Download Digital Computer Control Systems by G. S. Virk (auth.) PDF

By G. S. Virk (auth.)

ISBN-10: 033351405X

ISBN-13: 9780333514054

ISBN-10: 1349214906

ISBN-13: 9781349214907

ISBN-10: 1691761761

ISBN-13: 9781691761760

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Sample text

And the right-hand side gives the values y(O+), y(T+), y(2T+), .. If the output is continuous, then y(kT_) = y(kT+). 7. 5) Hold Plant Y(s) --- ------=1----• Y(z) T Delay Figure 2. 7 T ___. Y(z,m) Closed-loop system with fictitious time delay this system using the standard z-transform method. 75) where G (s) is the combined transfer function of the plant and zero-order hold unit. 81) Having calculated the standard discrete response, asnume this is not adequate and that inter-sampling values of the output are required.

Here one zero of G (s) at s = oo is mapped into z = oo and so the order of the numerator of G ( z) is one less than its denominator order. In this instance the series expansion of G (z) in powers of z- 1 will have no constant term, and hence the g (kT) has a delay of one sampling interval to a unit impulse. 58) - (s+5)(s+10) with T = 1/15 s. 513 • G (s) has a 2 zeros at s = oo and so G (z) has two zeros at z = -1. 513) Matching low frequency (DC) gains we have [ and so [{ (•+5)(~+10) _ [{ [ (z+1?

61) Starting with a continuous system, we have presented several methods for obtaining discrete equivalents. These included the numerical integration methods where the continuous transfer function, G (s), is represented as a differential equation and is used to derive a difference equation by approximating the integration. When G (s) is not in factored form the integration method is straightforward to apply, whereas the pole-zero mapping technique is suited to factorised transfer functions. All the digitisation methods give varying degrees of quantisation errors in different applications, and so an individual method cannot be said to be best in all cases (see Ogata [88]; Franklin and Powell [35]).

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Digital Computer Control Systems by G. S. Virk (auth.)

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