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Transcript of Interactive Modeling, Simulation, Animation, and Real-Time Control (MoSART) Flexible Inverted...
Interactive Modeling, Simulation, Animation, and Real-Time Control (MoSART) Flexible
Inverted Pendulum Environment
http://www.eas.asu.edu/~aar/research/mosart
Jose I. Hernandez Richard P. Metzger Jr. Chen-I Lim Armando A. Rodriguez
Ack : White House , NSF, WAESO/CIMD, Boeing, Intel, Microsoft, CADSI, Knowledge Revolution, MathWorks, Lego, Xilinx, Honeywell, National Instruments, Integrated Systems, ASU CIEE.
ASEE Pacific Southwest Meeting `99
Saturday, March 20th 1999
Harrah’s Hotel
Las Vegas, Nevada
Motivation
Flexible Inverted Pendulum (FIP) System Dynamics: Model & Control Laws
Description of Interactive MoSART FIP Environment
Utility of Environment
Summary and Future Directions
OutlineOutline
Advanced visualization tools are needed for system analysis and design.
Research/education can be enhanced with interactive multimedia environments.
PC platforms now offer substantial computing power for engineering design.
Motivation
New Technologies• Affordable High Performance Computing• Hi-fidelity Simulation Capability
– Simulink / MATLAB, etc…– Visual C++
• PC Animation Creation / Manipulation Technologies– 3D Modeling Software (e.g. 3D Studio, RPM D3D toolbox,
etc.)– Microsoft DirectX (provides: 3D-animation, sound, video,
user-input, etc.)
• Object Oriented Programming (OOP) Framework– ActiveX / OLE
New Technologies
• Accelerated-time simulation• Alter model/controller:
– structure– parameters (on-the-fly)
• Advanced visualization:– real-time graphics– visual indicators/aids– 3D animation models
• Direct user input via joystick, mouse, etc.• Integration with MATLAB and Simulink
Cartpend.exefxdbasepend.exe
RotaryPend.exe
Key Environment Features
System-specific interactive MoSART
environments
High performance: Windows/ C++
Advanced visualization tools: Direct-3D
Extensible: integration with MATLAB
User friendly
Contributions of Work
1
2
l
m
b
f
x
k t
1
2
h
c
in
1
c
l
m
b
d
l
c
1
m2
2b
Flexible Inverted Pendulum (FIP) System
Controls and OutputsControls and Outputs
xp
(N) ForceInput inf
Inputs, up Outputs, yp
x = Cart Position (m)
1= Link 1 Angle (rad)
ppp
ppppp
xCy
uBxAx
States, xpStates, xp
/sec)locity(radangular ve 2Link :6
(rad/sec)locity angular ve 1Link :5
(m/sec)ity Cart veloc x:4
(rad) angle 2Link :3
(rad) angle 1Link :2
(m)position Cart x :1
2
1
2
1
FIP Linear Model
FIP Linear Model
Unstable pole
Plant Analysis
Classical
Pole Placement
LQG/LTR
H (1)
H (2)
Control Laws
Pentium PC
Windows ’95/’98/NT
System Requirements: Pentium PC running Windows 95/NT. 32 MB RAM. Direct-3D 3.0.
Recommended: Pentium II 266 w/ MMX running Windows NT 4.0. 64 MB RAM. Direct-3D 3.0.
Visual C++/ MFC
Direct-3D v3.0MATLAB Engine
v5.0
About the Program
Communication Module (COM)
ProgramUser Interface
(PUI)
Simulation Module
(SIM)
Graphical Animation Module
(GAM)
Help/InstructModule(HIM)
Physical System Simulink MATLAB InternetOther
Applications
Interactive Environment Application
ActiveX
Interactive MoSART Environment Modules
(PUI)User Friendly Windows ’95/NT Interface
•Menus•Multiple windows•Program control toolbars
Interactive System Diagram
•Block diagram representation of system•Point-and-click access
Program User Interface
(SIM)Numerical Simulation
On-the-Fly Parameter Editing
•Fast compiled C++: >3000 Hz / 266MHz PII•Better than real-time simulation
•Plant models•Controller parameters•Reference Commands, Disturbances, Noise, etc.•Integration methods: Euler, Runge-Kutta 4, etc.
Extensibility
Simulation Module
(GAM)3D Animation
•Direct-3D•Texture-mapped, light-shaded polygons•Wireframe copters from previous simulations
•Real-Time Variable Display Window•2D Animation Window: pitch indicator•Real-time multiple-graph plotting
Visualization Tools & Indicators(SMAC)
Extensibility
Graphical Animation Module
(HIM)On-line Help
•Instructions on using the environment•Program reference
HTML / PDF Documents
•Model documentation/ references•Interactive tutorials
Help-Instruct Module
Cart Position<m> 0.3450 Link 1 Angle<rad> -0.2390 Link 1 Angle <rad> 0.3654 Cart Velocity<m/sec> 0.6288Link 1 Angular Vel.<rad/sec> 0.0234Link 1 Angular Vel. <rad/sec> 3.8054
Toolbar and Menu
Initial ConditionsMenu
3-D AnimationWindow
System Block Diagram
Variables WindowReal Time Plots
Simulation Parameters
MoSART Flexible Inverted Pendulum (FIP) Environment
Plant modal analysis
Plant flexibility analysis
H Controller design
Comparison of controllers
Utility of the Environment
Toppling Unstable Mode
Flexible Mode
Link Damping Mode
Modal Analysis
Visual animation of The Flexible Mode
Selecting To Work Open-Loop, No Controller,No Input
Plotting Cart Position and Link 1 and Link 2 Angles
VariableValues
Cart Position<m> 0.3450 Link 1 Angle<rad> -0.2390 Link 1 Angle <rad> 0.3654 Cart Velocity<m/sec> 0.6288Link 1 Angular Vel.<rad/sec> 0.0234Link 1 Angular Vel. <rad/sec> 3.8054
Visualization of Flexible Mode
M
xfin
m
l1
2
l
m
b
f x
kt
1
2
h
c
in
1
c
l
m
bd
l
c
1
m2
2b
Rigid Inverted Pendulum Flexible Inverted Pendulum
2
21
lll
mM
mmm
h
c
2
1
1
122
0
0
0
b
k
b
b
m
mmm
t
c
Plant Rigidity Analysis
As b2 Increases, Flexible Mode Damping Increases
As kt Increases, Natural Bending Frequency Increases
Rigidity Analysis: Pole Locations Varying b2 and kt
fin M
x
m
l
( )1m
M
g
ls=0,0,
(N) ForceInput inf
Inputs, upOutputs, yp
= Link Angle (rad)x = Cart Position (m)
States, xp
= Link angle (rad)d = Link angular velocity (rad/sec)x = Cart position (m)dx = Cart speed (m/sec)
Rigidity Analysis: Rigid Inverted Pendulum Linear Model
Fle
xibl
e In
vert
ed
Pen
dulu
m P
lant
High Frequency Peak Due to the Imaginary Poles
Rig
id I
nve
rte
d P
endu
lum
Pla
nt
Low Frequency Poles of Both Systems Are the Same
Rigidity Analysis: Transfer function comparison: Rigid vs Flexible Pendulums
r e udi do
K P
n
y
Controller Plant
• Design K based on model Po s.t. nominal CLS exhibits:
– Stability
– Good Command Following
– Good Disturbance Rejection
– Good Noise Attenuation
– Robust Performance
H Controller design
w1 w2
H Controller Design
Small Overshoot
No Steady State Error
Small Oscillations 1
2
Fast Response
SensitivitySensitivity
Complementary SensitivitySmall Control Force
Good Low FrequencyCommand Following
H Design
Classical
LQG/LTR
Pole Placement
H (design 1)
H (design 2)
Command Following (Cart Position)for a Unit Step Input
Controller Comparison
Sensitivity Transfer Functions (S)Complementary Sensitivity Transfer Functions (T)
Control Force
Command Following (Link 1 Angle)for a Unit Step Input
Controller Comparison
kt
Varying kt a Little Would Result in an Unstable Closed Loop System, for the H Controller
kt
Controller Comparison: Robustness to Flexibility Uncertainty. Varying kt
b2
When Using H (2) Controller, b2 Can Be Increased 3000% From Its Nominal Value Before Getting The System Unstable
b2
b2
Controller Comparison: Robustness to Flexibility Uncertainty. Varying b2
Closing the Loop and Selecting the LQG/LTR Controller
Selecting a Unit Step Command Input to The System
The MoSART FIP Environment PlotsAgree With The MATLAB Plots
Simulation of Closed-Loop System Response for a Step Command Input (LQG/LTR Controller)
Controller Comparison
• Versatile system-specific interactive MoSART environments
• Windows / C++ / Direct-X / MATLAB
• User friendly: accessible & intuitive
• User can alter model structures & parameters (on-the-fly)
• Highly extensible: ability to incorporate new simulation/animation models
Summary
Future Directions
… development of Facility
http://www.eas.asu.edu/~aar/research/mosart/Presentations/
VISIT:
-More visual indicators
-Advanced SIM and GAM (e.g. TLHS)
-Expanded HIM: web support, multimedia
-Develop Model Documentation Feature
-Enhanced integration with MATLAB / SIMULINK
LABVIEW / Excel….all are ActiveX Compatible
-Integrated design & analysis environment
-Develop Additional Environments