David E. Cox

Radiation modal expansion: Application to active structural acoustic control

This paper demonstrates active structural acoustic control using multiple input/output adaptive sensoriactuators combined with radiation filters and a feedback control paradigm. A new method of reduced order modeling/design of radiation filters termed radiation modal expansion (RME) is presented. For the experiments detailed in this paper, the RME technique reduced the modeling of the radiation matrix from 400 transfer functions to 6 transfer functions (multiplied by a constant transformation matrix). Experimental results demonstrate reductions of radiated sound power on the order of 5 dB over the bandwidth of 0-800 Hz.

Experimental Feedback Control of Flow Induced Cavity Tones

Discrete-time, linear quadratic methods were used to design feedback controllers for reducing tones generated by flow over a cavity. The dynamics of a synthetic-jet actuator mounted at the leading edge of the cavity as observed by two microphones in the cavity were modeled over a broad frequency range using state space models computed from experimental data. Variations in closed loop performance as a function of model order, control order, control bandwidth, and state estimator design were studied using a cavity in the Probe Calibration Tunnel at NASA Langley Research Center. The controller successfully reduced the levels of multiple cavity tones at the tested flow speeds of Mach 0.275,0.35, and 0.45. In some cases, the closed loop results were limited by excitation of sidebands of the cavity tones, or the creation of new tones at frequencies away from the cavity tones. The models were not able to account for nonlinear dynamics, such as interactions between tones at different frequencies. Nonetheless, the results validate the combination of optimal control and experimentally generated state space models for the cavity tone problem.

MULTI-VARIABLE STRUCTURAL ACOUSTIC CONTROL WITH STATIC COMPENSATION

The active control of turbulent boundary layer noise in commercial aircraft has gained significant interest in recent years, and, due to the stochastic nature of the disturbance, feedback control strategies are required. Linear quadratic Gaussian control has been proposed in the past [Baumann et al., J. Acoust. Soc. Am. (1991)], but compensators resulting from such control approaches are typically quite involved. The thrust of the current effort is to demonstrate that acceptable performance in structural acoustic control can be achieved with static compensation implemented through a multiple input, multiple output (MIMO) array of colocated transducers. Since static compensation requires a matrix of constant gains, it is easily realized in analog or digital hardware. By augmenting the system dynamics to include radiation filters, the dual Levine–Athans algorithm was implemented to design the appropriate static compensator. Results for various MIMO control cases are presented.

Analysis of Control Strategies for Aircraft Flight Upset Recovery

This paper proposes a framework for studying the ability of a control strategy, consisting of a control law and a command law, to recover an aircraft from ight conditions that may extend beyond the normal ight envelope. This study was carried out (i) by evaluating time responses of particular ight upsets, (ii) by evaluating local stability over an equilibrium manifold that included stall, and (iii) by bounding the set in the state space from where the vehicle can be safely own to wings-level ight. These states comprise what will be called the safely recoverable ight envelope (SRFE), which is a set containing the aircraft states from where a control strategy can safely stabilize the aircraft. By safe recovery it is implied that the tran- sient response stays between prescribed limits before converging to a steady horizontal ight. The calculation of the SRFE bounds yields the worst-case initial state corresponding to each control strategy. This information is used to compare alternative recovery strategies, determine their strengths and limitations, and identify the most e ective strategy. In regard to the control law, the authors developed feedback feedforward laws based on the gain scheduling of multivariable controllers. In regard to the command law, which is the mechanism governing the exogenous signals driving the feed- forward component of the controller, we developed laws with a feedback structure that combines local stability and transient response considera- tions. The upset recovery of the Generic Transport Model, a sub-scale twin-engine jet vehicle developed by NASA Langley Research Center, is used as a case study.

INDIRECT IDENTIFICATION OF LINEAR STOCHASTIC SYSTEMS WITH KNOWN FEEDBACK DYNAMICS

An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall dosed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open.loop plant dynamics from the identified rinsed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.

Aerodynamic Model Reduction Through Balanced Realization

ERODYNAMIC model reduction based on internal balancing is examined for incompressible potential flow and is shown to allow signification reduction in model complexity. The technique wa sv alidated against classical two-dimensional incompressible unsteady results, as well as an aeroelastic flutter boundary calculation. In particular, new insight is given into the relationship between balanced aerodynamic states and the fundamental physics of airfoil and wing motion. The form of the principal retained states suggests that the physics of a few dominant limiting-case airfoil motions characterize the flow. Comparison with exact solutions for a twodimensional case are shown to illustrate this point. A popular technique for aerodynamic model reduction is to per

Active control design for acoustic radiation using mixed‐norm optimization

Linear matrix inequalities were applied to design a mixed H2/H(infinity) feedback control compensator for a structural acoustic system. The compensator was designed to minimize the H2 norm of radiation filters while constraining the H(infinity) norm through the control path to be less than unity. A trade-off between minimizing sound power radiated and maximum rms gain in the control path resulted in a reliable and robust means of designing compensators for structural acoustic control.

Iterative LQG Controller Design Through Closed-Loop Identification

This paper presents an iterative Linear Quadratic Gaussian (LQG) controller design approach for a linear stochastic system with an uncertain open-loop model and unknown noise statistics. This approach consists of closed-loop identification and controller redesign cycles. In each cycle, the closed-loop identification method is used to identify an open-loop model and a steady-state Kalman filter gain from closed-loop input/output test data obtained by using a feedback LQG controller designed from the previous cycle. Then the identified open-loop model is used to redesign the state feedback. The state feedback and the identified Kalman filter gain are used to form an updated LQC controller for the next cycle. This iterative process continues until the updated controller converges. The proposed controller design is demonstrated by numerical simulations and experiments on a highly unstable large-gap magnetic suspension system.

Interaction Metrics for Feedback Control of Sound Radiation from Stiffened Panels

Interaction metrics developed for the process control industry are used to evaluate decentralized control of sound radiation from bays on an aircraft fuselage. The metrics are applied to experimentally measured frequency response data from a model of an aircraft fuselage. The purpose is to understand how coupling between multiple bays of the fuselage can destabilize or limit the performance of a decentralized active noise control system. The metrics quantitatively verify observations from a previous experiment, in which decentralized controllers performed worse than centralized controllers. The metrics do not appear to be useful for explaining control spillover which was observed in a previous experiment.

Experimental demonstration of a band-limited actuator/sensor selection strategy for structural acoustic control

A band-limited method of selecting actuators and sensors for structural acoustic control is reviewed, and experimental results are presented to demonstrate the approach. The selection methodology is based upon the decomposition of the Hankel singular values of a system model in terms of individual sensor and actuator configurations for lightly damped structures. The technique selects sensor and actuator combinations which couple well to structural modes that radiate efficiently. However, it rejects sensor and actuator combinations which couple well to modes that are inefficient acoustic radiators or are outside of the desired bandwidth of control. Selecting transducer combinations which filter modes outside of the desired bandwidth serves to minimize the potential for spillover and instability associated with unmodeled or poorly modeled dynamics. The approach is computationally efficient since it is based upon open-loop dynamics and does not require iterative nonlinear optimization.