# Dynamical modelling of a flexible motorised momentum exchange tether and hybrid fuzzy sliding mode control for spin-up

Chen, Yi (2010) Dynamical modelling of a flexible motorised momentum exchange tether and hybrid fuzzy sliding mode control for spin-up. PhD thesis, University of Glasgow.

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Printed Thesis Information: https://eleanor.lib.gla.ac.uk/record=b2747220

## Abstract

A space tether is a long cable used to couple
satellites, probes or spacecrafts to each other or to other masses, such as a spent booster rocket, space station, or an asteroid. Space tethers are usually made of thin strands of high-strength fibres or conducting wires, which range from a few hundred metres to several
kilometres and have a relatively small diameter. Space tethers can provide a mechanical connection between two space objects that enables a transfer of energy and momentum from one object to the other, and as a result they can be used to provide space propulsion
without consuming propellant. Additionally, conductive space tethers can interact with the Earth's magnetic field and ionospheric plasma to generate thrust or drag forces without expending propellant.

The motorised momentum exchange tether (MMET)
was first proposed by Cartmell in 1996 and published in 1998. The system comprises a specially designed tether connecting two payload modules, with a central launcher motor. For the purposes of fundamental dynamical modelling the launcher mass can be regarded as a two part assembly, where the rotor is attached to one end of each tether subspan, and the other side is the stator, which is attached to the rotor by means of suitable bearings. Both the launcher and the payload can be attached to the tether by means of suitable clamps or bearing assemblies, dependent on the requirements of the design.

The further chapters in this thesis focus on a series of dynamical models of the symmetrical MMET syste, including the dumbbell MMET system, the solid massless MMET system, the flexible massless MMET system, the solid MMET system and the discretised flexible MMET system. The models in this context have shown that including axial, torsional and pendular elasticity, the MMET systems have a
significant bearing on overall performance and that this effect should not be ignored in future, particularly for control studies. All subsequent analyses for control applications should henceforth include flexible compliance within the modelling procedure.

Numerical simulations have been given for all types of MMET models, in which, accurate and stable periodic behaviours are observed, including the rigid body motions, the tether spin-up and the flexible motions, with proper parameter settings. The MMET system's spin-up control methods design and analysis will henceforth be referenced on the results.

For the non-linear dynamics and complex control problem, it was decided to investigate fuzzy logic based controllers to maintain the desired length and length deployment rate of the tether. A standard two input
and one output fuzzy logic control (FLC) is investigated with numerical simulations, in which the control effects on the MMET system's spin-up are observed.

Furthermore, to make the necessary enhancement to the fuzzy sliding mode control, a specialised hybrid control law, named F$\alpha$SMC is proposed, which combines fuzzy logic control with a SkyhookSMC control law together, then it is applied for the control of motorised space tether spin-up coupled with an flexible oscillation phenomenon. It is easy to switch the control effects between the SkyhookSMC and the FLC modes when a proper value of $\alpha$ is selected $(0<\alpha<1)$ to balance the
weight of the fuzzy logic control to that of the SkyhookSMC control, and the hybrid fuzzy sliding mode controller is thus generated.

Next, the simulations with the given initial conditions have been devised in a connecting programme between the control code written in $MATLAB$ and the dynamics simulation code constructed within $MATHEMATICA$. Both the FLC and the hybrid fuzzy sliding mode control methods are designed for the control of spin-up of the discretised flexible MMET system with tether-tube subspans, and the results have shown the validated effects of both these control methods for the MMET system spin-up with included flexible oscillation.

To summarise, the objectives of this thesis are, firstly, to propose a series of new dynamical models for the motorised momentum exchange tethers; secondly, to discuss two types of control methods for the spin-up behaviour of a flexible motorised momentum exchange tether, which include a fuzzy logic control and a hybrid fuzzy sliding mode control. By the weight factor $\alpha$, fuzzy logic control and SkyhookSMC controllers can be balanced from one to each other, and there is observed difference for each of the elastic behaviour in the MMET system involving these MMET systems with different controllers - FLC($\alpha = 1$), F$\alpha$SMC($\alpha = 0.5$) and SkyhookSMC($\alpha = 0.0$). The results state the control effects for FLC, F$\alpha$SMC and FLC, which lead to stable spin-up behaviour with flexible oscillations.

Item Type: Thesis (PhD) Doctoral Motorised momentum exchange tether, fuzzy logic control, sliding mode control, spin-up, dynamical modelling T Technology > TJ Mechanical engineering and machinery College of Science and Engineering > School of Engineering Cartmell, Prof. Matthew and Lucas, Prof. Margaret 2010 Mr Yi Chen glathesis:2010-1844 Copyright of this thesis is held by the author. 25 May 2010 10 Dec 2012 13:47 http://theses.gla.ac.uk/id/eprint/1844