Home > Automation > Control Mode


[ pdf ] Neural network model to control an experimental chaotic pendulum

Neural network model to control an experimental chaotic pendulum Download
50
times
Topic under  Control Mode
Source: alexandria.tue.nl 
File size: 201.15 KB
File type: pdf
Last download on: Wed Nov 29, 2017 07:00:43 AM
Short Desciption:
A feedforward neural network was trained to predict the motion of an experimental, driven, and damped pendulum operating in a chaotic regime. The network learned the behavior of the pendulum from a time series of the pendulum’s angle, the single measured variable. The validity of the neural network model was assessed by comparing Poincare´ sections of measured and model-generated data. The model was used to find unstable periodic orbits ~UPO’s!, up to period 7. Two selected orbits were stabilized using the semicontinuous control extension, as described by De Korte, Schouten, and van den Bleek @Phys. Rev. E 52, 3358 ~1995!#, of the well-known Ott-Grebogi-Yorke chaos control scheme @Phys. Rev. Lett. 64, 1196 ~1990!#. The neural network was used as an alternative to local linear models. It has two advantages: ~i! it requires much less data, and ~ii! it can find many more UPO’s than those found directly from the measured time series.

Summary:
In the last ten years, many physical systems that exhibit seemingly random behavior have been demonstrated to be low-dimensional chaotic. In practice, the presence of chaos is often undesirable, and insights from nonlinear dynamics have been used to account for chaos in process design. At the same time, Ott, Grebogi, and Yorke ~OGY! @1# developed a control scheme that can be used to exploit chaotic behavior. The OGY method is based on the observation that the attractor of a chaotic system typically contains an infinite number of unstable periodic orbits ~UPO’s!. All that is needed to change the system behavior from chaotic to periodic is to select one of these UPO’s and stabilize it. Due to the sensitivity of chaotic systems for small perturbations, this can be achieved using only very small control actions. The possibility to select different kinds of periodic behavior by just selecting different UPO’s makes this type of control very appealing. Thus far, the OGY method has been applied to simple chaotic systems. To develop the chaos control methodology further, and make it applicable to more complex experimental systems, we have chosen to extend the method with a neural-network-based process model, and to first test this extension on a comprehensive experimental system, a driven and damped pendulum. For control, one needs ~i! a method to find UPO’s, and ~ii! a model that can predict future states of the system from the present, measured state. Hu¨binger et al. @2# controlled a pendulum of which all the state variables were measured. They used the equations of motion to calculate UPO’s and to make predictions, and they developed a semicontinuous control ~SCC! extension of the OGY method to cope with the large unstable eigenvalues of the stabilized UPOs. De Korte, Schouten, and van den Bleek @3# controlled a different, less ideal pendulum of which only one state variable, its angle, was measured. Delayed values of the angle were used to obtain a complete representation of the state. UPO’s were found by searching the measured data for close returning points, and the predictions were made by local linear models, fitted directly to the measured data.
Bookmark or share this info on Google+ and leave comment at below :

Bookmark and Share

People who downloaded this also viewed in this sites:

Plug and Play in Control Loop Design
If the PID has an autotuner, the autotuner needs to know the signal ranges in order to design its probing signals. The PID controller also has some...

PID Controller Tuning
Z-115 Temperature Control Tuning a PID (Three Mode) Controller Tuning a temperature controller involves setting the proportional, integral, and...

PID Control Theory
Matt Krass Email: mattkrass@gmail.com Last updated: April 10th, 2006 Team 358 http://www.team358.org/ One of the more difficult programming...

    Leave comment :
    "Neural network model to control an experimental chaotic pendulum"

    Name*

    Comment


    Related Free Files

    PID Control Theory... - Download: 157 times
    PID Controller Design with Guaranteed... - Download: 69 times
    ModelBased Tuning Methods for PID... - Download: 76 times
    Fuzzy expert systems... - Download: 111 times
    1 POLYNOMIAL AND RATIONAL MATRIX... - Download: 53 times
    Fuzzy logic systems for engineering... - Download: 62 times
    The PID Control Algorithm... - Download: 116 times
    Nonlinear Control Theory... - Download: 89 times
    LINEAR SYSTEMS AND CONTROL... - Download: 66 times
    ADAPTIVE CONTROL Correct... - Download: 68 times


    eXTReMe Tracker