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TECHNICAL BRIEFS

Sampled-data Control of a Class of Nonlinear Flat Systems With Application to Unicycle Trajectory Tracking

[+] Author and Article Information
N. Léchevin

 Defence Research and Development Canada—Valcartier, 2459 Pie-XI N., Val-Belair, Qc, G3J 1X5, Canada and Université du Québec à Trois-Rivières, Trois-Rivières, Qc, G9A 5H7, Canada

C. A. Rabbath

Defence Research and Development Canada—Valcartier and Department of Mechanical Engineering, McGill University, Montreal, Qc, H3A 2K6, Canada

J. Dyn. Sys., Meas., Control 128(3), 722-728 (Oct 03, 2005) (7 pages) doi:10.1115/1.2234491 History: Received October 18, 2004; Revised October 03, 2005

In this paper we propose a flatness-based nonlinear sampled-data control approach for the trajectory tracking of nonlinear differentially flat systems that can be expressed in cascade form. The nonlinear sampled-data control method relies on the flatness property for the generation of appropriate trajectories, with the design of one-step predictive control laws, and on controller discretization by means of an averaging-like method. In the paper we demonstrate that the causality problem that might arise in the implementation is avoided by using an estimator based on numerical integration techniques of sufficiently high order. Stability-like properties are proved. Numerical simulations show that the proposed sampled-data control law offers the best closed-loop performance when compared with nonlinear direct digital design for the trajectory tracking of a rotorcraft-like UAV modeled as the unicycle. The synthesis of the nonlinear sampled-data control law takes advantage of the feedback linearizability property of the unicycle model. Furthermore, the proposed nonlinear sampled-data control does not rely on approximated discretization techniques and is computed from exponentially convergent steering trajectories that result from the stabilization of the linearized unicycle model.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Structure of sampled-data control system

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Figure 2

The control of Eq. 31 with (i) a flatness-based SD control, (ii) a CT flatness-based control law followed by a ZOH, (iii) a DT feedback linearization control, and (iv) a CT feedback linearization control followed by a ZOH. (a) T=1ms and zoom around 0.025s; (b) T=2ms and zoom around 0.025s.

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Figure 3

UAV position (x,y) with (a) the proposed method and (b) the CT controller and hold (T=30ms)

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Figure 4

UAV error position (x−xd,y−yd) with (a) the proposed method and (b) the CT controller and hold (T=30ms)

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Figure 5

UAV speed (V) and orientation (alpha) with (a) the proposed method (T=30ms) and (b) the CT controller and hold (T=5ms, 30ms)

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Figure 6

Discrete-time control signals (T=30ms)

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