R-l-c circuit example - find input and output voltage wrt

Question

MATLAB Session on Signals, Systems Realization for n-th order system(SIMULINK)

MATLAB Session -

SIMULINK -

- Learn to use "SIMULINK" in MATLAB

- Learn to generate "SIMULINK" models

- Understand "Function Blocks" in SIMULINK

- Generate "Output Trace" using "Scope" and other function blocks in MATLAB SIMLULINK

R-L-C Circuit Example -

- Understand "Physical System", "Schematic System", "Mathematical System"

- Learn to convert "Mathematical System" into "SIMULINK model" and analyze RLC-circuit.

Using SIMULINK in MATLAB -

Creating SIMULINK model files:

INLAB Report (1):

• Create following SIMULINK model and save as file.
• Use a "sine" source block from SIMULINK library to generate -5 to 5 [V] sinusoidal signal.
• Use a "gain" block from SIMULINK library to create the amplitude gain of 3.
• Use two "scope" blocks to display signals - display input and output voltage signal by double clicking "scope" blocks.
• Adjust "scope" y-axis to display between -20 to 20 [V]

R-L-C circuit analysis (Differential Equation) using SIMULINK

R-L-C circuit example - Find input and output voltage w.r.t. time for below circuit

INLAB Report (1):

• Assume x(t) = u(t) unit step function has been applied to the circuit shown above.
• Find "math model" (differential equation) for the circuit.

INLAB Report (2):

• Create following SIMULINK model for the circuit.
• Use a "integrator" blocks from SIMULINK library to solve for multi-order time derivatives.

dy(t)/dt → ∫→ y(y)

• Apply "unit step" source block from SIMULINK library to the circuit. x(t) = u(t)
• Use two "scope" blocks to display signals - display input and output voltage signal by double clicking "scope" blocks.
• Adjust "scope" y-axis to display between -2 to 2 [V].

R-R-L circuit analysis (Differential Equation) using SIMULINK

R-R-L circuit

• Find input and output voltage w.r.t. time for circuit shown.

INLAB Report (1):

• Assume x(t) = u(t) unit step function has been applied to the circuit shown above.
• Find "math model" (differential equation) for the circuit.

R-R-L circuit

• Find input and output voltage w.r.t. time for circuit shown.

INLAB Report (2):

• Create following SIMULINK model for the circuit.
• Use a "integrator" blocks from SIMULINK library to solve for multi order time derivatives. dy(t)/dt →∫→ y(t)
• Apply "unit step" source block from SIMULINK library to the circuit.
• Use two "scope" blocks to display signals - display input and output voltage signal by double clicking "scope" blocks.
• Adjust "scope" y-axis to display between -2 to 2 [V].

R-R-C circuit analysis (Differential Equation) using SIMULINK

R-R-C circuit

• Find input and output voltage w.r.t. time for circuit shown.

INLAB Report (1):

• Assume x(t) = u(t) unit step function has been applied to the circuit shown above.
• Find "math model" (differential equation) for the circuit.

R-R-C circuit

• Find input and output voltage w.r.t. time for circuit shown.

INLAB Report (2):

• Create following SIMULINK model for the circuit.
• Use a "integrator" blocks from SIMULINK library to solve for multi order time derivatives. dy(t)/dt→ ∫→y(t)
• Apply "unit step" source block from SIMULINK library to the circuit. x(t) = u(t)
• Use two "scope" blocks to display signals - display input and output voltage signal by double clicking "scope" blocks.
• Adjust "scope" y-axis to display between -2 to 2 [V]

1^st Order Differential Eq

INLAB Report :

• Generate a time variable from -10 to 10 [sec] in 0.1[sec] step size.
• Use MATLAB function ode23 to plot resulting y(t) with respect to time for 1^st order differential equation given below.
• Assume y(0) = 15, use time span from 0 to 10 [sec] for ode23.
• Repeat same problem, but use MATLAB function dsolve to plot resulting y(t) with respect to time for 1st order differential equation given below 10(dy(t)/dt) + y(t) = -20 + 15sin(2t)

INLAB Report:

• Find the solution for the high order differential equation shown below.
• Use MATLAB function dsolve to plot resulting y(t) with respect to time.
• Use initial conditions: y(0) = 0 and y'(0) = 1

                  d²(y)/dt² + 8 (dy(t)/dt) + 2y(t) = cos(t)

Attachment:- Assignment File.rar