Feedback Control, Sensing and Discrete System

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Feedback Control, Sensing and Discrete System

• ME4803 Motion Control
• Teaching Associate Dalong Gao
• Instructor Dr. Wayne Book

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Physical System Example

• Simple mass damping model
• Input force u
• Output position y
• m 1 kg
• b 1 kg/s

y
m
u
b
How to get the unit for b?
b F / v N / (m/s)
F m a kg m / s2
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System Model

• Newtons law
• Laplace Transform
• Transfer function

y
m
u
b
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Proportional Control

• Considering the error between desired and
  measured output
• Input is proportional to the error signal

y
m
u
b
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Proportional Integral Control

• Steady State Error

y
m
u
b
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Proportional Derivative Control

• Transient behavior

y
m
u
b
Watch for step input.
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PID Control
y
m
u
b
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Sensing Motion Variables

• Variables
• Position
• Velocity
• Force
• Pressure

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Discrete System

• Ideal sampler
• Sampled data systems

t
T
2T
3T

A/D Converter
D/A Converter
Computer
Plant
Piecewise continuous analog control signal
Discrete signal
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Zero Order Hold

• Impulse response
• Output of zero-order hold

gZOH(t)
1
t
T
t
T
2T
3T

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For you to work through

• Mass-spring-damper system
• m 1 kg
• b 1 kg/s
• k 3 kg/s2
• Build P/PI/PD/PID controller for the system in
  Simulink, adjust gains for better performance.
• Compare the output of the controlled system, is
  this what you expected?

y
m
u
How to get the unit for k?
b
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Introduction to Digital ControlMotion Control

• Wayne Book
• HUSCO/Ramirez Chair
• In Fluid Power and Motion Control
• G.W.Woodruff School of Mechanical Engineering
• Georgia Tech

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Fundamental Differences between Analog and
Digital (Discrete Time)

• Analog
• Time is a continuous variable
• Amplitude is infinite in resolution
• Noise is inherent due to Brownian motion
• Programming is performed by wiring
• Calculations are typically approximate
• Variation can be at any time

• Digital
• Time is replaced by an index
• Amplitude is dependent on word size
• Noise can be reduced by calculation word length
• Programming by text or graphical languages
• Calculations can be made to high accuracy
• Changes occur only at sampling instants

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Fundamentals of dynamic behavior

• Continuous derivative and integral
• Discrete difference and summation

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Derivative Block Diagram
xn

xn
1/?t
_
z-1
One sample delay
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Integral Block Diagram


z-1
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Conversion from Continuous to Discrete Time
Transfer Functions

• Use finite difference (or other) ways to map
  differential into difference equation
• Solve
• for Y(z)
• Replace z-1 with a delay and replace Y(z) with
  y(k)

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The Complete Package

• Reference generator
• Step change of set point (often undesirable)
• Programmed reference change
• Generate trajectory of multiple variables to be
  tracked. e.g. position and velocity.
• Feedback control (as shown above)
• maybe modified e.g. by anti-windup
• Safety checks and limits
• Data logging