The present investigation deals with the application of an Adaptive Fuzzy Control Algorithm for active vibration control of an experimental flexible beam. The two-dimensional model of the experimental cantilever beam, given by an orthogonal tetrahedral space truss, represents a slender cantilever aluminum (7075-T6) beam of rectangular cross-section (1145 × 60 × 1.95 mm3). A variety of transient disturbances are introduced to excite the first four modes of the beam. The resulting transverse displacements are observed by a single sheet (50 × 50 mm2) of piezoceramic material placed at the clamped end of the beam. Active control of the beam is provided by one, two or three identical sheets of piezoceramic material collocated with the sensor. The control moments applied by the piezoceramic actuator are made to emulate the behavior of a discrete dynamic vibration absorber. The virtual absorber is tuned to the fundamental frequency using classical methods and the tuning ratios are time-invariant. However, the uniqueness of this approach is that the damping parameters of the emulated absorber are continuously varied by means of a fuzzy logic control algorithm to provide near minimum-time suppression of vibration. It is demonstrated that application of this methodology allows for its real-time implementation and provides relatively quick settling times in the closed-loop.
In this study a general approach is introduced for the design of a robust control law for suppression of structure borne vibration. This control law is based on a passive design in the form of dynamic vibration absorbers. Passive absorbers minimize vibration at a speci c frequency, but their performance is improved by introducing adaptive tuning of the absorber. An adaptive dynamic vibration absorber is tuned to the forcing frequency, using classical methods. The tuning ratio is time varying and adapts itself to variations in the forcing frequency. However, the uniqueness of the approach in this study is that the damping parameter of the absorber is continuously varied by means of a fuzzy-logic control algorithm to provide a lower sound pressure level. The inputs of the fuzzy control law are the displacement and velocity of the main structure. The effectiveness of the control algorithm for active vibration control is demonstrated using MATLAB® simulations of a single-degree-of-freedom plant. This methodology provides superior performance in the presence of signi cant mistuning compared to a more conventional approach.
Closed-loop control strategies were studied experimentally at low Reynolds and incompressible Mach numbers using periodic excitation to vector a turbulent jet. Vectoring was achieved by attaching a short, wide-angle diffuser at the jet exit and introducing periodic excitation from a slot covering one quadrant of the circumference of the round turbulent jet. Closed-loop control methods were applied to transition quickly and smoothly between different jet de ection angles. The frequency response of the zero-mass- ux piezoelectric actuatorwas at to about 0.5 kHz, but the jet responds up to 30–50 Hz only. This is still an order of magnitude faster than conventional thrust vectoring mechanism. System identi cation procedures were applied to approximate the system’s transfer function. A linear controller was designed that enabled fast and smooth transitions between stationary de ection angles and maintained desired jet vectoring angles under varying system conditions. The linear controller was tested over the entire range of available de ection angles, and its performance is evaluated and discussed.
For feedback control using low-dimensional proper orthogonal decomposition (POD) models, the mode amplitudes of the POD mode coefficients need to be estimated based on sensor readings. This paper is aimed at suppressing the von Kairman vortex street in the wake of a circular cylinder using a low-dimensional approach based on POD. We compare sensor placement methods based on the spatial distribution of the POD modes to arbitrary ad hoc methods. Flow field data were obtained from Navier-Stokes simulation as well as particle image velocimetry (PIV) measurements. A low-dimensional POD was applied to the snapshot ensembles from the experiment and simulation. Linear stochastic estimation was used to map the sensor readings of the velocity field on the POD mode coefficients. We studied 53 sensor placement configurations, 32 of which were based on POD eigenfunctions and the others using ad hoc methods. The effectiveness of the sensor configurations was investigated at Re = 100 for the computational fluid dynamic data, and for a Reynolds number range of 82-99 for the water tunnel PIV data. Results show that a five-sensor configuration can keep the root mean square estimation error, for the amplitudes of the first two modes to within 4% for simulation data and within 10% for the PIV data. This level of error is acceptable for a moderately robust controller The POD-based design was found to be simpler. more effective, and robust compared to the ad hoc methods examined.
A short computational program was undertaken to evaluate the effectiveness of a closed-loop control strategy for the stabilization of an unstable bluff-body flow. In this effort, the non-linear one-dimensional Ginzburg–Landau wake model at 20% above the critical Reynolds number was studied. The numerical model, which is a non-linear partial differential equation with complex coefficients, was solved using the FEMLAB®/MATLAB® software packages and validated by comparison with published literature. At first, a model independent approach was attempted for wake suppression using feedback control. The closed-loop system was controlled using a conventional proportional-integral-derivative (PID) controller as well as a non-linear fuzzy controller. A single sensor is used for feedback, and the actuator is represented by altering the boundary conditions of the cylinder. Simulation results indicate that for a single sensor scheme, the increase in the sophistication of the control results in significantly shorter settling times. However, there is only a marginal improvement concerning the suppression of the wake at higher Reynolds numbers. The feedback control design was then augmented by switching over to a model-dependent controller. Based on computationally generated data obtained from solving the unforced wake, a low-dimensional model of the wake was developed and evaluated. The low-dimensional model of the unforced Ginzburg–Landau equation captures more than 99.8% of the kinetic energy using just two modes. Two sensors, placed in the absolutely unstable region of the wake, are used for real-time estimation of the first two modes. The estimator was developed using the linear stochastic estimation scheme. Finally, the loop is closed using a PID controller that provides the command input to the variable boundary conditions of the model. This method is relatively simple and easy to implement in a real-time scenario. The control approach, applied to the 300 node FEMLAB® model at 20% above the unforced critical Reynolds number stabilizes the entire wake. Compared to the model-independent controllers, the controller based on the low-dimensional model is far more effective in the suppression of the wake at higher Reynolds numbers. Furthermore, while the latter approach employs only the estimated temporal amplitude of the first mode of the imaginary part of the amplitude, all higher modes are stabilized. This suggests that the higher order modes are caused by a secondary instability that is suppressed once the primary instability is controlled.
The effectiveness of a sensor configuration for feedback flow control on the wake of a circular cylinder is investigated in both direct numerical simulation as well as in a water tunnel experiment. The research program is aimed at suppressing the von Kármán vortex street in the wake of a cylinder at a Reynolds number of 100. The design of sensor number and placement was based on data from a laminar two-dimensional simulation of the Navier–Stokes equations for the unforced condition. A low-dimensional proper orthogonal decomposition (POD) was applied to the vorticity calculated from the flow field and sensor placement was based on the intensity of the resulting spatial eigenfunctions. The numerically generated data was comprised of 70 snapshots taken over three cycles from the steady state regime. A linear stochastic estimator (LSE) was employed to map the velocity data to the temporal coefficients of the reduced order model. The capability of the sensor configuration to provide accurate estimates of the four low-dimensional states was validated experimentally in a water tunnel at a Reynolds number of 108. For the experimental wake, a sample of 200 particle image velocimetry (PIV) measurements was used. Results show that for experimental data, the root mean square estimation error of the estimates of the first two modes was within 6% of the desired values and for the next two modes was within 20% of the desired values. This level of error is acceptable for a moderately robust controller.
The effect of feedback flow control on the wake of a circular cylinder at a Reynolds number of 100 is investigated in direct numerical simulation. The control approach uses a low-dimensional model based on proper orthogonal decomposition (POD). The controller applies linear proportional and differential feedback to the estimate of the first POD mode. The range of validity of the POD model is explored in detail. Actuation is implemented as displacement of the cylinder normal to the flow. It is demonstrated that the threshold peak amplitude below which the control actuation ceases to be effective is in the order of 5% of the cylinder diameter. The closed-loop feedback simulations explore the effect of both fixed-phase and variable-phase feedback on the wake. Whereas fixed-phase feedback is effective in reducing drag and unsteady lift, it fails to stabilize this state once the low drag state has been reached. Variable-phase feedback, however, achieves the same drag and unsteady lift reductions while being able to stabilize the flow in the low drag state. In the low drag state, the near wake is entirely steady, whereas the far wake exhibits vortex shedding at a reduced intensity. A drag reduction of 15% of the drag was achieved, and the unsteady lift force was lowered by 90%.