Dynamics and Control of Satellite Relative Motion in Proximity Operations

In this dissertation, the development of relative navigation, guidance, and control algorithms of an autonomous space rendezvous and docking system are presented. These algorithms are based on innovative formulations of the relative motion equations that are completely explicit in time. The navigation system uses an extended Kalman filter based on these formulations to estimate the relative position and velocity of the chaser vehicle with respect to the target vehicle and the chaser attitude and gyro biases. This filter uses the range and angle measurements of the target relative to the chaser from a simulated LIDAR system, along with the star tracker and gyro measurements of the chaser. The corresponding measurement models, process noise matrix, and other filter parameters are provided. The guidance and control algorithms are based on the glideslope used in the past for rendezvous and proximity operations of the Space Shuttle with other vehicles. These algorithms are used to approach, flyaround, and to depart from a target vehicle in elliptic orbits. The algorithms are general and able to translate the chaser vehicle in any direction, decelerate while approaching the target vehicle, and accelerate when moving away. Numerical nonlinear simulations that illustrate the relative navigation, attitude estimation, guidance, and control algorithm\u27s, as well as performance and accuracy are evaluated in the research study

Optimization of driving mode switching strategy for a multimode plug-in hybrid electric vehicle

Hybrid electric vehicles have become increasingly popular recently. Switching from internal combustion engine to battery as a clean source of energy is considered as a solution to reduce city pollution due to vehicle emissions. PHEV is a viable balance between the two sources of energy to achieve higher fuel economy with lower emissions. For a multimode PHEV, the car switches among three operation modes; namely electric mode, series mode, and parallel mode to maximize fuel economy based on the driving conditions. In this work, minimization of fuel consumption is used to optimize the mode switching strategy for a PHEV. The study is conducted using a reference vehicle that resembles 2014 Honda Accord Plug-in Hybrid vehicle. Global optimization with constraints using pattern search method is utilized. Starting from a switching strategy with 〖MPG〗_e = 30, optimization increased fuel economy to 〖MPG〗_e = 51.4 for a combined cycle (FTW75 and HWFET). Optimization proved to be a feasible method to improve mode switching strateg

Relative motion guidance, navigation and control for autonomous orbital rendezvous

In this paper, the dynamics of the relative motion problem in a perturbed orbital environment are exploited based on Gauss’ variational equations. The relative coordinate frame (Hill frame) is studied to describe the relative motion. A linear high fidelity model is developed to describe the relative motion. This model takes into account primary gravitational and atmospheric drag perturbations. In addition, this model is used in the design of a control, guidance, and navigation system of a chaser vehicle to approach towards and to depart from a target vehicle in proximity operations. Relative navigation uses an extended Kalman filter based on this relative model to estimate the relative position and velocity of the chaser vehicle with respect to the target vehicle and the chaser attitude and gyros biases. This filter uses the range and angle measurements of the target relative to the chaser from a simulated Light Detection and Ranging (LIDAR) system, along with the star tracker and gyro measurements of the chaser. The corresponding measurement models, process noise matrix and other filter parameters are provided. Numerical simulations are performed to assess the precision of this model with respect to the full nonlinear model.The analyses include the navigations errors, trajectory dispersions, and attitude dispersions

On The Solvability Of Some Diophantine Equations Of The Form ax+by = z2

The Diophantine equation ax+py = z2 where p is prime is widely studied by many mathematicians. Solving equations of this type often include Catalan’s conjecture in the process of proving these equations. Here, we study the non-negative integer solutions for some Diophantine equations of such family. We will use Mihailescu’s theorem (which is the proof of Catalan’s conjecture) and elementary methods to solve the Diophantine equations 16x −7y = z2, 16x − py = z2 and 64x − py = z2, then we will study a generalization where (4n)x − py = z2 and x, y, z,n are non-negative integers. By using Mihailescu’s theorem and a fundamental approach in the theory of numbers, namely the theory of congruence, we will determine the solution of the Diophantine equations 7x+11y = z2, 13x+17y = z2, 15x+17y = z2 and 2x+257y = z2 where x, y and z are non-negative integers. Also, we will prove that for any non-negative integer n, all non-negative integer solutions of the Diophantine equation 11n8x+11y = z2 are of the form (x, y, z) = (1,n,3(11) n2 ) where n is even, and has no solution when n is odd. Finally, we will concentrate on finding the solutions of the Diophantine equation 3x+ pmny = z2 where y = 1,2 and p > 3 a prime number

The effect of cold crystalloid versus warm blood cardioplegia on the myocardium during coronary artery bypass grafting

Background: The optimal cardioplegic solution is still debated. The objective of this study was to compare the effect of cold crystalloid versus warm blood cardioplegia on the myocardial injury during coronary artery bypass grafting. Methods: The study included 34 consecutive patients who underwent elective primary on-pump isolated coronary artery bypass grafting from 2016 to 2019. We randomly assigned the patients into two groups. Group (ICCC) (n= 17) received intermittent antegrade cold crystalloid cardioplegia and Group (IWBC) (n= 17) received intermittent antegrade warm blood cardioplegia. Results: There was no difference in the preoperative and operative variables between groups. The time taken by the heart to regain normal sinus rhythm was significantly longer in the cold crystalloid group (7.06 ± 1.8 vs. 2.17 ± 0.8 minutes, p<0.001) with a higher rate of reperfusion ventricular arrhythmia (35% versus 6%; p=0.03) compared to the warm blood cardioplegia group. Both coronary sinus acid production and lactate level were significantly higher in the warm blood group than in the cold crystalloid group (p< 0.001 and 0.043, respectively). The ischemic ECG changes and the severity of new segmental wall motion abnormalities were non-significantly different between both groups (p= 0.68 and 0.67, respectively). Postoperative CK-MB and cTnI levels in all-time points were not significantly different between groups (p= 0.46 and 0.37, respectively). ICU (2.29 ± 0.77 vs. 2.41 ± 0.87 days, p= 0.68) and hospital stay (9.28 ± 0.76 vs. 9.42 ± 0.88 days, p= 0.62) were non-significantly different between both groups. Conclusion: Intermittent antegrade cold crystalloid cardioplegia was associated with attenuated myocardial metabolism. However, it was associated with a longer time to regain normal sinus rhythm and more reperfusion ventricular arrhythmias. We did not find differences in the clinical and echocardiographic outcomes and cardiac enzymes between cold crystalloid and warm blood cardioplegia

A Model Predictive Control (MPC) approach on unit quaternion orientation based quadrotor for trajectory tracking

The objective of this paper is to introduce with a quaternion orientation based quadrotor that can be controlled by Model Predictive Control (MPC). As MPC offers promising performance in different industrial applications, quadrotor can be another suitable platform for the application of MPC. The present study consistently adopts unit quaternion approach for quadrotor orientation in order to avoid any axes overlapping problem, widely known as singularity problem whereas Euler angle orientation approach is unable to resolve so. MPC works based on the minimal cost function that includes the attitude error and consequently, the cost function requires quaternion error in order to proceed with process of MPC. Therefore, the main contribution of this study is to introduce a newly developed cost function for MPC because by definition, quaternion error is remarkably different from the attitude error of Euler angle. As a result, a unit quaternion based quadrotor with MPC can ascertain a smooth singularityfree flight that is influenced by model uncertainty. MATLAB and Simulink environment has been used to validate the cost function for quaternion by simulating several trajectories

Dynamics and control of quadcopter using linear model predictive control approach

This paper investigates the dynamics and control of a quadcopter using the Model Predictive Control (MPC) approach. The dynamic model is of high fidelity and nonlinear, with six degrees of freedom that include disturbances and model uncertainties. The control approach is developed based on MPC to track different reference trajectories ranging from simple ones such as circular to complex helical trajectories. In this control technique, a linearized model is derived and the receding horizon method is applied to generate the optimal control sequence. Although MPC is computer expensive, it is highly effective to deal with the different types of nonlinearities and constraints such as actuators’ saturation and model uncertainties. The MPC parameters (control and prediction horizons) are selected by trial-and-error approach. Several simulation scenarios are performed to examine and evaluate the performance of the proposed control approach using MATLAB and Simulink environment. Simulation results show that this control approach is highly effective to track a given reference trajectory

Trajectory tracking of quaternion based quadrotor using model predictive control

The aim of this paper is to introduce the trajectory tracking with a quaternion based quadrotor operation using model predictive con-trol (MPC). Since the efficacy of MPC on a system under noise and disturbance has been distinguished, it is a fair and successful attempt to apply MPC on the quaternion based quadrotor, which is a quite well-known system with uncertainties during operation. Quaternion approaches singularity-free orientation that is advantageous to design any trajectory for quadrotor wherein roll or pitch angle reaches at 90o. As a quaternion, with its four-tuple characteristics that incorporate vector elements, is different from Euler-angle orientation, a new cost function has been developed for the respective MPC controller. In order to achieve singularity-free ori-entations and abate the model infidelity of the system, the quaternion and MPC algorithm have been incorporated for quadrotor flight. Simulation based results elucidate the success of trajectory tracking of quaternion based dynamics of quadrotor using MPC approach

Impact of Culture Media Composition, Nutrients Stress and Gamma Radiation on Biomass and Lipid of the Green Microalga, Dictyochloropsis splendida as a Potential Feedstock for Biodiesel Production

يعتمد إنتاج الديزل الحيوي من الطحالب الدقيقة على إنتاج الكتلة الحيوية ومحتوى الدهون. يتم التحكم في زياده انتاج الكتلة الحيوية و تراكم الدهون بواسطة عدة عوامل.فى هذا العمل تم دراسة تأثيرات ثلاث اوساط غذائيه خاصة بزراعة الطحالب ( BG11, BBM, Urea media) وايضا بعض المغذيات)النيتروجين والفوسفورو المغنيسيوم والكربون) واشعة جاما على نمو وانتاج الدهون لطحالب Dictyochloropsis splendida. تم الحصول علي أعلي انتاج للكتله الحيويه والدهون لطحلب Dictyochloropsis splendida  عندما تم زراعة الطحلب على الوسط الغذائي BG11 . علاوة على ذلك كان اعلى انتاجية للكتله الحيويه عند 3000 مليجرام / لتر نيتروجين او 160 مليجرام / لتر فوسفور او 113 مليجرام/لتر مغنسيوم او 20 مليجرام/ لتر كربونات.  بينما عند غياب المغذيات فان تراكم الدهون زاد. من ناحية اخرى فان المحتوى الدهنى للطحلب وصل الى 18.26% عندما تعرضت خلايا الطحلب لجرعة 25 جراى من اشعة جاما. وكانت  الدهون المستخلصة من الطحلب تتكون من نسبة عالية من الاحماض الدهنية المشبعة (SFAs, 63.33% ) والاحماض الدهنية الغيرمشبعة (UFAs, 37.02%) وكانت السيادة لحمض البالمتيك (C16:0) ثم حمض اللينوليك (C18:2) فحمض بنتاديكانويك (C15:0) وحمض بالميتوليك (C16:1). و تمثل الاحماض الدهنية المستخلصه من طحلب Dictyochloropsis splendida بهذا التركيب مواد خام واعدة لانتاج الديزل الحيوي.Biodiesel production from microalgae depends on the biomass and lipid production. Both biomass and lipid accumulation is controlled by several factors. The effect of various culture media (BG11, BBM, and Urea), nutrients stress [nitrogen (N), phosphorous (P), magnesium (Mg) and carbonate (CO3)] and gamma (γ) radiation on the growth and lipid accumulation of   Dictyochloropsis splendida were investigated. The highest biomass and lipid yield of D. splendida were achieved on BG11 medium. Cultivation of D. splendida in a medium containing 3000 mg L−1 N, or 160 mg L−1 P, or 113 mg L−1 Mg, or 20 mg L-1 CO3, led to enhanced growth rate. While under the low concentrations of nutrients caused a marked increase in the lipid content. Cultures exposure to 25 Gy of γ-rays, led to an increase in lipid content up to 18.26 ± 0.81 %. Lipid profile showed the maximum presence of saturated fatty acids (SFAs, 63.33%), and unsaturated fatty acids (UFAs, 37.02%). Fatty acids (FAs) recorded the predominance of C16:0, C18:2, C15:0 and C16:1, which strongly proved D. splendida is a promising feedstock for biodiesel production.        

DYNAMICS AND CONTROL OF MINI AERIAL VEHICLE USING MODEL PREDICTIVE CONTROL

Nowadays Mini Aerial Vehicles (MAVs) are popular in many areas such as aerial photography, inspection, surveillance and search and rescue missions in complex and dangerous environments due to their low cost, small size, superior mobility, and hover capability. Multifarious applications of MAVs inspire researchers to concentrate on different types of controllers like linear, nonlinear or learning-based. The attention of this work is to design a robust controller and to develop an accurate mathematical model of Quadrotor, a type of MAV as it behaves roughly in uncertain environments. Quadrotor is an under-actuated and highly nonlinear system with six degrees of freedom (DOF). The mathematical model of quadrotor is derived based on Newton-Euler method that includes aerodynamic drag and moment that are sometimes overlooked in literatures. For higher precision modelling, model uncertainties are also included in the system. In addition, the kinematic model is derived utilizing Euler angles and Quaternion methods. Quaternion approach has the advantage of singularity free orientation while Euler angles are easy to visualize. This work investigates the performance of three different controllers which includes Proportional-Integral-Derivative (PID), Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC) based on several performance evaluation factors. PID offers fast response to the system comparing to other controllers although choosing proper gain is challenging for PID. However, it cannot handle directly under-actuated system and due to the fact, some states are required to be decoupled. LQR ensures fast response and can deal with Multiple Input Multiple Output (MIMO) system at the same time. The main drawback of the LQR controller is its incapability of dealing with steady-state error. Conversely, MPC has the functionalities of dealing with MIMO system with constraints and uncertainties while other controllers fail. The performance of the controllers are presented based on tracking accuracy using Root Mean Square Error (RMSE) method and control stability using control input norm method. MATLAB and Simulink environment is considered to carry out the simulations. Based on simulated experiments, it is found that MPC could track the trajectories more accurately with stable control effort comparing to PID controllers and LQR