Effect of feedback on stability, Electrical Engineering

Assignment Help:

Q. Effect of feedback on stability?

Let us consider the direct transfer function of the unstable first-order system of Figure (a). The transfer function is given by

396_Effect of feedback on stability.png

where p = d/dt is the differential operator. If a unit-step function is applied as the input quantity E, the output becomes

1886_Effect of feedback on stability1.png

for which the corresponding time solution is given by

c(t) = K(1 - et/τ)

which is clearly unstable, since the response increases without limit as time passes. By placing a negative feedback path H around the direct transfer function, as shown in Figure (b), the closed-loop transfer function is then

1979_Effect of feedback on stability2.png

where cf(t) denotes response with feedback. The system is now clearly stable with aK > τ . Thus, the insertion of feedback causes the unstable direct transmission system of Figure (a) to become stable. Such a technique is often used to stabilize space rockets and vehicles, which are inherently unstable because of their large length-to-diameter ratios. Note that the direct transfer function of Equation has a pole located in the right half p-plane at p = 1/τ , whereas the pole of the closed-loop transfer function of Equation with aK > τ is located in the left half p-plane.


Related Discussions:- Effect of feedback on stability

Measurment, emitter followers regulator

emitter followers regulator

Explain the alphanumeric coding - bcd to decimal conversion, Explain the Al...

Explain the Alphanumeric Coding - bcd to decimal conversion? For the inherently binary world of computer, it is necessary to put all symbols, letters, numbers, and so on into bin

Single phase meters, Single Phase Meters Single phase meters are commo...

Single Phase Meters Single phase meters are commonly rated for 240 V AC supply; the current ratings are 5/10, 10/20, 2.5/10 or 5/20 A or are for direct connection to the mains

What do you mean by internal data bus, What do you mean by internal data bu...

What do you mean by internal data bus? Internal Data Bus: A bus which operates only in the internal circuitry of the CPU, communicating between the internal caches of memory

Show principal source of energy, Q. Show Principal source of energy? Th...

Q. Show Principal source of energy? The principal source of energy comes from the burning of fossil fuels such as coal and oil to generate steam, which drives steam turbines, w

What is permeability, What is Permeability? Permeability: This is defin...

What is Permeability? Permeability: This is defined as the ability of the material to conduct flux. This is defined as the ratio of magnetic flux 'B' in a medium to the magneti

Corrosion, I want to know whether the circuits for both methods(linear pola...

I want to know whether the circuits for both methods(linear polarization resistance and electrochemical impedance spectroscopy) are same or not?

Energy stored in a magnetic field , Energy stored in a magnetic field ...

Energy stored in a magnetic field Consider a circuit consisting of a voltage supply,  switch,  resistor  and  a  coil  of  N turns wound on a toroid of length l, all in series

Electronics, why inductive load is use in electronics circuit?

why inductive load is use in electronics circuit?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd