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

What is synchronous data transfer, What is synchronous data transfer? I...

What is synchronous data transfer? It is a data method which is used when the I/O device and the microprocessor match in speed. To transfer a data to or from the device, the us

Determine the base current, Q. A transistor has a base current i B = 25 µA...

Q. A transistor has a base current i B = 25 µA, α = 0.985, and negligible ICBO. Find β, iE, and i .

Magnetic circuits, Suppose we have a coil wound onto a ring of material wit...

Suppose we have a coil wound onto a ring of material with relative permeability µ r . Provided that the relative permeability µ r  >> 1, then the magnetic flux lines will s

Power distribution, 1.  Establish importance of Distribution Planning with ...

1.  Establish importance of Distribution Planning with help of suitable example.     2.  Explain different distribution planning methods.       3.Explain the six level interv

Motor, What is the main function of the slip ring

What is the main function of the slip ring

About on line teaching, i am Eectrical engineer and i want to teach student...

i am Eectrical engineer and i want to teach students on line mode. let me know the procedure. thanks pushpendra

Preventing leakages at insulators, Preventing Leakages at Insulators L...

Preventing Leakages at Insulators Leakages at insulators, cracking of insulators and flashover across insulators frequent cause outages and give output in loss of revenue. Pol

Passive filters, Passive filters: Passive implementations of linear fi...

Passive filters: Passive implementations of linear filters are based upon combinations of inductors (L), resistors (R), and capacitors (C). These sorts are collectively termed

How to connect the coil to the supply, A coil has an inductance of 1.2H and...

A coil has an inductance of 1.2H and a resistance of 40? and is connected to a 200 V, d.c. supply. Verify the approximate value of the current flowing 60 ms after connecting the co

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