CONTROL OF THE DOUBLE INVERTED PENDULUM ON A CART USING THE NATURAL MOTION

This paper deals with controlling the swing-up motion of the double pendulum on a cart using a novel control. The system control is based on finding a feasible trajectory connecting the equilibrium positions from which the eigenfrequencies of the system are determined. Then the system is controlled during the motion between the equilibrium positions by the special harmonic excitation at the system resonances. Around the two equilibrium positions, the trajectory is stabilized by the nonlinear quadratic regulator NQR (also known as SDRE – the State Dependent Riccati Equation). These together form the control between the equilibrium positions demonstrated on the double pendulum on a cart

Synthesis of Mechanisms by Methods of Nonlinear Dynamics

This paper deals with a new method for parametric kinematic synthesis of mechanisms. The traditional synthesis procedure based on collocation, correction and optimization suffers from the local minima of objective functions, usually due to the local unassembled configurations which must be overcome. The new method uses the time varying values of the synthesized dimensions of the mechanism as if the mechanism had elastic links and guidances. The time varying dimensions form the basis for an accompanying nonlinear dynamical dissipative system and the synthesis is transformed into the time evolution of this accompanying dynamical system. Its dissipativity guarantees the termination of thesynthesis. The synthesis always covers the parametric kinematic synthesis, but it can be advantageously extended into the optimization of any further criteria. The main advantage of the method described here for dealing with mechanism synthesis is that it overcomes the unassembled configurations of the synthesized mechanisms and enables any further synthesis criteria to be introduced, and terminates due to dissipation of the accompanied dynamical system

Massive Parallelization of Multibody System Simulation

This paper deals with the decrease in CPU time necessary for simulating multibody systems by massive parallelization. The direct dynamics of multibody systems has to be solved by a system of linear algebraic equations. This is a bottleneck for the efficient usage of multiple processors. Simultaneous solution of this task means that the excitation is immediately spread into all components of the multibody system. The bottleneck can be avoided by introducing additional dynamics, and this leads to the possibility of massive parallelization. Two approaches are described. One is a heterogeneousmultiscale method, and the other involves solving a system of linear algebraic equations by artificial dynamics

AN INTERPOLATION METHOD FOR DETERMINING THE FREQUENCIES OF PARAMETERIZED LARGE-SCALE STRUCTURES

Parametric Model Order Reduction (pMOR) is an emerging category of models developed with the aim of describing reduced first and second-order dynamical systems. The use of a pROM turns out useful in a variety of applications spanning from the analysis of Micro-Electro-Mechanical Systems (MEMS) to the optimization of complex mechanical systems because they allow predicting the dynamical behavior at any values of the quantities of interest within the design space, e.g. material properties, geometric features or loading conditions. The process underlying the construction of a pROM using an SVD-based method [18] accounts for three basic phases: a) construction of several local ROMs (Reduced Order Models); b) projection of the state-space vector onto a common subspace spanned by several transformation matrices derived in the first step; c) use of an interpolation method capable of capturing for one or more parameters the values of the quantity of interest. One of the major difficulties encountered in this process has been identified at the level of the interpolation method and can be encapsulated in the following contradiction: if the number of detailed finite element analyses is high then an interpolation method can better describe the system for a given choice of a parameter but the time of computation is higher. In this paper is proposed a method for removing the above contradiction by introducing a new interpolation method (RSDM). This method allows to restore and make available to the interpolation tool certain natural components belonging to the matrices of the full FE model that are related on one side, to the process of reduction and on the other side, to the characteristics of a solid in the FE theory. This approach shows higher accuracy than methods used for the assessment of the system’s eigenbehavior. To confirm the usefulness of the RSDM a Hexapod will be analyzed

Kinematical and Dynamic Solution of Wing Flat

Cílem této práce je na zadaném mechanismu vztlakové klapky vyřešit jeho kinematické a dynamické chování se zaměřením na výpočet potřebných hnacích sil. K dosažení předem stanoveného pohybu je nutné řešit inverzní dynamickou úlohu. Celé řešení je provedeno v programu MATLAB a využívá již existujících programů KRESIC a DRESIC, které byly vytvořeny na FS ČVUT v Praze. DRESIC řeší pouze přímou dynamickou úlohu. Inverzní dynamická úloha proto tedy musela být naprogramována autorem.The aim of this work is to solve kinematic and dynamic behaviors of given planar wing flap mechanism. Special focus was devoted to the calculation of the required input forces. To achieve these results it is necessary to solve inverse dynamic problem. Entire solution is made in MATLAB and uses existing functions KRESIC and DRESIC which have been developed at FME CTU in Prague. The function DRESIC has to be modified to solve inverse dynamic problem