Implementation of Conventional and Neural Controllers Using...
Transcript of Implementation of Conventional and Neural Controllers Using...
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Implementation of Conventional andNeural Controllers Using Position
and Velocity Feedback
By
Christopher Spevacek
&
Manfred Meissner
Advisor
Dr. Gary Dempsey
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Contents
Summary
Previous Work
Modes Of Operation
Preliminary Design Work
Preliminary Lab Work
Equipment List
Schedule
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Summary
Design and Compare Conventional andNeural Controllers for a Small RobotArm
Position and Velocity Feedback Design
User Friendly Interface Design
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Previous Work
Quanser Consulting– Provided Software for Use with the Robot
Arm, A/D, D/A Converters
Dr. Dempsey– Research on different Velocity Algorithms
– Neural Network Architecture
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Modes of Operation
Default– Computer Generates the Command Signal
– User Set the Final Position of the RobotArm
Joystick– Connects to A/D Channel
– Generates Command Signal by theMovement of the Joystick
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Preliminary Design Work
High Level Block DiagramHigh Level Block Diagram
Control Block Diagram
Software
Velocity Algorithms
Neural Networks
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High Level Block Diagram
Robot Arm System
Pentium based PC
Position SensorA/D
Converter
D/AConverter
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High Level Block Diagram
Pentium Based PC– Generates Command Signal if Joystick is
not Present
– Implementation of Controllers
– Generates Real-Time Graphs
– Display the User Interface
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High Level Block Diagram
Robot Arm System– Power Amplifier
– DC Motor Assembly
– Gear Trains
– Load The Robot Arm
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Control Block Diagram
C(s)position
Gp(s)e+
+
F(s)b
H(s)Ampandfilter
Position Feedback
Gc(s)R(s)Command
+-
a c d
V(s)
To be usedlater forcontroller g
f
h
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Input And Outputs of System
A) R(s) is the Command Signal
+CMD
-CMD
t
Velocity
| |CMD ≤ °90
VELOCITYMAX = °45 sec
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Inputs and Outputs
C(s) is the Position of the Robot Arm– Percent Overshoot(%O.S.) = 5%
– Time To first Peak (tp) = 3s
– Magnitude of Peak in Frequency Domain(Mp) = 1.32dB
– Frequency of Peak In frequency Domain(wp)=170mHZ
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Inputs and Outputs
– Bandwidth Closed Loop (BW) = 290mHz
– Phase Margin (PM) = 50deg
– Gain Margin (GM) = 6dB
– Steady State Error = 2deg
Output should be the same as input
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Subsystems
F(s)– Feed-Forward Compensator
– Neural Network if Implemented
– Implemented in Software
Gc(s)– Plant Controller
– A PID-type controller
– Implemented in Software
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Subsystems
Gp(s)– Plant or Robot Arm System
– Hardware
H(s)– Position Sensor
– Hardware
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Subsystems
V(s)– Algorithm used for Velocity Feedback
– To Be Determined
Amp and Filter– Amplify signal
– Filter out the noise
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Software FlowchartInitialization Setup Interrupts
Interrupt Service Routine
Main ProgramRead Keyboard
to Determine Controller
Is Joystick Present
Generate Internal Position Command
Signal
Perform PID-Controller
Display Internal/External
Signals to Monitor
Return
Pentium-based PC
Yes No
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Subsystems
Initialization– Initializes the Interrupts to be set at 200Hz
Sampling Rate (5ms)
Main Program– Calculate the Values for the Display
– Check the Keyboard and Joystick
– If Present Read Joystick and Generate theCommand Signal
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Subsystems
Interrupt Service Routine andPerforming of PID Controller– Send Signal form Calculated Values of
Main Program and Interrupt ServiceRoutine to the Robot Arm
– Signals also Sent to the Monitor at UserSpecified Times
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Velocity Algorithms
Design S-Plane Lead Network useTustin Method(Bilinear Transformation)
Use Polynomial Curve Fit Algorithm toCalculate Velocity
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Neural Network
C(s)position
Gp(s)e+
+
F(s)b
H(s)Ampandfilter
Position Feedback
Gc(s)R(s)Command
+-
a c d
V(s)
To be usedlater forcontroller g
f
h
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Preliminary Lab Work
P Controller Design and Testing
C-Code– Filter Design using Tustin Method
– Filter Testing
– Improvement of Display
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P Controller Design
Gps s
=+1
1( )
K GpR C
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Calculation Results
For 0% OS k=0.25
Ts=11.7sec Tp=Infinity
For 5%OS k=0.525
Ts=8.4sec Tp=6sec
For 25%OS k=1.534
Ts=6.78sec Tp=2.76sec
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Circuitry Used
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Measurement 25% OS
Ts=6.75 Tp=2.7
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Calculation Vs. Measurement
0% Ts=11.7sec
5% Ts=8.4sec
Tp=6sec
25% Ts=6.78sec
Tp=2.76sec
BW=290mHz
fpeak=175mHz
Mp=1.32 norm.
0% Ts=12.5sec
5% Ts=7.4sec
Tp=5.75sec
25% Ts=6.75sec
Tp=2.7sec
BW=270mHz
fpeak=161.8mHz
Mp=1.354 norm.
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C-Code Development
Design of a digital filter @ 20Hz cutoff
Changing Real-Time Display Mode
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Filter Design
Using Tustin Method
With T=fixed sampling time=0.005sec
Filter Transfer Function to Obtain
ST
z
z=
−+
2 1
1
G s s( )
*
=+
1
120 2π
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Filter Output on PC Screen
Chose 1V@20Hz Input to see 3dB point
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Changing Real Time Display
Auto Scaling on y-Axis was given
Problem: Plot off the Screen
Improvement: now it takes the lasthighest value and adjusts it only byapproximately 20% up or down
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Equipment ListHardware & Software
500MHz IBM compatible Pentium III PC
Quansar Robot Arm System
A/D & D/A converter card
Amplifier
Borland 4.5 C-Compiler
Matlab 5.3
WinCom V2.0 Real-Time Workshop
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ScheduleChris=C Manfred=M Dr.Dempsey=D
12 weeks available till Presentation at the StudentExpo end of April
System Identification C&M&D 3Weeks
Menu C&M 1Week
P-Controller Design&Testing C 1Week
Investigate&Implement Neural Network
with P-Controller M&D 1Week
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Schedule Chris=C Manfred=M Dr.Dempsey=D
Velocity Algorithm C 1Week
Two Loop Design
With Neural Networks M&D 1Week
Redesign with Rotary Encoder C&M 1Week
Feed Forward Control & Implementation
in Neural Networks C&M&D 1Week
Digital Control Analysis C&M 2Weeks
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Additional Work
Presentation at Student Expo
miss one Lab Period
Expo Conference Report
Presentation Board
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The
End
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Design Equations 1
− −= ζπ ζ12
%OS e
nw k=nw = 12ξ
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Design Equations 2
Vo/Vi= 1kΩ /Rpot=k => R=1000/k
Transfer Function: 2nd order system
C/R=wn^2/(s*s+2*zeta*wn+wn^2)=
=k/(s*s+s+k)
Ts=<2% from final value
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Design Equations 3
Tustin or Bilinear z-Transformation
s=ln(z)*1/T~(2/T)*(z-1)/(z+1)
Truncating Laurent Series Expansion
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Calculation for Circuitry
Chose 1µF Capacitor for Integrator &Filter
→R=1MΩ for Integrator and Filter
Chosen 1 kΩ Resistors for Gain &Summer
→Rpot=1000/Gain
→Rpot= 4 kΩ for 0%OS
→Rpot= 1.905 kΩ for 5%OS
→Rpot=652 Ω for 25%OS
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Final C-code Function
Output = 0.239*Input+
+0.239*Past Input+
+0.522*Past Output
Past Input & Past Output had to be setzero to get started
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Subsystems
Keyboard– Gives the User a Choice of Which Signals
are to be Displayed and Controller type
– Command Signal Parameters
Display– Will Show all Internal and External Signals
Chosen by the User
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Subsystems
Joystick Check– If Present Joystick Position will be Read
and Sent to the Interrupt Service Routine
– If not the PC will Generate the CommandSignal
Generate Command Signal– This Option Occurs if the Joystick is not
Present.
– PC Performs the Calculations for theCommand Signal
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How Measurement was Obtained
Input Square Wave Chosen at LeastDouble the Settling Time
Potentiometer was Adjusted to Get
%OS Wanted
Read Results from Scope
Frequency Domain: Swept from 1mHztill Sine Wave to get BW(3dB) and Mp
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Measurement 0% OS
Ts=12.5sec
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Measurement 5% OS
Ts=7.4 sec Tp=5.75sec