Quantitative feedback theory
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Quantitative feedback theory (QFT), developed by Isaac 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 highly transparent, allowing a designer to see what trade-offs are necessary to achieve a desired performance level.
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[edit] Overview
Usually a system plant is represented by its Transform Function (Laplace in the continuous domain, Z-Transform in the discrete domain). In QFT every parameter of this function is represented as an interval of possible values, which have been obtained as a result of system modelling or system identification processes.
Therefore, the system is represented by a family of plants rather than by a standalone expression. After an analysis in the frequency domain, taking a finite number of frequencies, a set of templates is obtained which enclose the behaviour of the open loop system at each frequency.
QFT take care of the desired performance of system as a set of constraints represented in the frequency domain. Usually system performance is described as robustness to instability, rejection to input an output noise disturbances and reference tracking. All these considerations are summarized in a set of frequency constraints represented on the Nichols Chart (NC).
The controller design is undertaken on the NC with the frequency constraints and the nominal plant of the system, the plant which represents the frequency templates. At this point, the designer begins to introduce controller functions and tune their parameters, a process called Loop Shaping, until the best possible controller is reached without violation of the frequency constraints.
Finally, the QFT design may be completed with a pre-filter design when it is required. Post design analysis is then performed to ensure the system response is satisfactory.
The QFT design methodology was originally developed for single-input single-output (SISO) linear time invariant systems (LTI), with the design process being as described above. However, it has since been extended to weakly nonlinear systems, time varying systems, distributed parameter systems, and to multi-input multi-output (MIMO) systems (Horowitz, 1991). The development of CAD tools has been an important, more recent development, which simplifies and automates much of the design procedure (Borghesani et al, 1994).
[edit] References
- Horowitz, I., 1963, Synthesis of Feedback Systems, Academic Press, New York, 1963.
- Horowitz, I., and Sidi, M., 1972, “Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances,” International Journal of Control, 16(2), pp. 287-309.
- Horowitz, I., 1991, “Survey of Quantitative Feedback Theory (QFT),” International Journal of Control, 53(2), pp. 255-291.
- Borghesani, C., Chait, Y., and Yaniv, O., 1994, Quantitative Feedback Theory Toolbox Users Guide, The Math Works Inc., Natick, MA.
- Zolotas, A. (2005, June 8). QFT - Quantitative Feedback Theory. Connexions.
[edit] See also
- Control engineering
- Feedback
- Process control
- Robotic unicycle
- H infinity
- Optimal control
- Servomechanism
- Nonlinear control
- Adaptive control
- Robust control
- Intelligent control
- State space (controls)
[edit] External links
- Dr Charles J. Pritchard, Doctrate Thesis, University of the Witwatersrand, 1995
- Dr Murray Kerr, Doctrate Thesis, The University of Queensland, 2004
- Professor P.S.V. Nataraj, Interdisciplinary Programme in Systems and Control Engineering, Indian Institute of Technology Bombay, Powai, Mumbai – 400 076, India.
