Nyquist plot analysis in Simulink - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a Nyquist plot for a transfer function in Simulink.

Simulink

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

Drag options to blanks, or click blank then click option'

Anyquistplot

Bsys

Cplot

Dtf

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'plot' instead of 'nyquist' function.

Passing a string instead of the transfer function object.

The nyquist function in MATLAB/Simulink takes a transfer function object as input to plot its Nyquist plot.

2fill in blank

medium

Complete the code to define a transfer function with numerator 2 and denominator coefficients 1, 3, 2.

Simulink

sys = tf([1], [1, 3, 2]);

Drag options to blanks, or click blank then click option'

A[2]

B2

C[1, 2]

D2, 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using a scalar instead of a vector for numerator.

Using comma-separated values without brackets.

The numerator must be a vector (array) even if it has one element, so use [2].

3fill in blank

hard

Fix the error in the code to plot the Nyquist plot of system 'sys'.

Simulink

nyquist([1]);

Drag options to blanks, or click blank then click option'

Asys

Bsys()

Csys.plot

Dplot(sys)

Attempts:

3 left

💡 Hint

Common Mistakes

Adding parentheses after 'sys' making it a function call.

Using 'plot(sys)' which is incorrect for Nyquist plots.

The nyquist function expects the transfer function object directly, not a function call or method.

4fill in blank

hard

Fill both blanks to create a Nyquist plot with frequency range from 0.1 to 10 rad/s.

Simulink

w = logspace([1], [2], 100);
nyquist(sys, w);

Drag options to blanks, or click blank then click option'

A-1

B0.1

C1

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using actual frequency values instead of their log10 values.

Swapping the start and end values.

logspace(-1, 1, 100) creates 100 points from 10^-1 (0.1) to 10^1 (10).

5fill in blank

hard

Fill all three blanks to create a Nyquist plot and extract gain margin, phase margin, and crossover frequency.

Simulink

[Gm, Pm, Wcg, Wcp] = margin([1]);
nyquist([2]);
fprintf('Gain Margin: %f dB\nPhase Margin: %f degrees\nCrossover Freq: %f rad/s\n', [3], Pm, Wcp);

Drag options to blanks, or click blank then click option'

Asys

CGm

DWcg

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variables for margin and nyquist functions.

Printing the wrong variable for gain margin.

The margin function takes the system sys to calculate margins. The Nyquist plot is also for sys. The gain margin Gm is printed.

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