Tracking in a class of nonminimum-phase systems with nonlinear internal dynamics via sliding mode control using method of system center

Shkolnikov, I.A.; Shtessel, Yuri B.

doi:10.1016/s0005-1098(01)00275-8

Cited by 126 publications

(107 citation statements)

References 11 publications

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“…The tracking control of this kind of system is highly challenging, because of the unstable internal dynamic, which would drive the system to be unbounded. Traditional controller design methods of nonlinear system, such as backstepping control, sliding mode control, and dynamic inversion, are not suitable for a nonlinear system with non-minimum phase characteric, 17,18 especially when input delay occurs. The nonlinear dynamic of HFVs is a nonminimum phase system, and the actuators of HFVs are fuel-to-air ratio È and elevator deflection e .…”

Section: Introductionmentioning

confidence: 99%

Adaptive variable structure control of input delay non-minimum phase hypersonic flight vehicles

Huang

Yan

2017

International Journal of Advanced Robotic Systems

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An adaptive variable structure control strategy is proposed for the output tracking control of input delay non-minimum hypersonic flight vehicles. The problem is challenging because of the complex nonlinearity of hypersonic flight vehicles and the existence of input delay. The nonlinear model of hypersonic flight vehicles is partially linearized, and a state tracking model is constructed based on the ideal internal dynamics of hypersonic flight vehicles. A filtered tracking error is introduced to handle the input delay. A variable structure control strategy is proposed for the stability of filtered tracking error system, and an adaptive law is established for the unknown perturbations. Finally, the effectiveness of the proposed control method is shown by the simulation results.

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Section: Introductionmentioning

confidence: 99%

Adaptive variable structure control of input delay non-minimum phase hypersonic flight vehicles

Huang

Yan

2017

International Journal of Advanced Robotic Systems

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“…A slightly modified version of this work can be found in [15]. However, plant uncertainties may negatively impact on the output tracking performance in inversion based controllers.[5] contains acceptance bounds on the size of the uncertainties under which is advantageous to use inverse feedforward for linear, time-invariant systems.Approximate and asymptotic output tracking in sliding modes for certain classes of non-minimum phase and uncertain nonlinear systems is reported in [16] and [17]. The key is in the definition of a proper output reference profile to be followed by the system that avoids unstable internal states.…”

mentioning

confidence: 99%

“…Approximate and asymptotic output tracking in sliding modes for certain classes of non-minimum phase and uncertain nonlinear systems is reported in [16] and [17]. The key is in the definition of a proper output reference profile to be followed by the system that avoids unstable internal states.…”

mentioning

confidence: 99%

Galerkin method and approximate tracking in a non-minimum phase bilinear system

Fossas¹,

Olm²

2007

Discrete &Amp; Continuous Dynamical Systems - B

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Abstract. The tracking control of non-minimum phase systems is nowadays an open and challenging field, because a general theory is still not available. This article proposes an indirect control strategy in which a key role is played by the inverse problem that arises and their approximate solutions. These are obtained with the Galerkin method, a standard functional analysis tool. A detailed study of the effect on the output caused by the use of an approximate input is performed. Error bounds are also provided. The technique is motivated through its implementation in basic, DC-to-DC nonlinear power converters that are intended to be used as DC-to-AC voltage sources.1. Introduction. Exact tracking of a known output reference for non-minimum phase systems is developed in [6] and [7] both for the time-invariant and time-varying cases. The method tries to determine a bounded input-state trajectory that achieves a desired output behavior with an inversion-based procedure. If this is possible, a composite control law is used in such a way that its first component produces exact tracking and the second one stabilizes the overall system once linearized about the nominal trajectory. A slightly modified version of this work can be found in [15]. However, plant uncertainties may negatively impact on the output tracking performance in inversion based controllers.[5] contains acceptance bounds on the size of the uncertainties under which is advantageous to use inverse feedforward for linear, time-invariant systems.Approximate and asymptotic output tracking in sliding modes for certain classes of non-minimum phase and uncertain nonlinear systems is reported in [16] and [17]. The key is in the definition of a proper output reference profile to be followed by the system that avoids unstable internal states. It is known as the stable system center

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“…S. I. Zinober, Applied Mathematics Department, University of Sheffield, Sheffield S10 2TN, UK, (email: A.Zinober@shef.ac.uk) nonminimum phase systems employs the method of stable system center [10], [11]. This technique is based on the transformation of nonminimum phase output tracking in causal systems to state variable tracking.…”

Section: Introductionmentioning

confidence: 99%

“…This technique is based on the transformation of nonminimum phase output tracking in causal systems to state variable tracking. The bounded state reference profiles are generated using custom-designed equations of the system center [10], [11]. The Padé approximations yield the time delay function model of a reasonable accuracy within a limited bandwidth [12].…”

Section: Introductionmentioning

confidence: 99%

Output Tracking via Sliding Modes in Causal Systems with Time Delay Modeled by Higher Order Pade Approximations

Kosiba

Liu²,

Shtessel³

et al.

International Workshop on Variable Structure Systems, 2006. VSS'06.

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.Abstract-Output tracking in a SISO causal uncertain nonlinear system with an output subject to a time delay is considered using sliding mode control. A higher order Padé approximation to a delay function with a known time delay is used to construct a model of a transformed system without a time delayed output and is employed in a feedback sliding mode control. This model functions as a predictor of the plant states and the plant output, but is of nonminimum phase due to the application of the Padé approximation. The method of the stable system center is used to stabilize the internal dynamics of this plant model, and a control is developed using a sliding surface to allow the plant to track a arbitrary reference profile given by an exogenous system with a known characteristic equation. Simulations of the system are performed for the plant model using a first, second and third order Padé approximations and a controller in plant feedback mode. Numerical examples for Padé approximations of increasing order are considered and compared.

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Tracking in a class of nonminimum-phase systems with nonlinear internal dynamics via sliding mode control using method of system center

Cited by 126 publications

References 11 publications

Adaptive variable structure control of input delay non-minimum phase hypersonic flight vehicles

Adaptive variable structure control of input delay non-minimum phase hypersonic flight vehicles

Galerkin method and approximate tracking in a non-minimum phase bilinear system

Output Tracking via Sliding Modes in Causal Systems with Time Delay Modeled by Higher Order Pade Approximations

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