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By C. C. Bissell (auth.)

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The effective voltage across the armature resistance is therefore v - e, and Ohm's law for the circuit can be written v-e= iR Combining this with the torque equation gives Km R(v - KbQ) . = JQ Rearranging, we have In general, a differential equation may involve the derivatives with respect to time of either input or output or both. It is quite common in control engineering, however, to meet system models which involve derivatives of the output variable only, as in this case. Kmv _ J"' KmKbr-.

Solution This section and the previous one have dealt in some detail with the first-order lag model, which is a useful idealization of a number of commonly-occurring physical systems. Many systems, however, have properties which cannot be characterized adequately using such a model. In the remainder of this chapter a number of other simple standard models will be introduced, applying the time and frequencydomain techniques just discussed. All the models are applicable to many systems other than the examples presented.

So instead of substituting particular numerica! values of k 5 , kc and J into the antenna equation, let us examine in general terms how we can use a standard model to characterize second-order system behaviour. The standard form of the second-order equation is written .. 2 eo + 2(wneo + wneo Note again how cur modelling assumptions have been carefully chosen net only to be realistic, but also to lead to a tractable mathematical model. A non-linear viscous friction model for example might have been more realistic, but would not have led to a system model easy to handle!

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