Alejandro J. Malo Tamayo, Juan M Ibarra Zannatha, and Santos M Orozco Soto
under-actuated system control, spatial operator algebra, control flow diagram matrix, input-output feedback linearization
This paper deals with the modelling of multi-rotors using Spatial Operator Algebra and their control by feed- back linearization. Two dynamic models are presented; one where the speeds are projected on the inertial frame and other where the speeds are projected on the vehicle frame. Since a standard quadrotor is an under-actuated system, to understand it, the control flow diagram, proposed by Seto and Baillieul for this kind of systems, was drawn. Here the data for the hover equilibrium is presented as a ma- trix (an original contribution of this paper). It gives a very clear view of the causal relationships between variables of the system. This led to the partial input-output feedback linearization of the system, rendering linear the attitude- elevation (φ, θ, ψ, z) control and making posible, from it, the yaw-position (ψ, x, y, z) control. A control Lyapunov function is proposed to proof the stability of the controls. Simulation results for both controls are presented.
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