Stability analysis Bode criterion

All systems in Example 18.1 have an important common feature The AR and of the corresponding open-loop transfer functions decrease continuously as co increases. This is also true for the large majority of chemical processing systems. For such systems the Bode stability criterion leads to rigorous conclusions. Thus it constitutes a very useful tool for the stability analysis of most control systems of interest to a chemical engineer. 

An exact time-delay analysis, without the Fade approximation and based on the Bode stability criterion (see Example 14.6), indicates that the actual upper limit on Kc is 4.25, which is 23% lower than the approximate value of... 

Next, we state one of the most important results of frequency response analysis, the Bode stabihty criterion. It allows the stability of a closed-loop system to be determined from the open-loop transfer function. 

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... 

At this point, it is appropriate to summarize the relative advantages and disadvantages of the Bode and Nyquist plots. The Bode plot provides more information than the Nyquist plot, because the frequency is shown explicitly. In addition, it facihtates analysis over a wide range of frequencies due to its logarithmic frequency scale. Another advantage of the Bode plot is that it allows the open-loop frequency response characteristic to be graphically constructed from the characteristics for the individual transfer functions, G, Gy, Gp, and G, as shown in Chapter 14. The chief advantage of the Nyquist plot is that the Nyquist stability criterion is more widely applicable than the Bode stability criterion. 

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