Session has conducted through offline mode started with introduction of resource person Mr. K. Kishan Kumar Assistant Professor, Dept. of EEE, Malta Reddy College of Engineering for Women. by Mrs. Nomula Mounika. Resource person has explained about organization of control systems course. He also explained about importance of control systems and their real time applications. He explained about importance's of Bode plot & and polar plot, Nyquist plot in detailed. He delivered the effective lecture regarding Bode plot, Polar plot & Nyquist plot techniques in the session with technical examples
Bode plots
The Bode plot or the Bode diagram consists of two plots —
- Magnitude plot
- Phase plot
- In both the plots, x-axis represents angular frequency (logarithmic scale). Whereas, yaxis represents the magnitude (linear scale) of open loop transfer function in the magnitude plot and the phase angle (linear scale) of the open loop transfer function in the phase plot.
- The magnitude of the open loop transfer function in dB is -
- '**= ° * g1'*(J=)<(/=ll
- The phase angle of the open loop transfer function in degrees is
The magnitude plot is a line, which is having a slope of 20 dB/dec. This line started at m=0.lrad/sec having a magnitude of -20 dB and it continues on the same slope. It is touching 0 dB line at m=1 rad/sec. In this case, the phase plot is 900 line.
Consider the open loop transfer function iU 20 fnq s 1 + m2 dv G(s)H(s)=1+st. Magnitude j=tan’'wzdegrees
The magnitude plot is having magnitude of 0 dB upto m=11m=lz rad/sec. From z=1z rad/sec, it is having a slope of 20 dB/dec. In this case, the phase plot is having phase angle of 0 degrees up to m=1z rad/sec and from here, it is having phase angle of 900. This Bode plot is called the asymptotic Bode plot.
As the magnitude and the phase plots are represented with straight lines, the Exact Bode plots resemble the asymptotic Bode plots. The only difference is that the Exact Bode plots will have simple curves instead of straight lines. Similarly, you can draw the Bode plots for other terms of the open loop transfer function which are given in the table.
Rules for Construction of Bode Plots
Follow these rules while constructing a Bode plot.
- Represent the open loop transfer function in the standard time constant form. Substitute, s=jms=jm in the above equation.
- Find the corner frequencies and arrange them in ascending order.
- Consider the starting frequency of the Bode plot as 1/10th of the minimum corner frequency or 0.1 rad/sec whichever is smaller value and draw the Bode plot upto 10 times maximum comer frequency.
- Draw the magnitude plots for each term and combine these plots properly. Draw the phase plots for each term and combine these plots properly.
Note — The corner frequency is the frequency at which there is a change in the slope of the magnitude plot.
Stability Analysis using Bode Plots
From the Bode plots, we can say whether the control system is stable, marginally stable or unstable based on the values of these parameters.
- Gain cross over frequency and phase cross over frequency
- Gain margin and phase margin
- Phase Cross over Frequency
- The frequency at which the phase plot is having the phase of -1800 is known as phase cross over frequency. It is denoted by mpc. The unit of phase cross over frequency is rad/sec.
- Gain Cross over Frequency
- The frequency at which the magnitude plot is having the magnitude of zero dB is known as gain cross over frequency. It is denoted by mgc. The unit of gain cross over frequency is rad/sec.
- The stability of the control system based on the relation between the phase cross over frequency and the gain cross over frequency is listed below.
- If the phase cross over frequency mpc is greater than the gain cross over frequency mgc, then the control system is stable.
- If the phase cross over frequency mpc is equal to the gain cross over frequency zgc, then the control system is marginally stable.
- If the phase cross over frequency mpc is less than the gain cross over frequency age, then the control system is unstable.
- Gain Margin
- Gain margin GMGM is equal to negative of the magnitude in dB at phase cross over frequency. GM=20log(1Mpc)=20logMpc
- Where, Mpc is the magnitude at phase cross over frequency. The unit of gain margin (GM) is dB.
- Phase Margin
- The formula for phase margin PMPM is PM=1800+$gc
- Where, age is the phase angle at gain cross over frequency. The unit of phase margin is degrees.
- NOTE:
- The stability of the control system based on the relation between gain margin and phase margin is listed below.
- If both the gain margin GM and the phase margin PM are positive, then the control system is stable.
- If both the gain margin GM and the phase margin PM are equal to zero, then the control system is marginally stable
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