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Related Concept Videos

Physical Pendulum01:06

Physical Pendulum

When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
When dealing with complicated systems, the mass moment of inertia is an important parameter, as it describes the mass...
Simple Pendulum01:10

Simple Pendulum

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily life, pendulums have many uses, such as in clocks, on a swing set, and on a sinker on a fishing line.
The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period is completely independent of any other factors, such as mass or maximum displacement. For small displacements, a pendulum is...
Torsional Pendulum01:09

Torsional Pendulum

A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected.
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Real-World Applications of Power Series01:27

Real-World Applications of Power Series

The motion of a simple pendulum is governed by Newton’s Second Law in its rotational form, which relates the net torque on the bob to its angular acceleration. This physical law gives rise to a second-order differential equation in which the angular acceleration is proportional to the sine of the displacement angle.Because of the sin(𝜃) term, the governing equation is a nonlinear differential equation, which is difficult to solve analytically. To simplify the mathematical model, the sine...
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...

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Related Experiment Video

Updated: Jun 23, 2026

Online Virtual Reality Networked Control Laboratory Applied in Control Engineering Education
04:15

Online Virtual Reality Networked Control Laboratory Applied in Control Engineering Education

Published on: February 23, 2024

Modeling and control of a pneumatically actuated inverted pendulum.

Tihomir Zilić1, Danijel Pavković, Davor Zorc

  • 1Department of Robotics and Automation of Manufacturing Systems, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia. tihomir.zilic@fsb.hr

ISA Transactions
|April 29, 2009
PubMed
Summary

This study models a pneumatic inverted pendulum using low-cost sensors. Controllers were designed using linear quadratic (LQ) and LQ Gaussian (LQG) methods, compensating for friction for effective system stabilization.

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Experimental Methods to Study Human Postural Control
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Last Updated: Jun 23, 2026

Online Virtual Reality Networked Control Laboratory Applied in Control Engineering Education
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Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Area of Science:

  • Control Systems Engineering
  • Robotics
  • Mechatronics

Background:

  • Inverted pendulum systems are fundamental in control theory and robotics.
  • Pneumatic actuators offer cost-effectiveness but present nonlinear dynamics, including friction.
  • Accurate position sensing is crucial for effective control, with potentiometers offering a low-cost solution.

Purpose of the Study:

  • To model and control a pneumatically actuated inverted pendulum system.
  • To design and implement state feedback controllers using Linear Quadratic (LQ) and LQ Gaussian (LQG) optimization.
  • To address and compensate for nonlinear friction effects in the pneumatic system.

Main Methods:

  • Development of a nonlinear model for the inverted pendulum system, incorporating friction.
  • Derivation of a linearized model from the nonlinear system for controller design.
  • Design of LQ and LQG state feedback controllers.
  • Experimental identification and modeling of static friction.
  • Augmentation of controllers with a friction compensator.

Main Results:

  • A linearized model accurately represented the system dynamics for controller design.
  • LQ and LQG controllers, combined with friction compensation, demonstrated effective stabilization.
  • Experimental validation confirmed the performance of the proposed control strategies.
  • The system achieved stable control despite using low-cost position sensors.

Conclusions:

  • The study successfully demonstrated the efficacy of LQ/LQG control with friction compensation for a pneumatically actuated inverted pendulum.
  • Low-cost potentiometer-based sensing is viable for such systems.
  • The developed control approach offers a practical solution for stabilizing inverted pendulums in real-world applications.