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3. Random noise [2], n(t), may be introduced shown by the block diagram into the feedback signal, q(t), by the instrumentation such as the neutron detectors. In this section, the amount of error introduced into the optimum control system shown in Fig. 3 will be compared to the amount of error introduced into a typical state variable switching system shown in Fig. 4. 61 Switch off at t=T r 0 + Q(t) SECHMT2-tJ ] SECHMT 2-T|)1 SWITCH OFF AT t =T2" ø `˝˙[ø( 2-0] 7. km*(t) 1 s k y(t) + k n(t) + λ O Fig.

F/g . 5. T h e d e p e n d e n c e o f / ( « ) o n a secondar y parameter . α parameter . (w{p) α p 1 + ; = a const . i = 1 ax = 1 («1 + «2) Ø a2 = 2 See Fig. 5. const . 48 Example 2 In order to study the function f{a) for a typical control system, the transfer function was chosen (Fig. 6) with *(/) = white noise. <* I Models + process p(1+pT ) Fig. 6. ( l e f t ) . Typica l closed-loo p contro l syste m wit h u n k n o w gain . p(1+p) Fh. 7. ( r i e h t ) . Adaptiv e loop for th e syste m in Fig .

2). The symbols are the usual in analog computation. κ>-^]> Fig. 2. T h e /fa; instrumentatio n of th e m e a s u r e m e n t procedure . As is clearly seen from the figure, z{t) will not influence the measurement if x{t) and z(t) are uncorrelated and T0 large. As a result of the finite time of observation we shall get some errors when mea­ suring f(a). The reader is referred to ref. [2] for a detailed exposition of these questions. 44 APPLICATION IN ADAPTIVE CONTROL A major part of the literature of adaptive control is concerned with the identifi­ cation problem in general.

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