Output-feedback anti-disturbance predictor-based control for discrete-time systems with time-varying input delays

[EN] This paper investigates the robust stabilization of discrete-time systems with time-varying input delays and model uncertainties by predictor-based anti-disturbance output-feedback control strategies. Here, a novel predictor-feedback control combined with an extended state observer is proposed. The objective is to counteract the negative effects of input delays while actively rejecting disturbance signals typically encountered in engineering practice, such as steps or harmonics. Differently from previous approaches, unknown but bounded time-varying delays are taken into consideration. Moreover, the complexity of the algorithm for control synthesis is notably reduced. Finally, an illustrative example from the literature is provided to show that better robust performance can be achieved with the proposed method.This work was partially supported by projects TIN201786520C31R, Ministerio de Economia y Competitividad (Spain) , and PGC2018098719BI00, MCIU/AEI/FEDER, UE, and Group DGA T4517R, Spain. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Bin Zhou under the direction of Editor Ian R. Petersen.González Sorribes, A.; García Gil, PJ. (2021). Output-feedback anti-disturbance predictor-based control for discrete-time systems with time-varying input delays. Automatica. 129:1-8. https://doi.org/10.1016/j.automatica.2021.109627S1812

Sistemas dinámicos con retardos temporales: contribución al desarrollo de predictores robustos para el control de sistemas inestables

Una de las mayores dificultades en el diseño de un sistema de control es sin duda la presencia de retardos, máxime si el sistema que se pretende controlar es inestable en bucle abierto y/o de fase no mínima. Los retardos temporales pueden ser intrínsecos a los procesos a controlar, véase por ejemplo los procesos químicos, biológicos, columnas de destilación, procesos con intercambios térmicos, etc, o bien introducirse en el sistema de control por el propio diseño del mismo (tiempo de cómputo del algoritmo de control, sistemas distribuidos, control remoto, redes de comunicaciones, retardos introducidos por los sensores y/o actuadores, etc.). El Predictor de Smith, así como sus múltiples extensiones, y la técnica de Asignación Finita del Espectro, pueden considerarse como las estrategias de control más extendidas para el control de sistemas lineales sometidos a retardos de actuación y/o medida. Tanto el Predictor de Smith, como la técnica de Asignación Finita del Espectro, tienen en común que realizan una compensación del retardo en base a una predicción de la salida, o del estado, a partir de un modelo del sistema considerado. Si el proceso a controlar es inestable, los esquemas de control resultantes no cumplen la condición de estabilidad interna y por tanto serán inestables. Con objeto de poder aplicar estas técnicas al control de sistemas inestables con retardos temporales, se han propuesto diferentes modificaciones del esquema original del Predictor de Smith, denominadas genéricamente Compensadores de Tiempo Muerto (DTC), así como diferentes intentos de buscar una implementación numéricamente estable de la técnica de Asignación Finita del Espectro. Destacar sin embargo, que todas estas modificaciones han consistido en soluciones parciales del problema planteado, tanto en lo concerniente a la utilización de DTC para el control de sistemas inestables de fase mínima o no mínima, como en lo concerniente a la implementación numéricamente estable de la integral dGarcía Gil, PJ. (2007). Sistemas dinámicos con retardos temporales: contribución al desarrollo de predictores robustos para el control de sistemas inestables [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/79431Palanci

A generalized smith predictor for unstable time-delay SISO systems

[EN] In this work, a generalization of the Smith Predictor (SP) is proposed to control linear time-invariant (LTI) time-delay single-input single-output (SISO) systems. Similarly to the SP, the combination of any stabilizing output-feedback controller for the delay-free system with the proposed predictor leads to a stabilizing controller for the delayed system. Furthermore, the tracking performance and the steady-state disturbance rejection capabilities of the equivalent delay-free loop are preserved. In order to place this contribution in context, some modifications of the SP are revisited and recast under the same structure. The features of the proposed scheme are illustrated through simulations, showing a comparison with respect to the corresponding delay-free loop, which is here considered to be the ideal scenario. In order to emphasize the feasibility of this approach, a successful experimental implementation in a laboratory platform is also reported.This work was partially supported by the projects PROMETEOII/2013/004, Conselleria d'Educacio, Generalitat Valenciana; TIN2014-56158-C4-4-P-AR, Ministerio de Economia y Competitividad; and the FPI-UPV 2014 PhD Grant, Universitat Politecnica de Valencia, Spain.Sanz Díaz, R.; García Gil, PJ.; Albertos Pérez, P. (2017). A generalized smith predictor for unstable time-delay SISO systems. ISA Transactions. 72:197-204. https://doi.org/10.1016/j.isatra.2017.09.020S1972047

Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback

[EN] This paper deals with robust observer-based output-feedback stabilization of systems whose actuator dynamics can be described in terms of partial differential equations (PDEs). More specifically, delay dynamics (first-order hyperbolic PDE) and diffusive dynamics (parabolic PDE) are considered. The proposed controllers have a PDE observer-based structure. The main novelty is that stabilization for an arbitrarily large delay or diffusion domain length is achieved, while distributed integral terms in the control law are avoided. The exponential stability of the closed loop in both cases is proved using Lyapunov functionals, even in the presence of small uncertainties in the time delay or the diffusion coefficient. The feasibility of this approach is illustrated in simulations using a second-order plant with an exponentially unstable mode.This work was supported in part by Project TIN2017-86520-C3-1-R, Ministerio de Economia y Competitividad, in part by the 16/17 UPV Mobility Award, and in part by the FPI-UPV 2014 Ph.D. Grant, Universitat Politecnica de Valencia, Spain.Sanz Diaz, R.; García Gil, PJ.; Krstic, M. (2019). Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback. IEEE Transactions on Automatic Control. 64(9):3663-3675. https://doi.org/10.1109/TAC.2018.2887148S3663367564

Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay

[EN] This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.This work was partially supported by: Ministerio de Economía y Competitividad, Spain (TIN2017-86520-C3-1-R); Universitat Politècnica de València (FPI-UPV 2014 PhD Grant); and Israel Science Foundation (Grant No. 1128/14).Sanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2020). Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay. International Journal of Control. 93(2):217-225. https://doi.org/10.1080/00207179.2018.1562204S217225932Ahmed-Ali, T., Cherrier, E., & Lamnabhi-Lagarrigue, F. (2012). Cascade High Gain Predictors for a Class of Nonlinear Systems. IEEE Transactions on Automatic Control, 57(1), 221-226. doi:10.1109/tac.2011.2161795Artstein, Z. (1982). Linear systems with delayed controls: A reduction. IEEE Transactions on Automatic Control, 27(4), 869-879. doi:10.1109/tac.1982.1103023Basturk, H. I. (2017). Cancellation of unmatched biased sinusoidal disturbances for unknown LTI systems in the presence of state delay. Automatica, 76, 169-176. doi:10.1016/j.automatica.2016.10.006Basturk, H. I., & Krstic, M. (2015). Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay. Automatica, 58, 131-138. doi:10.1016/j.automatica.2015.05.013Bekiaris-Liberis, N., & Krstic, M. (2011). Compensation of Time-Varying Input and State Delays for Nonlinear Systems. Journal of Dynamic Systems, Measurement, and Control, 134(1). doi:10.1115/1.4005278Besançon, G., Georges, D. & Benayache, Z. (2007). Asymptotic state prediction for continuous-time systems with delayed input and application to control. 2007 European control conference (ECC) (pp. 1786–1791).Engelborghs, K., Dambrine, M., & Roose, D. (2001). Limitations of a class of stabilization methods for delay systems. IEEE Transactions on Automatic Control, 46(2), 336-339. doi:10.1109/9.905705Fridman, E. (2001). New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems. Systems & Control Letters, 43(4), 309-319. doi:10.1016/s0167-6911(01)00114-1Fridman, E. (2014). Introduction to Time-Delay Systems. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-09393-2Fridman, E. (2014). Tutorial on Lyapunov-based methods for time-delay systems. European Journal of Control, 20(6), 271-283. doi:10.1016/j.ejcon.2014.10.001Furtat, I., Fridman, E., & Fradkov, A. (2018). Disturbance Compensation With Finite Spectrum Assignment for Plants With Input Delay. IEEE Transactions on Automatic Control, 63(1), 298-305. doi:10.1109/tac.2017.2732279Germani, A., Manes, C., & Pepe, P. (2002). A new approach to state observation of nonlinear systems with delayed output. IEEE Transactions on Automatic Control, 47(1), 96-101. doi:10.1109/9.981726Guo, L., & Chen, W.-H. (2005). Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. International Journal of Robust and Nonlinear Control, 15(3), 109-125. doi:10.1002/rnc.978Karafyllis, I., & Krstic, M. (2017). Predictor Feedback for Delay Systems: Implementations and Approximations. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-42378-4Krstic, M. (2008). Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch. Automatica, 44(11), 2930-2935. doi:10.1016/j.automatica.2008.04.010Léchappé, V., Moulay, E., Plestan, F., Glumineau, A., & Chriette, A. (2015). New predictive scheme for the control of LTI systems with input delay and unknown disturbances. Automatica, 52, 179-184. doi:10.1016/j.automatica.2014.11.003Léchappé, V., Moulay, E. & Plestan, F. (2016). Dynamic observation-prediction for LTI systems with a time-varying delay in the input. 2016 IEEE 55th conference on decision and control (CDC) (pp. 2302–2307).Manitius, A., & Olbrot, A. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 24(4), 541-552. doi:10.1109/tac.1979.1102124Mazenc, F. & Malisoff, M. (2016). New prediction approach for stabilizing time-varying systems under time-varying input delay. 2016 IEEE 55th conference on decision and control (CDC) (pp. 3178–3182).Mondie, S., & Michiels, W. (2003). Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Transactions on Automatic Control, 48(12), 2207-2212. doi:10.1109/tac.2003.820147Najafi, M., Hosseinnia, S., Sheikholeslam, F., & Karimadini, M. (2013). Closed-loop control of dead time systems via sequential sub-predictors. International Journal of Control, 86(4), 599-609. doi:10.1080/00207179.2012.751627Najafi, M., Sheikholeslam, F., Hosseinnia, S., & Wang, Q.-G. (2014). Robust H ∞ control of single input-delay systems based on sequential sub-predictors. IET Control Theory & Applications, 8(13), 1175-1184. doi:10.1049/iet-cta.2012.1004Sanz, R., Garcia, P., & Albertos, P. (2016). Enhanced disturbance rejection for a predictor-based control of LTI systems with input delay. Automatica, 72, 205-208. doi:10.1016/j.automatica.2016.05.019Sanz, R., García, P., & Albertos, P. (2018). A generalized smith predictor for unstable time-delay SISO systems. ISA Transactions, 72, 197-204. doi:10.1016/j.isatra.2017.09.020Sanz, R., García, P., Fridman, E. & Albertos, P. (2017). A predictive extended state observer for a class of nonlinear systems with input delay subject to external disturbances. 2017 IEEE 56th annual conference on decision and control (CDC) (pp. 4345–4350).Sanz, R., Garcia, P., Fridman, E., & Albertos, P. (2018). Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer. International Journal of Robust and Nonlinear Control, 28(6), 2457-2467. doi:10.1002/rnc.4027Shustin, E., & Fridman, E. (2007). On delay-derivative-dependent stability of systems with fast-varying delays. Automatica, 43(9), 1649-1655. doi:10.1016/j.automatica.2007.02.009Suplin, V., Fridman, E., & Shaked, U. (2007). Sampled-data H∞ control and filtering: Nonuniform uncertain sampling. Automatica, 43(6), 1072-1083. doi:10.1016/j.automatica.2006.11.024Yao, J., Jiao, Z., & Ma, D. (2014). RISE-Based Precision Motion Control of DC Motors With Continuous Friction Compensation. IEEE Transactions on Industrial Electronics, 61(12), 7067-7075. doi:10.1109/tie.2014.2321344Zhong, Q.-C. (2004). On Distributed Delay in Linear Control Laws—Part I: Discrete-Delay Implementations. IEEE Transactions on Automatic Control, 49(11), 2074-2080. doi:10.1109/tac.2004.83753

Enhanced extended state observer-based control for systems with mismatched uncertainties and disturbances

[EN] This paper presents an enhanced Extended State Observer (ESO)-based control strategy to deal with the disturbance attenuation problem for a class of non integral-chain systems subject to non-linear mismatched uncertainties and external disturbances. The proposed control strategy does not assume the integral-chain form and it is formed by a state-feedback plus a dynamic disturbance compensation term, which is designed to reject the disturbance effect in the system output. From a theoretical point of view, the proposed strategy is reduced to the conventional ESO when the integral chain form and the matched condition hold. In this sense, this paper is presented as an extension of the ESO principles to cover a wider class of systems. The theoretical results show that the internal zero-dynamics plays an important role in ESO-based control design. Also, the closed-loop stability is analyzed and some numerical simulations show the effectiveness of the proposal in comparison with previous ESO-based techniques.This work was partially supported by projects FPU15/02008, FPI-UPV 2014 and TIN2014-56158-C4-4-P-AR, Ministerio de Economia y Competitividad, Spain.Castillo-Frasquet, A.; García Gil, PJ.; Sanz Díaz, R.; Albertos Pérez, P. (2017). Enhanced extended state observer-based control for systems with mismatched uncertainties and disturbances. ISA Transactions. 73:1-10. https://doi.org/10.1016/j.isatra.2017.12.005S1107

Disturbance Observer-Based Controllers: operating principles and design strategies

[EN] During the past decades, the scientific interest on the linear disturbance observer-based controllers has notably increased, mainly, due to their good properties for handling changes or uncertainties in the systems. In this tutorial, these type of controllers are reviewed by analyzing their characteristic elements which are: i) the disturbed models, ii) the disturbance observer algorithms, and iii) the feedback control-laws as well as their main design-techniques. Some aspects of the control theory that motivate and support the use of these regulators are also described, including: the model uncertainties, its relevance within the robust control paradigm, and the capability of the disturbed models to handle uncertainties. The tutorial concludes with an ilustrative example on the closed-loop glucose control for diabetic people (artificial pancreas).[ES] Durante las últimas décadas, los reguladores lineales basados en observadores de perturbaciones han experimentado un interés creciente entre la comunidad científica, principalmente, debido a sus buenas propiedades para tolerar cambios o incertidumbres en los sistemas. En este tutorial se aborda una revisión de dichos reguladores, analizando sus elementos más característicos esdecir: i) los modelos con entradas de perturbación, ii) los algoritmos observadores de perturbaciones, y iii) el diseño de leyes decontrol , así como sus principales técnicas de diseño. Se consideran también algunos aspectos de la teoría del control que motivan y justifican la utilización de estos reguladores; principalmente: la incertidumbre de los modelos, su importancia dentro del paradigma del control robusto y la capacidad de los modelos perturbados para representar sistemas inciertos. El tutorial concluye con u nejemplo ilustrativo sobre el diseño de este tipo de reguladores para el control de glucosa en personas diabéticas (páncreas artificial).Este trabajo ha sido financiado por la Union Europea-Next Generation EU –proyecto Margarita Salas, MS/38, Universitat Politècnica de València, Ministerio de Universidades, España.Castillo, A.; García Gil, PJ.; Albertos, P. (2022). Reguladores basados en observadores de perturbaciones: principios de funcionamiento y métodos de diseño. Revista Iberoamericana de Automática e Informática industrial. 19(4):343-355. https://doi.org/10.4995/riai.2022.16856OJS34335519

A sparse mesh for Compact Finite Difference Fourier solvers with radius-dependent spectral resolution in circular domains

This paper presents a new method for the resolution of elliptic and parabolic equations in circular domains. It can be trivially extended to cylindrical domains. The algorithm uses a mixed Fourier-Compact Finite Difference method. The main advantage of the method is achieved by a new concept of mesh. The topology of the new grid keeps constant the aspect ratio of the cells, avoiding the typical clustering for radial structured meshes at the center. The reduction of the number of nodes has as a consequence the reduction in memory consumption. In the case of fluid mechanics problems, this technique also increases the time step for a constant Courant number. Several examples are given in the paper which show the potential of the method. (C) 2014 Elsevier Ltd. All rights reservedThis work was supported by the Spanish Government in the frame of the Project "Metodos LES para la simulacion de chorros multifasicos", grant ENE2010-18542. We also are very grateful to one of the referees for his/her work.Torregrosa, AJ.; Hoyas, S.; Gil, A.; García Galache, JP. (2014). A sparse mesh for Compact Finite Difference Fourier solvers with radius-dependent spectral resolution in circular domains. Computers and Mathematics with Applications. 67(6):1309-1318. https://doi.org/10.1016/j.camwa.2014.01.020S1309131867

Artificial Pancreas System With Unannounced Meals Based on a Disturbance Observer and Feedforward Compensation

© 2021 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] This brief is focused on the closed-loop control of postprandial glucose levels of patients with type 1 diabetes mellitus after unannounced meals, which is still a major challenge toward a fully autonomous artificial pancreas. The main limitations are the delays introduced by the subcutaneous insulin pharmacokinetics and the glucose sensor, which typically leads to insulin overdelivery. Current solutions reported in the literature typically resort to meal announcement, which requires patient intervention. In this brief, a disturbance observer (DOB) is used to estimate the effect of unannounced meals, and the insulin pharmacokinetics is taken into account by means of a feedforward compensator. The proposed strategy is validated in silico with the UVa/Padova metabolic simulator. It is demonstrated how the DOB successfully estimates and counteracts not only the effect of meals but also the sudden drops in the glucose levels that may lead to hypoglycemia. For unannounced meals, results show a median time-in-range of 80% in a 30-day scenario with high carbohydrate content and large intrasubject variability. Optionally, users may decide to announce meals. In this case, considering severe bolus mismatch due to carbohydrate counting errors, the median time-in-range is increased up to 88%. In every case, hypoglycemia is avoided.This work was supported in part by the Ministerio de Economia y Competitividad under Grant DPI2016-78831-C2-1-R and in part by the European Union through FEDER Funds.Sanz Diaz, R.; García Gil, PJ.; Diez, J.; Bondía Company, J. (2021). Artificial Pancreas System With Unannounced Meals Based on a Disturbance Observer and Feedforward Compensation. IEEE Transactions on Control Systems Technology. 29(1):454-460. https://doi.org/10.1109/TCST.2020.2975147S45446029

Experimental application of Takagi-Sugeno observers and controllers in a nonlinear electromechanical system

[EN] In this paper, a systematic methodology to design fuzzy Takagi-Sugeno observers and controllers will be used to estimate the angular positions and speeds, as well as to stabilise an experimental mechanical system with 3 degrees of freedom (fixed quadrotor). Takagi-Sugeno observers and controllers are compared to observers and controllers based on the linearized model, both designed with the same optimization criteria and design parameters. Experimental results confirm that Takagi-Sugeno models and observers behave similarly to linear ones around the linearization point, but have a better performance over a larger operating range, as intuitively expected.The work of Zs. Lendek was supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-RU-TE-2011-3-0043, contract number 74/05.10.2011. Spanish authors are grateful to grants DPI2011-27845-C02-01 (A. Sala), DPI2011-27845-C02-02 (R. Sanchis), DPI2011-28507-C02-01 (P. Garcia) from Spanish Government, and PROMETEOII/2013/004 (A. Sala, P. Garcia) from Generalitat Valenciana.Lendek, Z.; Sala, A.; García Gil, PJ.; Sanchis Llopis, R. (2013). Experimental application of Takagi-Sugeno observers and controllers in a nonlinear electromechanical system. Control Engineering and Applied Informatics. 15(4):3-14. http://hdl.handle.net/10251/150453S31415