Derive the system equation for Figure 1 and find the value of Draw its free body diagram also.

<img src='./qimages/15556-1a.jpg'>

Write the differential equation and its transfer function for Figure 2 as given below:

<img src='./qimages/15556-1b.jpg'>

A block diagram is shown below in Figure 3. Draw its signal flow graph and determine the transfer function.

<img src='./qimages/15556-2a.jpg'>

What is a transfer function? Define the impulse response of a linear system.

3. Determine the overall gain of the signal flow graph given in Figure 4 and also determine y2/Y1,y4/yl and y6/y1

<img src='./qimages/15556-3.jpg'>

4. The open loop transfer function of a unity feedback system is given by



where K and Tare positive constants. By what factor should the amplifier gain be reduced so that the peak overshoot of unit step response of the system is reduced from 75% to 25%

5. The forward path transfer function of a unity feedback system is given by Sketch the root locus as K varies from 0 to infinite.

6. Sketch the Bode plot for the transfer function 1000/s(l 0·1s)(l 0·001s) Comment on the stability of the system.

7. Draw the state block diagram for the transfer function given below:



2s 2

8. Write short notes on the following:

PID Controllers

Nyquist Stability Criterion

Lag and Lead Compensator

Hydraulic and Pneumatic System