Link magnitude, phase, and pole-zero views to see how zero-pole spacing changes stability margin.
Parameters
Compensator gain K
dB
Overall compensator gain.
Zero frequency wz
rad/s
Compensator zero.
Pole frequency wp
rad/s
Compensator pole.
Target crossover
rad/s
Frequency where margin is read.
Results
—
Phase contribution
—
Gain at crossover
—
Pole-zero separation
—
Margin estimate
Bode magnitude plot
Bode phase plot
Pole-zero placement
Model and equations
$$C(s)=K\frac{1+s/\omega_z}{1+s/\omega_p}$$
A lead compensator places the zero below the pole to add phase around crossover. Lag compensation raises low-frequency gain but affects bandwidth and response speed.
How to read it
The magnitude plot shows gain change around crossover.
The phase plot shows the lift between zero and pole.
The pole-zero view shows why close pole-zero placement gives weak compensation.
Learn Bode Lead Lag Compensator by dialogue
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When reading Bode Lead Lag Compensator, where should I look first? Moving Compensator gain K changes both the plots and the result cards.
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Start with Phase contribution, but do not treat the number as the whole answer. Use Bode magnitude plot to confirm the assumed state, then read Bode phase plot for the distribution or trend. The magnitude plot shows gain change around crossover.
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I can see why Compensator gain K changes Phase contribution. How should I judge the influence of Zero frequency wz?
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Move Zero frequency wz in small steps and watch Gain at crossover. That reveals which term is controlling the result. A lead compensator places the zero below the pole to add phase around crossover. Lag compensation raises low-frequency gain but affects bandwidth and response speed. A single operating point is not enough; sweep the realistic scatter range.
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What is Pole-zero placement for? It feels like the ordinary curve already tells the story.
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Pole-zero placement is for finding boundaries where the condition becomes risky or margin collapses quickly. The phase plot shows the lift between zero and pole. In Improving phase margin around PID loops, the important question is often what happens after a small change, not only the nominal value.
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So if Phase contribution is within the target, can I accept the condition?
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Treat this as a first-pass review. It helps with Initial compensator design from Bode plots and Checking bandwidth versus stability margin tradeoff, but final decisions still need standards, measured data, detailed analysis, and vendor limits. The pole-zero view shows why close pole-zero placement gives weak compensation.
Practical use
Improving phase margin around PID loops.
Initial compensator design from Bode plots.
Checking bandwidth versus stability margin tradeoff.
FAQ
Start with Phase contribution and Gain at crossover. Then use Bode magnitude plot to confirm the assumed state and Bode phase plot to read distribution or bias. The magnitude plot shows gain change around crossover
Move Compensator gain K alone, then move Zero frequency wz by a comparable amount and compare the change in Phase contribution. Pole-zero placement shows combinations where margin or performance changes quickly.
Use it for Improving phase margin around PID loops. Instead of trusting a single point, widen the input range and check whether Phase contribution keeps enough margin before moving to detailed analysis.
A lead compensator places the zero below the pole to add phase around crossover. Lag compensation raises low-frequency gain but affects bandwidth and response speed. Final decisions still require standards, measured data, detailed analysis, and vendor limits.