arXiv subjects

Siamak Tafazoli

Publications and source records attributed to Siamak Tafazoli.

4 recordsLinked to original sources

arXiv2021

Calculation of the Vacuum Energy Density using Zeta Function Regularization

This paper presents a theoretical calculation of the vacuum energy density by summing the contributions of all quantum fields vacuum states which turns out to indicate that there seems to be a missing bosonic contribution in order to match the predictions of current cosmological models and all observational data to date. The basis for this calculation is a Zeta function regularization method used to tame the infinities present in the improper integrals of power functions.

physics.gen-ph↗

arXiv2020

On Attitude Recovery of Spacecraft using Nonlinear Control

The general objective of this Ph.D. thesis is to study the dynamics and control of rigid and flexible spacecraft supported by a high-fidelity numerical simulation environment. The demand for greater attitude pointing precision, attitude maneuvering or recovery with the increased use of lightweight and flexible materials necessitates the consideration of flexible dynamics in the control strategy. These highly nonlinear dynamics which increase the order of the system are extremely difficult to model with high degree of accuracy. A general model for attitude and flexible dynamics for a class of spacecraft is hence derived in detail based on the so-called hybrid coordinates approach. The spacecraft considered has a star topology with a rigid central bus and flexible plate-type appendages. Given that the flexible spacecraft is under-actuated, the input-output feedback linearization technique is specifically used to partition the system into two distinct parts, namely an external linear system and an internal unobservable nonlinear system. A general internal/zero dynamics theorem for a class of nonlinear systems is proved and then applied to a flexible spacecraft which results in a linear asymptotically stable zero dynamics. The overall closed-loop stability of the flexible spacecraft is also analyzed rigorously and shown to be locally asymptotically stable using the Lyapunov theory. The robustness of the controller against modeling and parametric uncertainties is examined through extensive numerical simulations. Overall, the feedback linearization control scheme has been proven to be feasible and efficient for the attitude recovery of a spacecraft and has also become front and center in other application areas in the recent years.

eess.SY↗

arXiv2018

A Closed Form Solution for the Normal Form and Zero Dynamics of a Class of Nonlinear Systems

The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms exist for determining the zero dynamics, but none is straightforward and all are difficult to apply to large dimensional problems. A Closed form solution to the zero dynamics problem would motivate more usage of this powerful technique. The author presents here a simple algebraic methodology for the normal form and zero dynamics calculation of a class of nonlinear systems, mostly found in dynamical mechanical systems. The solution is in closed form so that application of the theorem presented is straight forward. As an illustration, the zero dynamics calculations for the complex dynamics of a flexible spacecraft is presented to demonstrate the simplicity and usefulness of the proposed closed form solution. Keywords: Control, Differential Geometry, Normal Form, Zero Dynamics, Nonlinear Systems, Feedback Linearization, Attitude Dynamics, Flexible Spacecraft.

math.OC↗

arXiv2018

Analytical Solution to Improper Integral of Divergent Power Functions Using The Riemann Zeta Function

This paper presents an analytical closed-form solution to improper integral $μ(r)=\int_0^{\infty} x^r dx$, where $r \geq 0$. The solution technique is based on splitting the improper integral into an infinite sum of definite integrals with successive integer limits. The exact solution of every definite integral is obtained by making use of the binomial polynomial expansion, which then allows expression of the entire summation equivalently in terms of a weighted sum of Riemann zeta functions. It turns out that the solution fundamentally depends on whether or not $r$ is an integer. If $r$ is a non-negative integer, then the solution is manifested in a finite series of weighted Bernoulli numbers, which is then drastically simplified to a second order rational function $μ(r)=(-1)^{r+1}/(r+1)(r+2)$. This is achieved by taking advantage of the relationships between Bernoulli numbers and binomial coefficients. On the other hand, if $r$ is a non-integer real-valued number, then we prove $μ(r)=0$ by the virtue of the elegant relationships between zeta and gamma functions and their properties.

math.CA↗