Mixed continuous-discrete models in Simulink - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define a continuous state in Simulink.

Simulink

states = [1](2,1);

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

Aeye

Bones

Crand

Dzeros

Attempts:

3 left

💡 Hint

Common Mistakes

Using ones instead of zeros.

Using eye which creates an identity matrix.

We use zeros to initialize continuous states to zero.

2fill in blank

medium

Complete the code to sample a discrete signal at each time step.

Simulink

discrete_signal = [1](time_step);

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

Astep

Bsample

Ccontinuous

Dpulse

Attempts:

3 left

💡 Hint

Common Mistakes

Using sample which is not a Simulink function.

Using pulse which is unrelated.

The step function returns the value of the discrete signal at the given time step.

3fill in blank

hard

Fix the error in the code to update the continuous state derivative.

Simulink

dx = [1] * x + u;

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

A1

BA

CX

Da

Attempts:

3 left

💡 Hint

Common Mistakes

Using lowercase a which is undefined.

Using X which is a different variable.

Matrix A must be uppercase to match the variable name for system dynamics.

4fill in blank

hard

Fill both blanks to create a hybrid model with continuous and discrete parts.

Simulink

hybrid_model = [1](continuous_part, [2]);

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

Acombine

Bdiscrete_part

Csample_time

Dintegrate

Attempts:

3 left

💡 Hint

Common Mistakes

Using integrate which is for continuous integration.

Using sample_time which is a parameter, not a model.

The combine function merges continuous and discrete parts, where discrete_part is the discrete model.

5fill in blank

hard

Fill both blanks to define a discrete-time update rule with input and state.

Simulink

x_next = A[1]x + [2] * u;

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

A*

BB

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using - instead of + for addition.

Forgetting multiplication operators.

The discrete update rule multiplies state x by matrix A, adds input matrix B times input u.

Practice

1. What does a mixed continuous-discrete model in Simulink represent?

easy

A. A system combining smooth continuous changes and stepwise discrete changes

B. A system with only continuous changes

C. A system with only discrete changes

D. A system that cannot be simulated in Simulink

Solution

1. Step 1: Understand model types in Simulink

   Continuous models change smoothly over time, discrete models change at specific time steps.

2. Step 2: Define mixed continuous-discrete model

   It combines both smooth continuous changes and stepwise discrete changes in one system.

3. Final Answer:

   A system combining smooth continuous changes and stepwise discrete changes -> Option A

4. Quick Check:

   Mixed model = continuous + discrete changes [OK]

Hint: Mixed models combine smooth and step changes [OK]

Common Mistakes:

• Thinking mixed means only continuous
• Confusing discrete with continuous
• Believing Simulink can't simulate mixed models

2. Which Simulink block is used to represent discrete-time memory in mixed models?

easy

A. Integrator

B. Unit Delay

C. Gain

D. Sum

Solution

1. Step 1: Identify discrete memory blocks

   Discrete memory stores previous values at discrete time steps.

2. Step 2: Match block to function

   Unit Delay block holds the input value for one discrete time step, acting as memory.

3. Final Answer:

   Unit Delay -> Option B

4. Quick Check:

   Discrete memory = Unit Delay [OK]

Hint: Unit Delay stores previous discrete values [OK]

Common Mistakes:

• Choosing Integrator which is continuous
• Confusing Gain with memory
• Selecting Sum which adds signals

3. Consider a Simulink model with an Integrator block connected to a Unit Delay block. If the input is a step signal starting at 0 and stepping to 1 at time 1s, what is the output of the Unit Delay block at time 1.5s?

medium

A. 0.5

B. 0

C. 1

D. Undefined

Solution

1. Step 1: Understand signal timing

   The step input changes from 0 to 1 at 1s.

2. Step 2: Analyze Unit Delay output at 1.5s

   Unit Delay outputs the input value from the previous discrete time step. Assuming sample time 1s, at 1.5s it outputs input at 1s, which is 1 after the step.

3. Final Answer:

   1 -> Option C

4. Quick Check:

   Unit Delay outputs previous step input [OK]

Hint: Unit Delay outputs previous step input value [OK]

Common Mistakes:

• Assuming Unit Delay outputs current input
• Ignoring sample time effect
• Confusing Integrator output with Unit Delay

4. You have a mixed model with an Integrator and Unit Delay connected, but the simulation shows unexpected zero output from the Unit Delay. What is the most likely cause?

medium

A. Sample time of Unit Delay is not set correctly

B. Integrator block is not connected to Unit Delay

C. Step input is constant zero

D. Gain block is missing

Solution

1. Step 1: Check connections

   If Integrator not connected, output would be undefined, not zero.

2. Step 2: Verify Unit Delay sample time

   If sample time is incorrect or continuous, Unit Delay may output zero because it never updates.

3. Final Answer:

   Sample time of Unit Delay is not set correctly -> Option A

4. Quick Check:

   Incorrect sample time causes zero output [OK]

Hint: Check Unit Delay sample time for updates [OK]

Common Mistakes:

• Assuming connection issue without checking sample time
• Ignoring input signal values
• Thinking Gain block affects Unit Delay output

5. You want to model a system where a continuous temperature sensor feeds into a controller that updates every 0.1 seconds using discrete logic. Which approach correctly combines continuous and discrete parts in Simulink?

hard

A. Use only continuous blocks and ignore discrete timing

B. Use only discrete blocks with sample time 0.1s for both sensor and controller

C. Use a Unit Delay for temperature and Integrator for controller

D. Use an Integrator for temperature and a Unit Delay with sample time 0.1s for controller updates

Solution

1. Step 1: Identify continuous and discrete parts

   Temperature sensor is continuous, controller logic updates discretely every 0.1s.

2. Step 2: Choose appropriate blocks

   Integrator models continuous sensor output; Unit Delay with sample time 0.1s models discrete controller updates.

3. Final Answer:

   Use an Integrator for temperature and a Unit Delay with sample time 0.1s for controller updates -> Option D

4. Quick Check:

   Continuous sensor + discrete controller = Integrator + Unit Delay [OK]

Hint: Integrator for continuous, Unit Delay for discrete timing [OK]

Common Mistakes:

• Using only discrete blocks for continuous sensor
• Ignoring sample time for discrete controller
• Reversing block roles