By D. Welbourne and P. Hammond (Auth.)
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Another is to divide the integrator gains by 10. e. 10sec on the machine is 1 sec worth of "real" time on the physical system. So the final gains of the time-scaled circuit are 0-2, 0-32 and 0-5 in the integrators, and 1 in the summer. These correspond to the gains of 2¼, 3-2 and 5 in the integrators and 1 in the summer in the original analogue. The final circuit is shown in Fig. 19. I 0-20 —O |T\ 0-5 nv. ^>-^(-4÷)-Ç3^-[Ñ>— (20×Ç Ë 0-32 ^ \Jj FIG. I [-20f (t)] 19. Time scaling can cause a lot of confusion.
6) If time scaling is required, after the gains have been found, reduce integrator gains by a common factor for a simulation to behave slower than the physical system, and conversely. A WORKED EXAMPLE The uranium fuel elements in alloy cans which are pressed on humps can appear on the cans, the normalized height x of the equations , a nuclear reactor are encased in to the elements. **-lm* ±(φχ)=-2φα, (1) (2) where a is a parameter describing the elastic properties of the alloy can. We first construct the unsealed diagram of the simulation circuit of Fig.
Crudely, the differential of a spikey waveform is a much more spikey waveform. There is always some noise present at 50 c/s for a reason to be explained below, and the gain of a differentiator at 50 c/s is 100 times that at 0-5 c/s, which is a high frequency for an analogue problem, except in special applications. For this reason, pure differentiators are almost never successful in analogue circuits. All equations are transformed into terms of integration as the operation for solution of the differential 30 ANALOGUE COMPUTING METHODS equations for the system variables.
Analogue Computing Methods by D. Welbourne and P. Hammond (Auth.)