This paper presents the virtual laboratory software developed at the Department of Mathematical Modeling (BMSTU). The laboratory is designed as an educational tool for the nonlinear control courses. It allows to see 3D demonstrations of control processes for various nonlinear systems. The laboratory software package is developed using the Python programming language. It has open code and archit...

A novel demonstration of chaos in the double pendulum is discussed. Experiments to evaluate the sensitive dependence on initial conditions of the motion of the double pendulum are described. For typical initial conditions, the proposed experiment exhibits a growth of uncertainties which is exponential with exponent A = 7.5 ± 1.5 s• Numerical simulations performed on an idealized model give good...

In this study, we propose to simulate the center of mass trajectory during walking using a tridimensional Extended Inverted Pendulum model. For the single support trajectory simulation, we consider a modified tridimensional inverted pendulum introducing the forward displacement of its pivot point as the center of pressure translation. The model introduces a representation of the double support ...

This paper describes the method for trajectory tracking and balancing the Self Erecting Single Inverted Pendulum (SESIP) using Linear Quadratic Regulator (LQR). A robust LQR controller for stabilizing the SESIP is proposed in this paper. The first part of the controller is a Position Velocity (PV) controller to swing up the pendulum from its hanging position by moving the pendulum left and righ...

This paper proposes a reconsideration of use of computer simulations in science education. We discuss three studies of the use of science simulations for undergraduate distance learning students. The first one, The Driven Pendulum simulation is a computer-based experiment on the behaviour of a pendulum. The second simulation, Evolve is concerned with natural selection in a hypothetical species ...

The purpose of this paper is to present the design and program implementation of expansions made to the existing general algorithmic procedure which yields the mathematical model for a classical inverted pendulum system with an arbitrary number of pendulum links. The expansions include the option to define the reference position of the pendulum in a planar coordinate system, to choose the refer...

Using the basic concepts and design methods of Human Simulated Intelligent Control (HSIC), we have designed the master control level of an HSIC controller for the swinging-up and handstand control of a cart-double pendulum. Then, the self-tuning structure of the self-tuning level of the HSIC Controller is implemented using fuzzy logic rules. This structure has fuzzy self-tuning abilities in the...

We consider the double mathematical pendulum in the limit when the ratio of pendulum masses is close to zero and the ratio of pendulum lengths is close to infinity. We found that the limit system has a hyperbolic periodic trajectory, whose invariant manifolds intersect transversally and the intersections are exponentially small. In this case we obtain an asymptotic formula of the homoclinic inv...

Trying to extend a local deenition of a surface of section and the corresponding Poincar e map to a global one, one can encounter severe diiculties. We show that global transverse sections often do not exist for Hamiltonian systems with two degrees of freedom. As a consequence we present a method to generate so called W-section, which by construction will be intersected by (almost) all orbits. ...