Young Scholars Program,
Northeastern University
Feedback Control in Ball Beam Dynamics
- Experimenting Delay Effects
Benjamin Gertner
Mike Wilson
Framingham High School
Beverly High school
Professor Rifat Sipahi
Northeastern University
Background & Terminology
† What is “feedback control” ?
† Sensors
† Stability / Instability
† Cruise Control
Block Diagram Convention
(Controlled)
DC Motor
Comparator
Desired
Speed
Error
signal
Actual
Speed
Control
signal
Controller
Plant
Feedback
Sensor
(Encoder)
Block Diagram Convention
(Uncontrolled)
DC Motor
Comparator
Desired
Speed
Error
signal
Actual
Speed
Control
signal
Controller
Plant
Feedback
Sensor
(Encoder)
Block Diagram—Motor (PID
Controller)
RPM Error
du /dt
1
Derivative
Scope
Gain 3
Desired Speed
20 RPM
20
National Instruments
NIM DAC
1
Constant
Saturation
Gain 1
1
s
Analog Output
Integrator
Position Error
Sensor
(encoder)
Gain 2
2
Derivative
w/ filter
National Instruments
NIM ENC
50 s
-0.001533980787886
*60 /2/pi
s+50
RPM
Encoder Input
Gain
Voltage
Controller
Speed Control of the
Motor-Experiments
Speed Control with PI-Controller. Desired = 20 RPM
20
20
18
18
16
16
14
14
12
12
RPM
RPM
Speed Control with P-Controller. Desired = 20 RPM
10
10
8
8
6
6
4
4
2
2
0
0
0.05
0.1
Time [sec]
0.15
0.2
0
0
0.05
0.1
Time [sec]
0.15
0.2
Position Control of the MotorExperiments
Position Tracking with P-Controller, Red = Actual, Blue = Desired
1
0.8
0.8
0.6
0.6
0.4
0.4
Position [rad]
Position [rad]
1
0.2
0
-0.2
0.2
0
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
0
2
4
6
8
Time [sec]
10
Error = ±15°!!
12
14
Position Tracking with PID-Controller, Red = Actual, Blue = Desired
-1
0
5
Time [sec]
Error = ±3°
10
15
No Delay – Ball At Start
Introduction to Ball Beam Dynamics
What is Delay and Where is it?
† Time that it takes to receive a signal
† Where:
„
„
„
„
„
„
„
Remote surgery
Human reaction delays
Chemical processes
Robotics
Tele-operation
Missiles and targets
Light delay (circuits, all electronics)
Delay Effects
† How would you implement delay?
† Why does delay lead to instability?
† Compensation of undesirable effects
„ Wait before you act (observe trends)
„ Be less aggressive when compensating
„ Advanced controller development
(research)
Block Diagram—Ball Beam
Dynamics
5
Step
Command
in
centimeters
x
x_d
Simulated
Ball Position
Ball & Beam Simulation
Physical
Limitation
of Beam
Kp _bb
L/r
Outer Loop Kp
20 s
s+20
Derivative
w/ filter
Aplha to Theta
Theta D
Must
Opertate
in Linear
Region
Theta
SRV 02 Closed Loop
R2D
Radians
to Degrees
Theta
Kv_bb
D2R
Outer Loop Kd
56
Degrees to
Radians
R2D
Radians
to Degrees
Theta D
Offset in Degrees
National Instruments
NIM ADC
-L*2.54 /10
To
Calibrate Postion
to read in centimeters
(-20 to 20 )
Analog Input
Variable
Transport Delay
Ball Position
in centimeters
error
Delay 1
0
Step 1
Step 2
Step 3
delay
SRV02 - Experiment #3
BB01 - Ball & Beam
Double PV Controller : Experiment vs . Simulation
Run : Setup _SRV02 _Exp3
0.2 Second Delay– Ball At Start
Delay—Graph
Delay effect from start
15
10
Position (cm)
5
0
-5
-10
.2 seconds
No delay
-15
-20
0
1
2
3
4
5
6
7
8
Time (sec)
Kv_bb=.006
Kp_bb=.01
9
10
No Delay – Ball At Equilibrium
0.1 Second Delay– Ball At Equilibrium
0.2 Second Delay– Ball Equilibrium
Max Delay for Kv_bb
15
.3 Second Delay
Position (cm)
10
5
0
-5
-10
0
5
10
Time (sec)
15
8
.2 Second Delay
6
Delay
Position (cm)
4
2
0
-2
-4
-6
0
8
.1 Second Delay
4
Position (cm)
10
Time (sec)
6
2
0
-2
-4
-6
0
5
5
10
15
Time (sec)
Kv_bb
15
Getting Better
† Optimization
„ Energy efficient
„ Quickest result
„ Safest voltage
† Improving the Controller
„ New degrees of freedom—P, PI, PID controllers
„ Have the computer guess—Penalize the guess
† Gain, Too Much of a good thing?
„ Kp=1, Kp=1000
Thank you