Utilization of extrapolated integrators and differentiators in digital controller design and analysis

Mathematical tools that transform a continuous system-model to its digital counterpart are introduced. The work presented applies Richardson´s extrapolation integration technique in developing a discrete representation for integrators and differentiators that is less dependent on the sampling interval. An extrapolated integrator or differentiator element is related to a linear combination of trapezoidal rule or higher-order backward difference rule elements, respectively. The generalized integrators and differentiators are utilized to identify the transfer functions of extrapolated integrators and differentiators in the z domain. The discrete integrators and differentiators introduced are applied in the design of PID, PI, and PD digital controllers