry. Among the related analytical methods, Internal Model Control (IMC) has gained remarkable industrial acceptance due to its robust nature and good set-point responses. However, the traditional application of IMC results in poor load disturbance rejection for lag-dominant and integrating plants. This work presents an IMC-like design method which avoids this common pitfall and is devised to work well for plants of modest complexity, for which analytical PID tuning is plausible. For simplicity, the design only focuses on the closed-loop sensitivity function. The approach provides model-based tuning of single-loop PID controllers in terms of the robustness/performance and servo/regulator trade-offs. Although the robustness/performance compromise is commonly considered, it is not so common to also take into account, for example, the conflict between input and output disturbances, referred also as the servo/regulator trade-off. As interested in providing a unified tuning approach, it is shown how the proposed methodology allows to deal with different process dynamics in a unified way.[ES] El controlador PID es la opción más común en el ámbito de las aplicaciones de control, siendo la opción predominante en el control de procesos industriales. Entre los métodos analíticos más usuales utilizados para su diseño, el Control por Modelo Interno (IMC) ha ganado una notable aceptación industrial debido a su naturaleza robusta y buenas respuestas ante cambios de consigna. Sin embargo, la aplicación tradicional del IMC da como resultado un bajo rendimiento para el rechazo de perturbaciones en carga para plantas integradoras y/o con largas constantes de tiempo. Este trabajo presenta un método de diseño, basado en IMC, que evita esta deficiencia y está diseñado para funcionar bien en plantas de complejidad moderada para las cuales, por otro lado, el ajuste analítico de un controlador PID es plausible. Por simplicidad, el diseño solo se centra en la función de sensibilidad en lazo cerrado. El enfoque proporciona un ajuste basado en modelo en términos de los compromisos robustez/rendimiento y de servo/regulación. Aunque comúnmente se considera el compromiso robustez/rendimiento, no es tan común tener en cuenta también, por ejemplo, el conflicto entre las perturbaciones de entrada y salida, también conocido como el compromiso servo/regulación. Con el objetivo de proporcionar un enfoque de ajuste unificado, se muestra como la metodología propuesta permite tratar diferentes dinámicas de proceso de manera unificada.Los autores desean agradecer al Ministerio de Economía y Competitividad bajo las subvenciones DPI-2016-77271-R y PID2019-105434RB-C33 por la ayuda que han supuesto en la elaboración de los trabajos que han conducido a los desarrollos aquí presentados.Vilanova, R.; Alcántara, S.; Pedret, C. (2021). Sintonía de controladores PID: un enfoque analítico basado en el moldeo de la función de sensibilidad. Revista Iberoamericana de Automática e Informática industrial. 18(4):313-326. https://doi.org/10.4995/riai.2021.15422OJS313326184Alcántara, S., Vilanova, R., Pedret, C., 2013. PID control in terms of robustness/performance and servo/regulator trade-offs: A unifying approach to balanced autotuning. Journal of Process Control 23 (4), 527 - 542. https://doi.org/10.1016/j.jprocont.2013.01.003Alcántara, S., Pedret, C., Vilanova, R., 2010. On the model matching approach to PID design: Analytical perspective for robust Servo/Regulator tradeoff tuning. Journal of Process Control 20 (5), 596 - 608. https://doi.org/10.1016/j.jprocont.2010.02.011Alcántara, S., Pedret, C., Vilanova, R., Skogestad, S., 2011a. Generalized Internal Model Control for balancing input/output disturbance response. Industrial & Engineering Chemistry Research 50 (19), 11170-11180. https://doi.org/10.1021/ie200717zAlcántara, S., Vilanova, R., Pedret, C., 2020. PID Tuning: A Modern Approach via the Weighted Sensitivity Problem (1st ed.). CRC Press. https://doi.org/10.1201/9780429325335-1Alcántara, S., Vilanova, R., Pedret, C., Skogestad, S., 2012. A look into robustness/performance and servo/regulation issues in PI tuning. In: Proc. of the IFAC Conf. on Advances in PID Control PID'12. https://doi.org/10.3182/20120328-3-IT-3014.00031Alcántara, S., Zhang, W., Pedret, C., Vilanova, R., Skogestad, S., 2011b. IMC-like analytical H-inf design with S/SP mixed sensitivity consideration: Utility in PID tuning guidance. Journal of Process Control 21 (6), 976 - 985. https://doi.org/10.1016/j.jprocont.2011.04.007Alfaro, V. M., Vilanova, R., 2013a. Performance and Robustness Considerations for Tuning of Proportional Integral/Proportional Integral Derivative Controllers with Two Input Filters. Industrial & Engineering Chemistry Research 52, 18287-18302. https://doi.org/10.1021/ie4012694Alfaro, V. M., Vilanova, R., 2013b. Robust tuning of 2DoF five-parameters PID controllers for inverse response controlled processes. Journal of Process Control 23, 453-462. https://doi.org/10.1016/j.jprocont.2013.01.005Alfaro, V. M., Vilanova, R., September 2013c. Simple robust tuning of 2DoF PID controllers from a performance/robustness trade-off analysis. Asian Journal of Control 15 (5), 1-14. https://doi.org/10.1002/asjc.653Alfaro, V. M., Vilanova, R., 2016. Model-Reference Robust Tuning of PID Controllers. Springer International Publishing AG, Gewerbestrasse 11, 6330 Cham, Switzerland, ISBN 978-3-319-28213-8.Alfaro, V. M., Vilanova, R., Méndez, R., Lafuente, J., 2010. Performance/Robustness Tradeoff Analysis of PI/PID Servo and Regulatory Control Systems. In: Proc. of the IEEE International Conference on Industrial Technology. https://doi.org/10.1109/ICIT.2010.5472662Arrieta, O., Vilanova, R., 2012. Simple servo/regulation proportional-integralderivative (pid) tuning rules for arbitrary ms-based robustness achievement. Industrial & Engineering Chemistry Research 51 (6), 2666-2674. https://doi.org/10.1021/ie201655cArrieta, O., Vilanova, R., Rojas, J. D., Meneses, M., 2016. Improved pid controller tuning rules for performance degradation/robustness increase trade-off. Electrical Engineering 98 (3), 233-243. https://doi.org/10.1007/s00202-016-0361-xArrieta, O., Visioli, A., Vilanova, R., 2010. PID autotuning for weighted servo/regulation control operation. Journal of Process Control 20 (4), 472 -480. https://doi.org/10.1016/j.jprocont.2010.01.002Astrom, K., Hagglund, T., 2004. Revisiting the Ziegler-Nichols step response method for PID control. J. Process Control 14, 635-650. https://doi.org/10.1016/j.jprocont.2004.01.002Astrom, K., Hagglund, T., 2005. Advanced PID control. ISA - The Instrumentation, Systems, and Automation Society.Chien, I. L., Fruehauf, P. S., 1990. Consider IMC tuning to improve controller performance. Chemical Engineering Progress 86 (10), 33 - 41.Dehghani, A., Lanzon, A., Anderson, B., 2006. H1 design to generalize internalmodel control. Automatica 42 (11), 1959 - 1968.Grimholt, C., Skogestad, S., 2012. Optimal PI Control and Verifcation of the SIMC Tuning Rule. In: Proc. of the IFAC Conf. on Advances in PID Control PID'12. https://doi.org/10.3182/20120328-3-IT-3014.00003Horn, I. G., Arulandu, J. R., Gombas, C. J., VanAntwerp, J. G., Braatz, R. D., 1996. Improved Filter Design in Internal Model Control. Industrial & Engineering Chemistry Research 35 (10), 3437 - 3441. https://doi.org/10.1021/ie9602872Huba, M., 2012. Setpoint Versus Disturbance Responses of the IPDT Plant. In: Proc. of the IFAC Conf. on Advances in PID Control PID'12. https://doi.org/10.3182/20120328-3-IT-3014.00070J.Shi, W.S.Lee, 2004. Set Point Response and Disturbance Rejection Tradeoff for Second-Order Plus Dead Time Processes. In: Asian Control Conference.Kristiansson, B., Lennartson, B., 1998. Optimal PID controllers for unstable and resonant plants. In: Proc. of the IEEE Conference on Decision and Control. pp. 4380-4381.Kurokawa, R., Sato, T., Vilanova, R., Konishi, Y., 2019. Discrete-time firstorder plus dead-time model-reference trade-off pid control design. Applied Sciences 9 (16). https://doi.org/10.3390/app9163220Kurokawa, R., Sato, T., Vilanova, R., Konishi, Y., 2020. Design of optimal pid control with a sensitivity function for resonance phenomenon-involved second-order plus dead-time system. Journal of the Franklin Institute 357 (7), 4187-4211. https://doi.org/10.1016/j.jfranklin.2020.03.015Leva, A., Maggio, M., 2012. Model-Based PI(D) Autotuning. In: PID Control in the Third Millennium. Lessons Learned and New Approaches. Springer. https://doi.org/10.1007/978-1-4471-2425-2_2Mercader, P., Astrom, K. J., Baños, A., Hagglund, T., 2017a. Robust pid design based on qft and convex?concave optimization. IEEE Transactions on Control Systems Technology 25 (2), 441-452. https://doi.org/10.1109/TCST.2016.2562581Mercader, P., Baños, A., 2017. A pi tuning rule for integrating plus dead time processes with parametric uncertainty. ISA Transactions 67, 246-255. https://doi.org/10.1016/j.isatra.2017.01.025Mercader, P., Baños, A., Vilanova, R., 2017b. Robust proportional-integral-derivative design for processes with interval parametric uncertainty. IET Control Theory & Applications 11 (7), 016-1023. https://doi.org/10.1049/iet-cta.2016.1239Mercader, P., Soltesz, K., Baños, A., 2017c. Robust pid design by chance-constrained optimization. Journal of the Franklin Institute 354 (18), 8217-8231. https://doi.org/10.1016/j.jfranklin.2017.10.017Meza, G. R., Ferragud, X. B., Saez, J. S., Dur, J. M. H., 2016. Controller Tuning with Evolutionary Multiobjective Optimization: A Holistic Multiobjective Optimization Design Procedure, 1st Edition. Springer Publishing Company, Incorporated.Middleton, R. H., Graebe, S. F., 1999. Slow stable open-loop poles: to cancel or not to cancel. Automatica 35 (5), 877-886. https://doi.org/10.1016/S0005-1098(98)00220-9Morari, M., Zafiriou, E., 1989. Robust Process Control. Prentice-Hall International.Panagopoulos, H., Astrom, K. J., 2000. PID control design and H1 loop shaping. International Journal of Robust and Nonlinear Control 10 (15), 1249-1261. https://doi.org/10.1002/1099-1239(20001230)10:153.0.CO;2-7Pedret, C., Vilanova, R., Moreno, R., Serra, I., 2002. A refinement procedure for PID controller tuning. Computers & Chemical Engineering 26 (6), 903- 908. https://doi.org/10.1016/S0098-1354(02)00011-XRivera, D. E., Morari, M., Skogestad, S., 1986. Internal model control: PID controller design. Industrial & Engineering Chemistry Process Design and Development 25 (1), 252 - 265. https://doi.org/10.1021/i200032a041Rodriguez, C., September 2020. Revisiting the simplified imc tuning rules for low-order controllers: Novel 2dof feedback controller. IET Control Theory & Applications 14, 1700-1710(10). https://doi.org/10.1049/iet-cta.2019.0821Ruscio, D. D., 2010. On Tuning PI Controllers for Integrating Plus Time Delay Systems. Modeling, Identification and Control 31 (4), 145 - 164. https://doi.org/10.4173/mic.2010.4.3Samad, T., Feb 2017. A survey on industry impact and challenges thereof [technical activities]. CSM 37 (1), 17-18. https://doi.org/10.1109/MCS.2016.2621438Sanchez, H. S., Padula, F., Visioli, A., Vilanova, R., 2017a. Tuning rules for robust fopid controllers based on multi-objective optimization with fopdt models. ISA Transactions 66, 344-361. https://doi.org/10.1016/j.isatra.2016.09.021Sanchez, H. S., Visioli, A., Vilanova, R., 2017b. Optimal nash tuning rules for robust pid controllers. Journal of the Franklin Institute 354 (10), 3945-3970.https://doi.org/10.1016/j.jfranklin.2017.03.012Sato, T., Hayashi, I., Horibe, Y., Vilanova, R., Konishi, Y., 2019. Optimal robust pid control for first- and second-order plus dead-time processes. Applied Sciences 9 (9). https://doi.org/10.3390/app9091934Sato, T., Tajika, H., Vilanova, R., Konishi, Y., 2018. Adaptive pid control system with assigned robust stability. IEEJ Transactions on Electrical and Electronic Engineering 13 (8), 1169-1181. https://doi.org/10.1002/tee.22680Shamsuzzoha, M., Lee, M., 2007. IMC-PID Controller Design for Improved Disturbance Rejection of Time-Delayed Processes. Industrial & Engineering Chemistry Research 46 (7), 2077 - 2091. https://doi.org/10.1021/ie0612360Shamsuzzohaa, M., Skogestad, S., 2010. The setpoint overshoot method: A simple and fast closed-loop approach for PID tuning. Journal of Process Control 20 (10), 1220 - 1234. https://doi.org/10.1016/j.jprocont.2010.08.003Skogestad, S., 2003. Simple analytic rules for model reduction and PID controller tuning. J. Process Control 13, 291-309. https://doi.org/10.1016/S0959-1524(02)00062-8Skogestad, S., Grimholt, C., 2012. PID Tuning for Smooth Control. In: PID Control in the Third Millennium. Lessons Learned and New Approaches. Springer.Skogestad, S., Postlethwaite, I., 2005. Multivariable Feedback Control. Wiley.Smuts, J. F., 2011. Process Control for Practitioners: How to Tune PID Controllers and Optimize Control Loops. OptiControls.Vilanova, R., 2008. IMC based Robust PID design: Tuning guidelines and automàtic tuning. Journal of Process Control 18, 61-70. https://doi.org/10.1016/j.jprocont.2007.05.004Vilanova, R., Arrieta, O., 2007. PID design for improved disturbance attenuation: min max Sensitivity matching approach. IAENG International Journal of Applied Mathematics 37 (1).Vilanova, R., Arrieta, O., Ponsa, P., 2018. Robust pi/pid controllers for load disturbance based on direct synthesis. ISA Transactions 81, 177-196. https://doi.org/10.1016/j.isatra.2018.07.040Vilanova, R., Visioli, A., 2012. PID Control in the Third Millenium - Lessons Learned and New Approaches. Springer-Verlag London Limited. https://doi.org/10.1007/978-1-4471-2425-2Visioli, A., 2001. Optimal tuning of PID controllers for integral and unstable processes. IEE Proceedings. Part D 148 (2), 180 - 184. https://doi.org/10.1049/ip-cta:20010197Zhuang, M., Atherton, D. P., 1993. Automatic tuning of optimum PID controllers. IEE Proc. Part D 140 (3), 216-224. https://doi.org/10.1049/ip-d.1993.0030Ziegler, J. G., Nichols, N. B., 1942. Optimum settings for automatic controllers. Trans. Am. Soc. Mech. Eng. 64, 759-768

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools