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