Path following using transverse feedback linearization: Application to a maglev positioning system

Nielsen, Christopher; Fulford, Cameron; Maggiore, Manfredi

doi:10.1109/acc.2009.5159998

Cited by 38 publications

(37 citation statements)

References 18 publications

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“…Many magnetic levitation control design have been reported in the literature, including feedback linearization based controllers [4,6,[9][10][11], linear state feedback control design [6,12], the gain scheduling approach [13], observer-based control [5], neural network techniques [14], sliding mode controllers [8,15,16], backstepping control [17], model predictive control [18], cascade control [19] and PID controllers [20]. Since the governing differential equations are highly nonlinear, the nonlinear controllers are more attractive.…”

Section: Introductionmentioning

confidence: 99%

Cascade Control of Magnetic Levitation with Sliding Modes

Eroğlu

Ablay

2016

MATEC Web of Conferences

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Abstract. The effectiveness and applicability of magnetic levitation systems need precise feedback control designs. A cascade control approach consisting of sliding mode control plus sliding mode control (SMC plus SMC) is designed to solve position control problem and to provide a high control performance and robustness to the magnetic levitation plant. It is shown that the SMC plus SMC cascade controller is able to eliminate the effects of the inductance related uncertainties of the electromagnetic coil of the plant and achieve a robust and precise position control. Experimental and numerical results are provided to validate the effectiveness and feasibility of the method.

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Section: Introductionmentioning

confidence: 99%

Cascade Control of Magnetic Levitation with Sliding Modes

Eroğlu

Ablay

2016

MATEC Web of Conferences

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“…Firstly, it is desirable that the movement on the target manifold (tangential movement) can be influenced. Secondly, if the system is initialized exactly on the manifold (or more precisely in a corresponding controlled invariant subset of the state space) then it should stay on the manifold for all future times (in the nominal, undisturbed case) independent of the tangential movement [2]. This property is subsequently referred to as the invariance property.…”

Section: Introductionmentioning

confidence: 99%

“…when starting on the path (or in a corresponding controlled invariant subset of the state space) the system stays exactly on the path for all future times [1]. Note that trajectory tracking control does not necessarily share this property [2]. The paths are typically defined in the state space [5], [6] or output space [2], [7] of the system.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, we confine ourselves to the stabilization of manifolds in the flat output space, which renders the problem much simpler compared to the general case. In [1], [2], the stabilization of a one-dimensional manifold (curve) in the output space is considered where the motion along the curve shall meet certain application-specific requirements. In order to meet these requirements, the diffeomorphism mapping to TNF has to be completed by suitable functions determining the tangential dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Manifold stabilization and path-following control for flat systems with application to a laboratory tower crane

Böck

Kugi

2014

53rd IEEE Conference on Decision and Control

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This paper deals with the stabilization of manifolds for flat systems. Path-following control results as the special case of stabilizing a manifold with dimension one. The target manifold is defined in terms of the components of the flat output. A control strategy is developed which achieves the following objectives. Firstly, the error dynamics, which describe the deviation of the output from the target manifold, are to be asymptotically stabilized. Therefore, if the system is initialized such that all states of the error dynamics are zero, the invariance property holds. This means that in the nominal, undisturbed case the output of the system does not leave the target manifold for all future times. A further objective is that the movement of the system on the target manifold can be appropriately controlled. The degrees of freedom of this movement are given by the dimension of the manifold. Some nice features are gained by the restriction to flat systems. Amongst others, the controller which achieves the objectives of stabilization, invariance, and movement on the manifold can always be calculated in a systematic way. To this end, the equivalence of flat systems to linear controllable ones is exploited. The presented control methodology is applied to a laboratory experiment of a tower crane. The experimental results underline the feasibility of the proposed concept. 53rd IEEE Conference on Decision and Control

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“…In [12] Aguiar et al have used adaptive switched supervisory control combined with a non linear Lyapunov-based control to ensure the global convergence of the position tracking error to a small neighborhood of the origin, without assuring the convergence to zero. In spite of the inconvenience of convergence to a neighborhood, this work has been used as a base for many recent path following applications, such as [13], [14] and [15]. Lini et al [11] have provided theoretical results to show the connection between the geometric continuity of the trajectory and smoothness of control inputs under velocity, acceleration and jerk constraints.…”

Section: Introductionmentioning

confidence: 99%

Target-point based path following controller for car-type vehicle using bounded feedback

Laghrouche

Harmouche

Chitour

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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In this paper, we have studied the control problem of path following for car type vehicles. The target-point based path following problem has been transformed into a reference trajectory following problem, using bounded feedback control laws. The contribution of this work lies in the global asymptotic stability, without restrictions on initial conditions. The proof of global stability has been presented using Lyapunov based arguments, which show that the system converges to zero in boot-strap manner. The effectiveness of this controller has been illustrated through simulations.

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Path following using transverse feedback linearization: Application to a maglev positioning system

Cited by 38 publications

References 18 publications

Cascade Control of Magnetic Levitation with Sliding Modes

Cascade Control of Magnetic Levitation with Sliding Modes

Manifold stabilization and path-following control for flat systems with application to a laboratory tower crane

Target-point based path following controller for car-type vehicle using bounded feedback

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