STUPIDSID
Attempt any four:
1 (a)
Explain digital control system with neat block diagram.
5 M
1 (b)
State sampling theorem. What are the undesirable characteristics that may be exhibited in response if sampling theorem is not satisfied?
5 M
1 (c)
Specify the region in x plane that corresponds to the region in s plane as shown in Fig. 1
5 M
1 (d)
Explain controllability and observability of the system.
5 M
1 (e)
Explain sampler as an impulse modulator.
5 M
1 (f)
Explain various types of continuous and discrete time signals.
5 M
2 (a)
Obtain the pulse transfer function with sampling rate Ts=1sec. for the system shown in Fig. 2.
10 M
2 (b)
Determine the stability of the system having characteristic equation
P(z)=z3-z2-0.19z+0.28=0
using Routh's Stability criterion.
P(z)=z3-z2-0.19z+0.28=0
using Routh's Stability criterion.
10 M
3 (a)
Derive the transfer function for the ZOH.
10 M
3 (b)
Determine controllability and observability for the following system \[ x(k+1) = \begin{bmatrix}
0 &1 &0 \0
&0 &1 \0.24
&-1.28 &2.1
\end{bmatrix} x(k) + \begin{bmatrix}
0\0
\1 \end{bmatrix} u(k) \
y(k) = \begin{bmatrix}
1 &0 &0 \end{bmatrix} x(k) \]
10 M
4 (a)
Obtain the pulse transfer function for the digital control system described by
x(k+1)=Gx(k)+Hu(k)
y(k)=Cx(k)+Du(k)
x(k+1)=Gx(k)+Hu(k)
y(k)=Cx(k)+Du(k)
10 M
4 (b)
Represent the following system into the observable canonical form. \[ G(x)= \dfrac {z^2 - 1.2x + 0.35}{x^3 - 0.7 x^2 + 0.14z ? 0.008} \]
10 M
5 (a)
Obtain the solution to the system of equation \( x(k+1) = \begin{bmatrix}
0.5 &0 \0
&-0.1
\end{bmatrix} x(k).\) Assume initial condition x(0)=(1, 0)' and sampling times 1 sec.
10 M
5 (b)
prove using similarity transformation that state space representation is not unique. Also prove the invariance of eigenvalues under the similarity transformation.
10 M
6 (a)
Design the state feedback control for the following system to place the pole at 0.5 and 0.2. \[ \phi (k+1) = \begin{bmatrix}
0 &1 \\-0.88
&-1.9
\end{bmatrix} \phi (k) + \begin{bmatrix}
0\1 \end{bmatrix} \Gamma (k) \]
10 M
6 (b)
Determine the stability of the system using Lyapunov equation. \[ x(k+1) = \begin{bmatrix}
0 &1 \\-1.5
&2.5 \end{bmatrix} x(k) \]
10 M
7 (a)
Derive the state transition matrix via recursion for the system.
x(k+1)=Gx(k)
x(k+1)=Gx(k)
10 M
7 (b)
Explain pole placement method using Ackerman's formula.
10 M
More question papers from Digital Control System