Bode diagram amplitude ratio

Vary the magnitude of the frequency in the forcing disturbance and study its effect on the phase angle and amplitude ratio of the system. Use the information to construct the Bode diagram for the system, i.e., plots of phase angle and amplitude ratio versus frequency. 

The Bode diagram (Figure 7j) shows plots for GW, G2(s) and G(s) as amplitude ratio against frequency. Only the asymptotes (Section 7.10.4, Volume 3) are plotted. 

The polar plot is an alternative to the Bode diagram for representing frequency response data and is the locus of all points occupied by the tip of a vector in the complex plane whose magnitude and direction are determined by the amplitude ratio and phase shift, respectively, as the frequency of the forcing function applied to the system is varied from zero to infinity. 

The open-loop Bode diagram for all the components in the control loop, excepting the controller, is plotted and the cross-over frequency determined. If the total open-loop amplitude ratio at Bode criterion, the gain of a proportional controller which would cause the system to be on the verge of instability will be ... 

The Bode diagrams (in honour of H. W. Bode) constitute a convenient way to represent the frequency response characteristics of a system. As we can see from Eqs. (17.14a) and (17.14b), the amplitude ratio and the phase shift of the ultimate response of a system are functions of the frequency to. The Bode diagrams consist of a pair of plots showing ... 

The graphs in which the amplitude ratio and phase shift are plotted as a function of the frequency o), are called Bode diagrams. In the Bode plot, log(AR) and (j) are shown as a function of first-order process, this means ... 

The amplitude ratio and phase angle can easily be computed using Eqn. (9.32). Matlab can also be used to construct the Bode diagram, the result is shown in Fig. 9.3. 

As was derived in chapter 9, the amplitude ratio for a dead-time process is 1.0 and the phase shift -0)6. The amplitude ratio for the process becomes then AR (second-order process) x AR(dead-time process). The phase shift of the process becomes then (second-order process) + dead-time process). Figure 32.3 shows the Bode diagram in which the logarithm of the amplitude ratio and the phase shift are plotted against the frequency O). For the amplitude ratio two asymptotes emerge, one for low frequencies a>- ) (static behaviour) en one for high frequencies 0)- °° (high-frequency behaviour). The values can easily be calculated from ... 

Figure 32.4 shows the Bode diagram of a PI eontroller with integral action = 10. Rather than plotting the amplitude ratio, the ratio between amphtude ratio and controller gain is plotted on the vertieal axis. As can be seen from Eqn. (32.25), plotting log(AR) versus log(comer frequency, where the asymptotes interseet is at 1/t . The phase shift ranges from -90° to 0°. 

Frequency response techniques are powerful tools for the design and analysis of feedback control systems. The frequency response characteristics of a process, its amplitude ratio AR and phase angle, characterize the dynamic behavior of the process and can be plotted as functions of frequency in Bode diagrams. The Bode stability criterion provides exact stability results for a... 

Bode plot A type of frequency response diagram used for analysing the frequency response of a system to a disturbance signal. It is the plot of the logarithm of the amplitude ratio with the logarithm of the phase angle measurements. 

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