Modeling Energy Harvesting from Membrane Vibrations in COMSOL

Abstract: This paper presents an ongoing effort, motivated by developing self-contained sensors for structural health monitoring of inflatable structures, to model the process of extracting useable electrical power from the mechanical vibrations of thin, prestressed membrane structures. The multiphysics package COMSOL is being used to estimate the time-domain response of a piezoelectric patch placed onto a thin-film membrane to induced vibrations. Rayleigh damping coefficients will be used to represent the energy dissipated from the system through the harvesting process. Currently, prestress and eigenmodes have been successfully modeled in COMSOL. In following work, the prestressed solution will be used in the timedomain analysis for a more realistic representation of the added stiffness in the system

Modeling, design, and control of tensegrity structures with applications

Classical flexible structures dynamics and control suffer from several major deficiencies. First, reliable mathematical models involve partial differential equations which are difficult to deal with analytically as well as numerically. A partial differential equations mathematical model of a system\u27s dynamics is not practical for control system design, since most of the modern control systems design methodologies assume a state space representation. Second, from a practical perspective, the control of classical truss structures involves the use of expensive and short life mechanisms like telescopic struts. Third, the control of classical truss structures involves high energy, massive, hydraulic actuators. Fourth, classical controllable structures have many, complicated, bar to bar joints, which make the control task difficult. This thesis proposes a class of lightweight, space structures, called tensegrity structures, which can be reliably modeled using ordinary differential equations. Tensegrity structures offer excellent opportunities for physically integrated structure and control system design since their members can serve simultaneously as sensors, actuators, and load carrying elements. The actuating functions can be carried by tendons, controlled by electric motors. Thus, telescopic struts and hydraulic actuators can be eliminated. Additionally, tensegrity structures can be built without any bar to bar connections. The general prestressability conditions for tensegrity structures are derived from the principle of virtual work. In several cases these conditions are analytically solved, allowing for the parameterization of certain classes of prestressable configurations. A general methodology for the investigation of the prestressability conditions is also developed. The methodology uses symbolic and numeric computation, and it is meant to significantly reduce the complexity of the prestressability conditions for certain prestressable configurations. Mathematical models for tensegrity structures dynamics are developed using the Lagrangian approach. For certain classes of structures, particular motions are investigated and simpler dynamic equations are derived. These equations are next used for a simple, efficient, tendon control reconfiguration procedure. For certain classes of tensegrity structures linear parametric dynamical models are also developed. A tendon control deployment procedure for tensegrity structures is developed. The procedure is time optimal and uses continuous time control laws. It is based on the discovery of a connected equilibrium manifold to which the deployed and undeployed configurations belong. The deployment is conducted such that, in the state space, the deployment path is close enough to the equilibrium manifold. A force and torque sensor based on a tensegrity structure is proposed, enabling the simultaneous measurement of six quantities, three orthogonal forces and three orthogonal moments. An optimal estimator is designed, based on the linearized model of the structure. Finally, a motion simulator which exploits the intrinsic advantages of a tensegrity structure, is proposed. The actuating functions are carried out by the tendons, eliminating the telescopic actuators. A nonlinear robust tracking controller is designed to assure exponential convergence of the tracking error to a ball of prespecified radius, with a prespecified rate of convergence

Comfortable Helicopter Flight Via Passive/Active Morphing

This article offers a new perspective in defining comfortable helicopter flight along with two solutions based on passive and active main rotor morphing. Constrained optimization design problems aimed at minimizing flight control energy while satisfying variance constraints on flight parameters that are considered important in passenger comfort and noise reduction are formulated and solved. Output variance constrained (OVC) control is used for control system design and simultaneous perturbation stochastic approximation (SPSA) is employed to solve the resulting constrained optimization problems. Details on the computation of the control energy are given. Closed-loop responses of designs that satisfy prescribed variance constraints with a very small margin on the achievable variance bounds are compared with responses of designs that satisfy such constraints with a larger margin both for passively and actively morphing helicopters

Modeling and control of a helicopter slung-load system

This article investigates modeling and modern control for a helicopter and slung-load system. For this purpose complex, physics based, control oriented helicopter models are used. Point mass approach is used to model the external load's dynamics. The resulting nonlinear equations of motion are then trimmed for straight level flights and linearized around these flight conditions. Behaviors of representative trim variable values (i.e. cable angle and longitudinal and lateral cyclic blade pitch angles) and modes (i.e. flight dynamics and load modes) are thoroughly examined while some model parameters (e.g. cable length, load mass, and equivalent flat plate area) change. These behaviors are compared to data found in the literature. Furthermore, variance constrained controllers (i.e. output variance constrained and input variance constrained controllers) are applied for control system design. These controllers' performance is examined when they are aware of the slung-load's existence and when they are not aware of the slung-load. (C) 2013 Elsevier Masson SAS. All rights reserved.&nbsp;This article investigates modeling and modern control for a helicopter and slung-load system. For this purpose complex, physics based, control oriented helicopter models are used. Point mass approach is used to model the external load&rsquo;s dynamics. The resulting nonlinear equations of motion are then trimmed for straight level flights and linearized around these flight conditions. Behaviors of representative trim variable values (i.e. cable angle and longitudinal and lateral cyclic blade pitch angles) and modes (i.e. flight dynamics and load modes) are thoroughly examined while some model parameters (e.g. cable length, load mass, and equivalent flat plate area) change. These behaviors are compared to datafound in the literature. Furthermore, variance constrained controllers (i.e. output variance constrained and input variance constrained controllers) are applied for control system design. These controllers&rsquo; performance is examined when they are aware of the slung-load&rsquo;s existence and when they are not aware of the slung-load.&nbsp;</div

Variance-constrained control of maneuvering helicopters with sensor failure

This article presents the novel results obtained using variance-constrained controllers and maneuvering helicopters also when some helicopter sensors fail. For this purpose, complex, control oriented, and physics-based helicopter models are used. A nonlinear model of the helicopter, which includes blade flexibility, is first linearized around specific maneuvering flight conditions (i.e. level banked turn and helical turn). The resulting linearized models are used for the design of variance-constrained controllers (i.e. output and input variance-constrained controllers). Then, the robustness of the closed-loop systems with respect to modeling uncertainties (i.e. flight conditions and helicopter inertial parameters variations) is studied. Next, variance-constrained controllers are designed for these maneuvering helicopter models when some helicopter sensors fail. Several sensor failure cases are examined and robustness properties of the closed-loop systems with respect to modeling uncertainties are also examined. Limitations of the control design process due to the number and type of failed sensors are investigated as well. Finally, the possibility to adaptively switch between controllers in order to mitigate sensor failure is studied.This article presents the novel results obtained using variance-constrained controllers and maneuvering helicopters also when some helicopter sensors fail. For this purpose, complex, control oriented, and physics-based helicopter models are used. A nonlinear model of the helicopter, which includes blade flexibility, is first linearized around specific maneuvering flight conditions (i.e. level banked turn and helical turn). The resulting linearized models are used for the design of variance-constrained controllers (i.e. output and input variance-constrained controllers). Then, the robustness of the closed-loop systems with respect to modeling uncertainties (i.e. flight conditions and helicopter inertial parameters variations) is studied. Next, variance-constrained controllers are designed for these maneuvering helicopter models when some helicopter sensors fail. Several sensor failure cases are examined and robustness properties of the closed-loop systems with respect to modeling uncertainties are also examined. Limitations of the control design process due to the number and type of failed sensors are investigated as well. Finally, the possibility to adaptively switch between controllers in order to mitigate sensor failure is studied.</p

Flight Control Energy Saving via Helicopter Rotor Active Morphing

Helicopter main rotor active morphing is investigated to save helicopter flight control energy in the presence of constraints on outputs. For this purpose, the nonlinear equations of motion of the helicopter are linearized around straight level flight. Then, several main rotor active morphing scenarios such as blade radius, blade chord length, blade twist angle, and rotor angular speed variation are analyzed individually (i.e., each active morphing scenario is implemented one at a time). Output-variance-constrained control is used for helicopter flight control system design, and the control energy savings due to active morphing with respect to a conventional helicopter are evaluated. An extensive circumstance in which all active morphing concepts are implemented simultaneously is examined to obtain larger control energy savings. The possibility of using morphing controls for trimming is also considered, and stochastic optimization is used to solve the resulting simultaneous trimming and control design problem. Extensive analysis, including closed-loop system responses, is carried out for the most energy-efficient active morphing procedure. Comparisons with a helicopter designed using passive instead of active morphing are also performed. Finally, some robustness properties of the closed-loop system corresponding to the active morphing scenario are examined

Simultaneous Helicopter and Control-System Design

This article proposes simultaneous helicopter and control system design and illustrates its advantages. First, the traditional, sequential approach in which a satisfactory control system is designed for a given helicopter is applied. Then, a novel approach, in which the helicopter and control system are simultaneously designed, is applied to redesign the entire system. This redesign process involves selecting certain helicopter parameters as well as control system parameters. For both design procedures the key objectives are to minimize control energy and satisfy prescribed variance constraints on specific outputs. In order to solve the complex optimization problem corresponding to the simultaneous design approach, an efficient solution algorithm is developed by modifying the simultaneous perturbation stochastic approximation method to account for limits on optimization parameters. The algorithm is applied to redesign helicopters using models generated in straight level as well as maneuvering flight conditions. The performance of the designs obtained using the sequential and simultaneous design approaches is compared and the redesign process is thoroughly investigated. Finally, the robustness of the redesigned systems is also studied

Robustness of Variance Constrained Controllers For Complex, Control Oriented Helicopter Models

Complex helicopter models are used for variance constrained control design and robustness studies. The modeling process is briefly outlined and followed by output and input variance constrained control design. Extensive numerical investigations of closed loop systems eigenvalues variations and time responses indicate that these controllers are robustly stable for modeling uncertainties in flight speeds, inertial properties, initial conditions and noise intensities

Constrained predictive control of helicopters

Purpose - The purpose of this paper is to show the feasibility of constrained model predictive control (MPC) for sophisticated helicopter models which are derived by physical considerations