Repository logo

Infoscience

  • English
  • French
Log In
Logo EPFL, École polytechnique fédérale de Lausanne

Infoscience

  • English
  • French
Log In
  1. Home
  2. Academic and Research Output
  3. EPFL thesis
  4. On the use of input-output feedback linearization techniques for the control of nonminimum-phase systems
 
doctoral thesis

On the use of input-output feedback linearization techniques for the control of nonminimum-phase systems

Guemghar, Kahina  
2005

The objective of the thesis is to study the possibility of using input-output feedback linearization techniques for controlling nonlinear nonminimum-phase systems. Two methods are developed. The first one is based on an approximate input-output feedback linearization, where a part of the internal dynamics is neglected, while the second method focuses on the stabilization of the internal dynamics. The inverse of a nonminimum-phase system being unstable, standard input-output feedback linearization is not effective to control such systems. In this work, a control scheme is developed, based on an approximate input-output feedback linearization method, where the observability normal form is used in conjunction with input-output feedback linearization. The system is feedback linearized upon neglecting a part of the system dynamics, with the neglected part being considered as a perturbation. Stability analysis is provided based on the vanishing perturbation theory. However, this approximate input-output feedback linearization is only effective for very small values of the perturbation. In the general case, the internal dynamics cannot be crushed and need to be stabilized. On the other hand, predictive control is an effective approach for tackling problems with nonlinear dynamics, especially when analytical computation of the control law is difficult. Therefore, a cascade-control scheme that combines input-output feedback linearization and predictive control is proposed. Therein, inputoutput feedback linearization forms the inner loop that compensates the nonlinearities in the input-output behavior, and predictive control forms the outer loop that is used to stabilize the internal dynamics. With this scheme, predictive control is implemented at a re-optimization rate determined by the internal dynamics rather than the system dynamics, which is particularly advantageous when internal dynamics are slower than the input-output behavior of the controlled system. Exponential stability of the cascade-control scheme is provided using singular perturbation theory. Finally, both the approximate input-output feedback linearization and the cascade-control scheme are implemented successfully, on a polar pendulum 'pendubot' that is available at the Laboratoire d'Automatique of EPFL. The pendubot exhibits all the properties that suit the control methodologies mentioned above. From the approximate input-output feedback linearization point of view, the pendubot is a nonlinear system, not input-state feedback linearizable. Also, the pendubot is nonminimum phase, which prevents the use of standard input-output feedback linearization. From the cascade control point of view, although the pendubot has fast dynamics, the input-output feedback linearization separates the input-output system behavior from the internal dynamics, thus leading to a two-time-scale systems: fast input-output behavior, which is controlled using a linear controller, and slow reduced internal dynamics, which are stabilized using model predictive control. Therefore, the cascade-control scheme is effective, and model predictive control can be implemented at a low frequency compared to the input-output behavior.

  • Files
  • Details
  • Metrics
Loading...
Thumbnail Image
Name

EPFL_TH3175.pdf

Access type

openaccess

Size

788.29 KB

Format

Adobe PDF

Checksum (MD5)

f3f6e0648a813c11ae4b1d4bf4c94f54

Logo EPFL, École polytechnique fédérale de Lausanne
  • Contact
  • infoscience@epfl.ch

  • Follow us on Facebook
  • Follow us on Instagram
  • Follow us on LinkedIn
  • Follow us on X
  • Follow us on Youtube
AccessibilityLegal noticePrivacy policyCookie settingsEnd User AgreementGet helpFeedback

Infoscience is a service managed and provided by the Library and IT Services of EPFL. © EPFL, tous droits réservés