Reference no: EM13528184
Negative Feedback System with Time Delay:
The transfer function of the forward path is A(s) = 2/(1+2s+s2). There is also a delay of T seconds in the forward path. The transfer function of the delay is D(s) = exp(-sT). The feed back gain is B=1 and the sense is negative.
Use Matlab to make a Nyquist plot for T= 0 ). Is. It should show no poles in the RHP. Then increase T until the Nyquist plot just loops around .
What T is required? Use Matlab to make a Bode plot for this value of T.
Use Simulink to make simulate the step response of the system. Plot the step response with 1s and again with
T that you found was unstable. Use the block called "transport delay".
Signal Flow Graph of a Ladder Network:
The LC ladder is a very popular filter structure because it is not sensitive to component values. Here we will consider one with two inductive series branches and two capacitive shunt branches.
Define the series branches as impedances Z1 and Z2 and the shunt branches as admittances Y1 and Y2. Calculate the transfer function H. Replace ZN with sLN and YN with sCN for N=1,2 and write H(s) as a rational function of s.
Draw the signal flow graph to represent the equations of the circuit. Use Mason's Rule to find the transfer function H(s).
Show how to realize the signal flow graph representation with four opamp integrators and two opamp inverters (6 opamps in total).
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Negative feedback system with time delay
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