An input-output sampled data model for a class of continuous-time nonlinear systems having no finite zeros (original) (raw)
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Advanced Tools for Nonlinear Sampled-Data Systems’ Analysis and Control
European Journal of Control, 2007
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IFAC Proceedings Volumes, 2001
The study of some structural properties, namely controllability and spectrum distribution, in a hybrid system composed of a continuous-time system controlled by a digital controller is carried out in the lifting framework. The novelty of our approach lies in the infinite-dimensional nature of the state-space in the lifted domain due to the fact that the system evolves over a temporal continuum as opposed to the finite-dimensional state-space with infinite-dimensional input/output systems currently used in the literature. Different concepts of controllability related directly to the continuous-time behavior of sampled-data systems are introduced, namely exact, approximate and null controllability. It is shown that the two former notions never occur in sampled-data systems while the latter notion is a generic property for these systems. Some facts regarding the fundamental input/ output structure of sampled-data systems from the control viewpoint are drawn from these results. The spectrum distribution of sampled-data feedback systems is also characterized. Copyright
On the role of sampling zeros in robust sampled-data control design
1998
In this paper, we investigate the implications for robust sampled-data feedback design of minimum phase sampling zeros appearing in the transfer function of discrete-time plants. Such zeros may be obtained by zero-order hold (ZOH) sampling of continuous-time models having relative degree two or greater. In particular, we address the robustness of sampled-data control systems to multiplicative uncertainty in the model of the continuous-time plant. We argue that lightly damped controller poles, which may arise from attempting to cancel, or almost cancel, sampling zeros of the discretized plant are likely to introduce peaks into the fundamental complementary sensitivity function near the Nyquist frequency. This in turn makes the satisfaction of necessary conditions for robust stability difficult for all but the most modest amounts of modeling uncertainty in the continuous-time plant. Some H 2-and H 1-optimal discrete-time and sampled data designs may lead to (near-) cancellation, and we therefore argue that their suitability is restricted.
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3rd IFAC Conference on Analysis and Design of Hybrid Systems (2009), 2009
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2012
0.9.2 Développement du logiciel lxi 0.9.3 Applications lxii General Introduction 1 1 general introduction 3 1.1 Nonlinear sampled-data control 3 xiii xiv contents 1.2 CAD tools in nonlinear control 8 1.3 Notations and mathematical aspects 10 1.3.1 The class of systems 10 1.3.2 Vector fields 11 1.3.3 Lie derivative 11 1.3.4 Comparison functions 12 1.3.5 Relative degree 13 1.3.6 Baker Campbell Haussdorf (BCH) exponent 13 1.3.7 Sampled-data systems 14 1.3.8 Example 1. 18 i theoretical developments 23 2 lyapunov stability of nonlinear systems 25 2.1 Lyapunov stability in continuous-time 25 2.1.1 The linear case 27 2.2 Lyapunov stability of controlled systems 29 2.3 Lyapunov stability in discrete time 30 2.3.1 The linear case 31 2.4 Lyapunov stability for sampled-data systems 32 2.4.1 The case of the emulation of continuous-time state-feedback controllers 34 2.5 Example 2. 38 3 nonlinear input-lyapunov matching under digital feedback 41 3.1 The concept of Input-Lyapunov matching 41 3.2 Controller approximation 44 3.3 Example 2-corrective terms 46 3.3.1 First order controller 46 References , 28 45u c x k (0.25) Ces expressions sont bien définies puisque par construction L g c L i f c V m−i = 0, ∀x k = 0. Remark 6. La solution approchée d'ordre p à m + 1 échelles de temps uδ p d stabilise asymptotiquement le système avec m connections en cascade avec une erreur O(δ p+1) sur la reproduction de V m , respectivement une erreur O(δ p+m+1) pour W. Cela signifie que le contrôleur à m multi-échelles de temps sera capable de maintenir toutes les propriétés de stabilisation des dynamiques internes. La première dynamique z, ce qui dans de nombreuses situations pratiques a un intérêt majeur, est favorisée par cette conception. L'approche multiéchelles peut être utilisée avec succès dans le cas de systèmes avec une chaîne d'intégrateurs, lorsque les solutions émulées ne fonctionnent pas, mème pour des périodes d'échantillonnage plus faibles. 0.2.4.5 Quelques observations concernant d'autres stratégies similaires Dans l'article de [Nešić & Teel 2006] une conception échantillonnée calculée sur l'approximation d'Euler du modèle continu est proposée. Les résultats obtenus assurent une stabilisation semi-globale et pra-c (t) = (f + αg)(x c (t)) + v(t)βg(x c (t)) (1.4) y c (t) = h(x c (t)) (1.5) with α(•), β(•) as smooth functions and v(t) as an external time-signal. 2 An analytic function is a function that is locally given by a convergent power series. Also, an analytic function is an infinitely differentiable function such that the Taylor series at any point x 0 in its domain converges to f(x) for x in a neighborhood of x 0. 3 By denoting U m the space of measurable and and locally bounded control input functions u, then a system (1.2) is forward complete if for ∀ x 0 ∈ IR n , u ∈ U m the solution x(x(0), t) of (1.2) corresponding to input u exists ∀t 0.
IEEE Transactions on Automatic Control, 2004
This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.
In this paper, we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems. Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods, and it preserves important structures of the nonlinear systems. Also, the form of Euler-Maruyama model is simple and easy to be calculated. The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems, and may be useful to many practical control applications, such as tracking control in mechanical systems. And the effectiveness of the approach is demonstrated by a simulation example.
Towards a Simple Sampled-Data Control Law for Stably Invertible Linear Systems
IFAC-PapersOnLine, 2020
A new high gain control law is proposed for stably invertible linear systems. The continuous-time case is first studied to set ideas. The extension to the sampled-data case is made difficult by the presence of sampling zeros. For continuous-time systems having relative degree greater than or equal to two, these zeros converge, as the sampling rate approaches zero, to either marginally stable or unstable locations. A methodology which specifically addresses the sampling zero issue is developed. The methodology uses an approximate model which includes, when appropriate, the asymptotic sampling zeros. The core idea is supported by simulation studies. Also, a preliminary theoretical analysis is provided for degree two, showing that the design based on the approximate model stabilizes the true system for the continuous and sampled-data cases.