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. ...

Problem statement: The rotary inverted pendulum system was a highly nonlinear model, multivariable and absolutely unstable dynamic system. It was used for testing various design control techniques and in teaching modern control. The objectives of this study were to: (i) Develop a real rotary inverted pendulum which derived the mechanical model by using Euler-Lagrange and (ii) Design controller ...

To use numerical investigation of functional differential equations it is very important to know if difference analogues of the considered differential equations have the reliability to preserve some general properties of these equations, in particular, property of stability. This problem is considered here by investigation of a difference analogue of the linear mathematical inverted pendulum. ...

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conver...

The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart’s position. The inverted pendulum represents a challenging control problem, which continually moves toward ...

This article gives a practical overview of the popular biomechanically inspired, computationally efficient, algorithmically straightforward inverted pendulum technique for character-based systems. We explain the different flavours of inverted pendulum (e.g., springloaded and gravity compensated inverted pendulum), their viability for different situations (e.g., walking, running), simulation res...

The inverted pendulum is a highly nonlinear and open loop unstable system. To develop an accurate model of the inverted pendulum, different linear and nonlinear methods of identification will be used. However one of the problems encountered during modeling is the collection of experimental data from the inverted pendulum system. Since the output data from the unstable system does not show enoug...

We investigate experimentally liquid (oil) droplets vibrating over a bath of the same liquid and relate the phenomenon to the well-known effect of the stabilization of an inverted pendulum on a vibrating foundation (a “Kapitza pendulum”). Small fast vibrations can be substituted by an effective “levitation” force. We further discuss this effective stabilizing “spring force”. Besides the inverte...

The purpose of this paper is to present the design and program implementation of a general procedure which yields the mathematical model for a classical or rotary inverted pendulum system with an arbitrary number of pendulum links. Lagrange equations of the second kind with an integrated Rayleigh dissipation function are employed in model design, and the energetic balance relations, derived for...

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...