Jimmy Issa

Satellite attitude control using three reaction wheels

This work addresses the attitude control of a satellite by applying MIMO quantitative feedback approach. The objective is to design a set of proper controllers in presence of unknown disturbances and parametric uncertainties for a nonlinear MIMO system. The physical model of satellite utilizes three reaction wheels as actuators. The controller goal is to change the rotational speed of reaction wheels to adjust the satellite in desired course. First, the mathematical model of satellite and its actuators using angular kinematics and kinetic equations is developed. Quantitative feedback theory is then applied to synthesize a set of linear controllers that deals with both nonlinearities in the equations and unknown parameters or disturbance sources. By using basically non-interacting desired outputs and extracting sets of linear time invariant equivalent (LTIE) plants, the controllers set is designed for nine SISO systems. Simulation of closed loop system shows that all desired specifications of closed loop (tracking, stability, disturbance rejection) are robustly satisfied.

Energy Dissipation in Dynamical Systems Through Sequential Application and Removal of Constraints

A strategy to remove energy from finite-dimensional elastic systems is presented. The strategy is based on the cyclic application and removal of constraints that effectively remove and restore degrees of freedom of the system. In general, application of a constraint removes kinetic energy from the system, while removal of the constraint resets the system for a new cycle of constraint application. Conditions that lead to a net loss in kinetic energy per cycle and bounds on the amount of energy removed are presented. In linear systems, these bounds are related to the modes of the system in its two states, namely, with and without constraints. It is shown that energy removal is always possible, even using a random switching schedule, except in one scenario, when energy is trapped in modes that span an invariant subspace with special orthogonality properties. Applications to nonlinear systems are discussed. Examples illustrate the process of energy removal in both linear and nonlinear systems.

Vibration Suppression in Structures Using Cable Actuators

We investigate the use of cable tension for active vibration control in frame structures. A general formulation for this class of systems is developed using finite elements, which includes the dynamics of the structure and the effects of cable-structure interactions. It is found that the cable tension has two distinct effects on the structure. The first is a parametric effect in which the cable tension changes the stiffness of the structure, and the second is a direct effect that provides an external force on the structure. Based on this model, a general control scheme is developed that uses cable actuation to take advantage of these effects, both separately and together. The control scheme for all cases is based on modal amplitudes, and it applies and releases tension in such a manner that vibration energy is removed from the modes of the structure over a prescribed frequency range that depends on the bandwidth(s) of the actuator(s). The stability of the controlled systems is proven using nonlinear control theory. In addition, a method is developed for determining the optimal placement of cables for parametric stiffness control, which is verified via simulations. Finally, an experimental realization of the direct force control is tested on a frame structure and compared with simulations, demonstrating its effectiveness.

Ground motion isolation using a newly designed vibration absorber

A new vibration absorber setup for vibration attenuation in single degree of freedom systems subjected to harmonic base motion is proposed. The absorber is placed so as to separate between the vibrating ground and the main undamped system. It consists of a mas spring damper directly connected to the vibrating ground. The main system is modelled as a mass spring attached to the absorbers mass. The optimal absorber parameters are determined with the aim of reducing the steady-state amplitude of the main mass. It is shown that the amplitude of the main mass passes through three fixed points, two of which are used in the determination of the optimal shape of the transfer function. One of the fixed points is independent of the damping ratio and the second is independent of both the damping and tuning ratios. For this setup, the solution is not unique since the ultimate design is reached by a complete isolation of the main mass from the moving ground and is attained by removing the absorbers damper and stiffness. Since this solution is not physically achievable, for a given mass ratio of the system, the smallest tuning ratio which ensures structural integrity of the system is selected. The optimal damping ratio which yields the optimal shape of the objective function is determined analytically in terms of the mass and tuning ratios. A design flowchart is presented to be used for the design of such absorbers.

Design of a vibration absorber for harmonically forced damped systems

Vibration suppression in harmonically forced viscously damped systems is considered using a new vibration absorber setup. The absorber is placed between the primary system and the supporting ground. The optimal absorber parameters are obtained with the aim of minimizing the maximum of the primary system frequency response. For a given damping ratio of the primary system and mass ratio of the system, the optimal stiffness and damping ratios of the absorber are calculated numerically. Two different numerical approaches are used in solving the problem; the first is based on the genetic algorithm technique and the second on the downhill simplex method. It is shown that an optimal mass ratio exists and it is calculated along with the corresponding absorber parameters for a range of the primary system damping ratio. The utmost optimal parameters associated with the optimal mass ratios are tabulated to be used for the design of such absorbers. The absorber efficiency is discussed and it is shown that this absorber becomes detrimental as the mass ratio is increased or when damping in the primary system is high. The proposed and classical absorbers efficiencies are compared.

Vibration absorbers for simply supported beams subjected to constant moving loads

Vibration suppression in simply supported beams traversed by constant moving loads is explored using linear vibration absorbers. Assuming the Euler–Bernoulli beam theory, the beam is modeled using its first ten modes. The problem is formulated in terms of dimensionless parameters to render the results generic which are obtained for a range of the beam modal damping ratios and the system mass ratio. The objective is to minimize the maximum beam displacement for all load speeds. It is shown that the optimal absorber is an undamped absorber which should be attached at a fixed location irrespective of the modal damping or mass ratios. The optimal stiffness ratio is calculated numerically and a convenient analytical expression is obtained by curve fitting the numerical results to a second-order polynomial. The maximum error between the analytical model and the numerical solution is found to be negligible. The results are validated through comparison with a numerical example which was considered in the literature.

Optimal design of a new vibration absorber setup for randomly forced systems

In this work, vibration reduction in randomly forced systems is considered using a new vibration absorber setup. In the new setup, the absorber consists of a mass spring and damper, and is attached such that it separates the primary system from the fixed support. White noise excitation is assumed and the objective function is the mean square value of the primary system response function. For given damping and mass ratios of the system, the optimal stiffness and damping ratios of the absorber are determined. The optimal parameters are obtained in an analytical closed form when the primary system is undamped, and calculated numerically for damped primary systems. It is shown that an optimal mass ratio exists, unlike the case of classical absorbers where performance increases with increasing absorber mass. The optimal parameters associated with the optimal mass ratio are calculated and tabulated for a range of primary system damping ratios. The efficiency of the proposed absorber is discussed and compared to that of the classical absorber.

Optimal Design of a Damped Single Degree of Freedom Platform for Vibration Suppression in Harmonically Forced Undamped Systems

Vibration reduction in harmonically forced undamped systems is considered using a new vibration absorber setup. The vibration absorber is a platform that is connected to the ground by a spring and damper. The primary system is attached to the platform, and the optimal parameters of the latter are obtained with the aim of minimizing the peaks of the primary system frequency response function. The minimax problem is solved using a method based on invariant points of the objective function. For a given mass ratio of the system, the optimal tuning and damping ratios are determined separately. First, it is shown that the objective function passes through three invariant points, which are independent of the damping ratio. Two optimal tuning ratios are determined analytically such that two of the three invariant points are equally leveled. Then, the optimal damping ratio is obtained such that the peaks of the frequency response function are equally leveled. The optimal damping ratio is determined in a closed form, except for a small range of the mass ratio, where it is calculated numerically from two nonlinear equations. For a range of mass ratios, the optimal solution obtained is exact, because the two peaks coincide with the two equally leveled invariant points. For the remaining range, the optimal solution is semiexact. Unlike the case of the classical absorber setup, where the absorber performance increases with increasing mass ratios, it is shown that an optimal mass ratio exists for this setup, for which the absorber reaches its utmost performance. The objective function is shown in its optimal shape for a range of mass ratios, including its utmost shape associated with the optimal mass ratio of the setup. [DOI: 10.1115/1.4023811]

Control of Space Structures Using Cable Actuators

We explore the use of cable actuators for vibration suppression in space structures. The dynamics of the structure and cable-structure interaction are modeled using finite elements. It is found that the cable has two distinct effects on the structure. The first is a parametric effect, which changes the stiffness of the structure, and the second is a direct effect resulting from an external force on the structure. A general control scheme is designed using passivity analysis, where the input is the cable tension. The study is divided into two parts. In the first part, control by stiffness variation is investigated placing special emphasis on cable placement on the structure. In the second study, control by the direct force is examined and numerical and experimental results are presented.Copyright

An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

This work presents an exact and general model order reduction (MOR) technique for a fast finite element resolution of elastohydrodynamic lubrication (EHL) problems. The reduction technique is based on the static condensation principle. As such, it is exact and it preserves the generality of the solution scheme while reducing the size of its corresponding model and, consequently, the associated computational overhead. The technique is complemented with a splitting algorithm to alleviate the hurdle of solving an arising semidense matrix system. The proposed reduced model offers computational time speed-ups compared to the full model ranging between a factor of at least three and at best 15 depending on operating conditions. The results also reveal the robustness of the proposed methodology which allows the resolution of very highly loaded contacts with Hertzian pressures reaching several GPa. Such cases are known to be a numerical challenge in the EHL literature. [DOI: 10.1115/1.4035154]