Dual-rate sampled-data systems. Some interesting consequences from its frequency response analysis

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of General Systems on JUL 4 2019, available online: http://www.tandfonline.com/10.1080/03081079.2019.1608984[EN] The main goal of this contribution is to introduce a new procedure in order to analyse properly SISO dual-rate systems (DRS) and to provide straightforward answers to some common general questions about this kind of systems. Frequency response analysis based on DRS lifting modelling can lead to interesting results about stability margins or performance prediction. As a novelty, it is explained how to understand DRS frequency response and how to handle it for an easy computation of magnitude and phase margins keeping classical frequency domain methods. There are also some repetitive questions about DRS that can be analysed and answered properly using the results from this contribution: what the optimum relation between sampling periods is or what effects does delay have in a DRS. Every step is illustrated with examples that should clarify the understanding of the text.Salt Llobregat, JJ.; Alcaina-Acosta, JJ. (2019). Dual-rate sampled-data systems. Some interesting consequences from its frequency response analysis. International Journal of General Systems. 48(5):554-574. https://doi.org/10.1080/03081079.2019.1608984S55457448

Hierarchical Triple-Maglev Dual-Rate Control Over a Profibus-DP Network

© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising 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 worksThis paper addresses a networked control system application on an unstable triple-magnetic-levitation setup. A hierarchical dual-rate control using a Profibus-decentralized peripherals network has been used to stabilize a triangular platform composed of three maglevs. The difficulty in control is increased by time-varying network-induced delays. To solve this issue, a local decentralized H∞ control action is complemented by means of a lower rate output feedback controller on the remote side. Experimental results show good stabilization and reference position accuracy under disturbances.Manuscript received October 24, 2011; revised July 30, 2012; accepted September 9, 2012. Manuscript received in final form October 2, 2012. Date of publication November 12, 2012; date of current version December 17, 2013. The work of R. Piza, J. Salt, and A. Cuenca was supported in part by the Spanish Ministerio de Economia under Grant DPI2011-28507-C02-01, Grant DPI2009-14744-C03-03, and Grant ENE2010-21711-C02-01 and the Generalitat Valenciana Grant GV/2010/018. The work of A. Sala was supported in part by the Spanish Ministerio de Economia under Grant DPI2011-27845-C02-01 and the Generalitat Valenciana Grant PROMETEO/2008/088. Recommended by Associate Editor C. De Persis.Pizá, R.; Salt Llobregat, JJ.; Sala, A.; Cuenca Lacruz, ÁM. (2014). Hierarchical Triple-Maglev Dual-Rate Control Over a Profibus-DP Network. IEEE Transactions on Control Systems Technology. 22(1):1-12. https://doi.org/10.1109/TCST.2012.2222883S11222

A Multirate Control Strategy to the Slow Sensors Problem: An Interactive Simulation Tool for Controller Assisted Design

[EN] In many control applications, the sensor technology used for the measurement of the variable to be controlled is not able to maintain a restricted sampling period. In this context, the assumption of regular and uniform sampling pattern is questionable. Moreover, if the control action updating can be faster than the output measurement frequency in order to fulfill the proposed closed loop behavior, the solution is usually a multirate controller. There are some known aspects to be careful of when a multirate system (MR) is going to be designed. The proper multiplicity between input-output sampling periods, the proper controller structure, the existence of ripples and others issues need to be considered. A useful way to save time and achieve good results is to have an assisted computer design tool. An interactive simulation tool to deal with MR seems to be the right solution. In this paper this kind of simulation application is presented. It allows an easy understanding of the performance degrading or improvement when changing the multirate sampling pattern parameters. The tool was developed using Sysquake, a Matlab-like language with fast execution and powerful graphic facilities. It can be delivered as an executable. In the paper a detailed explanation of MR treatment is also included and the design of four different MR controllers with flexible structure to be adapted to different schemes will also be presented. The Smith's predictor in these MR schemes is also explained, justified and used when time delays appear. Finally some interesting observations achieved using this interactive tool are included.This work was supported in part by the Spanish Ministry of Economy and Competitiveness under Project DPI2012-31303. The authors J. Salt, A. Cuenca, are grateful to Grant TEC2012-31506, from the Spanish Ministry of Education. The work of A. Cuenca was supported in part by the Spanish Ministerio de Economia under Grant DPI2011-28507-C02-01.Salt Llobregat, JJ.; Cuenca Lacruz, ÁM.; Palau, F.; Dormido, S. (2014). A Multirate Control Strategy to the Slow Sensors Problem: An Interactive Simulation Tool for Controller Assisted Design. Sensors. 14(3):4086-4110. https://doi.org/10.3390/S140304086S4086411014

Optimal Control for Aperiodic Dual-Rate Systems With Time-Varying Delays

[EN] In this work, we consider a dual-rate scenario with slow input and fast output. Our objective is the maximization of the decay rate of the system through the suitable choice of the n-input signals between two measures (periodic sampling) and their times of application. The optimization algorithm is extended for time-varying delays in order to make possible its implementation in networked control systems. We provide experimental results in an air levitation system to verify the validity of the algorithm in a real plant.This work was supported in part by the Spanish Ministry of Economy and Competitiveness (MINECO) under the Projects DPI2012-31303 and DPI2014-55932-C2-2-R.Aranda-Escolástico, E.; Salt Llobregat, JJ.; Guinaldo, M.; Chacon, J.; Dormido, S. (2018). Optimal Control for Aperiodic Dual-Rate Systems With Time-Varying Delays. Sensors. 18(5):1-19. https://doi.org/10.3390/s18051491S119185Mansano, R., Godoy, E., & Porto, A. (2014). The Benefits of Soft Sensor and Multi-Rate Control for the Implementation of Wireless Networked Control Systems. Sensors, 14(12), 24441-24461. doi:10.3390/s141224441Shao, Q. M., & Cinar, A. (2015). System identification and distributed control for multi-rate sampled systems. Journal of Process Control, 34, 1-12. doi:10.1016/j.jprocont.2015.06.010Albertos, P., & Salt, J. (2011). Non-uniform sampled-data control of MIMO systems. Annual Reviews in Control, 35(1), 65-76. doi:10.1016/j.arcontrol.2011.03.004Cuenca, A., & Salt, J. (2012). RST controller design for a non-uniform multi-rate control system. Journal of Process Control, 22(10), 1865-1877. doi:10.1016/j.jprocont.2012.09.010Cuenca, Á., Ojha, U., Salt, J., & Chow, M.-Y. (2015). A non-uniform multi-rate control strategy for a Markov chain-driven Networked Control System. Information Sciences, 321, 31-47. doi:10.1016/j.ins.2015.05.035Kalman, R. E., & Bertram, J. E. (1959). General synthesis procedure for computer control of single-loop and multiloop linear systems (an optimal sampling system). Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry, 77(6), 602-609. doi:10.1109/tai.1959.6371508Khargonekar, P., Poolla, K., & Tannenbaum, A. (1985). Robust control of linear time-invariant plants using periodic compensation. IEEE Transactions on Automatic Control, 30(11), 1088-1096. doi:10.1109/tac.1985.1103841Bamieh, B., Pearson, J. B., Francis, B. A., & Tannenbaum, A. (1991). A lifting technique for linear periodic systems with applications to sampled-data control. Systems & Control Letters, 17(2), 79-88. doi:10.1016/0167-6911(91)90033-bLi, D., Shah, S. L., Chen, T., & Qi, K. Z. (2001). Application of dual-rate modeling to CCR octane quality inferential control. IFAC Proceedings Volumes, 34(25), 353-357. doi:10.1016/s1474-6670(17)33849-1Salt, J., & Albertos, P. (2005). Model-based multirate controllers design. IEEE Transactions on Control Systems Technology, 13(6), 988-997. doi:10.1109/tcst.2005.857410Nemani, M., Tsao, T.-C., & Hutchinson, S. (1994). Multi-Rate Analysis and Design of Visual Feedback Digital Servo-Control System. Journal of Dynamic Systems, Measurement, and Control, 116(1), 45-55. doi:10.1115/1.2900680Sim, T. P., Lim, K. B., & Hong, G. S. (2002). Multirate predictor control scheme for visual servo control. IEE Proceedings - Control Theory and Applications, 149(2), 117-124. doi:10.1049/ip-cta:20020238Xinghui Huang, Nagamune, R., & Horowitz, R. (2006). A comparison of multirate robust track-following control synthesis techniques for dual-stage and multisensing servo systems in hard disk drives. IEEE Transactions on Magnetics, 42(7), 1896-1904. doi:10.1109/tmag.2006.875353Wu, Y., Liu, Y., & Zhang, W. (2013). A Discrete-Time Chattering Free Sliding Mode Control with Multirate Sampling Method for Flight Simulator. Mathematical Problems in Engineering, 2013, 1-8. doi:10.1155/2013/865493Salt, J., & Tomizuka, M. (2014). Hard disk drive control by model based dual-rate controller. Computation saving by interlacing. Mechatronics, 24(6), 691-700. doi:10.1016/j.mechatronics.2013.12.003Salt, J., Casanova, V., Cuenca, A., & Pizá, R. (2013). Multirate control with incomplete information over Profibus-DP network. International Journal of Systems Science, 45(7), 1589-1605. doi:10.1080/00207721.2013.844286Liu, F., Gao, H., Qiu, J., Yin, S., Fan, J., & Chai, T. (2014). Networked Multirate Output Feedback Control for Setpoints Compensation and Its Application to Rougher Flotation Process. IEEE Transactions on Industrial Electronics, 61(1), 460-468. doi:10.1109/tie.2013.2240640Khargonekar, P. P., & Sivashankar, N. (1991). 2 optimal control for sampled-data systems. Systems & Control Letters, 17(6), 425-436. doi:10.1016/0167-6911(91)90082-pTornero, J., Albertos, P., & Salt, J. (2001). Periodic Optimal Control of Multirate Sampled Data Systems. IFAC Proceedings Volumes, 34(12), 195-200. doi:10.1016/s1474-6670(17)34084-3Kim, C. H., Park, H. J., Lee, J., Lee, H. W., & Lee, K. D. (2015). Multi-rate optimal controller design for electromagnetic suspension systems via linear matrix inequality optimization. Journal of Applied Physics, 117(17), 17B506. doi:10.1063/1.4906588LEE, J. H., GELORMINO, M. S., & MORARIH, M. (1992). Model predictive control of multi-rate sampled-data systems: a state-space approach. International Journal of Control, 55(1), 153-191. doi:10.1080/00207179208934231Mizumoto, I., Ikejiri, M., & Takagi, T. (2015). Stable Adaptive Predictive Control System Design via Adaptive Output Predictor for Multi-rate Sampled Systems∗∗This work was partially supported by KAKENHI, the Grant-in-Aid for Scientific Research (C) 25420444, from the Japan Society for the Promotion of Science (JSPS). IFAC-PapersOnLine, 48(8), 1039-1044. doi:10.1016/j.ifacol.2015.09.105Carpiuc, S., & Lazar, C. (2016). Real-Time Multi-Rate Predictive Cascade Speed Control of Synchronous Machines in Automotive Electrical Traction Drives. IEEE Transactions on Industrial Electronics, 1-1. doi:10.1109/tie.2016.2561881Roshany-Yamchi, S., Cychowski, M., Negenborn, R. R., De Schutter, B., Delaney, K., & Connell, J. (2013). Kalman Filter-Based Distributed Predictive Control of Large-Scale Multi-Rate Systems: Application to Power Networks. IEEE Transactions on Control Systems Technology, 21(1), 27-39. doi:10.1109/tcst.2011.2172444Donkers, M. C. F., Tabuada, P., & Heemels, W. P. M. H. (2012). Minimum attention control for linear systems. Discrete Event Dynamic Systems, 24(2), 199-218. doi:10.1007/s10626-012-0155-xQuevedo, D. E., Ma, W.-J., & Gupta, V. (2015). Anytime Control Using Input Sequences With Markovian Processor Availability. IEEE Transactions on Automatic Control, 60(2), 515-521. doi:10.1109/tac.2014.2335311Aranda Escolastico, E., Guinaldo, M., Cuenca, A., Salt, J., & Dormido, S. (2017). Anytime Optimal Control Strategy for Multi-Rate Systems. IEEE Access, 5, 2790-2797. doi:10.1109/access.2017.2671906Guinaldo, M., Sánchez, J., & Dormido, S. (2017). Control en red basado en eventos: de lo centralizado a lo distribuido. Revista Iberoamericana de Automática e Informática Industrial RIAI, 14(1), 16-30. doi:10.1016/j.riai.2016.09.007Van Loan, C. (1977). The Sensitivity of the Matrix Exponential. SIAM Journal on Numerical Analysis, 14(6), 971-981. doi:10.1137/0714065Hazan, E. (2016). Introduction to Online Convex Optimization. Foundations and Trends® in Optimization, 2(3-4), 157-325. doi:10.1561/2400000013Sala, A., Cuenca, Á., & Salt, J. (2009). A retunable PID multi-rate controller for a networked control system. Information Sciences, 179(14), 2390-2402. doi:10.1016/j.ins.2009.02.017Chacon, J., Saenz, J., Torre, L., Diaz, J., & Esquembre, F. (2017). Design of a Low-Cost Air Levitation System for Teaching Control Engineering. Sensors, 17(10), 2321. doi:10.3390/s1710232

Control Multifrecuencia en Tiempo Real Utilizando Herramientas CACSD

[ES] Ante la ausencia de una plataforma de simulación específica para sistemas con muestreo no-convencional, los autores desarrollaron durante varios años una aplicación validada en forma de una caja de herramientas en el entorno Simulink de Matlab – el "Multirate Control Toolbox". La herramienta permite el modelado, simulación y control multifrecuencia en tiempo real. Se presenta una aplicación de la herramienta en un entorno físico real y se muestra la potencialidad de un método de control multifrecuencia en el cual la selección de un esquema de muestreo permite la consecución de unos resultados inalcanzables en un ámbito convencional.Este trabajo fue posible debido al apoyo de la Universidad EAFIT, la cual de una manera clara y contundente apoya los proyectos de investigación realizados en los diferentes programas de la institución. Los aportes económicos y los recursos físicos fueron suficientes y su disponibilidad muy oportuna.Vélez, CM.; Salt, J. (2010). Control Multifrecuencia en Tiempo Real Utilizando Herramientas CACSD. Revista Iberoamericana de Automática e Informática industrial. 1(3):43-52. http://hdl.handle.net/10251/146617OJS43521

Dual-Rate Extended Kalman Filter Based Path-Following Motion Control for an Unmanned Ground Vehicle: Realistic Simulation

[EN] In this paper, a two-wheel drive unmanned ground vehicle (UGV) path-following motion control is proposed. The UGV is equipped with encoders to sense angular velocities and a beacon system which provides position and orientation data. Whereas velocities can be sampled at a fast rate, position and orientation can only be sensed at a slower rate. Designing a dynamic controller at this slower rate implies not reaching the desired control requirements, and hence, the UGV is not able to follow the predefined path. The use of dual-rate extended Kalman filtering techniques enables the estimation of the fast-rate non-available position and orientation measurements. As a result, a fast-rate dynamic controller can be designed, which is provided with the fast-rate estimates to generate the control signal. The fast-rate controller is able to achieve a satisfactory path following, outperforming the slow-rate counterpart. Additionally, the dual-rate extended Kalman filter (DREKF) is fit for dealing with non-linear dynamics of the vehicle and possible Gaussian-like modeling and measurement uncertainties. A Simscape Multibody (TM) (Matlab(R)/Simulink) model has been developed for a realistic simulation, considering the contact forces between the wheels and the ground, not included in the kinematic and dynamic UGV representation. Non-linear behavior of the motors and limited resolution of the encoders have also been included in the model for a more accurate simulation of the real vehicle. The simulation model has been experimentally validated from the real process. Simulation results reveal the benefits of the control solution.Grant RTI2018-096590-B-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF Away of making Europe" and Grant PRE2019-088467 funded by MCIN/AEI/10.13039/501100011033 and by "ESF Investing in your future".Carbonell-Lázaro, R.; Cuenca, Á.; Casanova Calvo, V.; Pizá, R.; Salt Llobregat, JJ. (2021). Dual-Rate Extended Kalman Filter Based Path-Following Motion Control for an Unmanned Ground Vehicle: Realistic Simulation. Sensors. 21(22):1-17. https://doi.org/10.3390/s21227557117212

Nonuniform Dual-Rate Extended Kalman-Filter-Based Sensor Fusion for Path-Following Control of a Holonomic Mobile Robot with Four Mecanum Wheels

[EN] This paper presents an extended Kalman-filter-based sensor fusion approach, which enables path-following control of a holonomic mobile robot with four mecanum wheels. Output measurements of the mobile platform may be sensed at different rates: odometry and orientation data can be obtained at a fast rate, whereas position information may be generated at a slower rate. In addition, as a consequence of possible sensor failures or the use of lossy wireless sensor networks, the presence of the measurements may be nonuniform. These issues may degrade the path-following control performance. The consideration of a nonuniform dual-rate extended Kalman filter (NUDREKF) enables us to estimate fast-rate robot states from nonuniform, slow-rate measurements. Providing these estimations to the motion controller, a fast-rate control signal can be generated, reaching a satisfactory path-following behavior. The proposed NUDREKF is stated to represent any possible sampling pattern by means of a diagonal matrix, which is updated at a fast rate from the current, existing measurements. This fact results in a flexible formulation and a straightforward algorithmic implementation. A modified Pure Pursuit path-tracking algorithm is used, where the reference linear velocity is decomposed into Cartesian components, which are parameterized by a variable gain that depends on the distance to the target point. The proposed solution was evaluated using a realistic simulation model, developed with Simscape Multibody (Matlab/Simulink), of the four-mecanum-wheeled mobile platform. This model includes some of the nonlinearities present in a real vehicle, such as dead-zone, saturation, encoder resolution, and wheel sliding, and was validated by comparing real and simulated behavior. Comparison results reveal the superiority of the sensor fusion proposal under the presence of nonuniform, slow-rate measurements.Grant RTI2018-096590-B-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe" and Grant PRE2019-088467 funded by MCIN/AEI/10.13039/501100011033 and by "ESF Investing in your future".Pizá, R.; Carbonell-Lázaro, R.; Casanova Calvo, V.; Cuenca, Á.; Salt Llobregat, JJ. (2022). Nonuniform Dual-Rate Extended Kalman-Filter-Based Sensor Fusion for Path-Following Control of a Holonomic Mobile Robot with Four Mecanum Wheels. Applied Sciences. 12(7):1-23. https://doi.org/10.3390/app1207356012312

A delay-dependent dual-rate PID controller over an ethernet network

n this paper, a methodology to design controllers able to cope with different load conditions on an Ethernet network is introduced. Load conditions induce time-varying delays between measurements and control. To face these variations an interpolated, delay-dependent gain scheduling law is used. The lack of synchronization is solved by adopting an event-based control approach. The dual-rate control action computation is carried out at a remote controller, whereas control actions and measurements are taken out locally at the controlled process site. Stability is proved in terms of probabilistic linear matrix inequalities. TrueTime simulations in an Ethernet case show the benefit of the proposal, which is later validated on an experimental test-bed Ethernet environment.Manuscript received June 07, 2010; revised September 05, 2010; accepted September 15, 2010. Date of publication October 18, 2010; date of current version February 04, 2011. The authors A. Cuenca, J. Salt, and R. Piza are grateful to Grant PAID06-08 by the Universidad Politecnica de Valencia, Grant dpi2009-14744-c03-03 from the Spanish Ministry of Education, and Grant gv/2010/018 by Generalitat Valenciana. In addition, A. Cuenca is grateful to Grant dpi2008-06737-c02-01 by the Spanish Ministry of Education, and A. Sala is grateful to the financial support of the Spanish Ministry of Education Research Grant dpi2008-06731-c02-01, and Generalitat Valenciana Grant prometeo/2008/088. Paper no. TII-10-06-0127.Cuenca Lacruz, ÁM.; Salt Llobregat, JJ.; Sala Piqueras, A.; Pizá Fernández, R. (2011). A delay-dependent dual-rate PID controller over an ethernet network. IEEE Transactions on Industrial Informatics. 7(1):18-29. doi:10.1109/TII.2010.2085007S18297

Delay-independent dual-rate PID controller for a packet-based networked control system

[EN] In this paper, a novel delay-independent control structure for a networked control system (NCS) is proposed, where packet-based control strategies with predictor-based and dual-rate control techniques are integrated. The control solution is able to cope with some networked communication problems such as time-varying delays, packet dropouts and packet disorder. In addition, the proposed approach enables to reduce network load, and usage of connected devices, while maintaining a satisfactory control performance. As a delay-independent control solution, no network-induced delay measurement is needed for controller implementation. In addition, the control scheme is applicable to open-loop unstable plants. Control system stability is ensured in terms of linear matrix inequalities (LMIs). Simulation results show the main benefits of the control approach, which are experimentally validated by means of a Cartesian-robot-based test-bed platform. (C) 2019 Elsevier Inc. All rights reserved.This work is funded by European Commission as part of Project H2020-SEC-2016-2017, Topic: SEC-20-BES-2016 Id: 740736 C2 Advanced Multi-domain Environment and Live Observation Technologies (CAMELOT). Part WP5 supported by Tekever ASDS, Thales Research & Technology, Viasat Antenna Systems, Universitat Politècnica de València, Fundação da Faculdade de Ciências da Universidade de Lisboa, Ministério da Defesa Nacional Marinha Portuguesa, Ministério da Administração Interna Guarda Nacional Republicana.Alcaina-Acosta, JJ.; Cuenca, Á.; Salt Llobregat, JJ.; Casanova Calvo, V.; Pizá, R. (2019). Delay-independent dual-rate PID controller for a packet-based networked control system. Information Sciences. 484:27-43. https://doi.org/10.1016/j.ins.2019.01.059S274348