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1 - S dhan Vol 33 Part 1 February 2008 pp 114 Printed in...

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S¯adhan¯a Vol. 33, Part 1, February 2008, pp. 1–14. © Printed in India LQG controller designs from reduced order models for a launch vehicle ASHWIN DHABALE, R N BANAVAR and M V DHEKANE Systems and Control Engineering, Indian Institute of Technology Bombay, Mumbai 400 076 Control and Guidance Group, Vikram Sarabhai Space Centre, Indian Space Research Organization, Thiruvananthapuram 695 022 e-mail: [email protected] MS received 6 April 2006; revised 28 August 2007 Abstract. The suppression of liquid fuel slosh motion is critical in a launch vehicle (LV). In particular, during certain stages of the launch, the dynamics of the fuel interacts adversely with the rigid body dynamics of the LV and the feedback controller must attentuate these effects. This paper describes the effort of a multi- variable control approach applied to the Geosynchronous Satellite Launch Vehicle (GSLV) of the Indian Space Research Organization (ISRO) during a certain stage of its launch. The fuel slosh dynamics are modelled using a pendulum model anal- ogy. We describe two design methodologies using the Linear-Quadratic Gaussian (LQG) technique. The novelty of the technique is that we apply the LQG design for models that are reduced in order through inspection alone. This is possible from a perspective that the LV could be viewed as many small systems attached to a main body and the interactions of some of these smaller systems could be neglected at the controller design stage provided sufficient robustness is ensured by the controller. The first LQG design is carried out without the actuator dynamics incorporated at the design stage and for the second design we neglect the slosh dynamics as well. Keywords. Launch vehicle; fuel slosh; LQG controller design. 1. Introduction The wave motion of liquids in finite containers, commonly known as slosh, is known to have adverse effects on aerospace vehicles Abramson (1966), Dodge & Garza (1967). For example, propellant slosh in rockets can have a detrimental effect during lift off, while fuel slosh in aircrafts and spacecrafts can effect control system performance during vehicle manoeuvers. To mitigate these effects a variety of techniques have been proposed including the use of baffles and dampers. These techniques are inherently passive in nature since energy dissipation is primary goal. To go beyond passive slosh suppression, several researches have investigated the feasibility of applying active feedback control (Reyhanoglu et al 1999, 2000). In this paper, the control of a LV with significant fuel slosh dynamics is considered. The objective is to simultaneously control the rigid body motion while suppressing the sloshing of 1
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2 Ashwin Dhabale, R N Banavar and M V Dhekane the fuel, using only the control effectors (strap-ons) that act on the rigid vehicle. Suppression of the unactuated fuel slosh degree of freedom must be achieved through the system coupling.
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