Mixed continuous-discrete models in Simulink - Mini Project: Build & Apply

Mixed Continuous-Discrete Models in Simulink

📖 Scenario: You are working on a simple control system that combines continuous and discrete parts. For example, a temperature control system where the temperature changes continuously, but the controller updates its output at fixed time steps.

🎯 Goal: Build a Simulink model that includes a continuous-time plant and a discrete-time controller. You will set up the continuous system, configure the discrete controller sample time, connect them, and observe the output.

📋 What You'll Learn

Create a continuous-time plant using an Integrator block

Add a Discrete-Time Controller with a sample time of 0.1 seconds

Connect the controller output to the plant input

Simulate the model and display the output signal

💡 Why This Matters

🌍 Real World

Mixed continuous-discrete models are common in control systems where sensors and controllers operate at discrete times but the physical system changes continuously.

💼 Career

Understanding how to model and simulate mixed systems is essential for control engineers, system modelers, and data scientists working with real-time systems.

1

Create the continuous-time plant

In your Simulink model, add an Integrator block to represent the continuous-time plant. Name this block Plant. This block will simulate the continuous change of the system state.

Simulink

% Add an Integrator block named 'Plant' to your Simulink model
% Your code here

Hint

Use the Simulink Library Browser to find the Integrator block under Continuous blocks. Drag it into your model and rename it to 'Plant'.

2

Add a discrete-time controller with sample time 0.1

Add a Discrete-Time Integrator block to your model to act as the controller. Set its sample time to 0.1 seconds. Name this block Controller.

Simulink

% Add a Discrete-Time Integrator block named 'Controller' with sample time 0.1
% Your code here

Hint

Find the Discrete-Time Integrator block under Discrete blocks. Set its sample time parameter to 0.1 seconds and rename it to 'Controller'.

3

Connect the controller output to the plant input

Connect the output port of the Controller block to the input port of the Plant block using a signal line. This models the controller sending commands to the plant.

Simulink

% Connect Controller output to Plant input
% Your code here

Hint

Use the add_line command or drag a line in Simulink to connect the output of Controller to the input of Plant.

4

Simulate the model and display the output

Run the simulation for 10 seconds. Add a Scope block connected to the output of the Plant block to visualize the continuous output signal.

Simulink

% Add a Scope block connected to Plant output
% Set simulation stop time to 10 seconds
% Run the simulation
% Your code here

Hint

Use add_block to add a Scope, connect it to Plant output with add_line, set stop time with set_param, and run simulation with sim.

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