Draw the block diagram of a digitally controlled plant with proper labelling.

Determine the Z-transform of the unit step function

Given the transfer function

0.3679z 0·2642/z^2 0.6321

determine the linear constant coefficient difference equation.

A second order system is represented as

z

What will be the time response, if the roots are real?

A linear constant coefficient discrete time system is represented as z^3 ­3z^2 2·25z -0·5 0.

Determine the stability using Jury's criterion.

Explain mapping of the primary strip in the left half of the s-plane into the z-plane by the Z-transform.

Explain cascade compensation "by continuous data controllers using bilinear transformation.

What are the compensation? degrees of freedom

For an open-loop transfer function with zero at and poles at and write down the circle equation for the root locus. Thus, write down the centre radius of the root locus.

For the open-loop transfer function 0·0175k(z 0·876)/(z ­0·67)(z

determine the centre and radius of the root locus and the points where the root locus enters or leaves the real axis.

Use the bilinear transformation z r to map the unit circle 1 onto the imaginary axis of the r-plane. Show pictorial presentation only.

Verify the stability of the system with characteristic equation

z^3 -l.25z^2 -1·375z -0.25 using the bilinear transformation

A state feedback model is given as

x(k g
d
u

Given

g [0.005]
0.1 0.1

Determine as a dead beat controller.

Define state space model (vector) of discrete data system. Use the similarity transformation to derive an equivalent model.

Use Cayley-Hamilton theorem to determine F^k from the eigenvalues of the matrix

F


Given the state space model
X(k
where
0.0787 0.0043]
0 0.6065 0.0787

Test the system for its controllability.

9. Write short notes on any two of the following:

Mathematical model of ZOH

Routh stability criterion on r-plane

Jordan canonical form