Sampled-data adaptive control for a class of nonlinear systems with parametric uncertainties (original) (raw)
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Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convexlike form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.
IET Control Theory & Applications, 2020
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Indirect sampled-data control with sampling period adaptation
International Journal of Control, 2011
It is known that if a continuous-time feedback system is exponentially stable, then the corresponding sampled-data system obtained by sample-hold discretization with constant sampling period is also exponentially stable, provided that the sampling period τ > 0 is sufficiently small. In general it is difficult to estimate how small the sampling period has to be in order to achieve stability of the sampled-data system. In this paper, we present an adaptive mechanism for adjusting the sampling period. This mechanism has the properties that, for every initial state, (i) the adaptation of the sampling period terminates after finitely many time steps and (ii) the state of the adaptive sampled-data system is integrable and converges to zero as time goes to infinity.
Sampled-data control of a nonlinear system
Chemical Engineering Science, 1978
AM-Sampled-data propomonai control of an exothermlc CSTR has been stuched usmg the classu=al lmear analysis and by the apphcatm~ al the averagmg techmque In order to use the latter method. the piecewise contmuous functions m the system equatmns were first approxunated by delay terms and subsequently replaced by Taylor senes expansions The subsldlary system equations thus obtamcd were then analyzed both by the linear and averagmg method The predicted response closely approximates the actual system behaviour for sampling penods less than half the residence time WtZtODUCTtON an adequate representation IS [l] Sampled-data control of linear systems IS well documented m the hterature In treating non-linear systems tradltlonally, the system equatlens are first hneanzed and classical methods are then apphed to the derwed linear system q(e) = v(e-e,)(i + KM*-e,))
Sampled-data fuzzy controller for continuous nonlinear systems
Iet Control Theory and Applications, 2008
This paper presents the sampled-data fuzzy control of nonlinear systems. The consequents of the fuzzy controller rules are linear sampled-data sub-controllers. As a result, the fuzzy controller is a weighted sum of some linear sampled-data sub-controllers which can be implemented by a microcontroller or a digital computer to lower the implementation cost. Consequently, a hybrid fuzzy controller consisting of continuoustime grades of memberships and discrete-time sub-controller is resulted. The system stability of the fuzzy control system is investigated. The proposed fuzzy controller exhibits a favourable property to alleviate the conservativeness of the stability analysis.
Sampling-Period Influence in Performance and Stability in Sampled-Data Control Systems
SAE Technical Paper Series, 2003
As already verified experimentally in foregoing works [1, 2] the dimensioning of the sampling period in sampleddata systems (analog plant and digital controller) aiming principally the stability is a very important task due the increasing of the lawsuit of this kind of systems. However, the theory to study this nature of systems is not complete today. In this work we search for to give the initial steps for design of discrete controllers for sampled-data systems considering an expression for the aliasing.
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IEEE Transactions on Automatic Control, 1993
Robust adaptive sampled-data control of a class of linear systems under structured perturbations is considered. The controller is a time-varying state-feedback law having a fixed structure, containing an adjustable parameter, and operating on sampled values. The sampling period and the controller parameter are adjusted with simple adaptation rules. The resulting closed-loop system is shown to be stable for a class of unknown perturbations. The same result is also shown to be applicable to decentralized control of interconnected system.
Continuous control of sampled data systems with robustness against bounded measurement errors
Transactions of the Institute of Measurement and Control, 2017
This paper considers the design of a generalized hold function to be used for the control of sampled-data systems. The proposed method suggests a continuous controller for sampled data systems. Ultimate boundedness of the proposed method in the presence of bounded measurement errors is also shown for linear and nonlinear systems. In linear time invariant cases, a cost function is suggested for the sake of ultimate bound minimization. In addition, this can answer how we choose a sensor for a real system to get a desired control outcome. Eventually, the effectiveness of the proposed control method is investigated through simulation and experimental implementation.
Journal of Dynamic Systems, Measurement, and Control, 2019
This paper deals with the robust stabilization of a class of linear parameter varying (LPV) systems in the sampled data control case. Instead of using a state observer or searching for a dynamic output feedback, the considered controller is based on output derivatives estimation. This allows the stabilization of the plant with very large parameter variations or uncertainties. The proof of stability is based on the polytopic representation of the closed-loop under Lyapunov conditions and system transformations. The result is a control structure with only one parameter tuned via very simple conditions. Finally, the effectiveness of the proposed method is verified via a numerical example of a second-order LPV system.
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.