12,728 research outputs found
Input-output decoupling and linearization of nonlinear two-input two-output time-varying delay systems
International audienceIn this paper, we study the input-output decoupling and linearization of nonlinear two-input two-output time-varying delay systems. When working with delay systems, two problems may arise when constructing a feedback transformation for which the input-output map of the feedback modified systems is linear. The first issue is the boundedness of the control and the second one is its causality. We develop an algorithm allowing the construction of a causal and bounded feedback which permits to solve the input-output decoupling and linearization problem. The idea of our algorithm is to introduce, at each step, when the input-output decoupling is not possible, an artificial delay for the input that appears " too early " in the system. To that end, we propose, at each step, a precise procedure for defining a simple feedback transformation
Robustness analysis of discrete predictor-based controllers for input-delay systems
In this article, robustness to model uncertainties are analysed in the context of discrete predictor-based state-feedback controllers for discrete-time input-delay systems with time-varying delay, in an LMI framework. The goal is comparing robustness of predictor-based strategies with respect to other (sub)optimal state feedback ones. A numerical example illustrates that improvements in tolerance to modelling errors can be achieved by using the predictor framework.The authors are grateful for grant nos. DPI2008-06737-C02-01, DPI2008-06731-C02-01, DPI2011-27845-C02-01 and PROMETEO/2008/088 from the Spanish and Valencian governments.GonzĆ”lez Sorribes, A.; Sala, A.; GarcĆa Gil, PJ.; Albertos PĆ©rez, P. (2013). Robustness analysis of discrete predictor-based controllers for input-delay systems. International Journal of Systems Science. 44(2):232-239. https://doi.org/10.1080/00207721.2011.600469S232239442Boukas, E.-K. (2006). Discrete-time systems with time-varying time delay: Stability and stabilizability. Mathematical Problems in Engineering, 2006, 1-10. doi:10.1155/mpe/2006/42489Du, D., Jiang, B., & Zhou, S. (2008). Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay. International Journal of Systems Science, 39(3), 305-313. doi:10.1080/00207720701805982El Ghaoui, L., Oustry, F., & AitRami, M. (1997). A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 42(8), 1171-1176. doi:10.1109/9.618250Gao, H., & Chen, T. (2007). New Results on Stability of Discrete-Time Systems With Time-Varying State Delay. IEEE Transactions on Automatic Control, 52(2), 328-334. doi:10.1109/tac.2006.890320Gao, H., Wang, C., Lam, J., & Wang, Y. (2004). Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proceedings - Control Theory and Applications, 151(6), 691-698. doi:10.1049/ip-cta:20040822Gao, H., Chen, T., & Lam, J. (2008). A new delay system approach to network-based control. Automatica, 44(1), 39-52. doi:10.1016/j.automatica.2007.04.020Garcia , P , Castillo , P , Lozano , R and Albertos , P . 2006 . Robustness with Respect to Delay Uncertainties of a Predictor Observer Based Discrete-time Controller . Proceeding of the 45th IEEE Conference on Decision and Control . 2006 . pp. 199 ā 204 .Guo , Y and Li , S . 2009 . New Stability Criterion for Discrete-time Systems with Interval Time-varying State Delay . Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference . 2009 . pp. 1342 ā 1347 .HƤgglund, T. (1996). An industrial dead-time compensating PI controller. Control Engineering Practice, 4(6), 749-756. doi:10.1016/0967-0661(96)00065-2V.J.S. Leite, and Miranda, M.F. (2008), āRobust Stabilization of Discrete-time Systems with Time-varying Delay: An LMI Approachā,Mathematical Problems in Engineering, 2008, 15 pages (doi:10.1155/2008/875609)Liu, X. G., Tang, M. L., Martin, R. R., & Wu, M. (2006). Delay-dependent robust stabilisation of discrete-time systems with time-varying delay. IEE Proceedings - Control Theory and Applications, 153(6), 689-702. doi:10.1049/ip-cta:20050223Lozano, R., Castillo, P., Garcia, P., & Dzul, A. (2004). Robust prediction-based control for unstable delay systems: Application to the yaw control of a mini-helicopter. Automatica, 40(4), 603-612. doi:10.1016/j.automatica.2003.10.007Manitius, 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.1979.1102124Michiels, W., & Niculescu, S.-I. (2003). On the delay sensitivity of Smith Predictors. International Journal of Systems Science, 34(8-9), 543-551. doi:10.1080/00207720310001609057Palmor, Z.J. (1996), āTime-delay Compensation ā Smith Predictor and Its Modificationsā, inThe Control Handbook, ed. W.S. Levine, Boca Raton: CRC Press, pp. 224ā237Pan, Y.-J., Marquez, H. J., & Chen, T. (2006). Stabilization of remote control systems with unknown time varying delays by LMI techniques. International Journal of Control, 79(7), 752-763. doi:10.1080/00207170600654554Richard, J.-P. (2003). Time-delay systems: an overview of some recent advances and open problems. Automatica, 39(10), 1667-1694. doi:10.1016/s0005-1098(03)00167-5Wang, Q.-G., Lee, T. H., & Tan, K. K. (1999). Finite-Spectrum Assignment for Time-Delay Systems. Lecture Notes in Control and Information Sciences. doi:10.1007/978-1-84628-531-8He, Y., Wu, M., Han, Q.-L., & She, J.-H. (2008). Delay-dependentHācontrol of linear discrete-time systems with an interval-like time-varying delay. International Journal of Systems Science, 39(4), 427-436. doi:10.1080/00207720701832531Yue, D., & Han, Q.-L. (2005). Delayed feedback control of uncertain systems with time-varying input delay. Automatica, 41(2), 233-240. doi:10.1016/j.automatica.2004.09.006Zhang, B., Xu, S., & Zou, Y. (2008). Improved stability criterion and its applications in delayed controller design for discrete-time systems. Automatica, 44(11), 2963-2967. doi:10.1016/j.automatica.2008.04.01
Feedback linearization control for a distributed solar collector field
This article describes the application of a feedback linearization technique for control of a distributed solar collector field using the energy from solar radiation to heat a fluid. The control target is to track an outlet temperature reference by manipulating the fluid flow rate through the solar field, while attenuating the effect of disturbances (mainly radiation and inlet temperature). The proposed control scheme is very easy to implement, as it uses a numerical approximation of the transport delay and a modification of the classical control scheme to improve startup in such a way that results compared with other control structures under similar conditions are improved while preserving short commissioning times. Experiments in the real plant are also described, demonstrating how operation can be started up efficiently.Ministerio de Ciencia y TecnologĆa DPI2004-07444-C04-04Ministerio de Ciencia y TecnologĆa DPI2005-0286
Flat systems, equivalence and trajectory generation
Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft
A unified view on weakly correlated recurrent networks
The diversity of neuron models used in contemporary theoretical neuroscience
to investigate specific properties of covariances raises the question how these
models relate to each other. In particular it is hard to distinguish between
generic properties and peculiarities due to the abstracted model. Here we
present a unified view on pairwise covariances in recurrent networks in the
irregular regime. We consider the binary neuron model, the leaky
integrate-and-fire model, and the Hawkes process. We show that linear
approximation maps each of these models to either of two classes of linear rate
models, including the Ornstein-Uhlenbeck process as a special case. The classes
differ in the location of additive noise in the rate dynamics, which is on the
output side for spiking models and on the input side for the binary model. Both
classes allow closed form solutions for the covariance. For output noise it
separates into an echo term and a term due to correlated input. The unified
framework enables us to transfer results between models. For example, we
generalize the binary model and the Hawkes process to the presence of
conduction delays and simplify derivations for established results. Our
approach is applicable to general network structures and suitable for
population averages. The derived averages are exact for fixed out-degree
network architectures and approximate for fixed in-degree. We demonstrate how
taking into account fluctuations in the linearization procedure increases the
accuracy of the effective theory and we explain the class dependent differences
between covariances in the time and the frequency domain. Finally we show that
the oscillatory instability emerging in networks of integrate-and-fire models
with delayed inhibitory feedback is a model-invariant feature: the same
structure of poles in the complex frequency plane determines the population
power spectra
Force feedback linearization for higher-order electromechanical sigma-delta modulators.
Abstract A higher-order electromechanical sigmaādelta modulator can greatly improve the signal-to-noise ratio compared with a second-order loop that only uses the sensing element as a loop filter. However, the electrostatic force feedback on the proof mass is inherently nonlinear, which will produce harmonics in the output spectrum and limits the total signal-to-noise and distortion ratio. High performance inertial sensors, which use sigmaādelta modulators as a closed-loop control system, have strict requirements on the output signal distortion. In this paper, nonlinear effects from the force feedback and pick-off circuits are analysed and a strategy for force feedback linearization is put forward which can considerably improve the signal-to-noise and distortion ratio. A PCB prototype of a fifth-order electromechanical modulator with a bulk micromachined accelerometer was used to demonstrate the concept
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