Nyquist plot analysis in Simulink - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Nyquist plot?

A Nyquist plot is a graph that shows how a system's output changes with frequency. It plots the system's response as a curve in the complex plane, using real and imaginary parts.

beginner

Why do we use Nyquist plots in control systems?

We use Nyquist plots to check if a system is stable and to understand how it reacts to different frequencies. It helps us see if the system might oscillate or behave badly.

intermediate

What does it mean if the Nyquist plot encircles the point (-1, 0)?

If the Nyquist plot encircles the point (-1, 0) in the complex plane, it indicates potential instability in the system. The number of encirclements relates to the number of unstable poles.

beginner

How can you generate a Nyquist plot in Simulink?

In Simulink, you can use the 'Bode Plot' or 'Frequency Response Estimator' blocks, or use MATLAB commands like 'nyquist' with your system model to create the Nyquist plot.

intermediate

What information does the Nyquist plot provide about gain and phase margins?

The Nyquist plot helps find gain and phase margins, which tell how much you can increase gain or shift phase before the system becomes unstable.

What does the Nyquist plot show in control systems?

A System response in the complex plane over frequency

B Time response of the system

C System input signal only

D System output signal only

The Nyquist plot shows how the system's output changes with frequency, plotted in the complex plane.

In Nyquist plot analysis, what does encircling the point (-1, 0) indicate?

A System stability

B System is linear

C No effect on system

D Potential system instability

Encircling (-1, 0) relates to system instability according to the Nyquist stability criterion.

Which Simulink tool can help generate a Nyquist plot?

A Integrator block

B Scope block

C Frequency Response Estimator

D Step block

The Frequency Response Estimator block helps generate frequency response plots like Nyquist plots.

What do gain and phase margins tell us from a Nyquist plot?

A The system's noise level

B How much gain or phase can change before instability

C The system's output delay

D The system's input amplitude

Gain and phase margins indicate how much the system can tolerate changes before becoming unstable.

Which part of the Nyquist plot corresponds to zero frequency?

A Point at the far right on the real axis

B Point at the origin

C Point at the far left on the real axis

D Point at the top on the imaginary axis

At zero frequency, the Nyquist plot starts at the system's DC gain, usually on the far right of the real axis.

Explain how a Nyquist plot helps determine system stability in control systems.

Think about how the plot's shape relates to the system's poles.

Describe the steps to generate and interpret a Nyquist plot using Simulink tools.

Consider both how to create the plot and what to look for in it.

Practice

1. What does a Nyquist plot primarily show in control system analysis?

easy

A. The error rate of a system over time

B. The time response of a system to a step input

C. The frequency response of a system in the complex plane

D. The physical layout of system components

Solution

1. Step 1: Understand Nyquist plot purpose

   A Nyquist plot maps the frequency response of a system onto the complex plane, showing gain and phase changes.

2. Step 2: Compare options to definition

   Only The frequency response of a system in the complex plane correctly describes this; others describe different system aspects.

3. Final Answer:

   The frequency response of a system in the complex plane -> Option C

4. Quick Check:

   Nyquist plot = frequency response [OK]

Hint: Nyquist plots map frequency response, not time or error [OK]

Common Mistakes:

• Confusing Nyquist plot with time-domain response
• Thinking Nyquist shows error rates
• Assuming it shows physical system layout

2. Which Simulink block is commonly used to generate a Nyquist plot?

easy

A. Step Response block

B. Bode Plot block

C. Frequency Response Estimator block

D. Nyquist Plot block

Solution

1. Step 1: Identify Simulink blocks for Nyquist plots

   Simulink provides a specific Nyquist Plot block to generate Nyquist plots directly.

2. Step 2: Eliminate other blocks

   Step Response shows time response, Bode Plot shows magnitude and phase separately, Frequency Response Estimator estimates frequency response but does not plot Nyquist directly.

3. Final Answer:

   Nyquist Plot block -> Option D

4. Quick Check:

   Nyquist plot uses Nyquist Plot block [OK]

Hint: Nyquist plots use the Nyquist Plot block in Simulink [OK]

Common Mistakes:

• Choosing Bode Plot block for Nyquist plot
• Confusing Step Response with frequency plots
• Selecting Frequency Response Estimator instead of Nyquist Plot block

3. Given the following MATLAB code snippet in Simulink environment:

sys = tf([1], [1, 2, 1]);
nyquist(sys)

What will the Nyquist plot show for this system?

medium

A. A plot showing no encirclement of the point -1+0i

B. A plot with multiple encirclements of the origin

C. A plot showing a clockwise encirclement of the point -1+0i

D. A plot showing a counterclockwise encirclement of the point -1+0i

Solution

1. Step 1: Analyze the transfer function

   The transfer function sys = 1/(s^2 + 2s + 1) has poles at s = -1 (double pole), stable system.

2. Step 2: Interpret Nyquist plot behavior

   For a stable system with no unstable poles, the Nyquist plot does not encircle the critical point -1+0i.

3. Final Answer:

   A plot showing no encirclement of the point -1+0i -> Option A

4. Quick Check:

   Stable system means no -1 encirclement [OK]

Hint: Stable poles mean no encirclement of -1 point [OK]

Common Mistakes:

• Assuming encirclement always occurs
• Confusing origin with -1+0i point
• Mixing clockwise and counterclockwise directions

4. You run a Nyquist plot in Simulink but the plot does not appear. Which of the following is the most likely cause?

medium

A. The system transfer function is not defined correctly

B. The Nyquist plot block is not connected to any input

C. The simulation time is set to zero

D. The plot window is minimized

Solution

1. Step 1: Check block connections in Simulink

   If the Nyquist plot block is not connected to a system input, it cannot generate data to plot.

2. Step 2: Evaluate other options

   Incorrect transfer function or zero simulation time may cause errors but usually show messages; minimized window does not prevent plot generation.

3. Final Answer:

   The Nyquist plot block is not connected to any input -> Option B

4. Quick Check:

   Block must be connected to input for plot [OK]

Hint: Always connect Nyquist block input to system [OK]

Common Mistakes:

• Ignoring block connections
• Assuming simulation time affects Nyquist plot
• Thinking minimized window stops plot generation

5. In a feedback control system modeled in Simulink, the Nyquist plot of the open-loop transfer function encircles the point -1+0i twice clockwise. What does this imply about the closed-loop system stability?

hard

A. The closed-loop system has two unstable poles

B. The closed-loop system is stable

C. The closed-loop system is marginally stable

D. The closed-loop system has no poles in the right half-plane

Solution

1. Step 1: Recall Nyquist stability criterion

   The number of clockwise encirclements of -1 equals the number of unstable closed-loop poles minus unstable open-loop poles.

2. Step 2: Apply to given scenario

   Assuming open-loop system has zero unstable poles, two clockwise encirclements mean two unstable closed-loop poles.

3. Final Answer:

   The closed-loop system has two unstable poles -> Option A

4. Quick Check:

   Clockwise encirclements = unstable poles count [OK]

Hint: Clockwise encirclements count unstable poles [OK]

Common Mistakes:

• Confusing clockwise with counterclockwise encirclements
• Ignoring open-loop pole count
• Assuming no encirclement means instability