# 0.1 Lecture 2: introduction to systems  (Page 2/8)

3/ Conclusion

A system is described structurally by specifying:

• the system topology,
• the rules of interconnection of the elements,
• functional descriptions of the elements — constitutive relations.

III. DYNAMIC ANALOGIES

Physically divergent systems can have similar dynamic properties.

1/ Mechanical free-body diagram

M = mass, B = friction constant,

K = spring constant,

f(t) = external force, and

v(t) = velocity of the mass.

Summing the forces yields

$f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

2/ Electric network

Summing the currents (Kirchhoff’s current law) yields

$i\left(t\right)=C\frac{\text{dv}\left(t\right)}{\text{dt}}+\frac{v\left(t\right)}{R}+\frac{1}{L}{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

3/ The mechanical and electrical systems are dynamically analogous

$\begin{array}{}f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }\\ i\left(t\right)=C\frac{\text{dv}\left(t\right)}{\text{dt}}+\frac{v\left(t\right)}{R}+\frac{1}{L}{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }\end{array}$

Thus, understanding one of these systems gives insights into the other.

4/ Block diagram

A block diagram using integrators, adders, and gains

$f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

5/ Electronic synthesis of block diagram

The integrator, adder, and gain blocks are other examples of functional descriptions of systems. We can produce a structural model of each of these blocks. For example, the gain block is easily synthesized with an op-amp circuit.

The op-amp itself is a functional model of a device that we can synthesize with an electronic circuit including a number of transistors.

Conclusion: We have seen several types of descriptions of systems

$f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

All four descriptions define a system with the same dynamic properties. We will develop methods that characterize these systems efficiently and that abstract their critical dynamic properties.

IV. CLASSIFICATION OF SYSTEMS

1/ Memoryless systems

The output of a memoryless system at some time to depends only on its input at the same time to. For example, for the resistive divider network,

${v}_{o}\left(t\right)=\frac{{R}_{2}}{{R}_{1}+{R}_{2}}{v}_{i}\left(t\right)$

Therefore, ${v}_{o}\left(\text{to}\right)$ depends upon the value of ${v}_{i}\left(\text{to}\right)$ and not on ${v}_{i}\left(t\right)$ for t ≠ to.

2/ Systems with memory

$i\left(t\right)=C\frac{\text{dv}\left(t\right)}{\text{dt}}$

$v\left(t\right)=\frac{1}{C}{\int }_{-\infty }^{t}i\left(\tau \right)\mathrm{d\tau }$

Note that v(t) depends not just on i(t) at one point in time t. Therefore, the system that relates v to i exhibits memory.

3/ Causal and noncausal systems

For a causal system the output at time to depends only on the input for t ≤ to, i.e., the system cannot anticipate the input.

Physical systems with time as the independent variable are causal systems. There are examples of systems that are not causal.

• Physical systems for which time is not the independent variable, e.g., the independent variable is space (x, y, z) as in an optical system.
• Processing of signals where time is the independent variable but the signal has been recorded or generated in a computer. Processing is not in real time.

4/ Stable and unstable systems

Stability can be defined in a variety of ways.

Definition 1: a stable system is one for which an incremental input leads to an incremental output.

An incremental force leads to only an

incremental displacement in the stable

system but not in the unstable system.

Definition 2: A system is BIBO stable if every bounded input leads to a bounded output. We will use this definition.

where we get a research paper on Nano chemistry....?
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
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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
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