non linear system
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Information ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 37
Author(s):  
James Andro-Vasko ◽  
Wolfgang Bein

We consider a power-down system with two states—“on” and “off”—and a continuous set of power states. The system has to respond to requests for service in the “on” state and, after service, the system can power off or switch to any of the intermediate power-saving states. The choice of states determines the cost to power on for subsequent requests. The protocol for requests is “online”, which means that the decision as to which intermediate state (or the off-state) the system will switch has to be made without knowledge of future requests. We model a linear and a non-linear system, and we consider different online strategies, namely piece-wise linear, logarithmic and exponential. We provide results under online competitive analysis, which have relevance for the integration of renewable energy sources into the smart grid. Our analysis shows that while piece-wise linear systems are not specific for any type of system, logarithmic strategies work well for slack systems, whereas exponential systems are better suited for busy systems.


2022 ◽  
Vol 12 (1) ◽  
pp. 67
Author(s):  
Abdul Rauf ◽  
Muhammad Jehanzeb Irshad ◽  
Muhammad Wasif ◽  
Syed Umar Rasheed ◽  
Nouman Aziz ◽  
...  

In the last few decades, the main problem which has attracted the attention of researchers in the field of aerial robotics is the position estimation or Simultaneously Localization and Mapping (SLAM) of aerial vehicles where the GPS system does not work. Aerial robotics are used to perform many tasks such as rescue, transportation, search, control, monitoring, and different military operations where the performance of humans is impossible because of their vast top view and reachability anywhere. There are many different techniques and algorithms which are used to overcome the localization and mapping problem. These techniques and algorithms use different sensors such as Red Green Blue and Depth (RGBD), Light Detecting and Range (LIDAR), Ultra-Wideband (UWB) techniques, and probability-based SLAM which uses two algorithms Linear Kalman Filter (LKF) and Extended Kalman filter (EKF). LKF consists of 5 phases and this algorithm is only used for linear system problems but on the other hand, EKF algorithm is also used for non-linear system. EKF is found better than LKF due to accuracy, practicality, and efficiency while dealing SLAM problem.


Author(s):  
Muhammad Rooman ◽  
Muhammad Asif Jan ◽  
Zahir Shah ◽  
Wejdan Deebani ◽  
Meshal Shutaywi

Purpose: The goal of this study is to investigate the entropy optimization of Jeffrey nanofluid flow with the homogeneous and heterogeneous reaction by stretching the rotating disk. The impact of Hall current is also being considered. The process of heat transmission is carried out. For heat transfer coefficient, temperature, concentration, velocity, Bejan number, and entropy generation rate and relevant equations are computed. The implications of various characteristics are investigated. The effect of emerging parameters of nanofluid flow is discussed and represented by a graph. To reduce partial differential equations into ordinary differential equations by using effective similarity transformation. The achieved non-linear system is resolved by the Homotopy analysis technique (HAM) to found the convergent solution of the designated flow problem. The impact of various pertinent parameters, i.e thermal radiations parameter, Brinkman number, Reynolds number, magnetic parameter, Hall Effects parameter, Jeffrey nanofluid parameters are discussed and presented by the graph. Engineering quantities such as Nusselt number and skin friction are also taken into account.


Author(s):  
K. Muhammad ◽  
T. Hayat ◽  
A. Alsaedi

Abstract This analysis emphasizes impacts of CNTs (Carbon nanotubes) during Darcy–Forchheimer squeezed flow. Melting heat transfer process is addressed. Water and gasoline are treated as baseliquid. By transformation method non-linear system of ODEs are obtained from the flow field equations (PDEs). Further the emerged flow problem is solved via OHAM. Influences of physical involved parameters on velocity, surface friction coefficient, temperature as well as Nusselt number are expressed graphically and interpreted physically.


Author(s):  
A. Alhadhrami ◽  
Hassan A. H. Alzahrani ◽  
B. M. Prasanna ◽  
N. Madhukeshwara ◽  
K. C. Rajendraprasad ◽  
...  

The features of ferromagnetic fluids make it supportive for an extensive usage in loudspeakers, magnetic resonance imaging, computer hard drives, directing of magnetic drug and magnetic hyperthermia. Owing to all such potential applications, the current investigation is to understand the relationship between the thermal distribution, magnetic field and resulting fluid flow of Maxwell liquid over a stretching sheet. Investigation of thermal energy and concentration is carried out in the presence of thermal radiation, non-uniform heat sink/source, chemical reaction, Stefan blowing, magnetic dipole, thermophoresis and Brownian motion. Also, microorganisms are considered just to stabilize the suspended nanoparticles. Boundary layer approximation is employed during mathematical derivation. Based on a new constitutive relation, the governing equations are formulated and are reduced into a coupled non-linear system of equations using appropriate transformations. Further, these equations are solved numerically using fourth-order Runge–Kutta method with shooting technique. The impact of involved parameters is discussed and analysed graphically. Outcomes disclose that Newtonian liquid shows high heat transfer when compared to non-Newtonian (Maxwell) liquid for increased values of Brownian motion and thermophoresis parameters. Increased values of Peclet number declines the rate of gyrotactic microorganisms. Finally, an increase in Brownian and thermophoresis motion parameters declines the rate of heat transfer.


2021 ◽  
Vol 84 (1) ◽  
pp. 77-83
Author(s):  
Mohamad Ikhwan Nordin ◽  
Jurifa Mat Lazi ◽  
Md Hairul Nizam Talib ◽  
Zulkifilie Ibrahim

In this paper, Sensorless Permanent Magnet Synchronous Motor (PMSM) using Extended Kalman Filter (EKF) is presented. The previous PMSM drive uses a sensor to measure the motor’s speed. Then the idea is to replace the sensor by using sensorless drives based on the observer. For the conventional observer, it’s only good for low current and low-speed applications. Moreover, it is hard to detect the phase voltage due to the non-existence of neutral wire. Therefore, this project proposes sensorless control using an EKF. This method provides an optional estimation algorithm for the non-linear system that can produce a fast and accurate estimation of state variables. The accurate estimation will reduce the noise and ripple of the system. Additionally, the EKF do not require the information of mechanical parameters and the initial position of the rotor, making the construction is easy and simple. In this paper, the fundamental of the EKF algorithm is explained and the simulation results for different speeds and loads are presented. The noise reduction test is also conducted to measure the flux current with and without the filter. The simulation study is achieved using MATLAB/Simulink to verify the effectiveness of the proposed method. The results of the simulation show that the sensorless PMSM drives using EKF have lower overshoot and faster rise time during start-up conditions and have lower undershoot during the loaded condition. It also can be concluded that the proposed sensorless PMSM drive using EKF has good speed control accuracy and can reduce the current noise.


Author(s):  
Mr. Sharan L Pais ◽  
Manoj Kumar M ◽  
Namratha ◽  
Mayoori K Bhat ◽  
Vibha Mohan

The Shrimp rover is highly suitable for planetary exploration missions because of its unconventional wheel order, in-built passive adaptability and good ability to climb obstacles. It is a spatial multi-body system and a multi-variable, multi-parameter coupled non-linear system. Thus, kinematic and dynamic analyses for such systems are complex and time consuming. Long-range robotic missions for Martian exploration imply a high degree of autonomy. The most advanced locomotion concepts are based on wheels or caterpillars (e.g. Sojourner, NASA or Nanokhod, ESA). These rovers have clear advantages regarding power efficiency and complexity if compared with walking robots. However, they still have quite limited climbing abilities. Typically they can only overcome obstacle smaller than their wheel size. In this paper we present Shrimp, an innovative long range rover architecture with 6 motorized wheels. Using a rhombus configuration, the rover has a steering wheel in both, the front and the rear, and two wheels arranged on a bogie on each side. The front wheel has a spring suspension to guarantee optimal ground contact of all wheels at any time. The steering of the rover is realized by synchronizing the steering of the front and rear wheel and the speed difference of the bogie wheels. This allows for high precision maneuvers and even turning on the spot with minimum slip. The use of parallel articulations for the front wheel and the bogies enables to set a virtual centre of rotation at the level of the wheel axis while maintaining a high ground clearance. This insures maximum stability and climbing abilities even for relatively low friction coefficients between the wheel and the ground. This rover is able to passively overcome unstructured obstacles of up to two times its wheel diameter. With this high mobility, this architecture is the perfect candidate for long range planetary missions.


Materials ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 6858
Author(s):  
Hanna Weber ◽  
Stefan Kaczmarczyk ◽  
Radosław Iwankiewicz

In high-rise buildings earthquake ground motions induce bending deformation of the host structure. Large dynamic displacements at the top of the building can be observed which in turn lead to the excitation of the cables/ropes within lift installations. In this paper, the stochastic dynamics of a cable with a spring-damper and a mass system deployed in a tall cantilever structure under earthquake excitation is considered. The non-linear system is developed to describe lateral displacements of a vertical cable with a concentrated mass attached at its lower end. The system is moving slowly in the vertical direction. The horizontal displacements of the main mass are constrained by a spring-viscous damping element. The earthquake ground motions are modelled as a filtered Gaussian white noise stochastic process. The equivalent linearization technique is then used to replace the original non-linear system with a linear one with the coefficients determined by utilising the minimization of the mean-square error between both systems. Mean values, variances and covariances of particular random state variables have been obtained by using the numerical calculation. The received results were compared with the deterministic response of the system to the harmonic process and were verified against results obtained by Monte Carlo simulation.


Sensors ◽  
2021 ◽  
Vol 21 (22) ◽  
pp. 7492
Author(s):  
Thijs Devos ◽  
Matteo Kirchner ◽  
Jan Croes ◽  
Wim Desmet ◽  
Frank Naets

To comply with the increasing complexity of new mechatronic systems and stricter safety regulations, advanced estimation algorithms are currently undergoing a transformation towards higher model complexity. However, more complex models often face issues regarding the observability and computational effort needed. Moreover, sensor selection is often still conducted pragmatically based on experience and convenience, whereas a more cost-effective approach would be to evaluate the sensor performance based on its effective estimation performance. In this work, a novel estimation and sensor selection approach is presented that is able to stabilise the estimator Riccati equation for unobservable and non-linear system models. This is possible when estimators only target some specific quantities of interest that do not necessarily depend on all system states. An Extended Kalman Filter-based estimation framework is proposed where the Riccati equation is projected onto an observable subspace based on a Singular Value Decomposition (SVD) of the Kalman observability matrix. Furthermore, a sensor selection methodology is proposed, which ranks the possible sensors according to their estimation performance, as evaluated by the error covariance of the quantities of interest. This allows evaluating the performance of a sensor set without the need for costly test campaigns. Finally, the proposed methods are evaluated on a numerical example, as well as an automotive experimental validation case.


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