Toolbox ninteger for MatLab, v. 2.3 (September 2005)

July 15, 2009 - Files for calculating variable-order derivatives (with orders both real and complex) may be found at Matlab's File Exchange website.

This toolbox implements non-integer controllers both in the frequency and the discrete time domains. Over thirty formulas are available for approximating a non-integer order derivative on-line. Structures such as non-integer PIDs are directly available and second and third-generation CRONE controllers may be reckoned. There are functions for finding norms, identifying models and plotting frequency diagrams. A graphical interface allows choosing parameters interactively and checking what the performance will be. The toolbox also includes a Simulink library.

Its code may be freely distributed and altered provided that the source of the code is acknowledged and this warning is kept in all further copies and/or alterations.

This version is a Beta release. Reports of eventual errors (the absence of which the author cannot ensure) and suggestions of improvements will be gladly accepted. Please use the author's e-mail given in the main page.

Files for download

You may find the toolbox at Matlab Code Exchange site, Control Design category. As an alternative you may use the link below.

  • Zip file with the entire toolbox (65 K)
  • PDF user and programmer manual (1135 K)

Requirements for running the toolbox

  • MatLab version 7.0 (release 14) or above. Actually most functions run under version 5; but the graphical interface and the Simulink library do not.
  • Control toolbox.
  • Optimisation toolbox.
  • Map toolbox. Actually this toolbox is only needed because of functions rad2deg and deg2rad. If these are not available, download these files and put them in some folder found in MatLab's path..

Version history

  • Version 2.3 - September 2005 - Simulink library and functions for computing norms, identifying models and plotting frequency responses added. A few minor enhancements were also incorporated.
  • Version 2.2 - July 2004 - Prompt user interface for fractional derivatives and PIDs was simplified. The manual's bibliography was significantly expanded and old publications included; more references were added in the text. A bug in the graphical interface preventing some functions from being plot or recovered was fixed.
  • Version 2.1 - February 2004 - Code for developing second and third generation CRONE controllers was improved and, for the digital case, enlarged.
  • Version 2.0 - January 2004 - All code was rewritten while the structure of the toolbox underwent a significant change. A serious bug in the reckoning of third generation CRONE controllers was corrected. The graphical interface was also completely rewritten. Non-integer identification methods were added.
  • Version 1.1 - 2001 - Everything in version 1.0 was translated to English. Matsuda, Carlson and discrete time domain methods were added, together with non-integer PIDs.
  • Version 1.0 - 2000/2001 - Toolbox in Portuguese implementing CRONE controllers of all three generations. A graphical interface was included.


The author thanks the following users (in alphabetical order) for their suggestions of improvement and / or bug reports. Of course, that the toolbox sould not have been improved further is solely the author's fault; the same can be said of still surviving bugs.

Blas Vinagre; Igor Podlubny