STUPIDSID
Attempt any four:
1 (a)
Derive the Lyapunov equation for a system x(k+1)=Gx(k).
5 M
1 (b)
State sampling theorem. Explain folding and aliasing in brief.
5 M
1 (c)
Specify the region in z-plane that corresponds to the shaded region in s-plane as shown in Fig. 1
5 M
1 (d)
Explain digital control system with neat block diagram.
5 M
1 (e)
Explain sampler as an impulse modulator.
5 M
1 (f)
Explain operation of extrapolative and interpolative FOH.
5 M
2 (a)
Define pulse transfer function. Obtain C(z)/R(z) for the system shown in Fig. 2.
10 M
2 (b)
Determine the stability of the system having characteristic equation
P(z)=z3-2.661z2+2.508z-0.8187=0.
using Jury's Stability criterion.
P(z)=z3-2.661z2+2.508z-0.8187=0.
using Jury's Stability criterion.
10 M
3 (a)
Derive the transfer function for the ZOH.
10 M
3 (b)
prove using similarity transformation that state space representation is not unique. Also prove the invariance of eigenvalues under the similarity transformation.
10 M
4 (a)
Obtain the pulse transfer function for the digital control system described by \[ x(k+1) = \begin{bmatrix}
0 &1 &0 \0
&0 &1 \\-0.06
&0.07 &0.6
\end{bmatrix}x(k)+ \begin{bmatrix}
0\0
\1\end{bmatrix} u(k) \ y(k) = \begin{bmatrix}
1 &0 &0 \end{bmatrix} x(k) \]
10 M
4 (b)
Represent the following system into the controllable canonical form. \[ G(z)=\dfrac {0.5z-0.25}{z^3-0.4z^2 ? 0.39z+0.126} \]
10 M
5 (a)
Obtain the steady state error constants for a digital control system for step, ramp and parabolic inputs.
10 M
5 (b)
Obtain the solution to the system of equation \( x(k+1) = \begin{bmatrix}0 &1 \\-0.15 & 0.8 \end{bmatrix} x(k) \). Assume initial condition x(0)=(1, 0)' and sampling time 0.5 sec.
10 M
6 (a)
Design the deadbeat observer for the following system. \[ \phi (k+1) = \begin{bmatrix}0 &1 \1 &2 \end{bmatrix} \phi (k), \ y(k)=[1 \ 0] \phi (k) \]
10 M
6 (b)
Write the steps for controller design via pole placement using ackermann's method.
10 M
7 (a)
Explain Lyapunov stability theorems for a digital control system.
10 M
7 (b)
Determine the stability of the system using lyapunov equation. \[ x(k+1) = \begin{bmatrix} 0 &1 \\-0.72 &1.8 \end{bmatrix} x(k) \]
10 M
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