Tracking control of second-order chained form systems by cascaded backstepping

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Abstract

A design methodology is presented for tracking control of second-order chained form systems. The methodology separates the tracking-error dynamics, which are in cascade form, into two parts: a linear subsystem and a linear time-varying subsystem. The linear time-varying subsystem, after the first subsystem has converged, can be treated as a chain of integrators for the purposes of a backstepping controller. The two controllers are designed separately and the proof of stability is given by using a result for cascade systems. The method consists of three steps. In the first step we apply a stabilizing linear state feedback to the linear subsystem. In the second step the second subsystem is exponentially stabilized by applying a backstepping procedure. In the final step it is shown that the closed-loop tracking dynamics of the second-order chained form system are globally exponentially stable under a persistence of excitation condition on the reference trajectory. The control design methodology is illustrated by application to a second-order non-holonomic system. This planar manipulator with two translational and one rotational joint (PPR) is a special case of a second-order non-holonomic system. The simulation results show the effectiveness of our approach.
Original languageEnglish
Pages (from-to)95-115
JournalInternational Journal of Robust and Nonlinear Control
Volume13
Issue number2
DOIs
Publication statusPublished - 2003

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