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

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.