Gotowa bibliografia na temat „MATLAB MATHEMATICAL MODELS”

<p>In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning.</p><p>Computation of parameters often includes as a part solution of linear system of equations <i>Ax = b</i>. The corresponding pseudoinverse solution depends on the properties of the matrix <i>A</i> and vector <i>b</i>. The singular value decomposition of <i>A</i> can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution <i>x</i>. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of <i>A</i> into account</p>

Thesis (DTech (Electrical Engineering))--Cape Peninsula University of Technology, 2018.<br>Industrial processes tend to have very complex mathematical models that in most instances result in very model specific optimal estimation and designs of control strategies. Such models have many composition components, energy compartments and energy inventories that result in many process variables that are intertwined and too complex to separate from one another. Most of the derived mathematical process models, based on the application of first principles, are nonlinear and incorporate unknown parameters and unmeasurable states. This fact results in difficulties in design and implementation of controllers for a majority of industrial processes. There is a need for the existing parameter and state estimation methods to be further developed and for new methods to be developed in order to simplify the process of parameters or states calculation and be applicable for real-time implementation of various controllers for nonlinear systems. The thesis describes the research work done on developing new parameter and state estimation methods and algorithms for bilinear and nonlinear processes. Continuous countercurrent ion exchange (CCIX) process for desalination of water is considered as a case study of a process that can be modelled as a bilinear system with affine parameters or as purely nonlinear system. Many models of industrial processes can be presented in such a way. The ion exchange process model is developed based on the mass balance principle as a state space bilinear model according to the state and control variables. The developed model is restructured according to its parameters in order to formulate two types of parameter estimation problem – with process models linear and nonlinear according to the parameters. The two models developed are a bilinear model with affine and a nonlinear according to the parameters model. Four different methods are proposed for the first case: gradient-based optimization method that uses the process output measurements, optimization gradient based method that uses the full state vector measurements, direct solution using the state vector measurements, and Lagrange’s optimization technique. Two methods are proposed for the second case: direct solution of the model equation using MATLAB software and Lagrange’s optimisation techniques.<br>National Research Foundation (NRF)

Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2009<br>This project was started as a result of strict environmental and health regulations together with a demand tor cost effective operation of wastewater treatment plants (VVWTPs). The main aim of this project is how to keep effluent concentration below a prescribed limit at the lowest possible cost. Due to large fluctuations in the quality and quantity of the influent concentrations, traditional control methods are not adequate to achieve this aim The major drawback with these methods is that the disturbances affect the process before the controller has time to correct the error (Olsson and Newell, 1999: 454). This problem is addressed through the use of modern control systems. Modern control systems are model based predictive algorithms arranged as feed-forward controllers (Olsson and Newell. 1999: 454). Normally a controller is equipped with a constant set point; the goal In this project is to calculate an optimal DO trajectory that may be sampled to provide a varying optimal set-point for the Activated Sludge Process, In this project an optimal control problem Is formulated using DO concentration as a control variable. This requires a model of the process to be controlled a mathematical expressions of the limitations on the process input and output variables and finally the objective functional. which consists of the objectives of the control. The structures of the Benchmark plant (developed within the COST 682 working group) and the Athlone WWTPs are used to implement this opt.mat control strategy in MATLAB. The plant's full models are developed based on the mass balance principle incorporating the activated sludge biological models: ,ASM1, ASM2, ASM2d and ASM3 (developed by the IWA working groups). To be able to develop a method that may later on be used for online control, the full models are reduced based on the technique In Lukasse (1996). To ensure that the reduced models keep the same prediction capabilities as the full models, parameters of the reduced models are calculated based on the Least Squares principle, The formulated optimal control problem is solved based on the decompostion-coorcdination method that involves time decomposition in a two layer structure. MATLAB software [5 developed to solve the problems for parameter estimation. fun and reduced mode! simulation. and optimal control calculation for the considered different cases of plant structures and biological models. The obtained optimal 00 trajectories produced the effluent state trajectories within prescribed requirements. These DO trajectories may be implemented in different SCADA systems to be tracked as set points or desired trajectories by different types of controllers.

The main goal of the master’s thesis SIMULATION OF INTERCONNECTION OF SOLAR CELLS IN MATLAB is introduction of conversion principle of solar radiation into electrical energy in photovoltaic cells. The thesis deals with mathematical models and equations that describe the solar cell and their interconnection. The main task was to develop a user interface program using MATLAB. The produced program is intended to simulate a single cells or series connection, parallel or in series – parallel cells, and so simulate a photovoltaic panel.

Cable-actuated manipulators (or 'cable robots') constitute a relatively new classification of robots which use motors, located at fixed remote locations, to manipulate an end-effector by extending or retracting cables. These manipulators possess a number of unique properties which make them proficient with tasks involving high payloads, large workspaces, and dangerous or contaminated environments. However, a number of challenges exist which have limited the mainstream emergence of cable robots. This thesis addresses two of the most important of these issues-- workspace analysis and disturbance compensation. Workspace issues are particularly important, as many large-scale applications require the end-effector to operate in regions of a particular shape, and to exert certain minimum forces throughout those regions. The 'Force-Feasible Workspace' represents the set of end-effector positions, for a given robot design, for which the robot can exert a set of required forces on its environment. This can be considered as the robot's 'usable' workspace, and an analysis of this workspace shape for point-mass cable robots is therefore presented to facilitate optimal cable robot design. Numerical simulation results are also presented to validate the analytical results, and to aid visualization of certain complex workspace shapes. Some cable robot applications may require mounting motors to moving bases (i.e. mobile robots) or other surfaces which are subject to disturbances (i.e. helicopters or crane arms). Such disturbances can propagate to the end-effector and cause undesired motion, so the rejection of motor mount disturbances is also of interest. This thesis presents a strategy for measuring these disturbances and compensating for them. General approaches and implementation issues are explored qualitatively with a simple one-degree-of-freedom prototype (including a strategy for mitigating accelerometer drift), and quantitative simulation results are presented as a proof of concept.

Current transformer saturation will cause the secondary current distortion. When saturation occurs, the secondary current will not be linearly proportional to the primary current, which may lead to maloperation of protection devices. This thesis researches and tests two detecting methods: Fast Fourier Transform (FFT) and Wavelet Transform based methods. Comparing these two methods, FFT has a better performance in steady state saturation, and Wavelet Transform can determine singularity to provide the moment of distortion. The Jiles-Atherton (J-A) theory of ferromagnetic hysteresis is one approach used in electromagnetics transient modeling. With decades of development, the J-A model has evolved into different versions. The author summarizes the different models and implements J-A model in both MATLAB and Simulink.

Tato práce se zabývá synchronním motorem s permanentními magnety na rotoru (PMSM), jeho modelováním a návrhu regulační struktury. V práci jsou uvedeny způsoby a výhody použití permanentních magnetů v elektrických motorech. Dále se práce zabývá transformací třífázové soustavy do dq0. Pomocí Parkovy transformace jsou v práci odvozeny rovnice stroje v dq0 souřadnicovém systému a vytvořeny náhradní schémata stroje v dq osách. Rovnice i schémata zahrnují jak ztráty v mědi, tak ztráty v železe. Náhradní schémata jsou popsány elektrickými a mechanickými rovnicemi a následně překresleny do grafické podoby v programu Matlab Simulink. Vytvořeny jsou dva modely PMSM, jeden s uvažováním ztrát v železe a druhý bez těchto ztrát. Pro oba dva modely je zde popsán postup návrhu regulátorů proudu a otáček. Pro model, u kterého jsou uvažovány ztráty v železe je navíc použito více druhů řídicích strategií a tyto strategie jsou mezi sebou navzájem porovnány.

The subject of my master’s thesis is creating a mathematical model of motor vehicle driving gear using the software programs MATLAB / Simulink. The results are presented via graphs of the data gained from the simulation of a car driving on a determined track. The parameters used in the model come from a specific file and they can be changed anytime in order to correspond with the particular vehicle.

Speech is intuitive, fast and easy to generate, but it is hard to index and easy to forget. What is more, listening to speech is slow. Text is easier to store, process and consume, both for computers and for humans, but writing text is slow and requires some intention. In this thesis, we study speech recognition which allows converting speech into text, making it easier both to create and to use information. Our tool of study is Hidden Markov Models which is one of the most important machine learning models in speech and language processing. The aim of this thesis is to do a rst study in Hidden Markov Models and understand their importance, particularly in speech recognition. We will go through three fundamental problems that come up naturally with Hidden Markov Models: to compute a likelihood of an observation sequence, to nd an optimal state sequence given an observation sequence and the model, and to adjust the model parameters. A solution to each problem will be given together with an example and the corresponding simulations using MatLab. The main importance lies in the last example, in which a rst approach to speech recognition will be done.