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The Tethered Satellite System (TSS) consisting of the Shuttle, tether, and an Italian satellite, has complex and non-linear dynamics because of the spring-like behavior of the tether and its interaction with two six degrees-of-freedom end-bodies. The TSS has natural librational and longitudinal oscillations, whose characteristics change as the tether is deployed and retrieved. When the finite mass of the tether is properly modeled, the TSS also exhibits 'skip rope' motion, particularly if the motion is excited by the interaction between the geomagnetic field and electric current in the tether. A conventional control system based on the linearization of the system dynamics is employed in the onboard software. Its inputs are sensed length, length rate, and tension parameters and it is expected to maintain not only the length but also the in-plane librational angle. Due to the complexity of this problem and the recent success of fuzzy logic techniques in controlling systems with non-linear dynamics using imprecise measurements as input from sensors, a fuzzy logic based tether length controller has been developed and implemented into the TSS simulation to investigate the usefulness and robustness that can be achieved with fuzzy control. In this chapter, a concept which utilizes fuzzy membership functions for length, length rate, and voltage parameters, and the rulebase used in generating the control voltage signal is described. Initially, a simple proportional controller was created based on length error only. Later, the length rate error was included as input, and the rulebase was expanded. In order to have a fair comparison between the conventional and fuzzy controllers, tension feedback was not included as an input to the controllers since it is not an input to the conventional controller. Test results indicate that the fuzzy controller keeps the length error smaller throughout the mission, and the amplitude of the tension oscillations during the retrieval phase is also smaller. One surprising benefit, in addition to better length control, is smaller in-plane librational oscillations during the retrieval phase. Overall the results of the study indicate that fuzzy logic based control can provide the simplicity and robustness desired for complex tethered operations in space.
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