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

Matlab, Exercise 1: Data array manipulation and selection using for loops ...

Exercise 1: Data array manipulation and selection using for loops These exercises demonstrate the use of for loops in array manipulation and selection. a) Write a user-defined fun

What is meant by regulation, Q. What is meant by regulation? The output...

Q. What is meant by regulation? The output of most power supplies should be a constant voltage. Unfortunately, this is difficult to achieve. There are two factors that can caus

Explain the effect of a dielectric on behaviour of capacitor, Explain the e...

Explain the effect of a dielectric on the behaviour of a capacitor. If two parallel plates are separated by a distance 'd' (meters) in vacuum and are kept at a potential diffe

Detection and handling of gas leakage, Detection and Handling of Gas Leakag...

Detection and Handling of Gas Leakage : If you are using a toxic gas or have a store for it you must have some devices to indicate the leakage, if any. Though numerous monitoring

Explain current-to-voltage amplifier, Q. Explain Current-to-Voltage Amplifi...

Q. Explain Current-to-Voltage Amplifier? The basic circuit is shown in Figure, which is similar to that of an inverting amplifier. The - input is connected directly to a curren

Dielectric heating - stepper motor , Dielectric Heating Dielectric  l...

Dielectric Heating Dielectric  losses  occur in  insulating materials. These are same  as hysteresis losses  in magnetic materials. When  an alternating  electric  field  is a

Determine about the satellite navigation, Determine about the satellite nav...

Determine about the satellite navigation In motor vehicles system is known as satellite navigation (sat nav). On board computer contains pre-stored road maps. Vehicle's exact

Light triggering - power semiconductor devices , Light Triggering Whe...

Light Triggering When  light is  thrown  on silicon the hole electron pair get excited an increases hence  the leakage  current of J 2   increases which  will increase I C1 a

What do you mean by companding, Q. What do you mean by Companding? In o...

Q. What do you mean by Companding? In order to lower the crest factor of a waveform, so as to produce better performance, a process known as companding is used. It works like a

Engine management systems for ic engines, In continuation of Part-B, the st...

In continuation of Part-B, the student is required to configure an engine management system for the proposed engine and produce a report including the following: A preamble

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