Simulink- Controller Tuning

Homework #9

1

CBE 403B (MWF 9-9:50 am) Due: April 15, 2020

Required reading: Chapters 11 & 12

1) Reduce the following block diagram for the 'servo' problem (i.e., for set-point changes only), and write an appropriate expression for the reduced TF, Y/Ysp, in terms of the original TFs. Figure 11.14 in Seborg will help with this.

2) In Homework #8, problem #4 you created the feedback loop below for a stirred-tank mixing problem in Simulink. Now add a 10 minute time delay to the forward path of that loop. Your block diagram should look like this:

Part a: Use the IMC tuning relations to obtain reasonable controller settings for a PID controller assuming you want 'aggressive' control such that tc = 0.5Q, and a filter coefficent of 0.1 (a = 0.1) for the derivative control mode. Report your values for Kc, tI, and tD, and include a screenshot of your scope output. (NOTE: for Simulink you need to translate a, Kc, tI, and tD to 'P', 'I', 'D', and 'N'... take care when you do this!)

Part b: Now use Ziegler-Nichols (Continuous Cycling Method) to tune a PI controller. Report your values for Kc, and tI, and include a screenshot of your scope output.

Part c: Using Ziegler-Nichols still, tune a PID controller. Report your values for Kc, tI, and tD, and include a screenshot of your scope output.

Part d: Which method and controller resulted in the fastest response? The slowest? In each case is it surprising, or not?

Homework #9

2

3) Use the direct synthesis (DS) method to find values for Kc and tI for a PI controller in a simple feedback loop where you know the process transfer function, (Gp), and all other transfer functions in the loop have gains of 1 and negligible dynamics.

G" = 191

5.1S + 1 ,(′K′ is in

min ∗ mm kg

,and ′τ′ is in minutes)

As an engineering decision, tc = 0.16 min (see equation 12-5 in Seborg et al.). Show all work in obtaining Kc and tI.