Question

Consider the simple series RLC circuit shown in figure below, the circuit has the following parameters, R=12, L = 0.2 Henry, and C = 0.05 Farad, R 1000 Vs The system is governed by the following equations: V = VR + V + V VR = IR V = Vc S(t)dt Or I = CM Construct a Simulink model for this system such that the input is the supply voltage Vs and the output is the voltage across the resistor VR, use a pulse generator source with an amplitude of Vs = 5 Volts a period of 10 seconds and pulse width of 20% of the time. Use a simulation time of 50 seconds M 16 Simulink models should be submitted to BlackBoard by Submission due date, incomplete/late submissions will receive a grade of 0.

Answer 1

Applying KVL, we get =l(t) *R+LICO) Sl(t)dt dt Assuming (t) is the amount of current flowingthrough the circuit Hence, applying Laplace transform on the above equation, we get V. (5) = 1(5) = R + LsI(9) +31(5) = (R+Ls +3:00) Now, as per question Valt) is the output ofthe system, hence, applying Laplace transform, we get the output equation as Vr(s) = R *I(S) Therefore, the transfer function of the system can be written as VR(S) R RCS G(s) = Vs(s) R+Ls + es Lcs- + Rcs +1 Inserting the values of R = 1 ohm, L = 0.2 Henry and C = 0.05 Farad, we get G(S) = 0.05s Vs(s) 0.015- + 0.05s +1 Now, as per the question, is a pulse generator havingavoltage of 5 V with a period of 10 sec and pulse width of 20% of the period. The total simulation time is 50 sec The corresponding Simulink model is shown below

File Edit View Display Diagram Simulation Analysis Code Tools Help 50 Normal 8:00 untitled Puntitled Vs(s) M 0.05s 0.0152+0.055+1 19 VR(S) Scope VR(S) Pulse Generator Vs(s) Transfer Fon G(s)

The parameters of the different blocks are shown below

1. Pulse Generator block parameters

Pulse Generator Output pulses: if (t >= Phase Delay) && Pulse is on Y(t) = Amplitude else Y(t) = 0 end Pulse type determines the computational technique used. Time-based is recommended for use with a variable step solver, while Sample-based is recommended for use with a fixed step solver or within a discrete portion of a model using a variable step solver. Parameters Pulse type: Time based Time (t): Use simulation time Amplitude: 5 Period (secs): 10 Pulse Width (% of period): 20 Phase delay (secs): o Interpret vector parameters as 1-D OK Cancel Help Apply

2. Transfer function block parameters

- Transfer Fun The numerator coefficient can be a vector or matrix expression. The denominator coefficient must be a vector. The output width equals the number of rows in the numerator coefficient. You should specify the coefficients in descending order of powers of s. Parameters Numerator coefficients: [0.05 0] Denominator coefficients: [0.01 0.05 1] Absolute tolerance: auto State Name: (e.g., "position') OK Cancel Help Apply

The corresponding output is shown below (where the yellow line represents the input (Vs(s)) and the magenta line represents the output VR(s)).