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By K. J. Astrom, T. Hagglund

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Lmin and the times /-u* and /-i,, when they occur are determined. 10) we 49 Chapter 2. 33 Determination by a doublet pulse. have of the parameters of an FOTD model by exciting the process J m a x: q Kp (\- e-rol r) J mi n: -d K p (t - n-r' tr 7' t^ur: L + To /min: L+2Tp. }max L ^r- ffi --aKP' and we get the following simple equations for the parameters of the model , ^t- K__rmax aJmin T_ T^ log(1 * y*u*/y*i,,) L _ t^ut - Tp L - t^rn - 2Tr. 46) The fact that the time delay L can be estimated in two ways can be used to asses if a process can be modeled by an FOTD model.

The oscillation will have the frequency raa16,o. This frequency is called the ultimate frequency. The parameter Ku is called the ultimate gain or the critical gain. The parameters Kes and ale6 have similar interpretations for a process with pure integral control. The gain ratio r is the ratio of the distances o and b. The Gain Ratio The gain ratio is an additional parameter that gives useful information about the system. 20) G(0) It is an indicator €-bo* difficult it is to control the process. Processes with a small K are easy to control.

31) for T : -2 Ilpical Process Models (dotted), -1, 0, 1 and 2 systems are said to have inverse responses. 'Examples of such systems are level dynamics in steam generators, dynamics of hydroelectric power stations, dynamics of backing cars, etc. Heat Conduction Temperature control is a very common application of PID control. Some models that are directly based on physics will now be discussed. Consider an infinitely long rod with thermal diffusivity 2. Assume that there is no radial heat transfer and that the input is the temperature at the left end of the rod.

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