Disturbance rejection in Simulink - Mini Project: Build & Apply

Disturbance Rejection in Simulink

📖 Scenario: You are working on a control system that needs to keep a machine running smoothly even when unexpected disturbances happen. Disturbance rejection means the system can handle these surprises and still work well.

🎯 Goal: Build a simple Simulink model that shows how a control system can reject disturbances and keep the output steady.

📋 What You'll Learn

Create a Simulink model with a plant and a disturbance input

Add a controller block to reduce the effect of disturbances

Configure a disturbance signal with a specific amplitude

Simulate the model and observe the output response

💡 Why This Matters

🌍 Real World

Disturbance rejection is used in machines like robots, cars, and airplanes to keep them working smoothly despite unexpected changes.

💼 Career

Control engineers and data scientists use disturbance rejection techniques to design reliable and stable systems in manufacturing and automation.

1

Create the Plant Model

Open Simulink and create a new model. Add a Transfer Function block named plant with numerator [1] and denominator [1 3 2]. This represents the system you want to control.

Simulink

% Add a Transfer Function block named plant with numerator [1] and denominator [1 3 2]
% Your code here

Hint

Use the Simulink Library Browser to find the Transfer Function block. Set its parameters exactly as instructed.

2

Add Disturbance Input

Add a Step block named disturbance to the model. Set its Step time to 5 and Final value to 1. Connect this disturbance to the plant input through a Sum block that adds the disturbance to the control signal.

Simulink

% Add Step block named disturbance with Step time 5 and Final value 1
% Add Sum block to add disturbance to control input
% Your code here

Hint

Use the Step block for disturbance and Sum block to combine signals. Make sure to name the blocks correctly.

3

Add Controller for Disturbance Rejection

Add a PID Controller block named controller to the model. Connect it so that it controls the plant input. Set the PID gains to Kp=2, Ki=1, and Kd=0.5 to help reject the disturbance.

Simulink

% Add PID Controller block named controller with Kp=2, Ki=1, Kd=0.5
% Connect controller to plant input
% Your code here

Hint

Find the PID Controller block in Simulink and set the gains exactly as given.

4

Simulate and Observe Output

Run the simulation for 15 seconds. Add a Scope block connected to the plant output to observe how the system responds to the disturbance. Print the final output value at the end of the simulation.

Simulink

% Run simulation for 15 seconds
% Connect Scope block to plant output
% Print final output value
% Your code here

Hint

Use the Simulink simulation command and get the output signal to print the final value.

Practice

1. What is the main goal of disturbance rejection in a Simulink control system?

easy

A. To keep the system output stable despite external changes

B. To increase the system's input signal strength

C. To remove all feedback loops from the system

D. To make the system run faster without delays

Solution

1. Step 1: Understand disturbance rejection purpose

   Disturbance rejection aims to keep the system output steady even when outside changes happen.

2. Step 2: Compare options to this goal

   Only To keep the system output stable despite external changes matches this goal by focusing on output stability despite disturbances.

3. Final Answer:

   To keep the system output stable despite external changes -> Option A

4. Quick Check:

   Disturbance rejection = output stability [OK]

Hint: Disturbance rejection means steady output despite changes [OK]

Common Mistakes:

• Confusing disturbance rejection with increasing input
• Thinking disturbance rejection removes feedback loops
• Assuming it speeds up the system only

2. Which Simulink block is commonly used to reduce the effect of disturbances in a control system?

easy

A. PID Controller block

B. Gain block

C. Scope block

D. Mux block

Solution

1. Step 1: Identify blocks that affect disturbance

   PID Controller blocks adjust system response to reduce disturbance effects.

2. Step 2: Eliminate unrelated blocks

   Gain changes signal strength, Scope shows signals, Mux combines signals but doesn't reduce disturbances.

3. Final Answer:

   PID Controller block -> Option A

4. Quick Check:

   PID Controller reduces disturbances [OK]

Hint: PID blocks help control disturbances in Simulink [OK]

Common Mistakes:

• Choosing Scope block which only displays signals
• Confusing Gain block with disturbance rejection
• Selecting Mux block which combines signals

3. Given this Simulink feedback loop with a disturbance input, what will happen if the PID controller gains are set too low?

Disturbance --> + --> System --> Output
               ^                 |
               |-----------------|
               PID Controller

medium

A. The system output will oscillate rapidly

B. The system output will closely follow the disturbance

C. The system output will reject the disturbance completely

D. The system output will be zero regardless of disturbance

Solution

1. Step 1: Understand low PID gains effect

   Low PID gains mean weak correction to disturbances, so system output follows disturbance closely.

2. Step 2: Analyze other options

   Complete rejection needs strong gains, oscillation usually comes from too high gains, zero output is unrealistic here.

3. Final Answer:

   The system output will closely follow the disturbance -> Option B

4. Quick Check:

   Low gains = poor disturbance rejection [OK]

Hint: Low PID gains mean weak disturbance correction [OK]

Common Mistakes:

• Assuming low gains cause oscillations
• Thinking output will be zero regardless
• Believing disturbance is fully rejected with low gains

4. You have a Simulink model with a disturbance rejection loop, but the output still shows large fluctuations. Which of these is the most likely error?

medium

A. The feedback loop is missing the disturbance input

B. The system has no input signal

C. The Scope block is not connected properly

D. The PID controller gains are set too high causing instability

Solution

1. Step 1: Identify cause of large output fluctuations

   High PID gains can cause the system to become unstable and oscillate, causing large fluctuations.

2. Step 2: Check other options

   Missing disturbance input means no disturbance effect, Scope connection affects display only, no input signal means no output but not fluctuations.

3. Final Answer:

   The PID controller gains are set too high causing instability -> Option D

4. Quick Check:

   High gains cause instability and fluctuations [OK]

Hint: Too high PID gains cause unstable output [OK]

Common Mistakes:

• Blaming Scope block for output fluctuations
• Ignoring PID gain settings
• Assuming missing disturbance input causes fluctuations

5. You want to design a Simulink model that rejects a sudden step disturbance affecting the system output. Which combination of blocks and settings is best to achieve fast disturbance rejection with minimal overshoot?

hard

A. Use a Scope block to monitor output and manually adjust input

B. Use only a Gain block with high gain and no feedback loop

C. Use a PID Controller block with tuned proportional and derivative gains, plus a feedback loop including the disturbance input

D. Use a Mux block to combine disturbance and input signals without control

Solution

1. Step 1: Identify blocks for disturbance rejection

   PID Controller with tuned gains helps react quickly and reduce overshoot; feedback loop is needed to correct disturbances.

2. Step 2: Evaluate other options

   Gain block alone cannot reject disturbances well; Scope only monitors signals; Mux combines signals but does not control.

3. Final Answer:

   Use a PID Controller block with tuned proportional and derivative gains, plus a feedback loop including the disturbance input -> Option C

4. Quick Check:

   PID + feedback = fast, minimal overshoot rejection [OK]

Hint: Combine PID with feedback loop for best disturbance rejection [OK]

Common Mistakes:

• Relying on Gain block without feedback
• Using Scope as control instead of monitoring
• Ignoring feedback loop importance