Ashraf Omran

Optimal vibration control for structural-acoustic coupling system

This paper proposes designing a static output feedback controller for a structural-acoustics coupling system using piezoelectric actuators. The system consists of a rectangular cavity with two flexible plates, one at the top of the cavity and the other at the bottom, and four other rigid boundaries. Piezoelectric pair patches are considered to be bonded to the top plate, and each pair is assumed to produce a pure moment actuation. The top plate is exposed to an external pressure excitation due to a planar wave generated by a sound source mounted above the cavity. The series solution is assumed for the displacements of the plates and the pressure inside the cavity. The responses of the coupled system are obtained using Galarkin’s method. In the control scheme, the controller gains have been optimally tuned using genetic algorithms. The proposed static output feedback controller shows an acceptable performance with simple implementation requirements compared to the linear quadratic Gaussian state feedback controller.

Nonlinearity Index Theory for Aircraft Dynamic Assessment

This paper introduces the nonlinearity index theory for assisting aircraft flight dynamics. The nonlinearity index theory was originally developed for orbital mechanics applications within the context of an initial value problem, while aircraft dynamic systems more commonly experience an input excitation as well as sensitivity to initial conditions. This current research proposes an algorithm for applying the index to aircraft dynamics. The algorithm starts by gridding down the flight envelope to a set of points. Around each point, an elliptical subregion is defined as ratios of the altitude and Mach number bands. A set of nominal linear models is then generated at each point. The maximum deviation of each nominal linear model from the equivalent linear models over the local subregion is presented as the basis for various nonlinear index measures. Visualizing these metrics over the entire flight envelope delivers a criterion to predict and identify flight regions of nonlinear phenomena such as limit cycli...

Full Envelope Nonlinear Parameter-Varying Model Approach for Atmospheric Flight Dynamics

This paper presents a nonlinear parameter-varying modeling approach to duplicate the aircraft dynamic behavior while moving from one flight region to another. This approach starts by generating a local two-term truncatedVolterra series, which is enough to capture the quadratic andbilinear nonlinearities, at different operating conditions over the flight envelope. The variation of these series’ coefficient matrices are then sought through different interpolation techniques. A nonlinear F-16 longitudinal model was used to assess the proposed approach. The improvement in the accuracy to predict, understand, and analyze the nonlinear aircraft behavior over the previous linear parameter-varying approach, which effectively ignored the second-order stability and control derivatives, is demonstrated through many numerical test cases.

Measuring Aircraft Nonlinearity Across Aerodynamic Attitude Flight Envelope

A new asymmetric level aerodynamic attitude flight envelope is introduced in this paper. Further, the nonlinearity of a six degree of freedom aircraft simulation model is analyzed with nonlinear index theory across this nontraditional flight envelope. The aerodynamic attitude envelope is an angle of attack vs. sideslip angle region describing the extent of where an aircraft can sustain a slipping horizontal flight condition, and is thus an extension of the more common speed-altitude symmetric level flight envelope. This new envelope can be used for design requirements, dynamic analysis, control synthesis, or performance comparison. Aircraft dynamic properties often change in a nonlinear way across operating conditions. Nonlinear index theory provides a new concept for measuring the strength of these changes and is applied to the asymmetric aerodynamic attitude envelope. This analysis provides new methodology and new insights to aircraft dynamics and control.

Analytical Response for the Prototypic Nonlinear Mass-Spring-Damper System

In this paper, a procedure to analytically develop an approximate nonlinear solution for the prototypic nonlinear mass-spring-damper system based on multi-dimensional convolution expansion theory is offered. An analytical nonlinear step response is also conducted to characterize the overall system response. The developed analytical step response provides an illumination for the source of differences between nonlinear and linear responses such as initial departure time, differences in settling times and steady value, and non-symmetric response. Feasibility of the proposed implementation is assessed by a numerical example. The developed kernel-based model shows the ability to predict, understand, and analyze the system behavior beyond that attainable by linear-based model.Copyright

Nonlinear cause-effect analysis for a second order system using Volterra kernels

In this paper, generalized analytical first and second Volterra kernels are developed for a nonlinear second order system as a paradigm for many dynamic systems. A step input is then employed to quantify and qualify the nonlinear response characteristics. The proposed analytical solution shows the ability of Volterra-based models to predict and understand the nonlinear system behavior beyond that attainable by linear-based models.

Measuring Aircraft Nonlinearity Across Aerodynamic Attitude Flight Envelope-Revisited With Symmetrized Aerodynamics

In previous research, the authors introduced a new asymmetric level aerodynamic attitude flight envelope. Further, nonlinearity of a six degree of freedom aircraft model was analyzed with nonlinear index theory across this nontraditional envelope. This paper revisits details concerning the experimental aerodynamic model used in the previous study after removing asymmetry and offset in the data. Asymmetry and offset in the force and moment coefficient data could originate from experimental error, model fabrication imperfections, vortex-dominated flow, data reduction flaws, or other sources. The purpose behind removing the asymmetry and offset is to facilitate analysis of the new aerodynamic attitude flight envelope with an ideal aircraft model so that fundamental relationships can be more easily observed, and to compare with the non-ideal case previously investigated. Literature shows that vortex-dominated flow causes side force, rolling moment, and yawing moment coefficient asymmetries. Based on the adapted and symmetrized aerodynamic data, a new aerodynamic attitude asymmetric level flight envelope is constructed and introduced. This angle of attack vs. sideslip angle envelope is an extension of the speed-altitude symmetric level flight envelope where in the former an aircraft can maintain a slipping horizontal flight condition. The new envelope provides enhanced insight to trimability-controllability regions for a model with ideal aerodynamic data characteristics. Aircraft dynamic characteristics frequently change in a nonlinear fashion across operating conditions. Nonlinear index theory is applied to the new symmetric aerodynamic attitude envelope. The index analysis exposes certain flight condition regions where nonlinearity strength is high.

Analytical Solution of Uniaxial Flight Systems Using Volterra Kernels in Frequency Domain

In previous research, a nonlinear analytical solution of the low-order flight system using Volterra kernels in the time domain was developed. In this paper, equivalent analytical solutions using Volterra kernels in the frequency domain is addressed. A two-term truncated Volterra series is developed for first-order and second-order generalized nonlinear single degree of freedom systems. The resultant models are given in the form of first and second kernels in the frequency domain. A parametric study of the influence of each linear and nonlinear term on kernel structures is investigated. Periodic input is then employed to quantify and qualify the nonlinear response characteristics. A uniaxial pitch motion example is presented as a low-order flight dynamic system. This example shows the ability of the proposed analytical Volterra-based model over the analytical linear model to predict, interpret, and analyze the nonlinear behavior.

Generalized frequency response of the nonlinear second order system

This paper develops generalized analytical first and second order transfer functions for the nonlinear second order system. A periodic input is also conducted to characterize the overall system response from the fundamental components. The proposed analytical solution provides more understanding of the influence of each linear and nonlinear component on the overall system behavior.

On the Influence of Structural Flexibility on Feedback Control Stability for Magnetically Suspended Vehicles

This paper presents a simple analysis evaluating the stability threshold for magnetically levitated flexible structures using dissipative colocated controllers. It is shown that with such a control structure, the controller that stabilizes a rigid levitated mass can also stabilize a simple flexible structure with the same overall mass and electrodynamics. Experimental and simulation results are presented to validate this conclusion.