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A controller design technique for shaping the frequency response of a processis described. A general linear model (GLM) is used to define the form of a lagor lead compensator in discrete time using a prescribed set of basis functions.The model is then transformed via the complex z-domain into a differenceequation for a recursive digital filter with an infinite impulse response(IIR). A polynomial basis set is better for shaping the frequency response inthe near-zero region; whereas a sinusoidal basis set is better for defining theresponse at arbitrary frequencies. The proposed compensator design method ismore flexible than existing low-order approaches and more suitable than othergeneral-purpose high-order methods. Performance of the resulting controller iscompared with digital proportional-integral-differential (PID) andlinear-state-space (LSS) algorithms in a real motor-control application.

Direct Digital Design of Loop-Shaping Filters for Sampled Control Systems