Control Engineering by C. C. Bissell (auth.)

By C. C. Bissell (auth.)

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Behaviour is needed to obtain a model in terms of standard system parameters. The system analysis route, on the other hand, involves the derivation of a differential equation model by applying physical laws to the interna! components of a system, and making appropriate modelling assumptions. In the examples presented in this chapter, for example, we chose to ignore friction in the case of the motor, but to include it in the case of the radio telescope. Again, experience and physical intuition are valuable aids to the designer in taking this sort of decision.

3. ) 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-.

25. (b) G2 (jw) may be viewed as two cascaded first-order lags, each with a lowfrequency gain of 1 and a time constant of 10s. Its Bode plot is shown in Fig. 25. 1 rad s- 1 . The phase shift is -90° at the corner frequency and tends to -180° as w increases indefinitely. 01 These days computer packages are used to generate Bode plots. It is stil! a good idea, however, to learn to appreciate how a higherorder ploi relates to ils lowerorder components. 1 -10 a:l "C o ·;:; ~ Q) "C -20 -30 -40 :J ·'= a.

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