# 0.11 Lecture 12:interconnected systems and feedback  (Page 3/5)

$Y\left(s\right)/X\left(s\right)⇒1/\beta \left(s\right)\begin{array}{cc}& \end{array}\text{and}\begin{array}{cc}& \end{array}Y\left(s\right)/D\left(s\right)⇒0$

4/ Improve dynamic characteristics

Our model of an op-amp was simplistic. A more realistic model that takes the finite bandwidth of the op-amp into account is shown below.

The finite bandwidth of the op-amp is modeled as

$K\left(s\right)=\frac{K}{s+\alpha }$

Using Black’s formula we obtain

$H\left(s\right)=\frac{K\left(s\right)}{1+\mathrm{\beta K}\left(s\right)}=\frac{\frac{K}{s+\alpha }}{1+\beta \frac{K}{s+\alpha }}=\frac{K}{s+\left(\alpha +\mathrm{\beta K}\right)}$

Therefore, the frequency response is

$H\left(\mathrm{j\omega }\right)=\frac{K/\left(\alpha +\mathrm{\beta K}\right)}{\mathrm{j\omega }/\left(\alpha +\mathrm{\beta K}\right)+1}$

the impulse response is

$h\left(t\right)={\text{Ke}}^{-\left(\alpha +\mathrm{\beta K}\right)t}u\left(t\right)$

and the step response is

$s\left(t\right)=\frac{K}{\alpha +\mathrm{\beta K}}\left(1-{e}^{-\left(\alpha +\mathrm{\beta K}\right)t}\right)u\left(t\right)$

We compare the open-loop with the closed-loop characteristics. We use typical parameters of a model 741 op-amp, $\text{K}=\text{8}×{\text{10}}^{6}$ and α = 40 rad/sec.

Effect on pole-zero diagram

As the loop gain is increased from 0 the pole moves out along the negative real axis from −40 rad/s and when β = 0.1 the pole reaches $-8×{\text{10}}^{5}\text{rad}/s$ . This type of diagram which shows the trajectory of the closed loop poles in the complex s-plane as the gain is changed is called a root locus plot.

Effect of feedback on frequency response.

B

Effect of feedback on step response.

As the loop gain is increased from 0 the time constant of the step response decreases, i.e., the system responds faster.

Summary of effect of feedback on dynamic characteristics.

5/ Reduce the effect of nonlinear distortion

A common power amplifier configuration found in many electronic systems (e.g., stereo amplifiers) is the push-pull emitter follower amplifier.

This configuration has an inherent nonlinearity. When ${v}_{i}>\text{0}\text{.}\text{6 V}$ , T1 conducts and when ${v}_{i}<\text{0}\text{.}\text{6 V}$ , T2 conducts. Thus, there is a dead zone between −0.6 and +0.6 V where neither transistor conducts.

The transfer characteristic, which contains an idealized dead zone, is shown below.

In an audio amplifier, the type of distortion caused by the dead zone is called crossover distortion.

We examine the use of feedback to reduce cross-over distortion with the aid of MATLAB’s block diagram language SIMULINK.

6/ Effect of cross-over distortion on simple signals and on music

The figure shows the effect of crossover distortion on a sinusoid obtained with Simulink. A demo will show the effect of cross-over distortion in an audio amplifier on simple signals and on music and the role of feedback to minimize this distortion.

IV. DYNAMIC PERFORMANCE OF FEEDBACK SYSTEMS

1/ Simple position control system with proportional controller

The objective of the position control system shown below is for the output position Y (s) to track the input signal X(s).

We can use Black’s formula to find H(s) as follows

$H\left(s\right)=\frac{\frac{K}{\left(s+1\right)\left(s+\text{100}\right)}}{1+\frac{K}{\left(s+1\right)\left(s+\text{100}\right)}}=\frac{K}{\left(s+1\right)\left(s+\text{100}\right)+K}$

How good is this system at controlling the motor position?

Let us examine the steady-state step response first. The system function is

$H\left(s\right)=\frac{K}{\left(s+1\right)\left(s+\text{100}\right)+K}$

The steady-state response to a unit step is simply the response to the complex exponential $x\left(t\right)=\text{1}\text{.}{e}^{0\text{.}t}=\text{1}$ which is y(t) = 1.H(0) ${e}^{0\text{.}t}=\text{K/}\left(\text{100}+K\right)$ . The position error ε=K/(100+K)−1=−100/(100+K). Hence, this position control system (with proportional controller) has an error that can be made arbitrarily small, although not zero, as the gain is made arbitrarily large.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!