BSE202 - Modeling and Simulation Assignment - Helwan University

Assignment Task

1. Use Matlab and Simulink Software to calculate the values of:

2. Use Matlab and Simulink Software to find the values of a, b, and c as given by the following expressions:

3. Create a matrix Use the colon operator to extract from this matrix the second row, the final column, and the top right hand corner sub-matrix 

4. Create a matrix X comprising two columns: the first being sin(2πt) , the second being cos(2 πt) and plot them against t from 0 to 1.

5. The number of weasels per acre in a field after x years is given by x y e 0.05x 2 . Write a program to plot the graph of y vs. x, with grid, title and axes labelling, for the range 0 < x>

6. Write a MATLAB program to compute the summation of the following three waves for the first 10 seconds. Label the summation as Y.

where, A1 = 3.5 cm, f1 = 1.25 Hz, A2 = 2.25 cm, f2 = 1.75 Hz, A3 = 7.5 cm, f3 = 0.75 Hz and x = 2f . Plot the waves Y, Y1, Y2, and Y3 on one figure using subplot command.

7. Write the mathematical equation for v that describes the following system.

8. Write the mathematical equation for v that describes the following system

9. Draw a Simulink model to simulate the following second order differential equation.

V + 0.5v - v = F

10. Draw a Simulink model to simulate the following first order differential equation.v = 2(4v + x − x)where x is a step input signal.

11. The following Matlab figure shows the simulation results of a coupled first order differential equations, v and P

v= 2v − 3vp

v= 4v − 3p

a. Use the ode45 Matlab solver to write the required programs to generate the same given figure.

b. Draw a Simulink model to simulate the previous coupled equations

12. Model and simulate a thermal heating house system using Simulink models controlled by ON/OFF control strategy to calculate the heating cost taking into account the outdoor environment, the thermal characteristics of the house, and the house heater system. Your answer should include Simulink models of the whole system showing the heat cost and a comparison between the in and out doors temperatures, the heater unit and the house. Also, write the mathematical equations of both heater and house.

13. Model and simulate a complete air conditioning system using Simulink models controlled by PID control strategy to calculate the electricity cost taking into account the outdoor environment, the thermal characteristics of the automotive cabin, and the compressor system. Your answer should include Simulink models of the whole system showing the fuel consumption cost and a comparison between the in and out doors temperatures, the compressor unit and the automotive cabin. Also, write the mathematical equations of both compressor and cabin.

14. Figure (1) shows a mechanical system with two masses, two springs and one damper. k ₁ = 2 N/m, k ₂ = 3 N/m, c = 10 Ns/m, m ₁ = 5 kg, and m ₂ = 50 kg.

1. Model the given system using the free body
2. Put the equations of motion in the general matrix
3. Put the equations of motion in state variable
4. Write a MATLAB program and draw a Simulink model to simulate and plot the dynamic performance of the given system.

15. Figure (2) shows a two degrees of freedom mechanical system with two masses, two springs and two dampers. k ₁ = 2 N/m, k ₂ = 3 N/m, c = 10 Ns/m, m ₁ = 5 kg, and m ₂ = 50 kg.

• Model the given system using the free body
• Put the equations of motion in the general matrix
• Put the equations of motion in state variable
• Write a MATLAB program and draw a Simulink model to simulate and plot the dynamic performance of the given system.

16. Figure (3) shows a quarter-car model, where m ₁ is the mass of one-fourth of the car body and m ₂ is the mass of the wheel–tire–axle assembly. The spring k ₁ represents the elasticity of the suspension and the spring k ₂ represents the elasticity of the tire. z(t) is the displacement input due to the surface of the road. The actuator force, f, applied between the car body and the wheel–tire–axle assembly, is controlled by feedback and represents the active components of the suspension system. The parameter values are m ₁ = 290 kg, m ₂ = 59 kg, b ₁ = 1000 Ns/m, k ₁ = 16,182 N/m, k ₂ = 19,000 N/m, and f is a step input with 500 N.

• Derive the equations of motion using the free body
• Put the equations of motion in the general matrix
• Put the equations of motion in state variable
• Write a MATLAB program and draw a Simulink model to simulate and plot the dynamic performance of the given system.

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