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Multiple Operation Simulation
Závada, Vladislav ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the numeric integration. The reader is acquainted with the numerical solution of differential equations using Taylor series method. Then describes the different variants integrators. The practical part describes the design double-input integrator with multiplication and its implementation in an FPGA. For this integrator is also provided a simulator demonstrate its function.
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Taylor Series Assembler
Valenta, Václav ; Kraus, Michal (referee) ; Kunovský, Jiří (advisor)
The objective of this work is to get familiar with numerical solution of differential equations. The solution is made by specialized microprocessor HC08. Basic arithmetic operations and algorithms which helps to make precise results are analyzed here.
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Parallel Computer Systems Based on Numerical Integrations
Kraus, Michal ; Kubátová, Hana (referee) ; Kollár,, Ján (referee) ; Kunovský, Jiří (advisor)
This thesis deals with continuous system simulation. The systems can be described by system of differential equations or block diagram. Differential equations are usually solved by numerical methods that are integrated into simulation software such as Matlab, Maple or TKSL. Taylor series method has been used for numerical solutions of differential equations. The presented method has been proved to be both very accurate and fast and also procesed in parallel systems. The aim of the thesis is to design, implement and compare a few versions of the parallel system.
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Control Systems
Vala, Jiří ; Konvalina, Jiří (referee) ; Kunovský, Jiří (advisor)
The MSc Thesis deals with real-time modelling, especially with the control circuits, where we focus on the regulation circuit with auxiliary model of the regulated system. The introduction contains the Theory of Controls and regulation. The work is divided into two basic parts. The first part deals with the problems from the theoretical point of view. The theoretical part is concerned with the general systems. Various definitions of systems, their partition and mathematical methods for their description are mentioned after introducing. A description the regulation circuits, their partition, structures and types follows. There are shown the particular regulators and different types of regulated systems in details. Mathematical methods applied to solve the differential equations that describe the models of the systems are summarized in the second part of the work. The end of this chapter is concerned with the TKSL system. In the practical part I have produced Microsoft Power Point program which summarizes the results of experiments, made in the TKSL and TKSL/C system. The output of simulation was transformed into the graphs in the format of Microsoft Excel. The last part deals with suggestion and implementation simulators of control circuits.
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Numerical Integrators in Control Theory
Novák, Adam ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This bachelor thesis deal with the topic of partial differential equations of parallel solutions from focus on control of dynamic systems working with real-time built-in control model. First, it is focused on real-time systems. The next section deals with the analysis of differential equations and types of differential equations. Consequently, numerical integration and derivation are discussed. The thesis deals with individual numerical methods, which are used to calculate a differential equations. This thesis also deals with individual fluids that can influence the calculation of differencial equations in the Modern Taylor method. The result is a competitive application that allows a quick and accurate solution of real-time management model and the subsequent calculation of the differential equations generated using the Modern Taylor Series Method.
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Numerical Integrators Development Environment
Vopěnka, Václav ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This term project describes transformation of system of diferential equations into polynomial form. Such transformed systems of diferential equations can be subsequently solved using Taylor series. This method enables computing of initial problem's numeric solution using dynamical order selection in order to achieve required accuracy. The work mathematically proves, that transformed systems of diferential equations have the same solution as the original systems. This transformation can be used for all mathematic functions commonly used in technical applications. The work also focuses on optimization of given problem and implements it in programme taylor. This progamme enables user to solve given diferential equations with chosen parameters.
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Control Systems
Vala, Jiří ; Konvalina, Jiří (referee) ; Kunovský, Jiří (advisor)
The MSc Thesis deals with real-time modelling, especially with the control circuits, where we focus on the regulation circuit with auxiliary model of the regulated system. The introduction contains the Theory of Controls and regulation. The work is divided into two basic parts. The first part deals with the problems from the theoretical point of view. The theoretical part is concerned with the general systems. Various definitions of systems, their partition and mathematical methods for their description are mentioned after introducing. A description the regulation circuits, their partition, structures and types follows. There are shown the particular regulators and different types of regulated systems in details. Mathematical methods applied to solve the differential equations that describe the models of the systems are summarized in the second part of the work. The end of this chapter is concerned with the TKSL system. In the practical part I have produced Microsoft Power Point program which summarizes the results of experiments, made in the TKSL and TKSL/C system. The output of simulation was transformed into the graphs in the format of Microsoft Excel. The last part deals with suggestion and implementation simulators of control circuits.
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SSI Dividing Numerical Integrator
Suntcov, Roman ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The thesis deals with numerical integration and hardware division operations. The reader is familiar with the numerical solution of differential equations through several different methods, for example Taylor's series. Furthermore, it is discussed the operation of division in the hardware and the method of its implementation in the FPGA. Subsequently, a parallel-parallel and serial-parallel integrator is designed. The practical aim of the thesis is to design and implement a serial-serial dividing integrator and create a simulator for it.
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Hardware Realization of Higher Order Numerical Integrator
Matečný, František ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This work describes numerical integration and solution for ordinary differential equations by the Taylor series by different types of integrators. The next part is a description of floating point and fixed point arithmetic. Subsequently, we are presenting designs and calculation methods for parallels multiplication and division integrators in floating point and fixed point arithmetic. The designs were realized in VHDL and implemented on FPGA. Finally we summarizes the proposed solution and compare time complexity with another numerical methods.
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Numerical Integrators in Control Theory
Novák, Adam ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This bachelor thesis deal with the topic of partial differential equations of parallel solutions from focus on control of dynamic systems working with real-time built-in control model. First, it is focused on real-time systems. The next section deals with the analysis of differential equations and types of differential equations. Consequently, numerical integration and derivation are discussed. The thesis deals with individual numerical methods, which are used to calculate a differential equations. This thesis also deals with individual fluids that can influence the calculation of differencial equations in the Modern Taylor method. The result is a competitive application that allows a quick and accurate solution of real-time management model and the subsequent calculation of the differential equations generated using the Modern Taylor Series Method.
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