Bode diagram asymptote

Asymptote interseetion (break frequeney) oeeurs at XjT, i.e. 2rad/s. The Bode diagram is shown in Figure 6.13. 

Construet, on log-linear graph paper, using asymptotes, and validate using MATLAB or a similar tool, the Bode diagrams for... 

Construct, using asymptotes, the Bode diagram and read off values of open-loop modulus and phase for the following frequencies... 

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 Bode diagrams are plotted for these in Figure 7o. The asymptotes on the AR plots are summed and the sums on the ft plots are obtained by linear measurement. 

The Bode diagram in this case (Fig. 7.46) is distinguished by the fact that f is a parameter which affects both the AR and the yr plots. However, the asymptotes may be determined in the same manner as for the first-order system. It is found that, for all , the AR high frequency asymptote is a straight line of slope -2 passing through the point (1,1) and the LFA is represented by the line AR = 1. The yr plots all tend to zero degrees as tor- 0 and to -180° as When toc= lr, y/--90°... 

For a system like the one in item 8, we claim that the slope of the overall asymptotes, in the log AR versus log to plot of its Bode diagram, can be given from the algebraic sum of the slopes of the asymptotes for the individual subsystems,... 

Explain why. Also, construct qualitatively the Bode diagram, indicating the slopes of the asymptotes for the overall system. 

We can use frequency response techniques (see Chapter 17) to identify experimentally a poorly known process. Do you have any ideas on how you could do it To help you in your thoughts, consider the Bode diagrams of various systems that were examined in Chapter 17. Notice the information provided by characteristics such as the corner frequency (determines the unknown time constant), the level of low-frequency asymptotes (determines the value of static process gains), the slope of high-frequency asymptotes (determines the order of a system), and the behavior of phase lag (keeps increasing for systems with dead time). Note For further details, consult Ref. 11.)... 

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°. 

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