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

Vector calculus in electromagnetic theory, can you please briefly explain a...

can you please briefly explain about significance of the word direction in vectors with some valid points

add instruction, ADD Instruction This  instruction use to add  content...

ADD Instruction This  instruction use to add  contents of any  register or memory  location with the  contents of accumulator. There are two  formats for ADD  instruction to ad

Coupling, advantages and disadvantages of direct and r c coupling

advantages and disadvantages of direct and r c coupling

Find the magnitude of the force, Q. A solenoid of cylindrical geometry is s...

Q. A solenoid of cylindrical geometry is shown in Figure. (a) If the exciting coil carries a steady direct current I, derive an expression for the force on the plunger. (b) F

Why do we cascade amplifiers, Q. Why do we cascade amplifiers? Why is RC co...

Q. Why do we cascade amplifiers? Why is RC coupling the most widely used coupling between 2 stages of a cascading amplifier? The voltage or power gain or frequency response obt

Determine l and c of the band pass filter circuit, Q. Determine L and C of ...

Q. Determine L and C of the band pass filter circuit of Figure to have a center frequency of 1 MHz and a bandwidth of 10 kHz. Also find the Q of the filter.

Power and power distribution, design a single phase distribution circuit fr...

design a single phase distribution circuit from a supply point to a load

Chemistry, write a note on vulcanization

write a note on vulcanization

Discuss the term d/a conversion, Discuss the term D/A conversion. D/A...

Discuss the term D/A conversion. D/A conversion: Digital-to-analog or analog-to-digital conversions are two very significant aspects of digital data processing.  Digital-to-

Clampers, just to put an assignment Give only short details that are impor...

just to put an assignment Give only short details that are important Specially bised clamper

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