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

Lossy transmission line, Q. The model of an elemental length of a lossy tra...

Q. The model of an elemental length of a lossy transmission line is shown in Figure (a), along with its parameters, where R is series resistance per unit length, L is serie

Show step-motor control system, Q. Show Step-motor control system? Figu...

Q. Show Step-motor control system? Figure illustrates a system in which the prime mover used in the disk-drive system is a step motor driven by pulse commands. In response to e

Circuit realization of the srff, Q. You are to construct a modified truth t...

Q. You are to construct a modified truth table for the circuit realization of the SRFF shown in Figure. As indicated in the text, you guess an output and then go back ato check it

What do you mean by bezier curve, What do you mean by Bezier curve? Shown B...

What do you mean by Bezier curve? Shown B0 (1,1), B1 (2,3), B2 (4,3), B3 (3,1) the vertices of Bezier polygon, calculate seven points on Bezier curve. Write in brief the differe

Find imax and imin, Q. (a) In the circuit shown in Figure the zener diode (...

Q. (a) In the circuit shown in Figure the zener diode (with zero zener resistance) operates in its reverse breakdown region while the voltage across it is held constant at VZ and t

Can you show binary number formats, Q. Can you show Binary Number Formats? ...

Q. Can you show Binary Number Formats? We in general write binary numbers as a sequence of bits (bits is short for binary digits) and we have defined boundaries for these bits.

Find the nature of the armature voltage, Q. The flux-density distribution p...

Q. The flux-density distribution produced in a two - pole synchronous generator by an acexcited field winding is B(θ, t) = B m sin ω 1 t cos θ Find the nature of the armatur

What do you mean by sub address, Q. What do you mean by sub address? A ...

Q. What do you mean by sub address? A sub address, though a part of the ISDN address, isn't considered as an integral part of the numbering scheme. Sub address is carried in a

Interpreter- high level language, Interpreter- High level language T...

Interpreter- High level language The interpreter is a program  which  translates the high  level  program  into  objects  program  statement wise . it reads one statement of

Explain cache structure in pentium, Explain cache structure in Pentium. ...

Explain cache structure in Pentium. Cache structure in Pentium: The cache in the Pentium has been changed by the one determined in the 80486 microprocessor. The Pentium has t

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