Question

Use the Transfer Function block to construct a Simulink model to plot the solution of the following equation for 0 ≤ t ≤ 4.

2x + 12x + 10x = 5us(t) - 5us(t −2) x(0) = x(0) = 0

Answer 1

The given equation is 2ẍ + 12ẋ + 10x = 5u, (t) – 5u, (t – 2)

 

Re-write this in terms of (from Laplace transform),

2s2x + 12sx + 10x = 5u, (t) – tu, (t – 2)

(2s2 + 12s + 10)x = 5[u,(t) – u, (t – 2)]

                          x = [1/(2s2 + 12s + 10)] × t[u, (t) – us(t – 2)]

 

The steps to create the Simulink model for this equation are as follows:

1. For input functions, place two Step blocks. Set the step time as 1 for u,(t) and -1 us(t – 2). 

2. Place the Sum block and set the signs |+-. Connect the Step block for us(t) to the ‘+ node and the Step block for us(t – 2) to the - node.

3. Place the Gain block. Set the gain to 5 and connect it to the output of Sum block. The output of this is 5us(t) – 5us(t – 2).

4. Place the Transfer function block. In the block parameters window, set the Numerator coefficient as [1] and Denominator coefficient [2 12 10].

5. Place the Scope block and connect it to the Transfer function block.

6. Set the Stop time to 4.

7. Run the simulation.

 

The Simulink model for 2ẍ + 12ẋ + 10x = 5us(t) – 5us(t - 2) is:

 

The scope obtained after simulation is:

 

Hence, the Simulink model is constructed to solve and plot the given equation, 2ẍ + 12ẋ + 10x = 5u, (t) – 5u, (t – 2).

Hence, the Simulink model is constructed to solve and plot the given equation, 2ẍ + 12ẋ + 10x = 5u, (t) – 5u, (t – 2).