Disturbance rejection in Simulink - Step-by-Step Execution

Concept Flow - Disturbance rejection

System Input

↓

Controller

→Plant

↓

Disturbance

↓

Error Calculation

↓

Controller adjusts output to reduce error

The system receives input and disturbance; the controller adjusts the plant input to keep output close to desired despite disturbances.

Execution Sample

Simulink

error = reference - output
control_signal = controller(error)
output = plant(control_signal + disturbance)

This code shows how the controller uses error to adjust control signal to reject disturbance and keep output near reference.

Execution Table

Step	Reference	Disturbance	Output Before Control	Error (Reference - Output)	Control Signal	Output After Control
1	10	2	8	2	3	11
2	10	3	11	-1	-1	9
3	10	1	9	1	2	11
4	10	4	11	-1	-1	9
5	10	0	9	1	2	11
Exit	-	-	-	-	-	-

💡 Simulation ends after 5 steps showing controller adjusting output to reject disturbances.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5
Reference	10	10	10	10	10	10
Disturbance	2	3	1	4	0	-
Output Before Control	8	11	9	11	9	-
Error	2	-1	1	-1	1	-
Control Signal	3	-1	2	-1	2	-
Output After Control	11	9	11	9	11	-

Key Moments - 2 Insights

Why does the output sometimes go above the reference value?

Because the controller reacts to error, it may overshoot to correct disturbance, as seen in steps 1 and 3 in the execution_table.

Why is the error negative in some steps?

Negative error means output is above reference; controller then reduces control signal to bring output down, shown in steps 2 and 4.

Visual Quiz - 3 Questions

Look at the execution_table at step 3. What is the error value?

A 1

B -1

C 0

D 2

💡 Hint

Check the 'Error' column in execution_table row for step 3.

At which step does the disturbance have the highest value?

A Step 1

B Step 4

C Step 2

D Step 5

💡 Hint

Look at the 'Disturbance' column in execution_table to find the max value.

If the controller did not adjust control signal, what would happen to output after disturbance?

A Output stays constant

B Output equals reference always

C Output equals disturbance plus previous output

D Output equals zero

💡 Hint

Consider output before control in execution_table and how disturbance affects it.

Concept Snapshot

Disturbance rejection uses a controller to keep system output close to reference despite disturbances.
Controller measures error (reference - output) and adjusts control signal.
Output changes due to disturbance but controller compensates.
Key: controller feedback reduces error caused by disturbances.

Full Transcript

Disturbance rejection means the system tries to keep output steady even if something disturbs it. The controller looks at the difference between what we want and what we get (error). It then changes the input to the system to fix the error. We saw in the steps how the controller changes the control signal to keep output near the reference value even when disturbance changes. Sometimes output goes a bit above or below reference because the controller is correcting. Negative error means output is too high, so controller lowers control signal. This way, the system stays stable despite disturbances.

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