In this paper, we have discussed the solutions of a system of n differential equations as a continuous dynamical system. Then we have discussed the nature of oscillations of a damped driven pendulum. We have analyzed the nature of fixed and periodic points of a damped driven pendulum for certain ranges of parameters. We have proved that oscillations of the pendulum are chaotic for certain range...

In recent years, Particle Swarm Optimization has evolved as an effective global optimization algorithm whose dynamics has been inspired from swarming or collaborative behavior of biological populations. In this paper, PSO has been applied to Triple Link Inverted Pendulum model to find its reduced order model by minimization of error between the step responses of higher and reduced order model. ...

BP Neural Network has a longer training time and a slow convergence. To deal with the defects of BP Neural Network a modified BP algorithm is proposed in the paper. The algorithm is applied for the control of Inverted Pendulum, a highly non linear system inherently being open loop unstable. Levenberg-Marquardt algorithm is used for the training purpose. The training samples are being collected ...

In this paper, a fuzzy controller for an inverted pendulum system is presented in two stages. These stages are: investigation of fuzzy control systemmodeling methods and solution of the “Inverted Pendulum Problem” by using Java programming with Applets for internet based control education. In the first stage, fuzzy modeling and fuzzy control system investigation, Java programming language, clas...

Several new types of regular and chaotic behavior of the parametrically driven pendulum are discovered with the help of computer simulations. A simple physical explanation is suggested to the phenomenon of subharmonic resonances. The boundaries of these resonances in the parameter space and the spectral composition of corresponding stationary oscillations are determined theoretically and verifi...

A switching control strategy for inverted pendulum systems is proposed based on the energy function and its transitions. We deal with a simplified second order model of cart-pendulum systems. Assume a virtual energy whose potential energy has an opposite sign. Paying attention to the motions of the pendulum, the energy changes are analyzed theoretically. According to these analyses, the conditi...

In this paper we describe the geometry of the energy momentum mapping of the complexified spherical pendulum. For background on the classical spherical pendulum we refer the reader to [4, chpt. IV]. We show that this complex Hamiltonian system is Mumford-Jacobi completely integrable [9, p.3.51–3.53] and admits an analogue of the period lattice [5] and action angle coordinates [4, Apend. D]. Fol...

The double pendulum is a classic dynamical system, capable of chaotic behavior in a four-dimensional phase space. The driven case introduces even more peculiar behaviors and opens the possibility for stable folded modes. In this paper, we explore the double pendulum in both driven and undriven cases through experimental observation and simulations, focusing on time-to-flip as a major measure of...

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...

This paper focuses on the flying inverted pendulum problem, i.e balancing a pendulum on a flying vehicle. After analyzing the system dynamic, a three loop cascade control strategy based on active disturbance rejection control (ADRC) is proposed. Not only the pendulum balancing, but also the trajectory tracking of the vehicle can be realized successfully even when strong disturbances exist. The ...