By K. J. Astrom, T. Hagglund

ISBN-10: 1556179421

ISBN-13: 9781556179426

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**Example text**

9. Parameter K is also related to the normalized time delay r. I0. This relation holds approximately for many other systems. As a crude approximation we can thus equate r and r. 6t. For the FOTD model it is also possible to find the parameters L and ? from r and arlse using the following equations T: f : A: '1{ T r-- l @no 1 -i- (tr ' - arctanrc-2- 11 f0rso G (latlse) | -I. 22) K 27 Chapter 2. 18). The dashed line shows the straight line approximation K: r. 5 TypicalProcessModels Much of the dynamic behavior encountered in control is relatively simple.

FrequencyResponse In frequency response analysis, a sinusoidal signal is instead introduced, and the steady-state response is analyzed. rg correlation techniques. The long experimental times is a drawback. It is also possible to introduce an arbitrary signal as perturbation. a The frequency response can be obtained as the raiio of the Fourier transforms of the output and the input signals. It is also possible to fit the parameters of a model with given structure to the data. A nice feature of using signals other than steps is that it is possible to make a trade-off between signal amplitude and duration.

44) T, - Tro and cg, Tg, and Tr, are the where xr: C - C O , X 2 : T - T O , a n d U equilibrium values. 44224 ( s + 0 . 0 8 7 1 7 ) (-r 0 . 03854 in the right half plane. 2 could be nonlinear. The dynamic models discussed so far have, however, been linear. Since nonlinearities are common in practice it is highly desirable to have nonlinear models. 27 A Hammerstein model a), and a Wiener model b). nonlinear. General models for nonlinear dynamics are complicated, and there are no good methods for designing PID controllers for such systems.

### Advanced PID Control by K. J. Astrom, T. Hagglund

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