1. Show that the digital first-order exponential filter output can be written as a function of previous measurements ym(k) and the initial filter output yF(0).

2.  Consider an integral plus dead time process 

Using the proportional-only controller, calculate the value of K_c that provides a phase margin of 30^o.0) 

3.  The distillation column in Fig. 3 has the following transfer function model

a.       Design a feedforward controller based on a steady-state analysis. 

b.      Design a feedforward controller based on a dynamic analysis.

4.  The discrete transfer function of a process is given by

a)  Is this system stable? 

b)  Convert the state space model to transfer function model 

6. The response of a particular system to the indicated input sequence is given in the table below. 

a.Describe that how you would identify a FIR model using linear regression. Write down the data matrix for identification. 

b.If you know that the process can be described by a first order ARX model, describe that how you would identify the model. Write down the data matrix for identification.

7. Indicate whether the given system is stable, unstable or unknown. Where necessary show your work on the given plots. Briefly explain your conclusions.

8)The shell and tube heat exchanger shown below is used to cool the product stream from a process. The product stream passes through the tube-side of the exchanger and cooling water passes through the shell-side of the exchanger. Both the shell and the tubes in the heat exchanger are completely full of liquid. The only two valves that can be used for control purposes are the cooling water inlet valve and the by-pass valve, with valve positions P_c and P_b, respectively. The flow through the tubes is held constant, but the cooling water system is subject to frequent supply pressure disturbances. You may assume that the sensor dynamics are negligible

Attachment:- Chemical process Control.rar