Mixed continuous-discrete models in Simulink - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple mixed continuous-discrete Simulink model

Consider a Simulink model with a continuous integrator block connected to a discrete zero-order hold (ZOH) block with a sample time of 0.1 seconds. The input to the integrator is a constant signal of value 2. What is the output of the ZOH block at time t = 0.3 seconds?

Simulink

Integrator input: constant 2
Integrator initial condition: 0
ZOH sample time: 0.1 seconds
Calculate output at t=0.3 seconds.

A 0.6

B 0.2

C 0.3

D 0.0

💡 Hint

Remember the integrator output is the integral of the input over time. The ZOH holds the value sampled at discrete intervals.

The integrator output at t=0.3 is integral of 2 from 0 to 0.3, which is 2 * 0.3 = 0.6. The ZOH samples at 0, 0.1, 0.2 seconds and holds the value until next sample. At t=0.3, the output is the value sampled at 0.3, which is 0.6.

❓ data_output

intermediate

Number of discrete samples in a mixed model simulation

A Simulink model runs a simulation for 5 seconds. It contains a discrete block with a sample time of 0.2 seconds. How many discrete samples will this block produce during the simulation?

Simulink

Simulation time: 5 seconds
Discrete block sample time: 0.2 seconds
Calculate number of samples generated.

A 20

B 24

C 25

D 26

💡 Hint

Divide total simulation time by sample time and consider the initial sample at time zero.

The samples occur at t=0, 0.2, ..., 4.8, 5.0 seconds, total 26 samples. Number of samples = (5 / 0.2) + 1 = 26.

❓ visualization

advanced

Plot behavior of a mixed continuous-discrete system

You have a continuous-time integrator with input u(t) = 1, connected to a discrete sampler with sample time 0.5 seconds. Sketch or describe the expected output plot of the discrete sampler over 3 seconds.

Simulink

Input: u(t) = 1 (constant)
Integrator initial condition: 0
Discrete sampler sample time: 0.5 seconds
Simulation time: 3 seconds

A A constant zero output for all times

B A continuous smooth curve from 0 to 3 over 3 seconds

C A stepwise increasing plot with values 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 at sample times 0, 0.5, ..., 3.0

D A sinusoidal wave oscillating between 0 and 1

💡 Hint

The integrator output increases linearly over time. The discrete sampler samples this output at fixed intervals, holding the value until next sample.

The integrator output at time t is integral of 1 dt = t. The discrete sampler samples this at 0, 0.5, 1.0, ..., 3.0 seconds, producing values 0, 0.5, 1.0, ..., 3.0. The output is a stepwise plot increasing by 0.5 every 0.5 seconds.

🔧 Debug

advanced

Identify the error in a mixed continuous-discrete Simulink model setup

A user sets up a Simulink model with a continuous integrator block feeding into a discrete unit delay block with sample time set to -1 (inherited). The simulation runs but the discrete block output remains constant zero. What is the most likely cause?

A The integrator block is not connected to the discrete block.

B The discrete block sample time is not properly defined, causing it not to update outputs.

C The input to the integrator is zero, so output stays zero.

D The simulation stop time is too short to see output changes.

💡 Hint

Check the sample time settings of discrete blocks when connected to continuous blocks.

Setting sample time to -1 means inherited sample time. If the discrete block inherits continuous sample time, it may not update properly. This causes output to remain constant zero. Defining a positive discrete sample time fixes the issue.

🚀 Application

expert

Design a mixed continuous-discrete model for a temperature control system

You want to model a temperature control system where the temperature changes continuously but the controller updates its output every 1 second. Which Simulink blocks and configuration best represent this mixed continuous-discrete system?

A Use a continuous integrator block for temperature dynamics and a discrete PID controller block with sample time 1 second.

B Use two discrete blocks both with sample time 1 second for temperature and controller.

C Use a discrete integrator block with sample time 1 second and a continuous controller block.

D Use only continuous blocks for both temperature and controller with no discrete blocks.

💡 Hint

Think about which parts of the system are continuous and which are discrete in time.

The temperature changes continuously, so a continuous integrator models it well. The controller updates at discrete intervals, so a discrete PID controller with sample time 1 second fits. This combination models the mixed continuous-discrete system correctly.

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