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