Why discrete-time matters for digital control in Simulink - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the sampling time for a discrete-time controller in Simulink.

Simulink

Ts = [1]; % Sampling time in seconds

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

A0.01

B1

C10

D100

Attempts:

3 left

💡 Hint

Common Mistakes

Using a very large sampling time causes slow response.

Using zero or negative values causes errors.

The sampling time defines how often the controller updates its output. A small value like 0.01 seconds is typical for digital control.

2fill in blank

medium

Complete the code to convert a continuous-time transfer function to discrete-time using zero-order hold method.

Simulink

sysd = c2d(sysc, Ts, '[1]');

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

Atustin

Bimpulse

Cfoh

Dzoh

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'tustin' changes the system behavior differently.

Using 'impulse' is not a discretization method.

The 'zoh' method stands for zero-order hold, which is commonly used to discretize continuous systems for digital control.

3fill in blank

hard

Fix the error in the code to correctly simulate a discrete-time system in Simulink.

Simulink

sim('model_name', [1]); % Simulation stop time

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

A10.0.0

B10

Cten

D'10s'

Attempts:

3 left

💡 Hint

Common Mistakes

Putting the time in quotes makes it a string, causing errors.

Using invalid formats like '10.0.0' causes syntax errors.

The simulation stop time should be a numeric value without quotes, like 10 seconds.

4fill in blank

hard

Fill both blanks to create a discrete-time transfer function with numerator and denominator coefficients.

Simulink

sysd = tf([1], [2], Ts);

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

A[0.1 0.2]

B[1 0.5]

C[1 -0.8]

D[0.5 0.3]

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping numerator and denominator coefficients.

Using invalid coefficient formats.

The numerator coefficients are [0.1 0.2] and denominator coefficients are [1 -0.8] for the discrete transfer function.

5fill in blank

hard

Fill all three blanks to create a discrete-time state-space model with matrices A, B, and sampling time Ts.

Simulink

sysd = ss([1], [2], C, D, [3]);

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

A[0.9 0.1; 0 0.8]

B[0.1; 0.2]

CTs

D0.1

Attempts:

3 left

💡 Hint

Common Mistakes

Using variable name 'Ts' instead of numeric value.

Incorrect matrix formatting.

The state matrix A is [0.9 0.1; 0 0.8], input matrix B is [0.1; 0.2], and sampling time Ts is 0.1 seconds.

Practice

1. Why is discrete-time important in digital control systems modeled in Simulink?

easy

A. Because discrete-time eliminates the need for sampling

B. Because continuous signals are easier to process digitally

C. Because it allows infinite precision in signal values

D. Because digital controllers update signals at fixed time intervals

Solution

1. Step 1: Understand digital controller operation

   Digital controllers work by updating signals at fixed intervals, not continuously.

2. Step 2: Connect discrete-time to Simulink modeling

   Simulink models this by using discrete blocks with sample times to represent these fixed updates.

3. Final Answer:

   Because digital controllers update signals at fixed time intervals -> Option D

4. Quick Check:

   Digital control = discrete updates [OK]

Hint: Digital control means fixed update times, not continuous [OK]

Common Mistakes:

• Thinking digital control is continuous
• Confusing sampling with elimination
• Assuming infinite precision in digital signals

2. Which Simulink block parameter correctly sets the discrete sample time for a digital controller?

easy

A. Continuous sample time set to 0

B. Sample time set to a positive fixed value

C. Sample time set to -1 for inherited

D. Sample time set to infinity

Solution

1. Step 1: Identify how discrete sample time is set

   Discrete blocks require a positive fixed sample time to update at intervals.

2. Step 2: Evaluate options

   Setting sample time to 0 means continuous, -1 means inherited, infinity is invalid.

3. Final Answer:

   Sample time set to a positive fixed value -> Option B

4. Quick Check:

   Discrete sample time = positive value [OK]

Hint: Discrete sample time must be positive fixed number [OK]

Common Mistakes:

• Using 0 which means continuous time
• Using -1 which inherits sample time
• Setting sample time to infinity

3. Given this Simulink discrete-time update code snippet:

y[k] = 0.5 * y[k-1] + u[k]

and input sequence u = [2, 4, 6], with initial y[0] = 0, what is y[3]?

medium

A. 8.5

B. 7.0

C. 9.5

D. 10.0

Solution

1. Step 1: Calculate y[1], y[2], y[3] step-by-step

   y[1] = 0.5* y[0] + u[1] = 0.5*0 + 2 = 2
   y[2] = 0.5* y[1] + u[2] = 0.5*2 + 4 = 1 + 4 = 5
   y[3] = 0.5* y[2] + u[3] = 0.5*5 + 6 = 2.5 + 6 = 8.5

2. Step 2: Verify calculations

   Check each step carefully to avoid off-by-one errors in indexing.

3. Final Answer:

   8.5 -> Option A

4. Quick Check:

   Discrete update sums to 8.5 [OK]

Hint: Calculate each step using previous output and input [OK]

Common Mistakes:

• Mixing up indices k and k-1
• Forgetting initial condition y[0]
• Adding instead of multiplying coefficients

4. Identify the error in this Simulink discrete-time block setup:

Sample time = 0
Initial condition = 5

What is wrong?

medium

A. No error, setup is correct

B. Initial condition cannot be 5

C. Sample time 0 means continuous, not discrete

D. Sample time must be negative

Solution

1. Step 1: Understand sample time meaning

   Sample time 0 means continuous time, not discrete updates.

2. Step 2: Check initial condition validity

   Initial condition 5 is valid; no issue there.

3. Final Answer:

   Sample time 0 means continuous, not discrete -> Option C

4. Quick Check:

   Discrete sample time ≠ 0 [OK]

Hint: Sample time 0 means continuous, use positive for discrete [OK]

Common Mistakes:

• Thinking initial condition causes error
• Believing sample time can be zero for discrete
• Ignoring sample time meaning

5. You want to design a digital controller in Simulink that samples input every 0.1 seconds and holds output constant between samples. Which setup correctly models this behavior?

hard

A. Use a discrete block with sample time 0.1 and a Zero-Order Hold block

B. Use a continuous block with sample time 0 and a Unit Delay block

C. Use a discrete block with sample time -1 and no hold block

D. Use a continuous block with sample time 0.1 and a Zero-Order Hold block

Solution

1. Step 1: Identify correct sample time setting

   Discrete block with sample time 0.1 means updates every 0.1 seconds.

2. Step 2: Understand output holding

   Zero-Order Hold block keeps output constant between samples, matching requirement.

3. Final Answer:

   Use a discrete block with sample time 0.1 and a Zero-Order Hold block -> Option A

4. Quick Check:

   Discrete sample + hold = correct model [OK]

Hint: Discrete block + Zero-Order Hold models sampled and held output [OK]

Common Mistakes:

• Using continuous block for discrete sampling
• Omitting Zero-Order Hold block
• Using inherited sample time (-1) incorrectly