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Dynamics of Snake Robots
Kubiena, Jaromír ; Doupovec, Miroslav (referee) ; Návrat, Aleš (advisor)
In this thesis, we deal with the mathematical description of the kinematics and the dynamics of mechanical systems. Then we focus on the particular mechanical system which is the Square robot with four legs with active joints and passive wheels, which moves on horizontal plane. The kinematics of the mechanical system is described by the control matrix, then we use it to express the equations of motion. We compute the dynamics the robot by using Lagrange equations. We verify that the mechanical system is nonholonomic constrained and we verify controllability by using Lie bracket and distribution. We find the singular postures of the robot.
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Control of linear systems
Cesneková, Ivana ; Milota, Jaroslav (advisor) ; Honzík, Petr (referee)
The aim of this work is to look into the theory of linear systems via population model represented by partial differential equations with boundary and initial condition. Special attention is devoted to the strongly continuous semig- roups on a complex Banach space. For this purpose, the notion of a homogeneous and inhomogeneous Cauchy problem is introduced and we solve our model in this abstract formulation. The system behaviour is based on properties of the resolvent set and spectrum. Controllability question limits to solve the uniformly exponen- tially stability and the exponentially stabilizability. The point of this problem is in the case of the unstability to show exponencially stability of the system by using feedback. Keywords: control, differential equations, stability, controllability 1
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Preliminary aerodynamic analysis of remotely controlled model with jet propulsion
Novák, Ondřej ; Zikmund, Pavel (referee) ; Popela, Robert (advisor)
This bachelor´s thesis deals with aerodynamic analysis of unmanned aircraft and subsequent changes to design of wing, its position and wing-fuselage junction. In this work emphasis is laid on flow separation, its interaction with other flow structures and its influence on aerodynamic properties. The goal of these changes to the aircraft is ensuring sufficient stability and controllability in low as well as high angle of attack flight. AVL, XFLR5 and CFD methods were used in the thesis. In case of inaccuracy of CFD calculation, two backup wing related modifications were prepared.
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Applications of fractional calculus in control theory
Kiša, Daniel ; Nechvátal, Luděk (referee) ; Kisela, Tomáš (advisor)
Tato bakalářská práce se zabývá matematickou teorií zlomkového kalkulu a jeho aplikacemi v oblasti teorie řízení. V první části jsou uvedeny základy řízení lineárních časově invariantních systémů, a jsou dále diskutovány tři klasické úlohy, a to určení stability, řiditelnosti a pozorovatelnosti. V druhé části je zaveden Riemann-Liouvillův a Caputův diferintegrál a jsou formulovány výše zmíněné problémy pro lineární časově invariantní systém zlomkého řádu. Opět jsou diskutována řešení a jejich odvození.
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Discrete linear dynamical systems with control
Procházková, Zuzana ; Tůma, Jiří (advisor) ; Růžička, Pavel (referee)
Discrete linear dynamical systems with control Author: Zuzana Procházková Department: Department of Algebra Supervisor: doc. RNDr. Jiří Tůma, DrSc., Department of Algebra Abstract: In this thesis we describe elementary property of discrete linear dyna- mical system. We define discrete linear dynamical system with control and its controllability and then we define descrete linear dynamical system with output and its observability. After that we show the duality of observability and con- trollability with definition of dual system and its description. There are three problems solved in the last chapter. 1
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Rebuilding of VUT 051 RAY into twin-engine conception
Jílek, Jan ; Mališ, Michal (referee) ; Píštěk, Antonín (advisor)
The master’s thesis is dealt with the design of rebuilding of VUT 051 RAY which is equipped electric powerplant to twin-engine conception named VUT 051 RAY-DUO. In the thesis was verified the range of centre of gravity position of VUT 051 RAY-DUO then powerplant in ducted fan configuration was designed, performances of the airplane were appointed and controllability during fail one of the engines was analysed. The design of new powerplant was verified by strength analysis and then costing calculation was established.
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Control of linear systems
Cesneková, Ivana ; Milota, Jaroslav (advisor) ; Honzík, Petr (referee)
The aim of this work is to look into the theory of linear systems via population model represented by partial differential equations with boundary and initial condition. Special attention is devoted to the strongly continuous semig- roups on a complex Banach space. For this purpose, the notion of a homogeneous and inhomogeneous Cauchy problem is introduced and we solve our model in this abstract formulation. The system behaviour is based on properties of the resolvent set and spectrum. Controllability question limits to solve the uniformly exponen- tially stability and the exponentially stabilizability. The point of this problem is in the case of the unstability to show exponencially stability of the system by using feedback. Keywords: control, differential equations, stability, controllability 1
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Linear Matrix Differential Equation with Delay
Piddubna, Ganna Konstantinivna ; Růžičková, Miroslava (referee) ; Dzhalladova, Irada (referee) ; Baštinec, Jaromír (advisor)
V předložené práci se zabýváme hledáním řešení lineární diferenciální maticové rovnice se zpožděním x'(t)=A0x(t)+A1x(t-tau), kde A0, A1 jsou konstantní matice, tau>0 je konstantní zpoždění. Dále se zabýváme odvozením podmínek stability řešení systému a řiditelnosti daného systému. Pro řešení tohoto systému byla použita metoda "krok za krokem". Řešení bylo nalezeno jak v rekurentní formě tak i v obecném tvaru. Je provedena analýza stability a asymptotické stability řešení systému. Jsou zformulovány podmínky stability. Hlavní roli v analýze stability měla metoda Lyapunovových funkcionálů. Jsou zformulovány nutné a postačující podmínky řiditelnosti pro případ systémů se stejnými maticemi a je zkonstruována řídící funkce. Jsou odvozeny postačující podmínky pro řiditelnost v případě komutujících matic a v případě obecných matic a je sestrojena řídící funkce. Všechny výsledky jsou ilustrovány na netriviálních příkladech.
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Solutions of inverse problems in the area of material and heat exchangers
Kůdelová, Tereza ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This master’s thesis deals with the dynamic behaviour of the heat exchangers which is described by a system of differential equations. In this connection, it contains general informations about heat transfer, heat exchangers and their arrangements. The main aim of this thesis is to solve the inverse problem of the antiparallel arrangement and discuss the question of the controllability, observability and identifiability of its parameters.
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Stability and controllability evaluation of the four-seater, single-engined airplane
Matějů, Jiří ; Zikmund, Pavel (referee) ; Daněk, Vladimír (advisor)
The diploma thesis deals with evaluation and suggestion of changes for the conceptual design of an airplane TL4000 in terms of stability and controllability. In the first part there are determined stability and controllability derivativations of the aircraft. Thereafter are estimated aircraft weight, moment of inertia and necessary geometric characteristics. In the second part there are calculated stability criteria for a sample case. In the third part, on the basis of this calculation, a program is created. This program combines the advantages of MS Excel, Matlab and Matlab Simulink. By means of this program criteria of stability and controllability were calculated parametrically for different regimes of flight, identified critical cases and compared with the requirements of CS-23rd. Based on this evaluation were recommanded modifications of the conceptual design TL4000.
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