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Meeting	ACGS Committee Meeting 98 - Williamsburg - October 2006
Agenda Location	7 SUBCOMMITTEE C - AVIONICS AND SYSTEM INTEGRATION 7.3 Switching Systems in Attitude Control
Title	Switching Systems in Attitude Control
Presenter	Prof. Karl Kienitz
Affiliation	Instituto Technolsgico de Aeronautica, Sco Josi dos Campos, SP, Brazil
Available Downloads*	presentation
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Abstract	Launch and space vehicles may use on-off thrusters as actuators for attitude control. Thrusters produce discontinuous control actions and are subject to switching constraints. In practical applications, switching constraints have been typically accommodated or accounted for with ad-hoc approaches, sometimes at the expense of system’s performance. This is an overview presentation that reports on ongoing work concerned with:  analysis of system behavior when actuators are operated at the limits of their switching constraints;  systematic handling of switching constraints at control design time.  Common approaches for thruster activation logic are direct activation and pulse modulation. The first part of the talk is devoted to pulse modulation. Pulse modulators convert continuous input commands in a sequence of switching signals suitable for the command of on-off thrusters. Discussed in this talk is a pulse modulation scheme based on a set of modulation curves which explicitly considers switching restrictions and implements arbitrary bounded functions between constant modulator input and averaged modulator output. Such an approach is particularly well suited for application in attitude control systems. The use of this modulation scheme does not rely on time-consuming tuning strategies. The second part of the talk addresses dynamical behavior patterns that may occur when actuators with switching restrictions are operated in direct activation, which consists of the use of a non-linear actuator “as is”. Based on an example attitude control system it is shown how some unusual motions can be observed arising from periodic attractors by means of bifurcations. During recent research on the issue of limit cycle control for systems with minimally spaced switching-times, it was observed that the optimal control parameter set, which guarantees minimum amplitude and minimum fuel consumption, lies on the frontier where the system bifurcates into nonperiodic persistent motion. Here the concern with the robustness of an optimal controller arises. In order to evaluate the system’s robust performance, some time is devoted to understanding these nonperiodic persistent motions. In particular, it is desirable to clarify how performance is affected by the emergence of these motions, and whether their amplitude or their appearance can be predicted. Dynamical systems tools, such as bifurcation diagrams, Poincaré maps and Lyapunov spectrum, can be used to characterize these motions. Their stability is verified and amplitudes predicted. Moreover, the coexistence of multiple attractors for a given value of the control parameter (multistability) is observed, and chaotic attractors are found. The last part of the talk addresses the issue of controller design for systems with actuators operated in direct activation, aiming at robust limit cycling behavior, i.e. avoiding nonperiodic motion. It is shown how to tackle such design problem via the describing function framework and the Tsypkin/Hamel method. Advantages and disadvantages of these approaches as well as the operation of controllers near bifurcations borders are addressed. Throughout the talk, open problems and directions for further research are outlined.