Derivative control effect in Simulink - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the derivative of the input signal.

Simulink

derivative = [1](input_signal);

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

Aintegrate

Bsum

Caverage

Ddiff

Attempts:

3 left

💡 Hint

Common Mistakes

Using integrate instead of diff.

Using sum or average which do not calculate change.

The diff function calculates the difference between consecutive elements, which approximates the derivative.

2fill in blank

medium

Complete the code to multiply the derivative by the derivative gain Kd.

Simulink

output = Kd * [1];

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

Aderivative

Binput_signal

Cintegral

Derror_signal

Attempts:

3 left

💡 Hint

Common Mistakes

Multiplying the original input signal instead of its derivative.

Using integral or error_signal which are unrelated here.

The derivative gain multiplies the derivative of the error signal to produce the derivative control effect.

3fill in blank

hard

Fix the error in the code to correctly compute the derivative control output.

Simulink

derivative = diff([1]);
output = Kd * derivative;

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

Aintegral_signal

Binput_signal

Coutput_signal

Dcontrol_signal

Attempts:

3 left

💡 Hint

Common Mistakes

Using integral_signal which is unrelated.

Using output_signal or control_signal which are results, not inputs.

The derivative should be calculated from the input signal to reflect its rate of change.

4fill in blank

hard

Fill both blanks to create a dictionary of derivative values for signals longer than 5 samples.

Simulink

derivative_dict = {signal: [1] for signal in signals if len(signal) [2] 5}

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

Adiff(signal)

B>

C<

Dlen(signal)

Attempts:

3 left

💡 Hint

Common Mistakes

Using < instead of > for length comparison.

Using len(signal) instead of diff(signal) for derivative.

We calculate the derivative using diff(signal) and select signals longer than 5 samples using len(signal) > 5.

5fill in blank

hard

Fill all three blanks to create a filtered dictionary of derivative values where derivative is positive and signal length is greater than 3.

Simulink

filtered_derivatives = {signal: [1] for signal in signals if len(signal) [2] 3 and [3][0] > 0}

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

Adiff(signal)

B>

Dsignal

Attempts:

3 left

💡 Hint

Common Mistakes

Using signal instead of diff(signal) for derivative.

Checking length < 3 instead of > 3.

Not indexing the derivative to check its first value.

The dictionary comprehension calculates the derivative with diff(signal), filters signals longer than 3 samples, and checks if the first derivative value is positive.

Practice

1. What is the main purpose of the derivative control effect in a control system?

easy

A. To delay the system response intentionally

B. To predict future error by analyzing its rate of change

C. To increase the system's steady-state gain

D. To eliminate steady-state error completely

Solution

1. Step 1: Understand derivative control role

   The derivative control looks at how fast the error changes over time.

2. Step 2: Identify its effect on system

   It predicts future error to reduce sudden jumps or overshoot in response.

3. Final Answer:

   To predict future error by analyzing its rate of change -> Option B

4. Quick Check:

   Derivative control predicts future error = D [OK]

Hint: Derivative control predicts error change rate [OK]

Common Mistakes:

• Confusing derivative with integral control
• Thinking it eliminates steady-state error
• Assuming it delays system response

2. Which Simulink block is typically used to implement the derivative control effect?

easy

A. Derivative block

B. Integrator block

C. Gain block only

D. Sum block

Solution

1. Step 1: Identify block for derivative

   The Derivative block calculates the rate of change of the input signal.

2. Step 2: Confirm implementation of derivative control

   Derivative control uses this block multiplied by a gain to affect the system.

3. Final Answer:

   Derivative block -> Option A

4. Quick Check:

   Derivative block implements derivative control = A [OK]

Hint: Derivative block calculates rate of change [OK]

Common Mistakes:

• Choosing Integrator block instead
• Thinking Gain block alone implements derivative
• Confusing Sum block with derivative

3. Consider this Simulink setup: An error signal e(t) passes through a Derivative block with gain 3. If e(t) = 2t, what is the output of the derivative control at t=4?

medium

A. 3

B. 2

C. 6

D. 0

Solution

1. Step 1: Calculate derivative of error signal

   Given e(t) = 2t, derivative de/dt = 2 (constant).

2. Step 2: Multiply derivative by gain

   Output = gain * derivative = 3 * 2 = 6 at t=4.

3. Final Answer:

   6 -> Option C

4. Quick Check:

   Derivative = 2, output = 3*2 = 6 [OK]

Hint: Derivative of 2t is 2, multiply by gain 3 [OK]

Common Mistakes:

• Calculating derivative as 2t instead of 2
• Forgetting to multiply by gain
• Using value of e(t) instead of its derivative

4. You have a Simulink model with a Derivative block followed by a Gain block set to 5. The output is unexpectedly zero for a changing error signal. What is the most likely cause?

medium

A. Sum block is missing before Derivative block

B. Gain block is set to zero

C. Derivative block is placed after the Gain block

D. The Derivative block input is constant, so derivative is zero

Solution

1. Step 1: Analyze derivative output behavior

   If input to Derivative block is constant, its derivative is zero.

2. Step 2: Check gain effect

   Multiplying zero derivative by gain 5 still results in zero output.

3. Final Answer:

   The Derivative block input is constant, so derivative is zero -> Option D

4. Quick Check:

   Constant input means zero derivative = A [OK]

Hint: Zero derivative means zero output despite gain [OK]

Common Mistakes:

• Assuming gain zero without checking
• Thinking block order causes zero output
• Ignoring input signal behavior

5. In a Simulink PID controller, how does increasing the derivative gain affect the system's response to a sudden step change in error?

hard

A. It reduces overshoot by reacting to error rate changes quickly

B. It increases steady-state error by ignoring error magnitude

C. It slows down the system response by adding delay

D. It eliminates the need for proportional control

Solution

1. Step 1: Understand derivative gain effect

   Increasing derivative gain makes controller react more strongly to error rate changes.

2. Step 2: Analyze impact on system response

   This reaction helps reduce overshoot and smooth sudden changes in error.

3. Final Answer:

   It reduces overshoot by reacting to error rate changes quickly -> Option A

4. Quick Check:

   Higher derivative gain reduces overshoot = C [OK]

Hint: Higher derivative gain smooths sudden error changes [OK]

Common Mistakes:

• Thinking derivative gain increases steady-state error
• Assuming it slows system response
• Believing it replaces proportional control