ECE 381: Laboratory 6

Winter 2006

Response of a RLC circuit

February 28

 Assignment   

 

 

 

 

  1. Using the MATLAB residue command, determine the inverse Laplace transform of each of the following functions (C.4.1):

           

 

  1. Using the feedback system of Fig.4.18d (Page 397) with G(s) = K/(s(s + 8)) and H(s) = 1, determine the transfer function for each of the following cases:

 

(a)    K = 7

(b)   K = 16

(c)    K = 80

 

                 Hint: Use the MATLAB function tf to determine transfer function.

 

 

  1.  

a.       Write down the differential equation for this circuit, in terms of V0.

b.      Find the transfer function of the system.

c.       Plot the step response of the system. Is the system under, critically, or overdamped? What are its poles? Are they real, imaginary, or complex?

d.      Select parameters such that the system is critically damped. Plot the resulting step response. What are its poles? Are they real, imaginary, or complex?

e.       Select parameters such that the system is overdamped. Plot the resulting step response. What are its poles? Are they real, imaginary, or complex?

f.        Summarize the relationship between the nature of the poles (distinct, idential, real, complex?) and the system’s behavior.

g.       Find the time-domain analytical expression for the step response of the overdamped circuit. (Use Matlab’s help to get the partial fraction expansion, and then look up Laplace transform pairs.)