Comparison of µ- and H-Synthesis Controllers 2 on an Experimental Typical Section

Abstract

An experimental comparison of H 2 -and ¹-synthesized utter suppression control systems was performed. A simple parametric uncertainty can be used to track changes in system dynamics as a function of dynamic pressure. The control system was implemented experimentally on a NACA 0012 test model of a typical section mounted in a low-speed wind tunnel. The pitching angle, ap angle, and plunge de ection of the airfoil were measured with sensors and fed back through the control compensator to generate a single control signal commanding the trailingedge ap of the airfoil. The model of the aeroelastic system, including the dynamics of the sensors and actuators in the bandwidth of interest, was obtained using system identi cation techniques. For comparison purposes, an H 2 control system with standard linear quadratic Gaussian weightings also was designed and implemented. When compared to the H 2 control system, the ¹-synthesis controller provided better disturbance rejection in the bandwidth of the unsteady aeroelastic dynamics. In addition, the ¹ controller required less control energy than the H 2 control system. The nal advantage of ¹-synthesis is the ability to design an aggressive ¹ control system that is stabilizing across the range of operating dynamic pressures. NomenclatureA; B; C; D = state-space representation of a system F u ; F l = upper and lower linear fractional transformations (LFT), respectively I = identity matrix J = cost functional K = controller L i = input return difference matrix, .I C KP/ L o = output return difference matrix, .I C PK/ P = generalized plant Q; R = performance and control penalties, respectively, for linear quadratic Gaussian (LQG) design u = control signal V ; W = process and sensor noise matrices, respectively, for LQG design V f = utter speed w = disturbance input to generalized plant w d ; w n = process and sensor noise, respectively, for LQG design y = measured plant variables z = output of generalized plant 1 = uncertainty model ¹ = structured singular value ¾ .!/ = plot of singular values vs frequency ! = natural circular frequency

Control of a Nonlinear Wing Section Using Leading- and Trailing-Edge Surfaces

“…1 designed a wing model for studies of flutter control, Wazak and Srinathkumar, 2 as well as Mukhopadhyay, 3 examined control with experimental validation for the active flexible wing, and Vipperman et al 4 developed a control strategy with experiment validation using µ-synthesis approaches.…”

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“…And once nonlinear aeroelastic models have reached a state of maturity sufficient for their consideration in the design process, then active and adaptive control can potentially provide for even greater flight vehicle performance. The discussion of active and adaptive control is beyond the scope of this paper, but the reader may wish to consult the work of Heeg [113], Lazarus, et al [114,115], Ko, et al [68][69][70], Block and Strganac [67], Vipperman, et al [116], Bunton and Denegri [8], Clark et al [117], Frampton et al [118], Rule et al [119], Richards et al [120] and Platanitis and Strganac [121].…”

Control of a Three-Degree-of-Freedom Airfoil with Limit-Cycle Behavior

“…The integration-basedinverse solver Genisa is essentiallya modication of that documented by Hess et al 2 and is driven by speci ed maneuver constraints. The starting point is, therefore, a mathematical de nition of the desired ight path to be followed by the subject vehicle.…”

“…In the context of helicopter ight dynamics, an inverse simulation generates the control time histories for the modeled helicopter performing a de ned task. To implement such a model in an inverse sense, it is necessary to adopt a numerical integration technique similar to that proposed by Hess et al 2 The generic inverse simulation algorithm (Genisa) used by Rutherford and Thomson is described in detail in Ref. 1, where the problem of numerical stability is also addressed.…”