1) a) Explain any 4 mathematical operations on discrete time signals, also give some of the examples.
b) Descirbe the sampled data control system with the help of suitable diagram?
2) a) Describe the reconstruction of the sampled signals using hold circuits?
b) Explain what is zero order hold? Describe in brief.
3) a) Determine the Z-transform of the following discrete sequence:
F(k) =( 1/2 )K U(k)
4) Verify for the stability of sampled data control system represented by following given characteristic equation using the Jury’s stability test.
z3-0.2 z2-0.25z+0.05=0
5) Deduce the expression for explaining the function of dead zone nonlinearity.
6) A second order system is represented by =AX. Find the stability of the system by Lyapunov’s theorem and thus calculate the appropriate the Lyapunov’s function.
7) A linear second order servo is described by the equation:
+2n+n 2e =0
Where =0.15,n=1 rad/sec , e(0)=1.5 and (0)=0. Find the singular point. Create the phase trajectory by using the method of isoclines.
8) Describe the concept of phase plane analysis of non- linear control systems.
9) a) Describe the Kalman’s test for the state controllability and observability.
b) The state model of the system is given by = X + U and Y= X. Find the transfer function of the system.