Quantitative Feedback Theory (QFT), a robust control design method introduced by Horowitz, has been shown to be useful in many cases of multi-input, multi-output (MIMO) parametrically uncertain systems. Prominent is the capability for direct design to closed-loop frequency response specifications. In this paper, the theory and development of optimization-based algorithms for design of minimum-gain controllers is presented, including an illustrative example. Since MIMO QFT design is reduced to a series of equivalent single-input, single-output (SISO) designs, the emphasis is on the SISO case.

Presented in this paper is a robust controller design methodology for a class of uncertain, multivariable, regulating systems required to maintain a prespecified operating condition within hard time domain tolerances despite a vector of step disturbances. The design methodology is a frequency domain approach and is based on sequential loop design where a Gauss elimination technique facilitates the various design steps. The specific class of systems addressed are those which can be modeled as square, multivariable systems with parametric uncertainty. One restriction imposed is that the system and its inverse are stable for all plant parameter combinations. The key features of this design methodology include (i) the design of a fully populated controller matrix, (ii) the ability to design for system integrity, and (iii) the direct enforcement of hard time domain tolerances through frequency domain amplitude inequalities.

In this work, a digital robust controller is designed via Quantitative Feedback Theory (QFT) to maintain a constant cutting force in the presence of parametric uncertainty for a time varying end milling process. The QFT controller is designed using the delta transform method for discrete systems. The controller is designed to limit the overshoot and settling time of the cutting force levels over a range of cutting parameters. Models are presented for the cutting process and machine dynamics including parametric uncertainty, and these models are used to develop a controller which meets given tracking and regulation specifications for all plant values. Experimental results are obtained by implementing the controller on a milling machine.

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