Quantizer effects on steady-state error specifications of digital feedback control systems

Suppose that for a linear, time-invariant, single-input single-output (SISO) plant a digital dynamic controller has been designed so that the corresponding discrete-time linear feedback control system will satisfy certain specified steady-state error criteria (e.g., the output v˜(kT) will follow the input r (kT) within a certain given error bound). Corresponding to this idealized linear system, the digital implementation of the dynamic controller will result in a nonlinear feedback control system. To what extent the resulting nonlinear digital feedback control system satisfies the steady-state-error criteria of the original idealized linear prototype feedback control system is investigated. Digital controller implementations which use fixed-point arithmetic or floating-point arithmetic are considered. Designs which are well scaled are assumed, i.e., overflow nonlinearities in digital controllers are not addressed