Event-based Stabilization of Nonlinear Time-Delay Systems

International audienceIn this paper, a universal formula is proposed for event-based stabilization of nonlinear time-delay systems affine in the control. The feedback is derived from the original one proposed by E. Sontag (1989) and previously extended to event-based control of nonlinear undelayed systems. Under the assumption of the existence of a control Lyapunov-Krasovsky functional, it enables smooth (except at the origin) asymptotic stabilization while ensuring that the sampling intervals do not contract to zero. Global asymptotic stability is obtain under the small control property assumption. Moreover, the control can be proved to be smooth anywhere under certain conditions. Some simulation results highlight the ability of the proposals

Event-Triggered Observer-based Output-Feedback Stabilization of Linear System with Communication Delays in the Measurements

International audienceIn this paper, an original framework is proposed for the stabilization of a linear system with delays in the measurements: i) an observer estimates the full state information of the plant from a partial measurement, ii) an event-based control technique computes and updates the control signal only when a certain condition is satisfied and iii) an event-based corrector updates the model used to calculate the control law when it deviates from the estimated state. It is notably proved that such a proposal renders the closed-loop system stable for larger delays in the measurements than in the classical continuous-time control case. Simulation results are provided

General Formula for Event-Based Stabilization of Nonlinear Systems with Delays in the State

International audienceIn this chapter, a universal formula is proposed for event-based stabilization of nonlinear systems affine in the control and with delays in the state. The feedback is derived from the seminal law proposed by E. Sontag (1989) and then extended to event-based control of affine nonlinear undelayed systems. Under the assumption of the existence of a control Lyapunov-Krasovskii functional (CLKF), the proposal enables smooth (except at the origin) asymptotic stabilization while ensuring that the sampling intervals do not contract to zero. Global asymptotic stability is obtained under the small control property assumption. Moreover, the control can be proved to be smooth anywhere under certain conditions. Simulation results highlight the ability of the proposed formula. The particular linear case is also discussed

Bounded attitude control of rigid bodies: Real-time experimentation to a quadrotor mini-helicopter

International audienceA quaternion-based feedback is developed for the attitude stabilization of rigid bodies. The control design takes into account a priori input bounds and is based on nested saturation approach. It results in a very simple controller suitable for an embedded use with low computational resources available. The proposed method is generic not restricted to symmetric rigid bodies and does not require the knowledge of the inertia matrix of the body. The control law can be tuned to force closed-loop trajectories to enter in some a priori fixed neighborhood of the origin in a finite time and remain thereafter. The global stability is guaranteed in the case where angular velocities sensors have limited measurement range. The control law is experimentally applied to the attitude stabilization of a quadrotor mini-helicopter

Position control system via active disturbance rejection for laser optical systems

[EN] In this work, an Active Disturbance Rejection Control scheme for a Laser Beam Stabilization system is presented in a pragmatic way. First, a Linear Extended State Observer is designed, which allows estimating external disturbances, non-model dynamics, and the transverse displacement speed of the beam. Subsequently, a control law is proposed for regulation and tracking tasks. The stability analysis in the Input-to-State-Stability framework shows that the closed-loop system, plant-observer-controller is stable when the total disturbance is viewed as the input, and the state is the beam position error. This analysis presents new perspectives to a now-classic result. The experimental results show the performance of the control scheme. Using the L2 norm and the Integral of the Squared Error, the closed-loop performance is evaluated and compared with three controls generally used in this type of systems: PID, observer-based state feedback, and linear quadratic gaussian regulator.[ES] En este trabajo se presenta de manera pragmática un esquema de control por rechazo activo a perturbaciones para un sistema de direccionamiento y estabilización de haz láser. Primeramente es diseñado un Observador Lineal de Estado Extendido, el cual permite estimar las perturbaciones externas e incertidumbres en el modelo, así como la velocidad de desplazamiento transversal del haz. Posteriormente, se propone una ley de control, la cual contiene términos de retroalimentación y precompensación, permitiendo realizar tareas de regulación y seguimiento. Mediante un análisis de estabilidad en el sentido entrada a estado, se muestra que el sistema en lazo cerrado, planta-observador-controlador, es robustamente estable, cuando la entrada es la perturbación total y el estado es el error de posición del haz. Dicho análisis presenta nuevas perspectivas en una técnica ahora madura. Los resultados experimentales muestran el funcionamiento del esquema de control y mediante la norma L2 y la Integral del Error Cuadrático se mide el desempeño en lazo cerrado, el cual es comparado con tres controles generalmente usados en este tipo de sistemas: PID, control por retroalimentación de estados con observador y regulador lineal cuadrático gaussiano.Benemérita Universidad Autónoma de PueblaGuerrero-Castellanos, JF.; González-Romeo, LL. (2021). Sistema de control de posición mediante rechazo activo de perturbaciones para sistemas ópticos láser. Revista Iberoamericana de Automática e Informática industrial. 19(1):61-73. https://doi.org/10.4995/riai.2021.14852OJS6173191Al-Alwan, A., Guo, X., N'Doye, I., Laleg-Kirati, T., Aug 2017. Laser beam pointing and stabilization by fractional-order PID control: Tuning rule and experiments. In: Proc. of the 2017 IEEE Conference on Control Technology and Applications (CCTA). https://doi.org/10.1109/CCTA.2017.8062699Alizadegan, A., Zhao, P., Nagamune, R., Chiao, M., 2018. Robust H∞ control of miniaturized optical image stabilizers against product variabilities. Con- trol Engineering Practice 80, 70 - 82. https://doi.org/10.1016/j.conengprac.2018.08.006Åstrom, K. J., Murray, R. M., 2010. Feedback systems: an introduction for scientists and engineers. Princeton university press.Baronti, F., Lazzeri, A., Lenzi, F., Roncella, R., Saletti, R., Saponara, S., 2009. Voice coil actuators: From model and simulation to automotive application. In: 2009 35th Annual Conference of IEEE Industrial Electronics. pp. 1805- 1810. https://doi.org/10.1109/IECON.2009.5414837Boyd, S. P., Barratt, C. H., 1991. Linear controller design: limits of performance. Prentice-Hall Englewood Cliffs, NJ.Carreno-Zagarra, J., Guzman, J., Moreno, J., Villamizar, R., 2019. Linear active disturbance rejection control for a raceway photobioreactor. Control Engineering Practice 85, 271-279. https://doi.org/10.1016/j.conengprac.2019.02.007Clark, R., 1961. Integral of the error squared as a performance index for automatic control systems. Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry 79 (6), 467-471. https://doi.org/10.1109/TAI.1961.6371690Deng, J., Xue, W., Zhou, X., Mao, Y., 2020. On disturbance rejection control for inertial stabilization of long-distance laser positioning with movable platform. Measurement and Control 53 (7-8), 1203-1217. https://doi.org/10.1177/0020294020935492Freidovich, L. B., Khalil, H. K., 2008. Performance recovery of feedback- linearization-based designs. IEEE Transactions on automatic control 53 (10), 2324-2334. https://doi.org/10.1109/TAC.2008.2006821Guerrero-Castellanos, J., Rifai, H., Arnez-Paniagua, V., Linares-Flores, J., Saynes-Torres, L., Mohammed, S., 2018. Robust active disturbance rejection control via control Lyapunov functions: Application to Actuated-Ank foot-Orthosis. Control Engineering Practice 80, 49 - 60. https://doi.org/10.1016/j.conengprac.2018.08.008Guo, B.-Z., Zhao, Z.-L., 2016. Active disturbance rejection control for nonlinear systems: An introduction. John Wiley & Sons.https://doi.org/10.1002/9781119239932Han, J., 2009. From PID to active disturbance rejection control. Transactions on Industry Electronics 56 (3), 900-906. https://doi.org/10.1109/TIE.2008.2011621Hernández-Méndez, A., Linares-Flores, J., Sira-Ram ́ırez, H., Guerrero- Castellanos, J., Mino-Aguilar, G., 2017. A backstepping approach to decentralized active disturbance rejection control of interacting boost converters. Transactions on Industry Applications 53 (4), 4063-4072. https://doi.org/10.1109/TIA.2017.2683441Kia, S. S., Van Scoy, B., Cortes, J., Freeman, R. A., Lynch, K. M., Martinez, S., June 2019. Tutorial on dynamic average consensus: The problem, its applications, and the algorithms. IEEE Control Systems Magazine 39 (3), 40-72. https://doi.org/10.1109/MCS.2019.2900783Kim, B.-S., S.Gibson, T-C. Tsao, June 2004. Adaptive control of a tilt mirror for laser beam steering. In: Proc. of the 2004 American Control Conference. https://doi.org/10.23919/ACC.2004.1384437Kim, Y., Keel, L., Bhattacharyya, S., 2003. Transient response control via characteristic ratio assignment. IEEE Transactions on Automatic Control 48 (12), 2238-2244. https://doi.org/10.1109/TAC.2003.820153Konadu, K. A., Yi, S., 2011. Design of controllers for a laser beam stabilizer using pid and observer-based state feedback control. In: 2011 ASME Early Career Technical Conference, ASME ECTC. Vol. 10. pp. 91-98.Konadu, K. A., Yi, S., Choi, W., Abu-Lebdeh, T., 2013. Robust positioning of laser beams using proportional integral derivative and based observer-feedback control. American Journal of Applied Sciences 10 (4), 374. https://doi.org/10.3844/ajassp.2013.374.387Landolsi, T., Dhaouadi, R., Aldabbas, O., 2011. Beam-stabilized optical switch using a voice-coil motor actuator. Journal of the Franklin Institute 348 (1), 1-11. https://doi.org/10.1016/j.jfranklin.2009.02.004Martinez, J., Sename, O., Voda, A., 2009. Modeling and robust control of Bluray disc servo-mechanisms. Mechatronics 19 (5), 715 - 725. https://doi.org/10.1016/j.mechatronics.2009.02.006Pérez-Arancibia, N., Chen, N., Gibson, J., Tsao, T.-C., 2006. Variable-order adaptive control of a microelectromechanical steering mirror for suppression of laser beam jitter. Optical Engineering 45 (10), 1 - 12. https://doi.org/10.1117/1.2363189Pérez-Arancibia, N., Gibson, J., Tsao, T.-C., June 2009. Frequency-weighted minimum-variance adaptive control of laser beam jitter. IEEE/ASME Transactions on Mechatronics 14 (3), 337-348. https://doi.org/10.1109/TMECH.2009.2017532Quanser, 2010. Laser beam stabilization instructor manual. Quanser Speciality Experiment Series: LBS Laboratory Workbook.Quanser, 2021. Qpide data acquisition device. URL: https://www.quanser.com/products/Sala, A., Pitarch, J. L., 2016. Optimisation of transient and ultimate inescapable sets with polynomial boundaries for nonlinear systems. Automatica 73, 82-87. https://doi.org/10.1016/j.automatica.2016.06.017Sira-Ramírez, H., Hernández-Méndez, A., Linares-Flores, J., Luviano-Juarez, A., 2016. Robust flat filtering dsp based control of the boost converter. Control Theory and Technology 14 (3), 224-236. https://doi.org/10.1007/s11768-016-6025-6Sira-Ramírez, H., Linares-Flores, J., Luviano-Juarez, A., Cortés-Romero, J., 2015. Ultramodelos globales y el control por rechazo activo de perturbaciones en sistemas no lineales diferencialmente planos. Revista Iberoamericana de Automática e Informática Industrial (RIAI) 12 (2), 133 - 144. https://doi.org/10.1016/j.riai.2015.02.001Sira-Ramírez, H., Luviano-Juarez, A., Cortés-Romero, J., 2011. Control lineal robusto de sistemas no lineales diferencialmente planos. Revista Iberoamericana de Automática e Informática Industrial RIAI 8 (1), 14-28. https://doi.org/10.1016/S1697-7912(11)70004-8Sira-Ramírez, H., Luviano-Juarez, A., Ramırez-Neria, M., Zurita-Bustamante, E., 2017. Active Disturbance Rejection Control of Dynamic Systems. Butterworth-Heinemann.Sontag, E. D., 2008. Input to State Stability: Basic Concepts and Results. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 163-220. https://doi.org/10.1007/978-3-540-77653-6_3Sontag, E. D., Wang, Y., 1995. On characterizations of the input-to-state stability property. Systems and Control Letters 24 (5), 351-360. https://doi.org/10.1016/0167-6911(94)00050-6Tran, M.-S., Hwang, S.-J., 2020. Design and simulation of electromagnetic linear actuators for jet dispensers. Applied Sciences 10 (5). https://doi.org/10.3390/app10051653Yue, Y., Song, Z., Aug 2015. An integral resonant control scheme for a laser beam stabilization system. In: Proc. of the 2015 IEEE International Conference on Information and Automation. https://doi.org/10.1109/ICInfA.2015.727965

Simple Lyapunov Sampling for Event-Driven Control

International audienceIn this paper, a simple Lyapunov sampling is proposed. Contrary to a periodic fashion which samples the system uniformly in time, an event-based scheme updates the control signal only when the system trajectory sufficiently changes. Furthermore, the present triggering mechanism is based on a Lyapunov function in order to enforce the events only when required from a stability point of view. Nevertheless, whereas the Lyapunov sampling mechanism initially introduced in Velasco et al. (2009) requires to execute a computationally heavy off-line algorithm, a fully on-line version is developed in this paper. The different approaches are tested (in simulation and practice) to show the efficiency of such an event-based control and, eventually, the performance remains ensured even if the constraint on the stability is relaxed

Improving control of quadrotors carrying a manipulator arm

International audienc

Control and Model-Aided Inertial Navigation of a Nonholonomic Vehicle

International audienceThe present work deals with the control and localization problem of wheeled-mobile robots with nonholonomic constraints. In the proposed method a simple nonlinear control law, composed of a position and heading direction controller, is designed to asymptotically stabilize the position error. The control law takes into account the constraints on the control signals in order to avoid saturation of the actuators. Furthermore, this paper considers a method of using the dynamic vehicle model and vehicle's nonholonomic constraints in order to aid position and attitude estimates provided by an Inertial Navigation System (INS). It is shown that dynamic model and vehicle's nonholonomic constraints can reduce the error growth in robot position estimates. Simulations are included to confirm the effectiveness of the proposed scheme

Event-triggered attitude control for flying robots using an event approach based on the control

International audienceThis paper presents the development of a quaternion-based nonlinear event-triggered control for the attitude stabilization of Flying robots. Firstly, it is proved the existence of a Control Lyapunov Function. Unlike some previously proposed schemes, the aim of this paper is to propose a new and simpler event function. The control law ensures the asymptotic stability of the closed-loop system to the desired attitude. The approach is validated in real-time using a quadrotor mini-helicopter. The experiments show that the event driven controller reduces the control update without deteriorating the closed-loop system performance

Biomimetic-Based Output Feedback for Attitude Stabilization of Rigid Bodies: Real-Time Experimentation on a Quadrotor

International audienceThe present paper deals with the development of bounded feedback control laws mimicking the strategy adopted by flapping flyers to stabilize the attitude of systems falling within the framework of rigid bodies. Flapping flyers are able to orient their trajectory without any knowledge of their current attitude and without any attitude computation. They rely on the measurements of some sensitive organs: halteres, leg sensilla and magnetic sense, which give information about their angular velocity and the orientation of gravity and magnetic field vectors. Therefore, the proposed feedback laws are computed using direct inertial sensors measurements, that is vector observations with/without angular velocity measurements. Hence, the attitude is not explicitly required. This biomimetic approach is very simple, requires little computational power and is suitable for embedded applications on small control units. The boundedness of the control signal is taken into consideration through the design of the control laws by saturation of the actuators' input. The asymptotic stability Micromachines 2015, 6 994 of the closed loop system is proven by Lyapunov analysis. Real-time experiments are carried out on a quadrotor using MEMS inertial sensors in order to emphasize the efficiency of this biomimetic strategy by showing the convergence of the body's states in hovering mode, as well as the robustness with respect to external disturbances