«Aeroservoelastic and structural dynamics research on smart structures conducted at NASA Langley Research Center Anna-Maria %vas McGowan, W. Keats ...»
This research will build upon the work of several other researchers who have developed analyses and numerical models to analyze piezoelectrically-controlled structure^^-'^. Some of these studies include: superelement modeling conducted by Hauch6;higher-order theory developed by Seeley’; and finite element modeling with a consideration of damping developed by Freed and Babuska’. These research efforts and many others clearly show that the key considerations in modeling in-plane piezoelectric actuation are capturing the sharply varying strain field around the piezoelectric actuator and modeling damping to more accurately capture the dynamic piezoelectric effect. Furthermore, to model larger, more complex structures with piezoelectric actuators, improved finite element modeling techniques are required. In particular, Seeley’s work (funded under a NASA Langley grant) showed that the strain field in the host structure in the vicinity of the piezoelectric actuator is nonlinear. Most analyses used to model piezoelectric actuation (including the one used during the PARTI program) assume the strain field through the thickness of the host structure is linear. Seeley used higher-order laminate theory, which was implemented using a finite element method, to model the piezoelectric actuation of composite plates.
2.3 Aeroservoelastic Modeling and Validation for Patch Piezoelectric Actuators During the PARTI program, Pototzky” developed a method of modeling the aeroservoelastic response of a structure controlled with piezoelectric actuators. He used a finely-meshed finite element model of a cantilevered beam as his test case.
This model did not have aerodynamic data with which to validate the aeroservoelastic results; therefore, this method was validated at air-off conditions only. His method consists of using a thermal mechanical analogy to create a static deflection shape of the host structure actuated by the piezoelectric actuators. This shape is then appended to the free vibration mode shapes and the new augmented modal matrix is then used in an aeroservoelastic analysis using the Interaction of Structures, Aerodynamics and Controls (ISAC)” code. In the aeroservoelastic analysis in ISAC, the appended static deflection shape is used as the control mode. Including this deflection shape as a mode in the aeroelastic analysis may allow for the aerodynamic influence of piezoelectric actuation to be computed. Since aerodynamic data for this test case is not available, this method of modeling the aerodynamic influence of the piezoelectric actuation has not been validated. However, the current research studies, to be discussed later, seek to assess the accuracy of this and other aeroservoelastic modeling techniques. When compared with experimental results at zero airspeed, the transfer function data of acceleration and strain with respect to piezo excitation agreed reasonably well in terms of both magnitude and phase. Also, note that a very finelymeshed finite element grid was used to ensure the accuracy of strain information. For larger, more complex models than the simple cantilevered beam model used for this test case, this may be computationally difficult.
Pototzky’s method is one of many developed to incorporate piezoelectric actuation in aeroservoelastic Much of this work uses simplified structural models and relies upon limited experimental data. To enable the study of more complex structures and to ensure analytical model accuracy through experimental validation, the objectives of the aeroservoelastic modeling and validation research in the Aircraft Morphing program are to: 1) assess the state-of-the-art in simulating piezoelectric actuation in aeroservoelastic modeling using simple and moderately complex models and 2) in the long term, develop and validate (via wind-tunnel testing) methods that may efficiently be used on larger, more complex structures. For this research, doublet lattice aerodynamics and the ISAC code will be used to perform the aeroservoelastic analyses. Existing data from the PARTI and ACROBAT programs will be used to assist in verifying the analysis methods. Verification of the analysis techniques will first be conducted at zero airspeed and then expanded to correspond to wind-on data. Data from ground modal tests conducted in the Aircraft Morphing program will be used to further verify zero-airspeed characteristics.
Additional simplified models may be constructed and ground and wind-tunnel tested to provide more experimental data to compare with the aeroservoelastic modeling development.
2.4 Ground Testing Using Patch Piezoelectric Actuators The research issues identified in the PARTI program include determining piezoelectric power consumption during active control and applying improved control and optimization techniques. Research in both of these areas at NASA Langley is focused toward the long-term goals of developing techniques to control larger, more realistic structures using piezoelectric actuators and assessing the economic viability of using piezoelectric actuators for control by examining power consumption.
This research also involves evaluating a variety of control techniques to ascertain the most efficient and/or effective technique for suppressing vibration.
One of the techniques being investigated in the Aircraft Morphing program is damping augmentation using shunted piezoelectric actuators. This method, which uses a parallel inductor and resistor to electrically shunt the piezoelectric actuator, may provide a simple, low power alternative to active control using piezoelectric actuators configured in the conventional, unshunted manner. Future research activities include conducting open- and closed-loop experimental ground tests on large-scale structures to assess trade-offs in piezoelectric control effectiveness, power consumption and optimal control strategies using both active and passive control techniques with shunted piezoelectric actuators and unshunted piezoelectric actuators. For the ground tests, an electrodynamic shaker will be used to provide a disturbance source.
2.4.1 Test Set-up and Approach The existing PARTI wind-tunnel model, a sketch of which is shown in Figure 1, is being used for the ground tests. This model consists of a composite plate in a sandwich construction (graphite epoxy facesheets with an aluminum honeycomb core) with 36 piezoelectric patches surface-bonded to each side of the plate as well as 14 conventional strain gages and 4 accelerometers. The 36 piezoelectric patches are arranged into 15 groups to be used as 15 actuators or sensors or a combination of both. The ground testing involves first identifying the natural kequencies, damping and mode shapes in a modal test of the PARTI model. Next, open-loop data to design the shunt circuit and the active control laws will be obtained. The data required to design the shunt circuit is the voltage output of each piezoelectric patch due to shaker disturbance of the model. This data is then used to determine the size of the inductor and resistor needed in the shunt circuit.
For active control law design, the data required is the voltage output of each sensor due to each actuator’s excitation and shaker disturbance. This open-loop frequency response function data is used to build an experiment-based analytical model of the wing using a time domain system identification technique. For active control, the sensors may be either the conventional sensors (strain gages and accelerometers) or the piezoelectric patches. Future testing is also planned for new models being constructed in support of the finite element modeling and validation effort mentioned previously.
Figure 1: PARTI Wind-Tunnel Model Two of the key benefits of using shunted piezoelectric actuators for active (active tuning of the shunt circuit) or passive damping augmentation is the very low power required for operation of the circuit and the simplicity of mechanical operation when the shunted actuators are used passively for control. This is in contrast to one of the main issues with using piezoelectric actuators for active vibration control: the potentially high amount of power needed and the corresponding power supplies and amplifiers required.
Figure 2: Parallel Shunt Circuit for Passive Vibration Some applications, however, may require active control to Control achieve the desired system performance.
where P(o) is the power required, w is the circular frequency, V(w) is the voltage of the control law output signal, C,(V(w)) is the effective capacitance of each piezoelectric actuator being used for control, and n is the total number of piezoelectric actuators being used by the control law. Although effective capacitance is often considered a constant quantity as quoted by the actuator manufacturer, measurements made at NASA Langley have shown that the effective capacitance is actually approximately a linear function of voltage. These capacitance values are best obtained through experimental tests over the bandwidth and voltage range of interest. More discussion of the voltage dependence of piezoelectric capacitance is given in reference 18.
The power expression in the equation was developed through both analysis and experimental tests using a cantilevered beam model with surface-bonded piezoelectric actuators. The tests showed that the maximum power required to control a structure using surface-bonded piezoelectric actuators can be estimated without modeling the complex dynamics between the piezoelectric actuator and the host structure. Experimental results demonstrated that for a perfectly-controlled structure (all motion is stopped), the power consumption of the piezoelectric actuators is a function of the material and geometric properties of the piezoelectric actuators. Furthermore, as control effectiveness decreases, the power consumption of the actuators decreases. Hence, maximum power consumption occurs when the structure is perfectly controlled. Experimental tests further demonstrated that the structural dynamics of the host structure and piezoelectric actuators have a minimal effect on the power consumed by the actuators during active control. Consequently, for typical surface-bonded piezoelectric actuators, the power required for active vibration control can be conservatively determined within 90% accuracy (generally within 97% accuracy) without modeling the complex structural dynamics of the actuator and host ~tructure”~’~.
2.4.3 Choosing Optimal Actuators and Sensors for Active Control Law Design Another important element of controlling large structures using several piezoelectric actuators is the effective use of optimization schemes. For example, wind-tunnel results from the PARTI program showed that at a given tunnel condition, one control law using all 15 actuators reduced gust loads by 75% while another control law used only 6 actuators to reduce gust loads by 72%. For many cases, such a minor loss of control effectiveness (3%) is inconsequential compared to the 60% reduction in the number of actuators required, which reduces weight and complexity. References 19 and 20 describe two optimal control studies conducted using data from the PARTI wind-tunnel tests. Both of these studies investigated optimally choosing a subset of actuators from a set already in place on the model. Placement of the actuators was specified a priori and was not a variable in the optimization studies. As an example, Lim’s studies in reference 19 focused on the selection of a “best” subset of actuators for improving the performance of an active control system at a single design point, namely, the onset of flutter. The formulation of an actuator selection metric, based on the Hankel singular value approach, was examined from a flutter control design perspective such that the degree of participation of the individual structural modes contributing to the flutter condition was used to weight the metric in the feedback loop. Simulation results using Hzand H, control law designs showed that the optimal actuator set gave improved closed-loop performance, independent of the control law design selected.
3. ACTIVE BUFFET LOAD ALLEVIATION
3.1 Actively Controlled Response of Buffet Affected Tails (ACROBAT) program The ACROBAT program*’,which took place from 1994-1997,focused on demonstrating the feasibility of using active controls to alleviate vertical tail buffeting experienced by twin-tail aircraft at high angles of attack. For these aircraft, buffeting of the vertical tails results when vortices, originating at the leading edge extensions, burst ahead of the vertical tails, engulfing the tails in highly turbulent flow. The resulting vibrations are a significant concern from fatigue and maintenance points of views since inspections and repairs are high cost items to military fleets.
Active control using piezoelectric actuators provides a potential solution to the buffeting problem. NASA Langley has partnered with DoD, industry, and international agencies to perform wind-tunnel and ground-vibration tests of buffet load alleviation systems that use smart materials. During the ACROBAT program, a M-scale rigid full-span model of the F/Aaircraft was tested in the Langley Transonic Dynamics Tunnel (TDT) using an active rudder and, separately, using active patch piezoelectric actuators to control buffeting. The arrangement used for the piezoelectric actuators (which were placed as opposing pairs on both surfaces of the vertical tail) is shown in Figure 3. A cover was placed over the actuators during tests to provide a smooth aerodynamic surface. The typical response of the vertical tail in the first bending mode is shown in Figure 4 as a plot of the normalized peak of the power spectral density of root bending moment versus angle of attack. These wind-tunnel tests showed that piezoelectric actuators reduced the power spectral density peak value and the root mean square value of the tail root bending moment by 60% and 19%, respectively. The tests effectively demonstrated that piezoelectric actuators provide a viable means for alleviating buffeting.