Download Digital Control: Fundamentals, Theory and Practice by W. Forsythe, R.M. Goodall PDF

By W. Forsythe, R.M. Goodall

The function of this article is to ascertain either the theoretical and sensible difficulties inherent within the use of a electronic processor for reasons of control.

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Extra resources for Digital Control: Fundamentals, Theory and Practice

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10(s + 1) G(s) = s + 10 (a) Determine the step response of the plant G(s) as a function of time. 1 sec. (c) Check the values derived from (b) against (a), for the first few steps. 4. 9 sec using {a) the Laplace transform; (b) the z-transform. 5. 5s) X 0 (s) =- xi(s) The input to the plant F(s) is a pulse of height 1 unit and duration 2 sec. (a) Use the z-transform tables to determine the value of the output at t = 0, 2, and 4 sec. 5 sec in two different ways. 6. 1 sec. (b) Express the discrete transfer function as a time-domain relationship, and as a block diagram.

It will be found that the values quoted for are correct. X0 2. 7 Why use the transform table? Values for X0 (t) could be computed from the s-domain model using a suitable numerical algorithm to perform the integration (fourth-order Runge-Kutta, for example, to obtain high accuracy). Why then should we resort to the z-domain and the transform tables? There are two reasons. In the first place the amount of computation performed by the computer is enormously reduced (and the programming greatly simplified if you are in the position of having to write your own integration algorithm).

We are able to use the transform table in this situation because the input to the plant is always a pulse; only the amplitude of the pulse changes from sample to sample. Thus the plant model performs a running summation of pulse responses of appropriate heights to determine the value of the output X0 from sample to sample. 8 Points of nomenclature (1) Variables are denoted in lower case (for example, the error Xe, the step response of the plant gp) and transfer functions in upper case (for example, the plant G(s)).

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