Quantitative feedback theory
In control theory, 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.
As a result of experimental measurement, values of coefficients in the Transfer Function have a range of uncertainty.
Therefore, in QFT every parameter of this function is included into an interval of possible values, and the system may be represented by a family of plants rather than by a standalone expression.
Usually system performance is described as robustness to instability (phase and gain margins), rejection to input and output noise disturbances and reference tracking.
In the QFT design methodology these requirements on the system are represented as frequency constraints, conditions that the compensated system loop (controller and plant) could not break.
With these considerations and the selection of the same set of frequencies used for the templates, the frequency constraints for the behaviour of the system loop are computed and represented on the Nichols Chart (NC) as curves.
To achieve the problem requirements, a set of rules on the Open Loop Transfer Function, for the nominal plant
The controller design is undertaken on the NC considering the frequency constraints and the nominal loop
) and tune their parameters, a process called Loop Shaping, until the best possible controller is reached without violation of the frequency constraints.
The experience of the designer is an important factor in finding a satisfactory controller that not only complies with the frequency restrictions but with the possible realization, complexity, and quality.
For this stage there currently exist different CAD (Computer Aided Design) packages to make the controller tuning easier.
Post design analysis is then performed to ensure the system response is satisfactory according with the problem requirements.
The QFT design methodology was originally developed for Single-Input Single-Output (SISO) and Linear Time Invariant Systems (LTI), with the design process being as described above.
The use of both phase and magnitude information for the design of pre-filter was first discussed in (Boje, 2003) for SISO systems.
