demonstrator of advanced controllers
DESCRIPTION
Master of Science assignment. Demonstrator of advanced controllers. Hans Dirne. May 25 th , 2005. Supervisors prof.dr.ir. J. van Amerongen dr.ir. J.F. Broenink dr.ir. T.J.A. de Vries ir. P.B.T. Weustink. Why this assignment?. The Major ‘Mechatronics’ provides several courses - PowerPoint PPT PresentationTRANSCRIPT
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Demonstrator ofadvanced controllers
Hans Dirne
Supervisorsprof.dr.ir. J. van Amerongen
dr.ir. J.F. Broeninkdr.ir. T.J.A. de Vriesir. P.B.T. Weustink
May 25th, 2005
Master of Science assignment
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May 25th, 2005 Demonstrator of advanced controllers 2
Why this assignment?
The Major ‘Mechatronics’ provides several courses in control theory, in which the theory is often supported by simulations.
A physical setup might, in addition to simulations,be an enrichment for demonstrating control theory.
Such a demonstration setup will be able to makethe theory more insightful and will show real limitations in practical setups.
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Objectives
1. To design, build and test a mechatronic demonstration setup, with which several control algorithms can be shown in practice
2. To be able to demonstrate performance differences of control algorithms in practice
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Overview
1. Demonstration setup options2. Control systems3. Design of the new demonstrator4. Experiments5. Demonstration6. Conclusions & recommendations
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Demonstration setup optionsDemonstration setup options
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1. Mechatronic system2. Portable and easy to set up3. Robust, safe and failsafe design4. High level of observability5. Representable by linear 4th order model6. Clear link with well known device
Criteria
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Three options
1. ‘Linix’ laboratory setup
2. Setup of ‘Controllab Products B.V.’
3. New build
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Option 1: ‘Linix’ Laboratory Setup
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‘Linix’ Laboratory Setup
motor
encoders
inertia 2
inertia 1transmission
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‘Linix’ Laboratory Setup
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‘Linix’ Laboratory Setup
Major disadvantage:
slip between belt and inertias
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Option 2: CLP setup
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CLP setup
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CLP setup
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Sensor positions
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Option 3: New Build
Advantage• Pure design freedom
Disadvantage• Requires very much time and
effort to design
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New build Linix CLP-setupMechatronic system √ √ √
Linear 4th order model √ limited linear to bedetermined
Portable, easy to set up √ √ not in currentform
Robust, safe, failsafe √ √ feasible
Observability √ yes, 2 positionSensors
yes, 4 positionsensors
Link with practical device √ transmission printer
Shows controller differences √ no, due tononlinearities
To bedetermined
Remarks Time constraint
Overview demonstrators
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Control SystemsControl Systems
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Mathematical model – 6th order
NMotorCurrent
m
Load
P
LoadSensorWorld
F
Motor
m
Frame
FrameFlex
m
MotorInertia
BeltFlex
P
MotorSensor
P
LoadSensorFrame
K
MotorGain
Damper
ViscousPLUScoulomb friction
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Focus
1. Linear Quadratic Gaussian (LQG)2. Proportional, Integral, Differential (PID)
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LQG explanation
u y
statesLQG
Reference PLANT Output
LQE
LQR
A LQG control algorithm is a combination of1. Lin. Quad. Regulator (state feedback)2. Lin. Quad. Estimator (state estimation)
4th order linear model required!
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4th order linear model
Nremoved at order downsizing
m
Load
P
LoadSensorWorld
F
Motor
m
Frame
FrameFlex
m
MotorInertia
BeltFlex
P
MotorSensor
P
LoadSensorFrame
K
MotorGain
Damper
Required steps:1. Downsize system order2. Linearize system: discard coulomb friction
Result: linear 4th order model (e.g. State Space)
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V A
Xref
LQR
PLANT
LQE
Estimated States
.
L
Cx(k|k)=x(k|k-1) +Le(k|k-1)
+_
m
Load
P
LoadSensorWorld
F
motor
m
FrameFrameFlex
P
LoadSensorFrame Damper
K
Motor
K
Amplifier
m
motortraagheid
motorflex
P
motorsensor
K counter
AD
DA1
ENC encoder
K
A2V
M
K
_
ENCencoder2
Kcounter2
Z-1
LQG controlled system
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PID
Plant
anti-windup reset
PID-controller
m
Load
P
LoadSensorWorld
F
motor
m
FrameFrameFlex
Damper
reference
K
Motor
K
Amplifier
m
motortraagheid
motorflex
K
counter
AD
DA1
ENC
encoder
K
A2V
K
Kp
-1zddt
-1z
K
Kd
K
Ki
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Tuning (1)
For proper comparison of the PID with the LQG controlled system, tuning with the same criteria is required.
1. Avoid actuator saturation2. Minimization of criterion:
dtuuJ TT RQ ee
position error controller output
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Tuning (2)
Tuning procedure:1. Set Q and R2. Minimize criterion J by optimizing
controller gains (KLQG and KP,KI,KD)
Xref
PID
ref
u
x
K
Kp
d/dt
K
Ki
K
Kd
Process
Criterion
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Tuning (3)
Xref
PID
LQR
K
Kp
-1zddt
K
Ki
-1z
K
Kd
Plant1
M
K
_ Plant2
Optimization results
KP = 15.7
KI = 42
KD = 1.6
KLQG= [3.7, 74, 8.2, 70]T
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model
0 0.5 1 1.5 2 2.5 3 3.5 4time {s}
0
0.1
0.2
0.3
0.4PowerPIDPowerLQG
model
0 0.5 1 1.5 2 2.5 3 3.5 4time {s}
-0.001
-0.0005
0
0.0005
0.001
FramePIDFrameLQG
PID vs LQG (1)
• The PID controlled system consumes twice the power of the LQG system
• The maximum frame movement in the PIDcontrolled system is twice compared to LQG
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PID vs LQG (2)
model
0 0.5 1 1.5 2 2.5 3 3.5 4time {s}
0
0.05
0.1
0.15 xPositionPID {m}PositionLQG {m}
The LQG control algorithm leads to an unacceptable position error with the nonlinear process
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LQG+
Xref
LQR
LQE
FRAMEWORLDPlant
Estimated States
.
L
Cx(k|k)=x(k|k-1) +Le(k|k-1)
+_
Z-1
AO526
analog_output
ENC526
Encoder1
KCounter1
ENC526
Encoder2
K Counter2
K
A2V
K Kcomp
-1z
M
K
_
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LQG+ vs LQG
System Results
-0.05
0
0.05
0.1Reference
-0.05
0
0.05
0.1Output {m}
0 0.5 1 1.5 2 2.5 3 3.5time {s}
-0.05
0
0.05
0.1Error
Effect of integrator:Static error is minimized!
Interesting to seethe performance ofLQG+ in practice…
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Design of the new demonstratorDesign of the new demonstrator
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Goal: to test a control algorithm on a physical setup
Procedure
How?
ModelingCode
GenerationLoad Codeat Target
Testing
PC PlantPC(realtime server)(client)
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System overview (1)
PC PlantPC(realtime server)(client)
Client:• Runs MS Windows• Generating models• Model control (start/stop/upload/delete)• Setting parameters of controlled system real-time• View parameters of controlled system real-timeServer:• Runs Linux, with real-time kernel• Runs control system• Performs I/O
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System overview (2)
CPU
I/O interface
RouterStorageDevice
Demonstrator Actuator & Sensors
MotorAmplifier
Encoders MotorCurrent
Cable to PC
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Realization
Mechatronics
Embedded PC+ I/O
Power (CPU)
Power (motor)
Motor amplifier
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ExperimentsExperiments
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Experiments
• Comparison of PID/LQG/LQG+ performanceon the new demonstration setup
• Same controller parameters used as insimulation (after tuning)
• Performance comparison on:1. Static error2. Frame vibration3. Power usage
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0 2 40
0.05
Time
Pos
. [m
]
LQG without I-term
0 2 40
0.05
Time
[m]
LQG with I-term
0 2 40
0.05
Time
[m]
PID
0 2 4-0.04
-0.02
0
0.020.04
Time
Err
. [m
]
0 2 4-0.04
-0.02
0
0.020.04
Time
[m]
0 2 4-0.04
-0.02
0
0.020.04
Time
[m]
0 2 4
-0.2
0
0.2
Time
Fra
me
[mm
]
0 2 4
-0.2
0
0.2
Time
[mm
]
0 2 4
-0.2
0
0.2
Time
[mm
]
0 2 4-1
0
1
Time
Cur
r. [
A]
0 2 4-1
0
1
Time
[A]
0 2 4-1
0
1
Time
[A]
0 2 40
500
1000
Time
Pow
er [
A2]
0 2 40
500
1000
Time
[A2]
0 2 40
500
1000
Time
[A2]
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Results
The LQG+ controlled system outperforms the PID controlled system:
• Maximum frame movement differs factor 3• Total power consumption differs a factor 2• Both control algorithms minimize the static error, but the
LQG controlled system is faster
More performance increase is expected with a better model
Differences in performance between 2nd order PID and 4th order LQG have now been
demonstrated in practice
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DemonstrationDemonstration
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Demonstration
What will be shown:1. ‘Homing’ of the demonstrator
1. Determining absolute position2. PID controller in practice with various controller gains
Furthermore:1. Online adjustment of parameters2. Real-time variable monitoring3. Real-time animation of demonstration setup
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Conclusions Conclusions &&
RecommendationsRecommendations
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Conclusions
1. The new mechatronic demonstration setup is a compact, integrated machine that forms a versatile developmentenvironment for testing various control algorithms in practice
2. The new demonstrator allows for easy comparison of differentcontrol algorithms
3. Non-linear friction elements in the process will lead to lowerperformance in position control of a 4th order LQG-controlled system compared to a 2nd order PID control algorithm
4. Addition of an integrating term leads to an ‘LQG+’ control algorithm that can compensate for differences betweenprocess and reference model.
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Recommendations
Hardware• Expand safety system• Reduce weight of the demonstrator (next version)• Add parallel processing (e.g. distributed control)
Software / control• Experiment with more control systems (MRAS, (L)FF, ILC etc)• Perform system identification
General1. Set up lab work assignments for student
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Questions…?Questions…?
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THANK YOU FOR THANK YOU FOR YOUR ATTENTIONYOUR ATTENTION
you are all invited for you are all invited for DRINKSDRINKS
at ‘De Tombe’, floor 0at ‘De Tombe’, floor 0