ABSTRACT
Compensators, in software or hardware, are commonly built with rational transfer functions. A design sequence is recommended for digital controllers. A complete compensator design example is presented with the derivation of a prototype analog compensator, including linear and nonlinear links, Tustin transform z-functions, equations of compensator links, and computer code. The effect of aliasing is described, and the loop response is considered for the reduction of the aliasing errors with the necessary reduction in the available feedback. Adding a lead link makes the loop gain Bode diagram locally shallower, thus reducing the gain at low frequencies and locally reducing the phase lag. Before deciding to introduce further compensation to improve the approximation to the desired response, one can use Bode’s phase integral to estimate the available improvement in the feedback. Complex poles can also be required to compensate for the plant response, and to shape the loop gain over the functional frequency band.
