A control engineer increases loop gain by 6 dB on a Nichols chart. What happens to the open-loop curve on the chart?
AThe entire curve shifts vertically upward by 6 dB while its horizontal position is unchanged
BThe entire curve shifts to the right by 6 degrees, increasing the phase margin
CThe curve rotates clockwise around the critical point at (−180°, 0 dB)
DOnly the high-frequency portion shifts; the low-frequency portion is unaffected by gain changes
On the Nichols chart, the vertical axis is open-loop magnitude in dB. A pure gain change multiplies all magnitudes by the same factor, which is a uniform vertical shift of the entire curve. Phase is unaffected by a real gain scalar, so the horizontal position stays fixed. This property makes gain tuning visually intuitive: you can slide the curve up or down and immediately read off the new performance from the fixed closed-loop contours.
Question 2 Multiple Choice
A designer reads the Nichols chart and finds the open-loop curve is tangent to the M = 4 dB closed-loop contour near crossover. This indicates:
AThe closed-loop peak magnitude is 4 dB (about 59% overshoot), which likely exceeds typical specifications
BThe gain margin is exactly 4 dB, meaning the system has minimal stability robustness
CThe phase margin equals 4 degrees, which is dangerously small
DThe closed-loop bandwidth is 4 rad/s, independently of the crossover frequency
The M-contours on a Nichols chart are loci of constant closed-loop magnitude. Where the open-loop curve is tangent to a contour, that contour value is the peak closed-loop magnitude M_p. An M_p of ~1.3 dB corresponds to about 20% overshoot; 4 dB is much larger, indicating a significant resonance peak and likely excessive overshoot. The chart lets you read this directly without computing the closed-loop transfer function.
Question 3 True / False
The M-contours and N-contours on a Nichols chart should be recalculated for each new plant, since they depend on the specific open-loop transfer function.
TTrue
FFalse
Answer: False
The M- and N-contours are fixed curves derived from the algebra of the unity-feedback closed-loop formula T = G/(1 + G). They are universal for any unity-feedback system and do not depend on the specific plant G(s). This is precisely the chart's power: a precomputed overlay converts open-loop magnitude-phase coordinates directly to closed-loop performance metrics for any plant.
Question 4 True / False
The Nichols chart allows a designer to simultaneously read gain margin, phase margin, and closed-loop peak overshoot from a single diagram.
TTrue
FFalse
Answer: True
Gain margin is the vertical distance from the open-loop curve to 0 dB at the −180° phase crossing; phase margin is the horizontal distance from the curve to −180° at the 0 dB gain crossing; and the M-contour tangent to the curve gives the closed-loop peak M_p. All three are readable simultaneously from the same Nichols plot, which is its key advantage over separate Bode plots.
Question 5 Short Answer
Why is the Nichols chart more useful for final design verification than for initially selecting the structure or poles/zeros of a compensator?
Think about your answer, then reveal below.
Model answer: Because the Nichols chart shows how the combined open-loop curve relates to closed-loop performance, but it doesn't reveal how individual compensator poles or zeros contribute to the curve's shape. Root locus and Bode plots give better insight into the frequency-domain effect of specific compensator elements during initial design. Once the structure is fixed, the Nichols chart efficiently verifies that all simultaneous specs are met.
The Nichols chart is a verification and tuning tool. Its strength — showing all performance metrics at once — is also a limitation: the curve's shape is the result of the entire open-loop transfer function, so it's hard to diagnose which compensator element to change. Bode magnitude and phase plots make the contribution of individual poles and zeros transparent, making them better for initial compensator design.