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8/17/2019 20080833 Jin Oh Jung.pdf
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
Block
Diagrams
Loops
PID Control
Root LocusMethod
Outline
1 Meaning of System Dynamics
2 The Laplace Transfrom Method
3 Transfer Functions
4 Block Diagrams
5 Loops
6 PID Control
7 Root Locus Method
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
Block
Diagrams
Loops
PID Control
Root LocusMethod
What is a System?
Definition
System: Combination of elements acting together
Input: Cause of the system
Output: Effect due to the input
Model: Mathematical description of the system
Inputs Outputs
Boundary
System
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
Block
Diagrams
Loops
PID Control
Root LocusMethod
We will deal with...
http://find/http://goback/
8/17/2019 20080833 Jin Oh Jung.pdf
5/61
8/17/2019 20080833 Jin Oh Jung.pdf
6/61
PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
Block
Diagrams
Loops
PID Control
Root LocusMethod
We will deal with...
ODE Models
Inital conditions at t = 0
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
Block
DiagramsLoops
PID Control
Root LocusMethod
We will deal with...
ODE Models
Inital conditions at t = 0
Use Laplace Transform!
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
8/61
PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Why are we doing this?
The real world looks simple...
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8/17/2019 20080833 Jin Oh Jung.pdf
9/61
PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Why are we doing this?
But it’s not!
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
http://find/http://goback/
8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
Describes system’s motion in frequency domain
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
Describes system’s motion in frequency domain
Ex) Damped harmonic oscillator
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
Describes system’s motion in frequency domain
Ex) Damped harmonic oscillator
ẍ + 4ẋ + 53x = 0
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
Describes system’s motion in frequency domain
Ex) Damped harmonic oscillator
ẍ + 4ẋ + 53x = 0
s 2X (s )− s x (0)− ẋ (0) + 4 [s X (s )− x (0)] + 53X (s ) = 0
(s 2 + 4s + 53)X (s ) = 8s + 13
X (s ) = 8s
+ 13s 2 + 4s + 53
x (t ) = 8e −2t cos 7t −3
7e −2t
sin7t
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
Thus, if s is the root of the characteristic equation
s 2 + 4s + 53 = 0
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
Thus, if s is the root of the characteristic equation
s 2 + 4s + 53 = 0
Re s → ζ
(Damping ratio)
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The Laplace Transform Method
Thus, if s is the root of the characteristic equation
s 2 + 4s + 53 = 0
Re s → ζ
(Damping ratio)
Im s → ωd
(Damped natural frequency)
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Transfer Functions
In general,A(s )X (s ) = B (s )F (s )
T (s ) = X (s )F (s )
, means OutputInput
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Transfer Functions
In general,A(s )X (s ) = B (s )F (s )
T (s ) = X (s )F (s )
, means OutputInput
T (s ) is called the Transfer Function
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Transfer Functions
In general,A(s )X (s ) = B (s )F (s )
T (s ) = X (s )F (s )
, means OutputInput
T (s ) is called the Transfer Function
Property of the system model only
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8/17/2019 20080833 Jin Oh Jung.pdf
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PID
Controllerand RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)T(s)
F(s)T(s)
X(s)
Y(s)
X(s) Z(s)+
X(s)
X(s)
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
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PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)T(s)
Multiply...
F(s)T(s)
X(s)
Y(s)
X(s) Z(s)+
X(s)
X(s)
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8/17/2019 20080833 Jin Oh Jung.pdf
25/61
PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)
T(s)
F(s)
T(s)
X(s)
Y(s)
X(s) Z(s)+
X(s)
X(s)
B D
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8/17/2019 20080833 Jin Oh Jung.pdf
26/61
PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)
T(s)
F(s)
T(s)
X(s)
Y(s)
X(s) Z(s)+
X(s)
X(s)
B D
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
27/61
PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)
T(s)
F(s)
T(s)
X(s)
Subtract... Y(s)
X(s) Z(s)+
X(s)
X(s)
B D
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8/17/2019 20080833 Jin Oh Jung.pdf
28/61
PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)
T(s)
F(s)
T(s)
X(s)
Y(s)
X(s) Z(s)+
X(s)
X(s)
B D
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
29/61
PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)
T(s)
F(s)
T(s)
X(s)
Extract...
Y(s)
X(s) Z(s)+
X(s)
X(s)
Block Diagrams
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8/17/2019 20080833 Jin Oh Jung.pdf
30/61
PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Block Diagrams
Visual representations with transfer functions
X(s)
T(s)
F(s)
T(s)
X(s)
Y(s)
X(s) Z(s)+
X(s)
X(s)
Loops
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
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PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Loops
Open Loop Control
Closed Loop Control
Loops
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PIDControllerand Root
Locus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Loops
In the closed loop,
T (s ) = Y (s )
R
(s
)
= G (s )D cl (s )
1 +G
(s
)D
cl (s
)
Loops
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Loops
In the closed loop,
T (s ) = Y (s )
R
(s
)
= G (s )D cl (s )
1 +G
(s
)D
cl (s
)
Set the denominator to 0
Loops
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Loops
In the closed loop,
T (s ) = Y (s )
R
(s
)
= G (s )D cl (s )
1 +G
(s
)D
cl (s
)
Set the denominator to 0
Shows how the system responses!
PID Controller
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
PID Controller
Proportional-Integral-Derivative Controller
Highly used in Mechanical, Aerospace Engineering
PID Controller
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
PID Controller
Proportional-Integral-Derivative Controller
Highly used in Mechanical, Aerospace Engineering
PID Controller
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
37/61
PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
PID Controller
Proportional-Integral-Derivative Controller
Highly used in Mechanical, Aerospace Engineering
Aileron
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Aileron
Example of a PID controller
Aileron
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Aileron
Ailerons are marked with red
Aileron
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Aileron
If tilted...
Aileron
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod The angle is measured
Aileron
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod PID Controller’s signal → Aileron
Aileron
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
The aileron actives!
Aileron
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod PID Controller’s signal → aileron
Aileron
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8/17/2019 20080833 Jin Oh Jung.pdf
45/61
PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod PID Controller’s signal → aileron
Aileron
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
46/61
PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod PID Controller’s signal → aileron
Aileron
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod Finally, at the right angle!
Aileron
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod Opps! Tilted again!
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
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Aileron
8/17/2019 20080833 Jin Oh Jung.pdf
50/61
PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod Opps! Tilted again!
Aileron
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
51/61
PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod Opps! Tilted again!
Aileron
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
52/61
PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod Opps! Tilted again!
http://find/
8/17/2019 20080833 Jin Oh Jung.pdf
53/61
P Control
8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Control signal is proportional to the error
P Control
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Control signal is proportional to the error
t (sec )
x (m)
0 1 2 3 4−2
−1
0
1
2
I Control
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Only P control: Constant error
I control: Accumulates error and gives feedback
I Control
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Only P control: Constant error
I control: Accumulates error and gives feedback
t (sec )
x (m)
0 1 2 3 4−2
−1
0
1
2
D Control
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Integral action produces oscillations
D control: Error approaches zero
D Control
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Integral action produces oscillations
D control: Error approaches zero
t (sec )
x (m)
0 1 2 3 4−2
−1
0
1
2
PID Control
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Altogether,
MV (t ) = K p e (t ) + K i
t 0
e (τ ) d τ + K d d
dx e (t )
In the frequency domain,
D cl (t ) = K p + K i
s + K d s
To obtain the gains → Use Root Locus method!
Root Locus Method
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8/17/2019 20080833 Jin Oh Jung.pdf
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PIDController
and RootLocus
Jin Oh Jung
Meaning of SystemDynamics
The LaplaceTransfromMethod
TransferFunctions
BlockDiagrams
Loops
PID Control
Root LocusMethod
Set transfer function’s denominator zero
Solve varying K p from 0 to ∞Find the position you want!
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