Akhilesh K. Jha

Optimal Sizes and Placements of Piezoelectric Actuators and Sensors for an Inflated Torus

One of the limitations of a piezoelectric actuator is the amount of force it can exert. Hence, it is important to optimize the locations and sizes of the actuators so that the required control effort is minimal. Similarly, to obtain good signal-to-noise ratio, sensors should be chosen to provide maximum output for the vibration in the modes of interests. These problems become more critical as the number of actuators and sensors increases, and the mode shapes become more complicated. This is true for the case of an inflated torus. In this study, we try to find optimum places and sizes of actuators and sensors attached to an inflated toroidal shell using a genetic algorithm. Using the expressions for the generalized forces and sensor voltages, modal forces and modal sensing constants are determined. To obtain a cumulative performance measure for all the controlled and observed modes, controllability and observability indices are used. Using these performance indices, optimal locations and sizes of the actuators and sensors are determined so that the actuators and sensors provide good control and sensing authorities in the considered modes. Finally, vibration suppression of the inflated torus using these actuators and sensors has been demonstrated using an optimal control technique.

Free Vibration Analysis of an Inflated Toroidal Shell

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkins method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

A literature review of ultra-light and inflated toroidal satellite components

Gossamer structures, also known as inflatable or membrane structures, have been a subject of renewed interest in recent years for space applications such as communication antennas, solar thermal propulsion, space solar power, and other large spacecraft applications. The major advantages of using inflatable structures in space are their extremely low weight, on-orbit deployability, and minimal stowage volume for launching. In this paper, we present a literature survey on different aspects of inflatable structures. Analytical and experimental studies of an inflated torus-the main structural support system for several inflatables-have drawn a considerable amount of attention from the vibration and control community. The inflated torus will be the main focus of this survey. First, we present an overview of gossamer spacecraft technology. Thereafter, we consider analytical studies of inflated tori and arches, and we cite several research papers on these topics. Next, we present a brief overview of research work on experimental studies of tires, inflated tori, and other types of gossamer structures, and we outline the future for ultra-flexible spacecraft technology.

Intelligent Control of a Morphing Aircraft

A morphing aircraft is able to drastically alter its planform to optimize performance at very dissimilar flight conditions. Despite significant strides to develop wing structure and actuation systems, much work remains to effectively control both the morphing wing as well as the entire morphing aircraft. The control solution presented in this paper uses modelbased methods that provide precise, closed-loop control of the morphing planform (i.e. wing-shape control) and simultaneously enforce prescribed closed-loop aircraft dynamics (i.e. flight control). The specific planform that is the focus of this research is the N-MAS wing designed by NextGen Aeronautics. At the wing-shape control level, the authors sought to answer two questions: (1) What is the most efficient means of actuating the underlying structure of the N-MAS wing? and (2) Given a fixed set of actuators, how does one precisely manipulate a morphing structure given inherent physical limitations? At the flight-control level, the authors sought to develop a control methodology that can: (1) accommodate different planforms that result in drastically changing plant dynamics, and (2) make the transition between any two configurations while maintaining the stability of the morphing aircraft.

Sliding Mode Control of a Gossamer Structure Using Smart Materials

Gossamer structures have been a subject of renewed interest for space applications because of their low weights, on-orbit deploying capabilities, and minimal stowage volumes. In this study, vibration suppression of an inflated structure using piezoelectric actuators and sensors has been attempted. These actuators and sensors can be suitably used for gossamer structures since they can conform to curved surfaces and provide distributed actuation and sensing capabilities. Using the natural frequencies and mode shapes of the system (structure, actuators, and sensors), a state-space model is derived. For designing a robust vibration controller, we used a sliding mode technique. The derivations of the sliding model controller and observer are presented in details. Finally, by means of numerical analysis, the method was demonstrated for an inflated torus considering Macro-Fiber Composite (MFC™) as actuators and Polyvinylidene Fluoride (PVDF) as sensors. The simulation studies show that the piezoelectric actuators and sensors are suitable for vibration suppression of an inflatable torus. The robustness properties of the controller and observer against the parameter uncertainty and disturbances are also studied.

Vibration of dynamic systems under cyclostationary excitations

This paper proposes a new method for calculating the response of structural systems subjected to a special type of nonstationary, random excitation, called cyclostationary. The main characteristic of this type of excitation is that its statistical properties (e.g., the RMS) vary periodically in time in contrast to a traditional, random stationary model, which assumes constant statistical properties. Systems like a submarine propeller, a turbine blade and an internal combustion engine are subjected to this type of excitation. The paper presents a method for modeling the excitation and for calculating the response of such systems. It demonstrates that a cyclostationary model yields considerably more accurate estimates of the RMS of the response of a vehicle driven on rough pavement compared to a traditional stationary model.

Fatigue reliability of cars under road-induced cyclostationary excitation

This paper has two goals: (a) describe a method for modelling special types of nonstationary loads on cars, called cyclostationary loads, and (b) demonstrate the importance of this method. Cyclostationary excitations are encountered in many real-life problems involving systems subjected to periodic, random loads. Using a two-degree-of-freedom model of a car travelling on a road made of slabs, the paper demonstrates that the proposed model estimates the statistics of the vehicle response and the fatigue life of its components more accurately than a traditional stationary model.

Optimal sizes and placements of piezoelectric actuators and sensors on an inflated torus

One of the limitations of a piezoelectric material is the amount of force it can exert. Hence, it is important to optimize the locations and sizes of the actuators so that the required control effort is minimum. Similarly, to obtain good signal to noise ratio, sensors should be chosen to provide maximum output for the vibration in the modes of interest. These problems become more critical as the number of actuators and sensors increases. In this study, we find optimum places and sizes of actuators/sensors on an inflated toroidal shell using genetic algorithm. Using the expressions for the generalized forces and sensor voltages developed previously, modal forces and modal sensing constants are determined. To obtain a cumulative performance measure of all the controlled modes, controllability and observability indices are used. Using these performance indices, optimal locations and sizes of the actuators and sensors are determined so that the actuators require minimum energy and the sensors provides maximum output energy. Finally, using an optimal control, the vibration suppression of the inflated torus using these actuators and sensors has been demonstrated.