Design and Experimental Validation of a Flutter Suppression Controller for the Active Flexible Wing

The synthesis and experimental validation of an active utter suppression controller for the Active Flexible Wing wind-tunnel model is presented. The design is accomplished with traditional root locus and Nyquist methods using interactive computer graphics tools and extensive simulation-based analysis. The design approach uses a fundamental understanding of the utter mechanism to formulate a simple controller structure to meet stringent design speci cations. Experimentally, the utter suppression controller succeeded in simultaneous suppression of two utter modes, signi cantly increasing the utter dynamic pressure despite modeling errors in predicted utter dynamic pressure and utter frequency. The utter suppression controller was also successfully operated in combination with another controller to perform utter suppression during rapid rolling maneuvers. Introduction Modern aircraft designs emphasize the reduction of structural weight to maximize e ciency and agility. Reduced structural weight, however, results in reduced sti ness and increases the likelihood of structural dynamic instabilities ( utter). Active utter suppression is an attractive solution to the problems associated with reduced weight. Developing methods to suppress utter and reduce structural loads by utilizing active control systems was an objective of the Active Flexible Wing (AFW) program. The AFW program was a joint venture between NASA Langley Research Center and Rockwell International, North American Aircraft. The program occurred in two phases. Only the second phase, which focused on active utter suppression, will be addressed herein. Two wind-tunnel tests were conducted during the second phase. These tests were performed in the Transonic Dynamics Tunnel (TDT) at NASA Langley with a wind-tunnel model of the Active Flexible Wing (see g. 1) that was built and supported by Rockwell. The goals of the AFW program were to develop and apply advanced control system design and analysis methodologies to utter suppression and maneuver load control. The program objectives as they pertain to utter suppression were to (1) develop mathematical aeroelastic models L-89-12445 Figure 1. AFW wind-tunnel model mounted in TDT. 1 of the wind-tunnel model, (2) design and implement control systems to perform active utter suppression and verify controller performance by means of windtunnel experiments, and (3) develop analysis tools to compare experimental and analytical controller performance (Noll et al. 1989). This paper focuses on the design and wind-tunnel test of an active utter suppression (AFS) system. The operation of the utter suppression controller in steady ight and while performing rapid rolling maneuvers is speci cally addressed. Developing such a system requires a mathematical model that accurately describes aeroelastic behavior, an understanding of the physical phenomena involved, and the ability to analyze the behavior of the system in the context of likely model errors. The role each of these aspects played in accomplishing the program objectives will be discussed herein with an emphasis on developing an understanding of key physical phenomena through a variety of analysis methods. Characterization of AFWWind-Tunnel Model in Flutter Wind-Tunnel Model and Digital Controller The AFW wind-tunnel model, depicted in gure 1, is an actively controlled, statically and aeroelastically scaled, full-span wind-tunnel model of an advanced tailless ghter aircraft. The fuselage is rigid, and the wings are exible. The vehicle is supported by a sting with a ball bearing and brake mechanism that allows the vehicle to be xed relative to the sting axis or free to roll about it (i.e., roll brake on and roll brake o , respectively). Four control surfaces, controlled by hydraulic actuators, are located on each wing semispan: leading edge outboard (LEO), leading edge inboard (LEI), trailing edge outboard (TEO), and trailing edge inboard (TEI). Only three of these surfaces (LEO, TEO, and TEI) were e ective for utter suppression. The vehicle is extensively instrumented with accelerometers, strain gauges, rotary variable di erential transducers, and a rate gyro. Of particular interest for active utter suppression are the four accelerometers on each wing semispan. Three of the accelerometers are located near the hinge line of the LEO, TEO, and TEI control surfaces near the surface midspan, and one is located near the wingtip at about midchord. A more detailed description of the wind-tunnel model is presented in Noll et al. (1989) and Miller (1988). The active utter suppression controller consists of a digital computer running at 200 samples per second and a variety of other electronic equipment that allows the digital computer to interface with the wind-tunnel model. In addition to computing the control system commands, the controller samples the analog vehicle responses, converts them to digital signals, and converts the digital control system outputs to analog control surface commands. The analog measurements are pre ltered by a rst-order, 25Hz antialiasing lter and can also be passed through notch lters (though this capability was not used in the control law described herein). A schematic diagram of the AFW wind-tunnel model and controller is depicted in gure 2. A detailed description of the digital controller is presented in Hoadley et al. (1991). AAA AAA AA Accelerometer s Control s Antialiasing & notch filters A | D Digital controller D | A Figure 2. Schematic of AFW wind-tunnel model and AFS controller. Mathematical Model The mathematical model of the AFW windtunnel model used for control law synthesis and analysis consists of representations of the structural and aerodynamic characteristics, the control surface actuator dynamics, wind-tunnel turbulence, and the digital controller dynamics (including the processing required to transfer signals to and from the vehicle). A detailed description of the mathematical model can be found in Buttrill and Houck (1990). The structural representation was developed by Rockwell and was provided to NASA Langley Research Center in a form that consisted of a lumped mass matrix and a structural in uence coe cient matrix. The mass and sti ness information was used to compute a set of in vacuo vibration mode shapes, frequencies, and generalized masses for the 10 lowest frequency elastic modes for both symmetric motion and antisymmetric motion. The structural vibration modes were generated for both the roll brake on conguration and the roll brake o con guration. The model was then modi ed to match natural vibration 2 frequencies measured during ground vibration tests. E ective modal viscous damping of 1.5 percent was assumed, since structural damping was not addressed in the structural modeling process. The modal information was then used to compute linear unsteady aerodynamics. The aerodynamic representations were generated with the Interaction of Structures, Aerodynamics, and Controls (ISAC) computer codes (Newsom et al. 1984 and Peele and Adams 1979). ISAC utilizes modal characteristics of the structure and a doublet lattice lifting surface method to compute unsteady aerodynamic force coe cients for a set of reduced frequencies for a given Mach number. The unsteady aerodynamic force coe cients at the various reduced frequencies were used to generate the rational function approximations that were then used to formulate mathematical models of the vehicle. The methods by which this was accomplished are documented in Noll et al. (1989) and Ti any and Adams (1988). The control surface actuator representations were generated with parameter estimation techniques to match frequency response data obtained by experiment. The experimental results indicate that the actuators could be accurately modeled over a wide frequency range, containing the predicted utter frequency, by third-order transfer functions with no numerator dynamics. Each actuator has a unique transfer function such that corresponding leftand right-side control surfaces have di erent actuator models. This is the primary source of asymmetry in the mathematical model. However, individual control surface rate and de ection limits were also modeled. Within the mathematical model, the digital controller was represented by a set of di erence equations to characterize the dynamic compensation and by a set of di erential equations to characterize the antialiasing lters. Representations of analog-todigital and digital-to-analog converters and quantization e ects were also part of the controller model. The complete mathematical model of the AFW wind-tunnel model was obtained by combining the structural, aerodynamic, control surface actuator, and digital controller representations described above. The model was implemented with the Advanced Continuous Simulation Language (ACSL) computer program (Anon. 1987). The linear equations of motion for the structural dynamics, unsteady aerodynamics, and controller dynamics are included. In addition, nonlinearities associated with control surface de ection limits, actuator rate limits, and quantization e ects were characterized. The e ects of wind-tunnel turbulence were also incorporated into the simulation model by using an appropriately calibrated Dryden spectrum representation (Buttrill and Houck 1990). Linear models, used extensively in the control system design and analysis process, were obtained by linearizing the ACSL model about equilibrium points at various conditions. Linear models were also obtained directly from ISAC. By generating linear models that addressed di erent boundary conditions (e.g., roll brake status), wind-tunnel operating conditions (e.g., dynamic pressure), modeling assumptions (e.g., number of modes, number of aerodynamic lags), etc., many issues regarding controller performance and robustness could readily be considered. This capability was extremely helpful in achieving the design goals. Flutter Mechanism The predicted symmetric dynamic characteristics of the AFW wind-tunnel model are summarized by the dynamic pressure root loci presented in gure 3. The root loci describe the variation in pole and zero locations with variations in dynamic pressure of the open-loop transfer function associated with symmetric tip accelerometer response due to symmetric TEO actuator command. The upper plot depicts the loci of all the symmetric structural modes contained in the model, while the lower plot depicts a close-up of the utter region. These root loci are representative of all the control surface and accelerometer pairs when symmetric deformations are considered. The root loci are also representative of the utter behavior for antisymmetric structural deformations with the roll brake on. The root loci in gure 3 predicted that the AFW wind-tunnel model would exhibit classical wing bending/torsion utter (Bisplingho and Ashley 1962). The utter mode is characterized by coupling between the rst wing bending mode and the rst wing torsion mode. At low dynamic pressures these two modes are distinct with characteristic bending and torsion mode shapes. As the dynamic pressure increases, these two modes become coupled so that the bending and torsion modal frequencies tend to coalesce to a common frequency and take on mode shapes that exhibit characteristics of both wing bending and wing torsion. Eventually, one mode becomes unstable and manifests itself as a divergent oscillation displaying both bending and torsion motions. 3