Key Concept – To draw Bode diagram there are four steps:
Because the denominator was already factored in this case, each factored term must have unity as the lowest order power of s (zero in this case). As a result, the numerator and denominator polynomials are both equal to unity.
2. Separate the transfer function into its constituent parts.
A constant, a zero at the origin, real Poles, real Zeros, and complex conjugate zeros are the seven types of parts that make up a polynomial function. The most common way to express this is to use the standard notation for a second order polynomial.
3. Draw the Bode diagram for each part.
The rules for drawing the Bode diagram are outlined below, with examples provided at the bottom of the page.
Examples: Draw Bode Diagrams for the following transfer functions
Complex poles are simple functions with multiple poles and zeros at their origin, such as repeated poles, a zero at the origin, and a negative constant and a complex function.
How do you find the slope of a Bode plot?
The magnitude plot has a magnitude of 0 dB up to =1 rad/sec, and from there, it has a slope of 20 dB/dec. In this case, the phase plot has a phase angle of 0 degrees up to =1 rad/sec, and from there, it has a phase angle of 90sup>0/sup>.
Where can I start a Bode plot?
Plot of the straight-line phase
- If is positive, begin line (with zero slope) at.
- If is negative, begin line (with zero slope) at.
- If the number of unstable zeros and poles is odd, add 180u00b0 to that basis.
- At every (for stable zeros), increase the slope by degrees per decade, beginning one decade before (E.g.: )
What is the difference between Bode plot and Nyquist plot?
As a result, the Bode plot shows a constant of 90 degrees and a linear curve with a negative slope, whereas the Nyquist plot shows a straight line along the ordinate (see Figure 6.4). It is clear from this example that the Nyquist plot does not show the frequency at which a value was recorded.
What is GM and PM in Bode plot?
Gm and Pm of a system indicate the relative stability of the closed-loop system formed by applying unit negative feedback to sys, as shown in the following figure; Gm is the amount of gain variance required to make the loop gain unity at the frequency Wcg where the phase angle is u2013180u00b0 (modulo 360u00b0); Pm is the amount of gain variance required to make the loop gain unity at the frequency Wcg where the phase angle is u2013180u00b0 (modulo 360u00b0);
Why Bode plot is used?
A Bode Plot is a useful tool that displays the gain and phase response of a given LTI system for various frequencies. Bode Plots are typically used with the Fourier Transform of a given system, with the Magnitude plot on top and the Phase plot on the bottom.
What are the advantages of Bode plot?
Benefits of a Bode Plot With the help of this plot, we can directly comment on the system’s stability without having to do any calculations. Bode plots provide relative stability in terms of gain margin and phase margin, and they cover the frequency range from low to high.
What is the initial slope of Bode magnitude plot of a Type 2 system?
If there are no poles or zeros at the origin, the initial slope is zero.
How do you plot a Nyquist plot?
To plot the Nyquist plots, follow these guidelines.
- Locate the poles and zeros of the open loop transfer function G(s)H(s) in the’s’ plane.
- Draw the polar plot by varying from zero to infinity.
- Draw the mirror image of the above polar plot by varying from zero to zero (0sup>/sup> if any pole or zero present at s=0).
How do you draw a polar plot of a transfer function?
Drawing Polar Plots Rules
- Substitute s=j in the open loop transfer function.
- Write the expressions for magnitude and phase of G(j)H(j).
- Find the starting magnitude and phase of G(j)H(j) by substituting=0.
- Find the ending magnitude and phase of G(j)H(j) by substituting=.