Essay Available:

You are here: Home → Math Problem → Engineering

Pages:

1 page/≈275 words

Sources:

2 Sources

Level:

Harvard

Subject:

Engineering

Type:

Math Problem

Language:

English (U.S.)

Document:

MS Word

Date:

Total cost:

$ 5.4

Topic:

# Physical System Modelling, Time Response And Stability (Math Problem Sample)

Instructions:

THE TASK WAS TO SOLVE CONTROL SYSTEMS MATH PROBLEMS AND SIMULATE USING MATLAB SOFTWARE

source..Content:

PHYSICAL SYSTEM MODELING, TIME RESPONSE AND STABILITY

Student’s Name

Course

Professor’s Name

University

City (State)

Date

Physical System Modeling, Time Response and Stability

1 A differential equation that relates ea(t) and θL(t)

We know that eat=Raia(t)+Kbdθm(t)dt and θmt=N2N1θL(t)

dθm(t)dt =ddt(θmt)=N2N1dθL(t)dt

Substituting the value of dθm(t)dt in eat gives:

eat=KbN2N1dθLtdt+Raia(t)

Therefore, eat=Raia(t)+(KbN2N1dθL(t)dt)

2 GS=θL(S)Ea(S) of the system

eat=Raia(t)+Kbdθm(t)dt in the s-Domain becomes Eas=RaIa(s)+KbSθm(s)

Also, TmS=KtIa(s), IaS=TmSKt

EaS=RaTmSKt+Kbsθms………..(i)

We also know that TmS=(Jms2+Dms)θms………..(ii)

Substituting equation (ii) in equation (i)

EaS=RaKt(Jms2+Dms)θms+Kbsθms

EaS=sθmsRaKt(Jms+Dm+Kb)

After simplification, θmsEaS is found to be:

θmsEaS=Kt(RaJm)s+1Jm(Dm+KtKbRa)s

But from θmt=N2N1θL(t) we find θms=N2N1θL(s) ,

Hence θLsEaS=KtRaN1N2Jms+1Jm(Dm+KtKbRa)s

3 Time response of the system given that the input is a unit impulse input

Jm=Ja+JL(N1N2)2=5+700(1001000)2=12

Dm=Da+DL(N1N2)2=2+800(1001000)2=10

To get the electrical constant KtRa we use the torque-speed curve.

Figure 1: Torque Speed Curve

KtRa=Tstallea=500100=5

θLsEaS=500100×1001000×12s+112(10+500×2100)s=0.0417s(s+1.667)

4 The response of the system to a unit-step input

For a unit-step input, Rs=1s

For a gain of K=40, the transfer function becomes 40×0.0417s(s+1.667)=1.668s(s+1.667)

...

Get the Whole Paper!

Not exactly what you need?

Do you need a custom essay? Order right now:

### Other Topics:

- Research And Describe Car Braking System Modeling & ControlDescription: The stopping distance of a vehicle can be calculated using a number of formulas dependent on the nature of the braking system....1 page/≈275 words| 3 Sources | Harvard | Engineering | Math Problem |
- Reengineering of Legacy Systems vs. Development of New Systems: A Mathematical ModelDescription: Based on rational thinking processes without application of a single rationally conceptualized mathematical model that can increase confidence in the decision....5 pages/≈1375 words| 4 Sources | Harvard | Engineering | Math Problem |