Question

Assignment: Let us consider the same network of HW3, Figure 1, with the parameter reported in Table 1. 10 V 1 2 ΙΩ R2 1 H Figure l Table l 1. Which is the order of the system How many input it has? Comment your answer. 2. Obtain (manually) a state space representation of the circuit in the form x(t) - Ax(t) + Bu(t) 3. Assuming that you variable of interest is the current is resistor R1, write an output equation that give you IR1 and arrange it in the form: y(t) - Cx(t) + Du(t) 4. Write a Matlab script that simulates the circuit of Figure 1 on the base of the obtained description and plots IRi. Compare the results obtained integrating the system of equation using Euler Forward, Euler Backward, Trapezoidal Rule for three different time step sizes: 0.1 s, ls, 2s. Select a proper final time for the simulation 5. Write a Matlab script that compares the results obtained modeling the circuit using resistive companion and using state space representation. Use Euler Backward as integration method and IRi for the comparison Comment the results obtained. Use a time step sizes equal to 0.1 s. Select a proper final time for the simulation

Answer 1

34ea di dt- d- diat) [-1-制 Tel+, Rt.uk 4) _ T .

SLO dt dtf Vi 21 1D 2 丸(4) 火(+)