Linearization of nonlinear models in Simulink - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to linearize the Simulink model at the operating point.

Simulink

op = findop('[1]');

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

AsimulinkModel

BmodelName

CnonlinearModel

DlinearModel

Attempts:

3 left

💡 Hint

Common Mistakes

Using variable names instead of the model name string.

Passing the linear model name instead of the nonlinear one.

The findop function requires the model name as input to find the operating point.

2fill in blank

medium

Complete the code to linearize the model using the operating point.

Simulink

linsys = linearize('[1]', op);

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

AmodelName

BlinearModel

CsimulinkModel

DnonlinearModel

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the linear model name instead of the nonlinear model name.

Using the operating point variable incorrectly.

The linearize function needs the model name and the operating point to create the linear model.

3fill in blank

hard

Fix the error in the code to get the operating point of the model.

Simulink

op = [1]('[2]');

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

Afindop

Blinearize

Csim

Dopen_system

Attempts:

3 left

💡 Hint

Common Mistakes

Using linearize instead of findop.

Not passing the model name as a string.

The function to find the operating point is findop. The second blank is the model name string.

4fill in blank

hard

Fill both blanks to create a linear state-space model from the linearization data.

Simulink

sys = ss([1], [2], C, D);

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

Alinsys.A

Blinsys.B

Clinsys.C

Dlinsys.D

Attempts:

3 left

💡 Hint

Common Mistakes

Using output matrices C or D instead of A and B.

Mixing up the order of matrices.

The state-space model requires matrices A and B from the linearized system.

5fill in blank

hard

Fill all three blanks to extract the state-space matrices from the linearized system.

Simulink

A = [1];
B = [2];
C = [3];

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

Alinsys.A

Blinsys.B

Clinsys.C

Dlinsys.D

Attempts:

3 left

💡 Hint

Common Mistakes

Using matrix D instead of C.

Confusing the order of matrices.

Extract matrices A, B, and C from the linearized system object for further analysis.

Practice

1. What is the main purpose of linearizing a nonlinear model in Simulink?

easy

A. To make the model run faster in simulation

B. To simplify the model around an operating point for easier analysis

C. To convert the model into a discrete-time system

D. To add noise to the model for robustness testing

Solution

1. Step 1: Understand linearization concept

   Linearization approximates a nonlinear system by a linear one near a specific operating point.

2. Step 2: Identify the purpose in Simulink

   This simplification helps in easier analysis and controller design by using linear system tools.

3. Final Answer:

   To simplify the model around an operating point for easier analysis -> Option B

4. Quick Check:

   Linearization = Simplify near operating point [OK]

Hint: Linearization means simplify near a point [OK]

Common Mistakes:

• Thinking linearization speeds up simulation
• Confusing linearization with discretization
• Assuming linearization adds noise

2. Which Simulink function is used to linearize a nonlinear model at a specified operating point?

easy

A. linmod

B. ode45

C. step

D. sim

Solution

1. Step 1: Recall Simulink linearization functions

   Simulink provides linmod and linearize functions to get linear models from nonlinear ones.

2. Step 2: Identify the correct function

   linmod is a common function used to linearize models at operating points.

3. Final Answer:

   linmod -> Option A

4. Quick Check:

   Linearize function = linmod [OK]

Hint: Use linmod to linearize nonlinear models [OK]

Common Mistakes:

• Choosing sim which runs simulation
• Selecting step which plots step response
• Using ode45 which solves ODEs

3. Given the following MATLAB code snippet for linearizing a Simulink model:

sys = 'myModel';
op = operpoint(sys);
[A,B,C,D] = linmod(sys, op);
disp(size(A));

What will be the output of disp(size(A)) if the system has 4 states?

medium

A. [4 1]

B. [1 4]

C. [4 4]

D. [1 1]

Solution

1. Step 1: Understand linmod output matrices

   linmod returns state-space matrices A, B, C, D. A is the state matrix with size (number_of_states x number_of_states).

2. Step 2: Apply to given system

   Since the system has 4 states, A will be a 4x4 matrix.

3. Final Answer:

   [4 4] -> Option C

4. Quick Check:

   State matrix A size = (states x states) = [4 4] [OK]

Hint: A matrix size is states by states [OK]

Common Mistakes:

• Confusing A size with input or output dimensions
• Assuming A is a vector instead of a matrix
• Mixing up B or C matrix sizes

4. You tried to linearize a nonlinear Simulink model using linmod('modelName') but got an error. What is the most likely cause?

medium

A. The MATLAB path is incorrect

B. The model has no inputs defined

C. The model is already linear

D. The model is not loaded or compiled before linearization

Solution

1. Step 1: Understand linmod requirements

   linmod requires the model to be loaded and compiled to access its operating point and states.

2. Step 2: Identify common error cause

   If the model is not loaded or compiled, linmod throws an error.

3. Final Answer:

   The model is not loaded or compiled before linearization -> Option D

4. Quick Check:

   Model must be loaded before linmod [OK]

Hint: Load and compile model before linmod [OK]

Common Mistakes:

• Assuming no inputs cause error
• Thinking linear model can't be linearized
• Blaming MATLAB path without checking model status

5. You want to design a controller using a linearized model of a nonlinear Simulink system. Which step is essential before controller design?

hard

A. Linearize the nonlinear model at the desired operating point

B. Convert the nonlinear model to a discrete-time model directly

C. Simulate the nonlinear model without linearization

D. Add random noise to the nonlinear model

Solution

1. Step 1: Understand controller design needs

   Controller design often requires a linear model to apply linear control techniques.

2. Step 2: Identify necessary preparation

   Linearizing the nonlinear model at the operating point provides the linear approximation needed.

3. Step 3: Recognize incorrect options

   Direct discretization or simulating nonlinear model alone does not prepare for linear controller design.

4. Final Answer:

   Linearize the nonlinear model at the desired operating point -> Option A

5. Quick Check:

   Linearize before controller design [OK]

Hint: Always linearize model before designing controller [OK]

Common Mistakes:

• Skipping linearization and designing controller on nonlinear model
• Trying to discretize nonlinear model first
• Adding noise instead of linearizing