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.
The control of exible structures employing the passivity approach has been extended to systems having noncollocated input/output pairs by introducing an observer that incorporates the nominal dynamical model of the plant. The passive observer-based control is applied to the American Control Conference benchmark problem, whereby, the control force emulates a dynamic vibration absorber attached to a virtual wall with passive control elements (spring, mass, and dashpot). The springs and mass elements of the controller are constant, whereas the damping coef cients are selected as time dependent in an attempt to choose continuously the most appropriate amount of damping in compliance with the design goals. A novel approach is introduced, whereby the passive observer-based control law is modi ed by varying the damping coef cient of the virtual dashpot by means of an adaptive fuzzy logic algorithm. This modi ed system exhibits quick settling times and desirable performance characteristics. Results from the statistical robustness analysis for the developed controller are compared to 10 other (linear) solutionsof the benchmarkproblem. The comparisonis based onrobust stability, robust performance (settling time), and control effort. The results obtained by the adaptive fuzzy logic algorithm are superior to those obtained by all other methods, and, consequently, further application of the fuzzy algorithm is advocated.
The present study deals with an AFCA (Adaptive Fuzzy Control Algorithm) for an Euler-Bernoulli approximation of a two-dimensional version of a cantilever beam-like orthogonal tetrahedral space truss. Transient disturbances, modeled as a unit impulse, excite all the modes of the beam. The resulting transverse displacement at the free end of the beam and its corresponding rate are observed by sensors placed there, and active control of the beam is provided by a collocated force actuator.
A design methodology for the closed-loop control algorithm that is independent of an exact mathematical model (space-state model, F.E.M., etc.) of plant dynamics and which is based on fuzzy logic is presented. First, the behavior of the open-loop system is observed. Then, the control force applied to the system emulates the behavior of a dynamic vibration absorber which is tuned to the measured fundamental frequency. This approach not only assures inherent stability associated with passive absorbers, but also circumvents the phenomenon of modal spillover. The damping and the mass ratios of the absorber adapt themselves by using a fuzzy decision-making process. This results in relatively quick settling times, low overshoots and dying out of vibration within a few seconds.
When the control force is turned off after a mere 16 seconds, almost all the vibrational energy is dissipated. In addition, the performance of the AFCA is insensitive to varying initial conditions. To demonstrate the robustness of the control system to changes in the temporal dynamics of the cantilever beam, the transient response to a considerably perturbed plant is simulated. The Young's modulus of the beam was raised as well as lowered substantially, thereby significantly perturbing the natural frequencies of vibration. The mode shapes, however, remain unchanged. For these cases, too, the AFCA provides similar settling times and rates of vibrational energy dissipation.
A genetic algorithm was used to optimize performance of a fuzzy inference system acting as a controller for a magnetically actuated CubeSat. A solely magnetically controlled satellite is a nonlinear, underactuated system for which the uncontrollable axis varies as a function of orbit position and attitude; variation is approximately periodic with orbit position. Therefore, controllability is not guaranteed, making solely magnetic control a less than ideal option for spacecraft requiring a high degree of pointing accuracy or spacecraft subject to relatively large disturbances. However, for small spacecraft, such as CubeSats, with modest pointing and disturbance rejection requirements, solely magnetic actuation is a good option. The genetic-algorithm-tuned fuzzy controller solution was compared to a similar linear quadratic regulator solution that was tuned to minimize the cost function used by the genetic algorithm. Both were optimized with respect to a single set of initial conditions. The genetic-algorithm-tuned fuzzy controller was found to be a lower-cost solution than the linear quadratic regulator for the optimized set of initial conditions. Additionally, a Monte Carlo analysis showed the genetic-algorithm-tuned fuzzy controller tended to settle faster than the linear quadratic regulator over a variety of initial conditions.
For a Timoshenko beam model the equations of motion, representing the anisotropic continuum model of a two-dimensional, latticed, large space structure, are extended to include coupling between the extensional, shear and bending modes. This analytical model, applied to a 20-bay, orthogonal, tetrahedral, cantilevered truss structure, is used to determine the transient response when subjected to a unit impulse. It is demonstrated that for beam-like structures having a fixed bending stiffness and beam mass an increase in diagonal stiffness, on account of the stiffness of the vertical girder, leads to a rise in the transverse shear rigidity. This results in higher natural frequencies and a reduction in peak displacement. In addition, in an asymmetrical truss configuration, coupling between the extensional and shear modes raises the maximum peak displacement compared to that obtained for a symmetric truss. The model is modified to investigate the introduction of passive damping in the form of several dynamic vibration absorbers. For a fixed absorber mass budget, a simple yet efficient absorber parameter optimization procedure, based on the classical steady state criteria of a 2-DOF system, is developed to design several absorbers each tuned to a different modal frequency. It is found that inclusion of transverse shear rigidity, as a design parameter in damping augmentation studies, reduces settling time for predetermined maximum peak displacements.
This research was conducted within the framework of a National Science Foundation sponsored summer Research Experience for Undergraduate (REU) students. This research considers small-scale and mathematical models of simple one-story structures that are subjected to free and base-motion excitations and installed with and without passive damping devices to gain an understanding of their dynamic behavior while reviewing active and semi-active damping means being applied and researched today. Using computer programming and numerical methods, the goal is to understand and counteract catastrophic disasters to structures caused by earthquakes. The research is broken down into a number of MATLAB simulations and experiments in order to understand basic dynamic and control features required to design earthquake resilient buildings. These experiments include free vibration experiments to test for the stiffness of columns for different heights and to test for the natural frequency and damping ratio of a one-story structure under different mass loads. Active PD control was then applied to an experimental system experiencing accelerations attributed to the Northridge 1994, Kobe 1995, El Centro 1940, and Mendocino 1992 earthquakes. Robustness comparisons were made between (1) P control; (2) D control; and (3) PD control for the above earthquake inputs to the shaker. A fuzzy logic controller was developed to effectively control transient vibrations. The uniqueness of this control concept is that the fuzzy control continuously varies the damping characteristics of a semi-active tuned mass damper (TMD). It was concluded that a fuzzy logic based TMD was more effective than a regular passive TMD, by providing half the settling times.
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%.
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.
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.
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 the systematic development of feedback flow controllers, a numerical model that captures the dynamic behaviour of the flow field to be controlled is required. This poses a particular challenge for flow fields where the dynamic behaviour is nonlinear, and the governing equations cannot easily be solved in closed form. This has led to many versions of low-dimensional modelling techniques, which we extend in this work to represent better the impact of actuation on the flow. For the benchmark problem of a circular cylinder wake in the laminar regime, we introduce a novel extension to the proper orthogonal decomposition (POD) procedure that facilitates mode construction from transient data sets. We demonstrate the performance of this new decomposition by applying it to a data set from the development of the limit cycle oscillation of a circular cylinder wake simulation as well as an ensemble of transient forced simulation results. The modes obtained from this decomposition, which we refer to as the double POD (DPOD) method, correctly track the changes of the spatial modes both during the evolution of the limit cycle and when forcing is applied by transverse translation of the cylinder. The mode amplitudes, which are obtained by projecting the original data sets onto the truncated DPOD modes, can be used to construct a dynamic mathematical model of the wake that accurately predicts the wake flow dynamics within the lock-in region at low forcing amplitudes. This low dimensional model, derived using nonlinear artificial neural network based system identification methods, is robust and accurate and can be used to simulate the dynamic behaviour of the wake flow. We demonstrate this ability not just for unforced and open-loop forced data, but also for a feedback-controlled simulation that leads to a 90% reduction in lift fluctuations. This indicates the possibility of constructing accurate dynamic low-dimensional models for feedback control by using unforced and transient forced data only.
Feedback flow control of the wake of a circular cylinder at a Reynolds number of 100 is an interesting and challenging benchmark for controlling absolute instabilities associated with bluff body wakes. A two dimensional computational fluid dynamics simulation is used to develop low-dimensional models for estimator design. Actuation is implemented as displacement of the cylinder normal to the flow. The estimation approach uses a low dimensional model based on a truncated 6 mode Double Proper Orthogonal Decomposition (DPOD) applied to the streamwise velocity component of the flow field. Sensor placement is based on the intensity of the resulting spatial modes. A non-linear Artificial Neural Network Estimator (ANNE) was employed to map the velocity data to the mode amplitudes of the DPOD model. For a given four sensor configuration, developed using a previously validated strategy, ANNE performed better than two state-of-the-art approaches, namely, a Quadratic Stochastic Estimator (QSE) and a Linear Stochastic Estimator with time delays (DSE).
The methods and outcome of a senior undergraduate project related to the control of a turbulent cylinder wake flow using plasma actuators are summarized in this article. The study integrates computational fluid dynamics (CFD) with experimentation and combines fluid mechanics with flow control research, crossing the boundaries between engineering disciplines.Comput. Appl. Eng. Educ.
Comparison of approximate approaches to solving the Travelling Salesman Problem and its application to UAV swarming. International Journal of Unmanned Systems Engineering. 3(1): 1-16. The Travelling Salesman Problem (TSP) is a widely researched Non-deterministic Polynomial-time hard optimization problem with a range of important applications in a wide spectrum of disciplines including aerospace engineering. In this paper, a comparison of different approaches to solve the TSP and also its application towards swarming of UAVs is considered. The objective of the TSP is to determine the optimal route associated with the shortest tour connecting all targets just once. Genetic Algorithms (GA) are one of the most widely applied techniques for solving this class of optimization problems. Two other techniques, 2-opt and Particle Swarm Optimization, are used and the results are compared with those obtained using GA. The comparison is made for different numbers of targets, using salient figures of merit such as computational time required and the cost function which is the minimum solution (distance) obtained. Results show that the 2-opt approach with the closest neighbour as initial starting point for the search yields superior performance. In the Multiple Travelling Salesman Problem, we propose a cluster-first approach which allocates each specific UAV to a subset of targets. The 200 targets are divided into four clusters corresponding to the four UAVs and then TSP algorithms like 2-opt and GA are employed to solve each cluster. This approach drastically reduces the computational time and also gives much better results than the conventional technique of directly applying GA over the 200 targets.
Fuzzy logic is used in a variety of applications because of its universal approximator attribute and non-linear characteristics. But, it takes a lot of trial and error to come up with a set of membership functions and rule-base that will effectively work for a specific application. This process could be simplified by using a heuristic search algorithm like Genetic Algorithm (GA). In this paper, genetic fuzzy is applied to the task assignment for cooperating Unmanned Aerial Vehicles (UAVs) classified as the polygon visiting multiple traveling salesman problem (PVMTSP). The PVMTSP finds a lot of applications including UAV swarm routing. We propose a method of genetic fuzzy clustering that would be specific to PVMTSP problems and hence more efficient compared to k-means and c-means clustering. We developed two different algorithms using genetic fuzzy. One evaluates the distance covered by each UAV to cluster the search-space and the other uses a cost function that approximates the distance covered thus resulting in a reduced computational time. We compare these two approaches to each other as well as to an already benchmarked fuzzy clustering algorithm which is the current state-of-the-art. We also discuss how well our algorithm scales for increasing number of targets. The results are compared for small and large polygon sizes.
There are a variety of scenarios in which the mission objectives rely on an unmanned aerial vehicle (UAV) being capable ofmaneuvering in an environment containing obstacles in which there is little prior knowledge of the surroundings. With an appropriate dynamicmotion planning algorithm, UAVs would be able tomaneuver in any unknown environment towards a target in real time. This paper presents a methodology for two-dimensional motion planning of a UAV using fuzzy logic. The fuzzy inference system takes information in real time about obstacles (if within the agent’s sensing range) and target location and outputs a change in heading angle and speed. The FL controller was validated, andMonte Carlo testing was completed to evaluate the performance.Not only was the path traversed by the UAV often the exact path computed using an optimal method, the low failure rate makes the fuzzy logic controller (FLC) feasible for exploration. The FLC showed only a total of 3% failure rate, whereas an artificial potential field (APF) solution, a commonly used intelligent control method, had an average of 18% failure rate. These results highlighted one of the advantages of the FLC method: its adaptability to complex scenarios while maintaining low control effort.
The present study deals with an AFCA (Adaptive Fuzzy Control Algorithm) for an Euler-Bemoulli approximation of a two-dimensional version of a cantilever beam-like orthogonal tetrahedral space truss. Transient disturbances, modeled as a unit impulse, excite all the modes of the beam. The resulting transverse displacement at the free end of the beam and its corresponding rate are observed by sensors placed there, and active control of the beam is provided by a collocated force actuator.
A design methodology, based on fuzzy logic which assumes no a priori knowledge of plant dynamics, for the closed-loop control algorithm results in relatively quick settling times, low overshoots and dying out of vibration within a few seconds. The control algorithm is enhanced and made much faster by eliminating the need of repeatedly solving the set of differential equations of motion of an emulated dynamic vibration absorber. When the control force is turned off after a mere 15 seconds, almost all the vibrational energy is dissipated as the beam returns to its undisturbed state throughout its length. In addition, the performance of the AFCA is insensitive to varying initial conditions. To examine the robustness of the control system to changes in the temporal dynamics of the cantilever beam, the transient disturbance response to a considerably perturbed plant is simulated. The Young's modulus of the beam was raised as well as lowered by 60%, substantially perturbing the natural frequencies of vibration compared to the nominal plant. The AFCA provided similar settling times and rates of vibrational energy dissipation, satisfying the aim of plant model independence.
Breakthroughs in genetic fuzzy systems, most notably the development of the Genetic Fuzzy Tree methodology, have allowed fuzzy logic based Artificial Intelligences to be developed that can be applied to incredibly complex problems. The ability to have extreme performance and computational efficiency as well as to be robust to uncertainties and randomness, adaptable to changing scenarios, verified and validated to follow safety specifications and operating doctrines via formal methods, and easily designed and implemented are just some of the strengths that this type of control brings. Within this white paper, the authors introduce ALPHA, an Artificial Intelligence that controls flights of Unmanned Combat Aerial Vehicles in aerial combat missions within an extreme-fidelity simulation environment. To this day, this represents the most complex application of a fuzzy-logic based Artificial Intelligence to an Unmanned Combat Aerial Vehicle control problem. While development is on-going, the version of ALPHA presented withinwas assessed by Colonel (retired)Gene Lee who described ALPHA as “the most aggressive, responsive, dynamic and credible AI (he’s) seen-to-date.” The quality of these preliminary results in a problem that is not only complex and rife with uncertainties but also contains an intelligent and unrestricted hostile force has significant implications for this type of Artificial Intelligence. This work adds immensely to the body of evidence that this methodology is an ideal solution to a very wide array of problems.
This work presents a methodology for real-time estimation of wildland fire growth, utilizing afire growth model based on a set of partial differential equations for prediction, and harnessing concepts of space-time Kalman filtering and Proper Orthogonal Decomposition techniques towards low dimensional estimation of potentially large spatio-temporal states. The estimation framework is discussed in its criticality towards potential applications such as forest fire surveillance with unmanned systems equipped with onboard sensor suites. The effectiveness of the estimation process is evaluated numerically over fire growth data simulated using a well-established fire growth model described by coupled partial differential equations. The methodology is shown to be fairly accurate in estimating spatio-temporal process states through noise-ridden measurements for real-time deploy ability.