A Convex Approach to Fault Tolerant Control

Peiman G. Maghami *NASA Goddard Space Flight Center, Greenbelt, MD 20771David E. Cox tNASA Langley Research Center, Hampton, VA 23581The design of control laws for dynamic systems with the potential for actuator failuresis considered in this work. The use of Linear Matrix Inequalities allows more freedom incontroller design criteria than typically available with robust control. This work proposesan extension of fault-scheduled control design techniques that can find a fixed controllerwith provable performance over a set of plants. Through convexity of the objectivefunction, performance bounds on this set of plants implies performance bounds on arange of systems defined by a convex huH. This is used to incorporate performancebounds for a variety of soft and hard failures into the control design problem.IntroductionThe control design of lightly damped dynamic sys-tems is a challenging area for incorporating fault tol-erance. Loss of an actuator or sensor can greatlydegrade, or even destabilize, the closedqoop perfor-mance. This is particularly true for optimal controllaws that are tuned to a specific operating condition.Ahhough robust control can account for real paramet-ric uncertaimy, in the case of full actuator failure theuse of broadband 100_ input uncertainty severely lim-its loop gains, and often results in conservative controllaws.An alternative approach is considered here thatmakes use of the flexibility offered by posing controldesign problems as Linear Matrix Inequalities (LMIs).The use of LMIs in control theory has been studiedextensively in recent years. _,2 Of particular interest isthe design of linear parameter varying (LPV) controllaws, thar are implicitly gain scheduled with changesin the plant. 3 One application of LPV control is inthe design of fault-scheduled (FS) controllers whichaxe scheduled with measured fault parameters in thesystem. Here we examine a modification to the FScontrol design that allows for fixed controllers and re-moves the need for griding the parazneter space.The design technique is tested on a simple coupledma_ss-spring-damper system. Although quite simplethis system possess the same qualitative characteristicsas more complex flexible body systems. Contro]lersare designed using the proposed LMI framework andanalyzed under various fault conditions. These fau/tsinclude hard failure - a complete loss of an actuatorand soft failures - dynamically altered capability of an*Senior Engineer, Fligh_ Dynamics and Control Branch, Se-nior Member AIAA.tResearch Engineer, Guidance and Control Branch.