WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

The electric power system is currently undergoing a period of unprecedented changes. Environmental and sustainability concerns lead to replacement of a significant share of conventional fossil fuel-based power plants with renewable energy resources. This transition involves the major challenge of substituting synchronous machines and their well-known dynamics and controllers with power electronics-interfaced generation whose regulation and interaction with the rest of the system is yet to be fully understood. In this article, we review the challenges of such low-inertia power systems, and survey the solutions that have been put forward thus far. We strive to concisely summarize the laid-out scientific foundations as well as the practical experiences of industrial and academic demonstration projects. We touch upon the topics of power system stability, modeling, and control, and we particularly focus on the role of frequency, inertia, as well as control of power converters and from the demand-side.

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Foundations and Challenges of Low-Inertia Systems (Invited Paper)

The study of rotor blade aerodynamic performances of wind turbine has been presented in this thesis. This study was focused on aerodynamic effects changed by blade surface distribution as well as grid solution along the airfoil. The details of numerical calculation from Fluent were described to help predict accurate blade performance for comparison and discussion with available data. The direct surface curvature distribution blade design method for two-dimensional airfoil sections for wind turbine rotors have been discussed with the attentions to Euler equation, velocity diagram and the factors which affect wind turbine performance and applied to design a blade geometry close to an existing wind turbine blade, Eppler387, in order to argue that the blade surface drawn by direct surface curvature distribution blade design method contributes aerodynamic efficiency. The FLUENT calculation of NACA63-215V showed that the aerodynamic characteristics agreed well with the available experimental data at lower angles of attack although it was discontinuities in the surface curvature distributions between 0.7 and 0.8 in x/c. The discontinuities were so small that the blade performance could not be affected. The design of Eppler 387 blade performed to reduce drag force. The discontinuities of surface distribution matched the curve of the pressure coefficients. It was found in the curvature distribution that the leading edge pressure side had difficulties to connect to Bezier curve and also the trailing edge circle was never be tangent to the lines of trailing edge pressure and suction sides due to programming difficulties.

Aerodynamics of wind turbines

A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed optimization technique which uses a piecewise polynomial representation for the state and controls, and collocation, thus converting the optimal control problem into a nonlinear programming problem, which is solved numerically. This technique has been modified to provide efficient handling of those portions of the trajectory which can be determined analytically, i.e., the coast arcs. Among the problems that have been solved using this method are optimal rendezvous and transfer (including multirevolution cases) and optimal multiburn orbit insertion from hyperbolic approach.

Optimal finite-thrust spacecraft trajectories using collocation and nonlinear programming

 Abstract—The present paper describes the structure and the design aspects of a robust PID controller for higher-order systems. A design scheme that combines deadbeat response, robust control, and model reduction techniques to enhance the performances and robustness of PID controller is presented. Unlike conventional deadbeat controllers, the tuning parameters are reduced to one cascade gain which yields a practical tuning method. The design scheme is illustrated on a pitch-axis autopilot design of an Unmanned Aerial Vehicle (UAV). Computer simulations show that the proposed method improves time-domain response performances and exhibits stronger robustness property to conquer system uncertainties.

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Robust PID Controller Design for an UAV Flight Control System

In this paper, an automatic control system design based on Integral Squared Error (ISE) parameter optimization technique has been implemented on longitudinal flight dynamics of an UAV. It has been aimed to minimize the error function between the reference signal and the output of the plant. In the following parts, objective function has been defined with respect to error dynamics. An unconstrained optimization problem has been solved analytically by using necessary and sufficient conditions of optimality, optimum PID parameters have been obtained and implemented in control system dynamics.

https://works.bepress.com/kamran_turkoglu/6/download/

PID Parameter Optimization of an UAV Longitudinal Flight Control System

Nonlinear consensus strategies for multi-agent networks under switching topologies: Real-time receding horizon approach

Distributed Real-Time Non-Linear Receding Horizon Control Methodology for Multi-Agent Consensus Problems

This paper investigates the utilization of differential thrust to help a commercial aircraft with a damaged vertical stabilizer regain its lateral/directional stability. In the event of an aircraft losing its vertical stabilizer, the consequential loss of the lateral/directional stability and control is likely to cause a fatal crash. In this paper, an aircraft with a completely damaged vertical stabilizer is investigated, and a unique differential thrust based adaptive control approach is proposed to achieve a stable flight envelope. The propulsion dynamics of the aircraft is modeled as a system of differential equations with engine time constant and time delay terms to study the engine response time with respect to a differential thrust input. The proposed differential thrust control module is then presented to map the rudder input to differential thrust input. Model reference adaptive control based on the Lyapunov stability approach is implemented to test the ability of the damaged aircraft to track the model aircraft's (reference) response in an extreme scenario. Investigation results demonstrate successful application of such differential thrust approach to regain lateral/directional stability of a damaged aircraft with no vertical stabilizer. Finally, the conducted robustness and uncertainty analysis results conclude that the stability and performance of the damaged aircraft remain within desirable limits, and demonstrate a safe flight mission through the proposed adaptive control methodology.

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Adaptive Differential Thrust Methodology for Lateral/Directional Stability of an Aircraft with a Completely Damaged Vertical Stabilizer

This paper presents real-time practical strategies for enhancing the endurance of Unmanned Aerial Vehicle (UAV) flights by utilizing wind energy. Consistent with actual flight, no regional knowledge of the wind field is assumed. Rather, the technique relies solely on making “optimal” decisions at each successive time instant, given the instantaneous values of estimated local wind speeds. Based on these estimates, optimal airspeed and/or heading angle corrections are determined to minimize the instantaneous power requirement for steady level flight. UAV dynamics are described in terms of a dynamic point-mass model, and vehicle motion is constrained via boundary controls to a three-dimensional region around a specified target point. Models of closed-loop trajectory tracking are developed using the method of dynamic inversion for both airspeed vector tracking and boundary trajectory tracking. A nominal reference trajectory is assumed in which the UAV flies a fixed radius, constant altitude orbit with an airspeed that would maximize the endurance in zero wind. Simulations conducted for varying wind patterns compare the average power consumption of the proposed strategy with that of the reference trajectory. Obtained results indicate a potential saving in power consumption and in endurance of the UAV by simply using the appropriate wind component instantaneously during the flight regime.

Kamran Turkoglu

Papers

PID Parameter Optimization of an UAV Longitudinal Flight Control System

Nonlinear consensus strategies for multi-agent networks under switching topologies: Real-time receding horizon approach

Distributed Real-Time Non-Linear Receding Horizon Control Methodology for Multi-Agent Consensus Problems

Adaptive Differential Thrust Methodology for Lateral/Directional Stability of an Aircraft with a Completely Damaged Vertical Stabilizer

Real-Time Insitu Strategies for Enhancing UAV Endurance by Utilizing Wind Energy