1. Develop a discrete equation for the following transfer functions. Determine stability and realizability.





2. Develop a differential equation for both the mechanical and the electrical system below. Find the transfer function for the module using the backshift operator ‘B’ for a time step of T = 1 sec.



4. a) Given the following transfer function, and the input function, find the resulting output for the first 5 time steps, if T=0.5 seconds.



b) What will the steady state output be for the system in part a)?


5. Develop a process model for one of the systems below. Assume the system starts at rest.



a) Write the differential equations for one of the systems above.


b) Convert the equation to a transfer function using the backshift operator (use T=1sec).


c) Assume there is a step input of magnitude 1. Find the output function for the system in terms of the backshift operator. Do not convert the output function to numerical values in time.


d) Determine the steady state value for the system. Is the value consistent with what you would expect from the system? Explain.




6. Given the following output function,



a) Find the steady state response as a function of time using the tables (assume T=0.2sec).


b) Find the first three values of the output in time using long division. Check that these values agree with the solution found in part a).