Additional Exercises

1:	Compare step responses of the transfer function and state space models for the van de Vusse reactor. Transfer function: Perform the open-loop simulation for a step input change from 0 to 1 at t = 1, as shown in Figure M2-5. State space: Replace the transfer function block shown in Figure M2-5 with a state space block. Enter the following matrices in the MATLAB command window: Show that the resulting step responses of the transfer function and state space models are identical.
2:	Consider the closed-loop SIMULINK diagram for the van de Vusse reactor (Figure M2-8). Replace the default PID controller with a "Real PID" controller, as shown below in both the masked and unmasked versions. How do your results compare with ones obtained using the default PID controller?
3:	The following control algorithm uses a filtered derivative of the process output (see Chapter 5). Develop a SIMULINK implementation of this algorithm, where e(s) = r(s) - y(s).