## Principles of Control Systems - May 2016

### Electronics Engineering (Semester 4)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.

### Attempt any Four questions

**1(a)** Explain Adaptive control system.(5 marks)
**1(b)** Explain lead and lag compensator(5 marks)
**1(c)** Explain Controllability and Observability with its necessity for stability.(5 marks)
**1(d)** Determine whether the following systems are stable, marginally stable, and unstable

(i) -2,0; (ii) -2+j, -2-j; (iii) -2+j4, -2-j4, -2; (iv) x(t) = cosωt; (v) x(t) = e^{-t} sin4t.(5 marks)
**1(e)** Examine the stability of s^{5}+2s^{4}+2s^{3}+4s^{2}+4s+8=0 using Routh's method.(5 marks)
**2(a)** Obtain the overall transfer function from block diagram.

**2(b)**Sketch the complete root locus for the system

G(s)H(s) = [K (s+1)(s+2)] / [(s+0.1)(s-1)], where K>0.(10 marks)

**3(a)**Obtain the state variable model of the parallel RLC network. (10 marks)

**3(b)**Explain P, PI and PID controller.(10 marks)

**4(a)**The state equation of a linear time-invariant system is given below: $$\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 1 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 0\\ 1 \end{bmatrix}u$$

Where u>0.

Determine the following:

(i) The state transition matrix.

(ii) Controllability of the system.(10 marks)

**4(b)**Sketch the bode plot for the open loop transfer function given by:

G(s) = [288(s+4)] / [s(s+1) (s

^{2}+4.8s+144)] and H(s) = 1.(10 marks)

**5(a)**Derive the expression of Peak Overshoot when step input applied to the system.(5 marks)

**5(b)**Sketch the polar plot of G(s) = 12 / [s(s+1)].(5 marks)

**5(c)**For G(s)H(s) = 1+4s / [s

^{2}+(1+s)(1+2s)], draw the Nyquist plot examine the stability of the system.(10 marks)

### Attempt any two

**6(a)** Write a short note on Robust control system.(10 marks)
**6(b)** Construct the signal flow graphs for the following set of equations:

Y_{2} = G_{1}Y_{1} - G_{2}Y_{4}

Y_{3} = G_{3}Y_{2} + G_{4}Y_{3}

Y_{4} = G_{5}Y_{1} + G_{6}Y_{3}

Where Y_{4} is the output.(10 marks)
**6(c)** Explain the Correlations between time and frequency domain specifications of the system.(10 marks)