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)=[010\001\0.24−1.282.1]x(k)+[0\0\1]u(k) y(k)=[100]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)=z2−1.2x+0.35x3−0.7x2+0.14z?0.008
10 M
5 (a)
Obtain the solution to the system of equation x(k+1)=[0.50\0−0.1]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. ϕ(k+1)=[01−0.88−1.9]ϕ(k)+[0\1]Γ(k)
10 M
6 (b)
Determine the stability of the system using Lyapunov equation. x(k+1)=[01−1.52.5]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
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