Integral control on nonlinear spaces: two extensions

Zhifei Zhang 1, 2 Zhihao Ling 2 Alain Sarlette 3, 1
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, MINES ParisTech - École nationale supérieure des mines de Paris, CNRS - Centre National de la Recherche Scientifique : UMR8551
Abstract : This paper applies the recently developed framework for integral control on nonlinear spaces to two non-standard cases. First, we show that the property of perfect target stabilization in presence of actuation bias holds also if this bias is state dependent. This might not be surprising, but for practical purposes it provides an easy way to robustly cancel nonlinear dynamics of the uncontrolled plant. We specifically illustrate this for robust stabilization of a pendulum at arbitrary angle, a problem posed as non-trivial by some colleagues. Second, as previous work has been restricted to systems with as many control inputs as configuration dimensions, we here provide results for integral control of a non-holonomic system. More precisely, we design robust steering control of a rigid body under velocity bias.
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Zhifei Zhang, Zhihao Ling, Alain Sarlette. Integral control on nonlinear spaces: two extensions. IFAC conference on Nonlinear Control Systems (NOLCOS), International Federation of Automatic Control (IFAC), Aug 2016, Monterey, United States. ⟨hal-01395593⟩

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