Modelling the Dynamics of an Arc-shaped Kite for Control Law Design: Design of a rigid body model for real-time simulation using a multi-body reference
S. G. C. de Groot · Research Repository (Delft University of Technology) · 2010
The need and interest for sustainable energy solutions is rising.A new branch in this field is high altitude wind power (HAWP).One novel concept is the Laddermill under development at the ASSET institute (TU Delft).The Laddermill uses kites to reel a tether from a drum which drives a generator.One of the key factors for success is the ability to control kites automatically.Currently successful test have been conducted with leading edge inflatable or arc-shaped kites.Arc-shaped kites are extensively used and developed in the field of kite surfing.Due to their high traction and control capabilities arc-shaped kites are the choice for the Laddermill prototypes.A literature review is conducted to obtain an overview of the current status of technology regarding arc-shaped kite modelling and control.For automatic control of kites several advanced control techniques exist like model predictive control and nonlinear dynamic inversion.Different kite models exist with specific applications.An example is the complex Multi-Body Kite model designed in Msc.Adams.It is concluded that fast models are required for online implementation.A formal methodology is developed to reduce the Multi-Body Arc-shaped Kite model to a Rigid Body Arc-shaped Kite model.In more general terms: any flying object modelled with multi-bodies can be reduced to a set of rigid body states.The numerous states of the Multi-Body model designed in Adams are reduced to a set of states describing the motion as a rigid body.For every body, flexible and rigid, holds that the inertial linear and rotational acceleration follow Newton's second law: the sum of external forces is equal to the time derivative of the linear momentum and the sum of external moments is equal to the time derivative of the angular momentum.On this principle the state reduction is applied and verified for the Multi-Body model.The acceleration, velocity and displacement components are obtained on the basis of conservation of linear momentum.The inertia tensor and angular momentum are derived with a particle based method.It is proven that the particle based method makes up a very good approximation to derive the rotational quantities.The Rigid Body model is developed to describe the dynamic motion of an arc-shaped kite.It is attempted to reduce the aerodynamics and structural deformation of the Multi-Body Kite model to a parametric aerodynamic model and a quasi-static structural model.To accomplish the reduction of the the Multi-Body Kite model to a Rigid Body Kite model it is required that the aerodynamics and the structural properties can be formulated by a set of rigid body states.The rigid body states are defined by the state reduction process.Due to the tight interaction between the flight condition and kite shape the aerodynamic model and structural model are variant with the flight condition.The aerodynamic model is formulated on the basis of Taylor expansions and written in dimensionless form.This results in a linear decomposition of the dependency of each state.The effective Modelling the Dynamics of an Arc-shaped Kite for Control Law Design vi Summary contribution of each aerodynamic state is given by respective dimensionless aerodynamic derivatives.The aerodynamic derivatives are obtained with the parameter identification technique.Flight test simulations are performed to identify the aerodynamic model.The structural model is constituted on a quasi-static basis by formulating functions describing the initial conditions of the flight test simulations.Functions are formulated for the inertia tensor properties, mean wing chord, wing span, projected surface area and the tether attachment points.Test simulations are performed to validate the Rigid Body model with respect to the Multi-Body model.The validation proves that the proposed methodology for model reduction is a qualitative manner for model reduction of the Multi-Body Kite model and for multi-body model reduction of flying objects in general.It results in kite models almost ten times faster than real-time, whereas simulating the Multi-Body Kite model in Adams takes more than ten times real-time.The development of an arc-shaped kite model which is appropriate for controller design has come to a detailed level.Control techniques which require fast and accurate models like model predictive control and nonlinear dynamic inversion can be designed on the basis of this modelling approach.For future work it is recommended to investigate on advanced model identification techniques and to perform a structural modal analysis. Modelling the Dynamics of an Arc-shaped Kite for Control Law Design