STUPIDSID
Attempt any four:
1 (a)
Define singular point of the system. How do you identify them in the phase portrait?
5 M
1 (b)
Draw the sinusoidal response of saturation with dead zone nonlinearity. Write the response equations.
5 M
1 (c)
Define positive definite matrix. What are the properties of the positive definite matrix if it is symmetric?
5 M
1 (d)
Compute the 2-norm for the matrices i) A=[0135]ii) F=[1005]
5 M
1 (e)
What are the limitations of plant inverse controller?
5 M
1 (f)
Obtain the linear system matrix at the operating point xT0=[1 0.5 0.5] for the system of equations. [x1x2x3]=[x22x23−3x21−11x22−12x3] Comment whether the operating point is stable?
5 M
2 (a)
Draw the phase trajectory for the following system using delta method. Assume initial condition. x=1, ˙x=0 ¨x+2˙x+4x=0
10 M
2 (b)
Derive the describing function for relay with dead zone nonlinearity.
10 M
3 (a)
Obtain via analytical method the solution of the following system and write the equation of trajectory. Assume initial condition x10=1, x20=0.˙x1=x2˙x2=−2x1−3x2
10 M
3 (b)
Explain Lyapunov stability analysis with neat phase trajectories.
10 M
4 (a)
Design IMC controller for plant model. ˜G(s)=(−s+1)2s+1 in order to achieve the response with time constant of 1.5 sec.
10 M
4 (b) (i)
Explain choice of filters in IMC for step and ramp reference inputs.
5 M
4 (b) (ii)
What is NMP system? Explain inverse response.
5 M
5 (a)
Design the optimal controller via Riccati equation for the system ˙x=[012−1]x+[01]u to minimize the performance index J=∫∞0(x21+x22+u2)dt.
10 M
5 (b)
Write the steps for constructing the Lyapunov function via Krasovskii method.
10 M
6 (a)
Investigation stability of the given system using describing function method.
10 M
6 (b)
Write steps for linearizing the nonlinear system using feedback linearization: ˙x=f(x)+g(x)uy=h(x)
10 M
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