English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Received: 15 December 2019 Accepted: 27 February 2020 In this paper, a simple flatness condition for the two degree of freedom underactuated mechanical system has been derived. Differential geometry was used as a mathematical tool in the derivation of the flatness condition. The flatness condition has been found as a direct inner product between the covariant derivative of a vector field which annihilate the codistribution, that spanned by the force matrix and the force matrix itself. Several examples of underactuated mechanical systems are 2DOF systems, or mechanical systems underactuated by one control which can be reduced to 2DOF system. Systems that are classified as differentially flat have many useful features, which can be used in designing an effective controller for the nonlinear systems. The Translational Oscillator with Rotational Actuator (TORA) system is considered here as an example of a typical flat 2DOF underactuated mechanical system. The flat output is derived based on the obtained result here, and then a nonlinear controller is designed for a TORA system based on the flatness property, and using a Backstepping method to overcome the under actuation problem. The simulation results demonstrate the effectiveness of the proposed controller.

Simple Flatness Condition for 2DOF Underactuated Mechanical Systems with Application to Controller Design