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Articles 4561 - 4590 of 11146
Full-Text Articles in Engineering
Experimental Investigation Of Mixtures Of 1-Ethyl-3-Methylimidazolium Ethyl Sulfate And Ethylammonium Nitrate With Electrospray Propulsion Applications, Mitchell J. Wainwright, Joshua L. Rovey, Shawn W. Miller, Benjamin D. Prince
Experimental Investigation Of Mixtures Of 1-Ethyl-3-Methylimidazolium Ethyl Sulfate And Ethylammonium Nitrate With Electrospray Propulsion Applications, Mitchell J. Wainwright, Joshua L. Rovey, Shawn W. Miller, Benjamin D. Prince
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Physical properties, performance metrics, and mass spectra of mixtures of two ionic liquids (1-ethyl-3-methylimidazolium ethyl-sulfate aka [Emim][EtSO4] and ethyl ammonium nitrate aka EAN) are investigated from the standpoint of electrospray propulsive characteristics. Spectra suggest that as the [Emim][EtSO4] mixture fraction increases, the intensity of [Emim][EtSO4] related species in the plume also increases, while the presence of EAN decreases. Spectra also show presence of both EAN proton transfer species and species related to chemical reaction of [EtSO4] and water. Despite the volatility of EAN, it emits stably into vacuum at low flow rates when mixed with 25% [Emim][EtSO4]. Spectra also show …
Hydroxylammonium Nitrate Species In A Monopropellant Electrospray Plume, Mitchell J. Wainwright, Joshua L. Rovey, Shawn W. Miller, Benjamin D. Prince, Steven P. Berg
Hydroxylammonium Nitrate Species In A Monopropellant Electrospray Plume, Mitchell J. Wainwright, Joshua L. Rovey, Shawn W. Miller, Benjamin D. Prince, Steven P. Berg
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A mixture of 1-ethyl-3-methylimidazolium ethyl sulfate ([Emim][EtSO4]) and hydroxylammonium nitrate (HAN) is an energetic monopropellant potentially suitable in a multi-mode chemical-electric microtube-electrospray micro propulsion system. In this work, electrospray plume mass spectra are compared between the monopropellant mixture and neat [Emim][EtSO4]. This comparison clearly indicates new and additional species present in the plume due to the addition of HAN. Mass spectra from 20-600 amu/q were obtained over a variety of angles and flow rates from 2 pL/sec to 3 nL/sec in both cation and anion extraction modes. Mass spectrum dependence on flow rate and angular orientation agree qualitatively well with …
Real-Time Electrical Impedance Monitoring Of Carbon Fiber-Reinforced Polymer Laminates Undergoing Quasi-Static Indentation, Khaled Almuhammadi, Arief Yudhanto, Gilles Lubineau
Real-Time Electrical Impedance Monitoring Of Carbon Fiber-Reinforced Polymer Laminates Undergoing Quasi-Static Indentation, Khaled Almuhammadi, Arief Yudhanto, Gilles Lubineau
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Laminated composites are vulnerable to damage from out-of-plane loading, particularly impact loading, and the incurred damage is often only detected by evaluating the post-impact condition of the composites. Real-time monitoring techniques are desirable for early detection of damage. Utilizing changes in the electrical properties of composites to track incurred damage is promising, but the interpretation of such measurements is still challenging. Here, an electro-mechanical system is introduced to understand how well we could detect mechanical degradation in carbon-fiber-reinforced polymer (CFRP) plates undergoing a quasi-static indentation (QSI) test, which is representative of an impact load. The system measures the in situ, …
Traditional Vs Gesture Based Uav Control, Sam J. Holley, Brian Sanders, Dennis Vincenzi, Yuzhong Shen
Traditional Vs Gesture Based Uav Control, Sam J. Holley, Brian Sanders, Dennis Vincenzi, Yuzhong Shen
Publications
Abstract. The purpose of this investigation was to assess user preferences for controlling an autonomous system. A comparison using a virtual environment (VE) was made between a joystick based, game controller and a gesture-based system using the leap motion controller. Command functions included basic flight maneuvers and switching between the operator and drone view. Comparisons were made between the control approaches using a representative quadcopter drone. The VE was designed to minimize the cognitive loading and focus on the flight control. It is a physics-based flight simulator built in Unity3D. Participants first spend time familiarizing themselves with the basic controls …
Effects Of Uncertainty Refinement On Satellite Collision Probability, Bruce Thomas Morrison
Effects Of Uncertainty Refinement On Satellite Collision Probability, Bruce Thomas Morrison
Masters Theses
"Due to the drastic increase in orbital debris about the Earth, the likelihood for new and current mission satellites to collide with other objects grows. When a mission satellite is placed in a highly populated orbit in the vicinity of other satellites or debris, it is necessary to consider the probability of collision to assess any possible conjunctions. The computation of the collision probability is heavily dependent on the relative position and velocity of the objects during conjunction, as well as the combined covariance. There are two main types of analytic collision probability computations; the first assumes that the objects …
Analyzing The Effects Of Attitude Errors When Quantifying The On-Orbit Performance Of A Cubesat Micropropulsion System, Andrew Orion Watson
Analyzing The Effects Of Attitude Errors When Quantifying The On-Orbit Performance Of A Cubesat Micropropulsion System, Andrew Orion Watson
Masters Theses
"CubeSats and small satellites have become popular methods of performing space research. Accordingly, interest has also grown in designing micropropulsion systems to increase the lifespan of these satellites. This work describes the framework for analyzing the effects of imperfect attitude determination and control when quantifying the on-orbit performance of a micropropulsion system. The Gauss variation of parameters equations were implemented to model the orbital mechanics, with perturbing models for the zonal harmonics, atmospheric drag, and solar radiation pressure included. Two common sources for imperfections in a spacecraft's attitude were considered. The first was to consider the effect of the spacecraft …
Small Satellite Earth-To-Moon Direct Transfer Trajectories Using The Cr3bp, Garrett Levi Mcmillan
Small Satellite Earth-To-Moon Direct Transfer Trajectories Using The Cr3bp, Garrett Levi Mcmillan
Masters Theses
"The CubeSat/small satellite field is one of the fastest growing means of space exploration, with applications continuing to expand for component development, communication, and scientific research. This thesis study focuses on establishing suitable small satellite Earth-to-Moon direct-transfer trajectories, providing a baseline understanding of their propulsive demands, determining currently available off-the-shelf propulsive technology capable of meeting these demands, as well as demonstrating the effectiveness of the Circular Restricted Three Body Problem (CR3BP) for preliminary mission design. Using the CR3BP and derived requirements from NASA's Cube Quest Challenge, five different trajectory scenarios were analyzed for their propulsive requirements. Results indicate that the …
Conceptual Design Of Male Uavs, Vincent Spada
Conceptual Design Of Male Uavs, Vincent Spada
Graduate Theses, Dissertations, and Problem Reports (ETD)
The conceptual design process of aircraft involves the creation of a product, in this case UAVS (unmanned aerial vehicles), using the most effective means possible across multiple subdisciplines of Aerospace Engineering. This paper will outline a unique methodology that involves calculating certain design variables such as wing loading, power loading, aspect ratio and cruise altitude in the conceptual design phase for MALE (medium altitude long endurance) UAVs. Aircraft characteristics from MALE UAVs such as the MQ-9 predator and MQ-1 reaper will used for a comparative aircraft study as “jumping off” points in order to carry out the initial calculations. An …
Artificial Immune System For Unmanned Aerial Vehicle Abnormal Condition Detection And Identification, Ryan G. Mclaughlin
Artificial Immune System For Unmanned Aerial Vehicle Abnormal Condition Detection And Identification, Ryan G. Mclaughlin
Graduate Theses, Dissertations, and Problem Reports (ETD)
A detection and identification scheme for abnormal conditions was developed for an unmanned aerial vehicle (UAV) based on the artificial immune system (AIS) paradigm. This technique involves establishing a body of data to represent normal conditions referred to as “self” and differentiating these conditions from abnormal conditions, referred to as “non-self”. Data collected from simulation of the UAV attempting to autonomously fly a pre-decided trajectory were used to develop and test a scheme that was able to detect and identify aircraft sensor and actuator faults. These faults included aerodynamic control surface locks and damages and angular rate sensor biases. The …
Utilization Of Scale In Keypoint Detection And Feature Description, Andrew P. Rhodes
Utilization Of Scale In Keypoint Detection And Feature Description, Andrew P. Rhodes
Graduate Theses, Dissertations, and Problem Reports (ETD)
Ubiquitous availability of inexpensive three dimensional (3D) sensors has led to an abundance of keypoint detection and feature description techniques for point-clouds. While some recent methods utilize color along with geometric information, most only implicitly discuss -- if not completely disregard -- the information provided by scale. Scale is an inherent characteristic of any keypoint or feature that describes its physical size or region of support.
Exploiting information provided by scale facilitates the processes of keypoint detection and feature description. A 3D scale-space, extended from robust and popular 2D methods, is constructed to diffuse a signal on triangulated meshes. Methods …
Enabling Robust State Estimation Through Covariance Adaptation, Ryan Magnum Watson
Enabling Robust State Estimation Through Covariance Adaptation, Ryan Magnum Watson
Graduate Theses, Dissertations, and Problem Reports (ETD)
Several robust state estimation frameworks have been proposed over the previous decades. Underpinning all of these robust frameworks is one dubious assumption. Specifically, the assumption that an accurate a priori measurement uncertainty model can be provided. As systems become more autonomous, this assumption becomes less valid (i.e., as systems start operating in novel environments, there is no guarantee that the assumed a priori measurement uncertainty model characterizes the sensors current observation uncertainty).
In an attempt to relax this assumption, a novel robust state estimation framework is proposed. The proposed framework enables robust state estimation through the iterative adaptation of the …
Improving Solder Joints Formed In Microgravity By Use Of Magnetic Soldering Paste Additives, Aaron Dunkle
Improving Solder Joints Formed In Microgravity By Use Of Magnetic Soldering Paste Additives, Aaron Dunkle
Graduate Theses, Dissertations, and Problem Reports (ETD)
With the expansion of the space industry, the need for the capability to repair electronics in space grows. Previous researchers have found that soldering in microgravity has yielded joints of poorer quality than those made on Earth, with increased interior porosity. WVU’s microgravity research team (MRT) constructed an experiment to solder onboard a microgravity aircraft to explore this problem and to test a possible solution. MRT’s experiment collected solder samples both in microgravity and a ground test, which were then cross-sectioned to allow the interior porosity of the joints to be studied. This determined that there was an increase in …
Immunity-Based Framework For Autonomous Flight In Gps-Challenged Environment, Mohanad Al Nuaimi
Immunity-Based Framework For Autonomous Flight In Gps-Challenged Environment, Mohanad Al Nuaimi
Graduate Theses, Dissertations, and Problem Reports (ETD)
In this research, the artificial immune system (AIS) paradigm is used for the development of a conceptual framework for autonomous flight when vehicle position and velocity are not available from direct sources such as the global navigation satellite systems or external landmarks and systems. The AIS is expected to provide corrections of velocity and position estimations that are only based on the outputs of onboard inertial measurement units (IMU). The AIS comprises sets of artificial memory cells that simulate the function of memory T- and B-cells in the biological immune system of vertebrates. The innate immune system uses information about …
Scaling Analysis And Experimental Investigation Of A Rotating Detonation Engine, David Thomas Billups
Scaling Analysis And Experimental Investigation Of A Rotating Detonation Engine, David Thomas Billups
Graduate Theses, Dissertations, and Problem Reports (ETD)
Pressure gain combustion (PGC) technologies, specifically rotating detonation engines (RDEs), are poised to provide the next big leap in gas turbine engine advancement, significantly increasing the thermal. RDEs make use of thermodynamic advantages of isochoric as opposed to isobaric combustion. Theorized to increase thermal efficiency by up to 7% [1], the RDE would have significant impact on reducing anthropogenic carbon emissions. In addition to efficiency gains, the RDE also provides mechanical simplicity and reduced size advantages compared to it’s traditional counterparts and PGC competition.
The United States (U.S.) Department of Energy (DOE) National Energy Technology Laboratory (NETL) maintains and operates …
Real-Time Path Planning In Constrained, Uncertain Environments, Randall Christensen, Robert C. Leishman
Real-Time Path Planning In Constrained, Uncertain Environments, Randall Christensen, Robert C. Leishman
Faculty Publications
A key enabler of autonomous vehicles is the ability to plan the path of the vehicle to accomplish mission objectives. To be robust to realistic environments, path planners must account for uncertainty in the trajectory of the vehicle as well as uncertainty in the location of obstacles. The uncertainty in the trajectory of the vehicle is a difficult quantity to estimate, and is influenced by coupling between the vehicle dynamics, guidance, navigation, and control system as well as any disturbances acting on the vehicle. Monte Carlo analysis is the conventional approach to determine vehicle dispersion, while accounting for the coupled …
Dynamic Response Of A Hingeless Helicopter Rotor Blade At Hovering And Forward Flights, Pratik Sarker
Dynamic Response Of A Hingeless Helicopter Rotor Blade At Hovering And Forward Flights, Pratik Sarker
LSU New Orleans Theses and Dissertations
The helicopter possesses the unrivaled capacity for vertical takeoff and landing which has made the helicopter suitable for numerous tasks such as carrying passengers and equipment, providing air medical services, firefighting, and other military and civil tasks. The nature of the aerodynamic environment surrounding the helicopter gives rise to a significant amount of vibration to its whole body. Among different sources of vibrations, the main rotor blade is the major contributor. The dynamic characteristics of the hingeless rotor consisting of elastic blades are of particular interest because of the strongly coupled equations of motion. The elastic rotor blades are subjected …
Operating Different Displays In Military Fast Jets Using Eye Gaze Tracker, Jeevitha Shree Dv, L. R. D. Murthy, Kamalpreet Singh Saluja, Pradipta Biswas
Operating Different Displays In Military Fast Jets Using Eye Gaze Tracker, Jeevitha Shree Dv, L. R. D. Murthy, Kamalpreet Singh Saluja, Pradipta Biswas
Journal of Aviation Technology and Engineering
This paper investigated the use of an eye-gaze-controlled interface in a military aviation environment. We set up a flight simulator and used the gaze-controlled interface in three different configurations of displays (head down, head up, and head mounted) for military fast jets. Our studies found that the gaze-controlled interface statistically significantly increased the speed of interaction for secondary mission control tasks compared to touchscreen- and joystick-based target designation system. Finally, we tested a gaze-controlled system inside an aircraft both on the ground and in different phases of flight with military pilots. Results showed that they could undertake representative pointing and …
Cfd Modeling Of Smoke Movement In An Atrium, Robin Wu
Cfd Modeling Of Smoke Movement In An Atrium, Robin Wu
UNLV Theses, Dissertations, Professional Papers, and Capstones
The purpose of this paper is to better understand the behavior of smoke movement in an atrium. Thus gives first responders and civilians in and out of building a better understanding
With the advancements of modern technology, computers and softwares make simulation models possible such as fire models to simulate fire and smoke movements. In this paper, a computational fluid dynamic (CFD) software Fire Dynamic Simulator (FDS) is used to conduct a series of atrium tests to investigate the effectiveness of smoke exhaust systems. FDS solves the Navier-Stokes equations appropriate for low speed flows (Ma < 0.3) with an emphasis on smoke, heat transport and CO2 concentrations from fires. The default turbulence model used in FDS simulation is the Large Eddy Simulation (LES), which is the solution of Navier-Stokes equations at low speed.
The compartment tested was 9 …
Effects Of Secondary Stall And Unsteady Free-Stream On Blade Drag And Pitching Moments, Michael Malick
Effects Of Secondary Stall And Unsteady Free-Stream On Blade Drag And Pitching Moments, Michael Malick
McKelvey School of Engineering Graduate Student Theses & Dissertations
Dynamic stall is a complex aerodynamic phenomenon occurring in helicopter rotors, limiting the flight envelope and causing control linkage damage and instabilities. The Peters-Modarres semi-empirical dynamic stall model is extended to simulate pitching moment and drag in unsteady freestream and yawed flow, including the effects of secondary stall. The aerodynamics are implemented as a state-space model, suitable for time-marching or aeroelastic analyses. With small modifications to the original stall model, secondary stall effects and unsteady freestream can be simulated without adding additional states. An optimization routine determines sets of parameters that minimize the error between the modeled solution and experimental …
Effects Of Secondary Stall And Unsteady Free-Stream On Blade Drag And Pitching Moments, Michael Malick
Effects Of Secondary Stall And Unsteady Free-Stream On Blade Drag And Pitching Moments, Michael Malick
McKelvey School of Engineering Graduate Student Theses & Dissertations
Dynamic stall is a complex aerodynamic phenomenon occurring in helicopter rotors, limiting the flight envelope and causing control linkage damage and instabilities. The Peters-Modarres semi-empirical dynamic stall model is extended to simulate pitching moment and drag in unsteady freestream and yawed flow, including the effects of secondary stall. The aerodynamics are implemented as a state-space model, suitable for time-marching or aeroelastic analyses. With small modifications to the original stall model, secondary stall effects and unsteady freestream can be simulated without adding additional states. An optimization routine determines sets of parameters that minimize the error between the modeled solution and experimental …
Rotating Mount For Complex Fluid Flow Research, Kirsten Murphy
Rotating Mount For Complex Fluid Flow Research, Kirsten Murphy
Honors Theses
Fluid flow around rotating objects is mathematically complex and there is currently limited experimental data on the subject. To make Western Michigan University capable of this research, a rotating wind tunnel mount was developed. The mount design was integrated into the existing setup at the Applied Aerodynamics Laboratory (AAL) to allow seamless transitions between different research projects. Non-rotating and rotating disk prototypes were created from 3D-printed materials to test the mount’s capabilities. Experimental data gathered from utilizing this rotating mount was analyzed to understand the aerodynamic effects on rotating disks in a fluid stream. From testing the rotating disk prototype …
Rotating Mount For Complex Fluid Flow Research, Kirsten Murphy
Rotating Mount For Complex Fluid Flow Research, Kirsten Murphy
Honors Theses
Fluid flow around rotating objects is mathematically complex and there is currently limited experimental data on the subject. To make Western Michigan University capable of this research, a rotating wind tunnel mount was developed. The mount design was integrated into the existing setup at the Applied Aerodynamics Laboratory (AAL) to allow seamless transitions between different research projects. Non-rotating and rotating disk prototypes were created from 3D-printed materials to test the mount’s capabilities. Experimental data gathered from utilizing this rotating mount was analyzed to understand the aerodynamic effects on rotating disks in a fluid stream. From testing the rotating disk prototype …
Nonupdating Methods For The Characterization Of Nonlinear Stress-Strain And Delamination Fracture Properties Of Fiber Reinforced Composites, Bastiaan Corstiaan Van Der Vossen
Nonupdating Methods For The Characterization Of Nonlinear Stress-Strain And Delamination Fracture Properties Of Fiber Reinforced Composites, Bastiaan Corstiaan Van Der Vossen
Mechanical and Aerospace Engineering Dissertations - Archive
Efforts to develop strength and life prediction analysis tools for aircraft composite structures have shown a great need to understand the complexity and interaction of failure modes. Many failure models are highly sensitive to transverse nonlinear shear stress-strain and delamination fracture properties, which are notoriously hard to measure. Without proper input parameters, life predictions analyses will not be successful. The objective of this work was to accurately characterize these mechanical properties of carbon fiber reinforced polymer composites through advanced experimental methods. Full-field noncontact deformation measurements using Digital Image Correlation are used to quantify all surface strains components, enabling the design …
Evaporative Hotspot Cooling Of Microprocessors Using Electrowetting On Dielectric (Ewod), Arvind Venkatesan
Evaporative Hotspot Cooling Of Microprocessors Using Electrowetting On Dielectric (Ewod), Arvind Venkatesan
Mechanical and Aerospace Engineering Dissertations - Archive
The increased use of smart devices and great strides in fabrication technologies have resulted in densely packed electronics. Combined with 3D packaging, high heat uxes have become the norm. The need for advanced thermal management solutions has risen. Most devices based on their load pro le and architecture are susceptible to non-uniformities in heat uxes. These non-uniformities with very high heat uxes are known as hotspots. Mitigation of hotspots is very important for the normal functioning and long term reliability of microprocessors. Multiple attempts have been made at developing microscale thermal solutions. Most prominent among them are microchannels and heat …
Design Principles For Large Foil Bearings Based On Scaling Laws: Analyses And Experiment, Srikanth Honavara Prasad
Design Principles For Large Foil Bearings Based On Scaling Laws: Analyses And Experiment, Srikanth Honavara Prasad
Mechanical and Aerospace Engineering Dissertations - Archive
Gas foil bearings are used for supporting high speed turbomachinery systems. They are characterized by complex physical and thermal interactions between the lubricating fluid and the structural elements. Mathematically, the behavior of such systems is governed by nonlinear partial differential equations and pose substantial computational challenges. However, their potential applications in aerospace systems and power generation systems have renewed research and development efforts aimed at simplifying their design and analyses methods. Commercialization of gas foil bearings in Mega Watt scale applications necessitate the development of simple tools for estimating bearing design parameters such as load capacity, radial clearance, and support …
Surface Roughness Formation During Tensile Plastic Deformation Of Nickel Polycrystals, Kranthi Balusu
Surface Roughness Formation During Tensile Plastic Deformation Of Nickel Polycrystals, Kranthi Balusu
Mechanical and Aerospace Engineering Dissertations - Archive
Understanding the formation of surface roughness could help better diagnose a metal component’s health and could potentially help in making better microstructure design decisions. Both of these, in turn, contribute to the design of efficient structural components. In this work, the research objective is to understand the relationship between the surface microstructure (i.e., grain orientations) and the surface-height changes in nickel polycrystals undergoing small amounts of tensile plastic deformation. The secondary objective is to determine the relationship between surface height and strain localization. Primarily simulations were used, along with experimental surface roughness observations, to validate the simulation results. Discrete dislocation …
Performance Modeling And Experimental Investigations Of Rotating Detonation Engines, Andrew Ryan Mizener
Performance Modeling And Experimental Investigations Of Rotating Detonation Engines, Andrew Ryan Mizener
Mechanical and Aerospace Engineering Dissertations - Archive
The rotating detonation engine (RDE) is a promising propulsion concept that has the potential to offer increased thermodynamic performance in a compact package with no moving parts. A series of analytical and experimental investigations was carried out on RDEs with the joint goal of investigating swirl, torque, and a range of other design parameters of interest. The model and experimental facility were then applied to related problems with the goal of advancing the understanding of RDE applications. A flexible, low-order, semi-empirical model for a rotating detonation engine was presented. The model was formulated to be able to run broad parametric …
Direct Numerical Simulation Of Homogeneous Isotropic Turbulence - A Methodology And Applications, Sarah Moussa Hussein
Direct Numerical Simulation Of Homogeneous Isotropic Turbulence - A Methodology And Applications, Sarah Moussa Hussein
Mechanical and Aerospace Engineering Dissertations - Archive
Turbulence has been a topic of scientific research for years. Characterized by unorganized chaotic motion and irregular fluctuations, it persists as one of the most challenging topics in fluid mechanics despite volumes of documented research and crucial findings. This begs the question: What is turbulence and why is it so challenging? Turbulence research studies cover a wide spectrum of branches from fundamental flow propagation to different turbulence interactions. This research project investigates the simplest class of turbulent flow studies, homogeneous isotropic turbulence. In a quest to advance the fundamental understanding of turbulence physics, a direct numerical simulation tool is developed. …
Observation Of The Interaction Between A Transonic Shock Wave And A Wingtip Vortex||, Troy T. Bushmire
Observation Of The Interaction Between A Transonic Shock Wave And A Wingtip Vortex||, Troy T. Bushmire
Mechanical and Aerospace Engineering Theses - Archive
The present study observes the interaction between two fundamental phenomena in fluid mechanics: the transonic shock wave and the wingtip vortex. While these are two areas of fluid mechanics in which extensive experimental and numerical research has been conducted, there is little information on the interaction between the two. The present study numerically simulates a wing with a NACA-0012 section at Mach 0.758 and observes the interaction between the transonic shock wave and wingtip vortex for various angles of attack. The focus of the study is on the surface flow topology and the flow exterior to the boundary layer. Results …
Reachable Set Computation And Analysis For Perturbed Linear Systems, Prabhjeet Singh Arora
Reachable Set Computation And Analysis For Perturbed Linear Systems, Prabhjeet Singh Arora
Mechanical and Aerospace Engineering Theses - Archive
Determination of the set of all possible states, which a system can attain, plays an important role in safety for critical application. Prior knowledge of this set for the complete run-time provides critical information about how a system may evolve, providing accurate information of all the states, which could violate constraints. The knowledge of these states, helps in estimating control input, which can control the system, such that, these states are eliminated from the reachable set. Computation of reachable set of a dynamic system for a set of initial conditions can be easily performed, provided the analytical solution of the …