Skip to content Skip to navigation


You are here: Home » Content » QFT - Quantitative Feedback Theory


Recently Viewed

This feature requires Javascript to be enabled.

QFT - Quantitative Feedback Theory

Module by: Argyrios Zolotas. E-mail the author

Summary: Introduction to the QFT control method. QFT stands for Quantitative Feedback Theory, which emphasises the use of feedback in order to achieve adequate robust system performance tolerances despite the presence of plant and disturbances uncertainties. The robust control problem is formulated by a "quantitative means" for control design. The method is a very good introduction for students to become familiar with the idea of robust control.

* The site undergoes major re-structuring. It is expected that the new version will be published during this summer.

Quantitative Feedback Theory (QFT) developed by Horowitz (Horowitz, 1963; Horowitz and Sidi, 1972), is a frequency domain technique utilising the Nichols Chart (NC) in order to achieve a desired robust design over a specified region of plant uncertainty. Desired time-domain responses are translated into frequency domain tolerances, which lead to bounds (or constraints) on the loop transmission function. The design process is very transparent allowing a designer to see what trade-offs are necessary to achieve the desired performance.

  1. BRYANT G.F. and HALIKIAS G.D., 1995, Optimal loop shaping for systems with large parameter uncertainty via linear programming. International Journal of Control, 62, 557-568.
  2. HOROWITZ, I.M., 1973, Synthesis of linear Systems (Academic Press).
  3. HOROWITZ, I.M. and SIDI, M., 1972, Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances. International Journal of Control, 16, 287-309.
  4. HOROWITZ, I.M. and SIDI, M., 1978, Optimum synthesis of non-minimum phase systems with plant uncertainty, International Journal of Control, 27, 361-386.
  5. MACIEJOWSKI, J.M., 1989, Multivariable Feedback Design (Addison-Wesley).

An updated and more complete version will follow in the near future. You can check two papers on QFT aspects: on Optimal PID design (IEE CTA Proceedings, Vol. 146, Nov. 1999) and on Optimisation of Fixed-Structure Controllers (Proceedings 2002 IEEE International Symposium on CACSD). You will need Adobe Acrobat to view the above files, a free version can be found in Acrobat Reader Download.

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens


A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks