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Authors: Michael A. Unbehauen, Gregory D. Sloan, Alberto J. Squatrito

Abstract:

Missile proliferation and global stability are intrinsically linked. Missile threats continually appear at the forefront of global security issues. North Korea’s recently demonstrated nuclear and intercontinental ballistic missile (ICBM) capabilities, for the first time since the Cold War, renewed public interest in strategic missile defense capabilities. To protect from limited ICBM attacks from so-called rogue actors, the United States developed the Ground-based Midcourse Defense (GMD) system. This study examines if the GMD missile defense shield has contributed to a safer world or triggered a new arms race. Based upon increased missile-related developments and the lack of adherence to international missile treaties, it is generally perceived that the GMD system is a destabilizing factor for global security. By examining the current state of arms control treaties as well as existing missile arsenals and ongoing efforts in technologies to overcome U.S. missile defenses, this study seeks to analyze the contribution of GMD to global stability. A thorough investigation cannot ignore that, through the establishment of this limited capability, the U.S. violated longstanding, successful weapons treaties and caused concern among states that possess ICBMs. GMD capability contributes to the perception that ICBM arsenals could become ineffective, creating an imbalance in favor of the United States, leading to increased global instability and tension. While blame for the deterioration of global stability and non-adherence to arms control treaties is often placed on U.S. missile defense, the facts do not necessarily support this view. The notion of a renewed arms race due to GMD is supported neither by current missile arsenals nor by the inevitable development of new and enhanced missile technology, to include multiple independently targeted reentry vehicles (MIRVs), maneuverable reentry vehicles (MaRVs), and hypersonic glide vehicles (HGVs). The methodology in this study encapsulates a period of time, pre- and post-GMD introduction, while analyzing international treaty adherence, missile counts and types, and research in new missile technologies. The decline in international treaty adherence, coupled with a measurable increase in the number and types of missiles or research in new missile technologies during the period after the introduction of GMD, could be perceived as a clear indicator of GMD contributing to global instability. However, research into improved technology (MIRV, MaRV and HGV) prior to GMD, as well as a decline of various global missile inventories and testing of systems during this same period, would seem to invalidate this theory. U.S. adversaries have exploited the perception of the U.S. missile defense shield as a destabilizing factor as a pretext to strengthen and modernize their militaries and justify their policies. As a result, it can be concluded that global stability has not significantly decreased due to GMD; but rather, the natural progression of technological and missile development would inherently include innovative and dynamic approaches to target engagement, deterrence, and national defense.

Keywords: Arms control, arms race, global security, GMD, ICBM, missile defense, proliferation.

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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