Why continuous-time models represent physical systems in Simulink - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define a continuous-time transfer function in Simulink.

Simulink

sys = tf([1], [1 [1] 1]);

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

A2

B3

C0

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using zero causes a first-order system, not continuous second-order.

The coefficient 2 in the denominator represents the damping term in the continuous-time transfer function.

2fill in blank

medium

Complete the code to simulate the continuous-time system response in Simulink.

Simulink

sim('model_name', [1]);

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

A'stopTime'

B'startTime'

C10

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using a string instead of a numeric value for simulation time.

The number 10 sets the simulation stop time in seconds for the continuous-time model.

3fill in blank

hard

Fix the error in the code to correctly define a continuous-time state-space model.

Simulink

A = [0 1; -[1] -2]; B = [0; 1]; C = [1 0]; D = 0; sys = ss(A,B,C,D);

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

A5

B1

C0

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using zero or negative values that do not represent physical stiffness.

The value 5 represents the system stiffness in the state matrix A for a continuous-time model.

4fill in blank

hard

Fill both blanks to create a continuous-time transfer function with numerator and denominator polynomials.

Simulink

sys = tf([[1] 3], [1 [2] 2]);

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

A1

B4

C5

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing numerator and denominator coefficients incorrectly.

The numerator starts with 1, and the denominator's middle coefficient is 4 for the continuous-time system.

5fill in blank

hard

Fill all three blanks to create a continuous-time state-space model with matrices A, B, and C.

Simulink

A = [[0 1]; [-[1] -[2]]]; B = [[0]; [[3]]]; C = [1 0]; sys = ss(A,B,C,0);

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

A6

B2

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using zero for input gain or incorrect signs in A matrix.

The values 6 and 2 represent stiffness and damping in A, and 1 is the input gain in B for the continuous-time model.

Practice

1. Why do continuous-time models best represent physical systems in Simulink?

easy

A. Because continuous models use only discrete steps, making them simpler.

B. Because physical systems change smoothly over time, which continuous models capture.

C. Because physical systems do not change over time, so continuous models are static.

D. Because continuous models ignore time, focusing only on space.

Solution

1. Step 1: Understand physical system behavior

   Physical systems like temperature or speed change smoothly and continuously over time.

2. Step 2: Match model type to system behavior

   Continuous-time models use differential equations to represent smooth changes, matching real system behavior.

3. Final Answer:

   Because physical systems change smoothly over time, which continuous models capture. -> Option B

4. Quick Check:

   Continuous models = smooth real changes [OK]

Hint: Physical systems change smoothly; continuous models match that [OK]

Common Mistakes:

• Thinking continuous models use discrete steps
• Believing physical systems are static
• Confusing time with space in models

2. Which Simulink block is typically used to represent continuous-time dynamics of a physical system?

easy

A. Step block

B. Discrete-Time Integrator block

C. Constant block

D. Continuous-Time Integrator block

Solution

1. Step 1: Identify block types for continuous dynamics

   The Continuous-Time Integrator block solves differential equations continuously over time.

2. Step 2: Compare with other blocks

   Discrete-Time Integrator works in steps, Constant and Step blocks do not model continuous dynamics.

3. Final Answer:

   Continuous-Time Integrator block -> Option D

4. Quick Check:

   Continuous integrator = continuous dynamics [OK]

Hint: Continuous integrator block models smooth changes [OK]

Common Mistakes:

• Choosing discrete integrator for continuous systems
• Confusing constant or step blocks as dynamic
• Ignoring block function descriptions

3. Given this Simulink continuous-time model snippet:

dx/dt = -2*x + u
where u = 1 (constant input)

What is the steady-state value of x?

medium

A. 0.5

B. 2

C. -0.5

D. 1

Solution

1. Step 1: Set derivative to zero for steady state

   At steady state, dx/dt = 0, so 0 = -2*x + 1.

2. Step 2: Solve for x

   Rearranged: 2*x = 1, so x = 1/2 = 0.5.

3. Final Answer:

   0.5 -> Option A

4. Quick Check:

   0 = -2*0.5 + 1 = 0 [OK]

Hint: Set dx/dt=0 to find steady state [OK]

Common Mistakes:

• Forgetting to set derivative to zero
• Solving for wrong variable
• Ignoring input u value

4. In a Simulink continuous-time model, this equation is used:

dx/dt = 3*x + 2*u

But the simulation shows unstable growth. What is the likely error?

medium

A. The equation should use discrete time, not continuous.

B. The input u should be zero for stability.

C. The sign of the coefficient 3 should be negative for stability.

D. The coefficient 2 should be 3 for correct scaling.

Solution

1. Step 1: Analyze system stability from coefficient

   A positive coefficient on x (3) causes exponential growth, making system unstable.

2. Step 2: Correct sign for stability

   Changing 3 to -3 makes the system stable by causing decay over time.

3. Final Answer:

   The sign of the coefficient 3 should be negative for stability. -> Option C

4. Quick Check:

   Positive feedback = instability [OK]

Hint: Positive feedback causes instability; check signs [OK]

Common Mistakes:

• Assuming input u causes instability
• Confusing discrete vs continuous time
• Changing coefficients without reason

5. You want to model a physical system with a mass-spring-damper in Simulink using continuous-time blocks. Which approach best represents the system?

hard

A. Use differential equations with continuous integrator blocks to model velocity and position.

B. Use discrete integrator blocks with very small step size to approximate continuous behavior.

C. Use only constant blocks to represent forces and ignore dynamics.

D. Use step blocks to simulate sudden changes ignoring smooth motion.

Solution

1. Step 1: Understand physical system dynamics

   Mass-spring-damper systems are described by differential equations involving velocity and position.

2. Step 2: Choose modeling approach

   Continuous integrator blocks solve these differential equations smoothly, capturing real system behavior accurately.

3. Final Answer:

   Use differential equations with continuous integrator blocks to model velocity and position. -> Option A

4. Quick Check:

   Continuous integrators = accurate physical modeling [OK]

Hint: Use continuous integrators for smooth physical system modeling [OK]

Common Mistakes:

• Using discrete integrators instead of continuous
• Ignoring system dynamics with constants
• Using step blocks that cause unrealistic jumps