ABSTRACT
Digital computers are general-purpose devices designed with the flexibility to do many tasks other than the control function. This chapter delineates the theory necessary to design algorithms that will be programmed into the digital computer to provide the control efforts at the outputs of the digital-to-analog converter based on the input to the analog-to-digital converter. It examines the fundamental mathematics necessary to discuss the discrete-time control problem on a rational basis. The z-transform is developed as a tool for the solution of linear difference equations with constant coefficients. Whenever possible the parallel structure with the Laplace transform is pointed out. Usage of the transfer function results in the frequency response function for sinusoidal excitation. The significance of the location of the z-domain poles of sampled functions and how these locations reflect the nature of the sequence itself is also pointed out.
