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MAS107 - L2b

First / second order systems

Martin Choux

on 22 August 2013

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Transcript of MAS107 - L2b

MAS107 - L2b
Modeling: Introduction

Simple integrator models
Input: Flow u(t)
Drop of water
Area A
Output: level y
How can we model this?
No disturbance
Water flowing into a bucket
First order linear differential equation
Rate of change of height (m/s)
Cross sectional
area (m²)
Flow into
the bucket
Integral causality
Time derivative of output
Many systems have inputs that control the time derivatives of their outputs:
Input: Flow u(t)
Drop of water
Area A
Output: level y
How can we model this?
Water flowing out
There is a hole in the bucket!
Model of bucket with hole
Block diagram
First Order system
How can we model this?
Mass Spring Damper
Newtons second law
Block diagram
Second Order system
Solve diff. equations
time response
y(t) = ...

Previously on MAS107...
The design process
Practical PID
Laplace transform

Transfer function

Block diagram
Reduce the
block diagram
Frequency response
Bode plot
Stability analysis
Stability criteria
Phase margin
Gain margin
Controller design using Frequency response techniques
Proportional Controller

Lag Controller

Lead Controller

Cascade Controller
Plant /
How do we
model this?
Full transcript