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Unformatted text preview: 1 REVIEW OF CONTROL SYSTEM ANALYSIS IN FREQUENCY DOMAIN (Ch 8) One advantage of the frequency response approach is that we can use the data obtained from measurements on the physical system without deriving its mathematic model. Bode Diagram A Bode diagram consists of two graphs: Plot of the logarithm of the magnitude Plot of the phase angle. Both are plotted against the frequency on a logarithmic scale. The main advantage of using the Bode diagram is that multiplication of magnitudes can be converted into addition. 2 3 General procedure for plotting Bode diagram • Write the sinusoidal transfer function as a product of basic factors. • Identify the corner frequencies associated with these basic factors. • Draw the asymptotic curves with proper slops between the corner frequencies. • The exact curve can be obtained by adding proper corrections, especially for a second order system. Example Figure 89 Frequency response of a second order system 4 Relative stability In designing a control system, we require that the system be stable. Furthermore, it is necessary that the system have adequate relative stability. It is common practice to represent the closeness in terms of phase margin and gain margin. Phase margin The gain crossover frequency is the frequency at which G(jw) is unity. The phase margin is 180 degree plus the phase angle of the open loop transfer function at the gain crossover frequency, φ γ + = 180 For a stable system, the phase margin is positive. 5 6 Gain Margin The phase crossover frequency is defined to be the frequency at which the phase angle of the open loop transfer function equals –180 degree. The gain margin is the reciprocal of the magnitude G(jw) at the phase crossover frequency....
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This note was uploaded on 06/02/2010 for the course HET 489 taught by Professor Zhenwei during the Three '08 term at Swinburne.
 Three '08
 ZHENWEI
 Frequency, Ode

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