Interactive Modeling Simulation Animation and Real-Time Control Mo

Interactive Modeling, Simulation, Animation, and Real-Time Control (Mo. SART) Flexible Inverted Pendulum Environment Jose I. Hernandez Richard P. Metzger Jr. Chen-I Lim Armando A. Rodriguez ASEE Pacific Southwest Meeting `99 Saturday, March 20 th 1999 Harrah’s Hotel Las Vegas, Nevada Ack : White House , NSF, WAESO/CIMD, Boeing, Intel, Microsoft, CADSI, Knowledge Revolution, Math. Works, Lego, Xilinx, Honeywell, National Instruments, Integrated Systems, ASU CIEE. http: //www. eas. asu. edu/~aar/research/mosart

Outline Motivation Flexible Inverted Pendulum (FIP) System Dynamics: Model & Control Laws Description of Interactive Mo. SART FIP Environment Utility of Environment Summary and Future Directions

Motivation 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.

New Technologies • Affordable High Performance Computing • Hi-fidelity Simulation Capability – Simulink / MATLAB, etc… – Visual C++ • PC Animation Creation / Manipulation Technologies – 3 D Modeling Software (e. g. 3 D Studio, RPM D 3 D toolbox, etc. ) – Microsoft Direct. X (provides: 3 D-animation, sound, video, user-input, etc. ) • Object Oriented Programming (OOP) Framework – Active. X / OLE

Key Environment Features • Accelerated-time simulation • Alter model/controller: – structure – parameters (on-the-fly) • Advanced visualization: – real-time graphics – visual indicators/aids – 3 D animation models • Direct user input via joystick, mouse, etc. • Integration with MATLAB and Simulink

Contributions of Work System-specific interactive Mo. SART environments High performance: Windows/ C++ Advanced visualization tools: Direct-3 D Extensible: integration with MATLAB User friendly

Flexible Inverted Pendulum (FIP) System 2 lh kt b 2 1 b 1 m 2 m 1 l 2 l 1 f in d mc bc xc

Controls and Outputs Inputs, up Outputs, yp x = Cart Position (m) 1= Link 1 Angle (rad) xp

States, xp

FIP Linear Model

FIP Linear Model

Plant Analysis Unstable pole

Control Laws Classical Pole Placement LQG/LTR H (1) H (2)

About the Program MATLAB Engine Direct-3 D v 3. 0 v 5. 0 Visual C++/ MFC Windows ’ 95/’ 98/NT Pentium PC System Requirements: Pentium PC running Windows 95/NT. 32 MB RAM. Direct-3 D 3. 0. Recommended: Pentium II 266 w/ MMX running Windows NT 4. 0. 64 MB RAM. Direct-3 D 3. 0.

Interactive Mo. SART Environment Modules Interactive Environment Application Program User Interface (PUI) Simulation Module (SIM) Graphical Animation Module (GAM) Help/Instruct Module (HIM) Communication Module (COM) Physical System Simulink MATLAB Other Applications Active. X Internet

Program User Interface User Friendly Windows ’ 95/NT Interface • Menus • Multiple windows • Program control toolbars Interactive System Diagram • Block diagram representation of system • Point-and-click access UI) (P

Simulation Module Numerical Simulation IM) (S • Fast compiled C++: >3000 Hz / 266 MHz PII • Better than real-time simulation On-the-Fly Parameter Editing • Plant models • Controller parameters • Reference Commands, Disturbances, Noise, etc. • Integration methods: Euler, Runge-Kutta 4, etc. Extensibility

Graphical Animation Module 3 D Animation M) (GA • Direct-3 D • Texture-mapped, light-shaded polygons • Wireframe copters from previous simulations (SMAC) Visualization Tools & Indicators • Real-Time Variable Display Window • 2 D Animation Window: pitch indicator • Real-time multiple-graph plotting Extensibility

Help-Instruct Module On-line Help • Instructions on using the environment • Program reference HTML / PDF Documents • Model documentation/ references • Interactive tutorials IM) (H

Mo. SART Flexible Inverted Pendulum (FIP) Environment 3 -D Animation Window Toolbar and Menu Initial Conditions Menu System Block Diagram Cart Position Link 1 Angle Link 1 Angle Cart Velocity Link 1 Angular Vel. Simulation Parameters Variables Window 0. 3450 -0. 2390 0. 3654 0. 6288 0. 0234 3. 8054 Real Time Plots

Utility of the Environment Plant modal analysis Plant flexibility analysis H Controller design Comparison of controllers

Modal Analysis Flexible Mode Toppling Unstable Mode Link Damping Mode

Visualization of Flexible Mode Selecting To Work Open-Loop, No Controller, No Input Visual animation of The Flexible Mode Cart Position Link 1 Angle Link 1 Angle Cart Velocity Link 1 Angular Vel. Plotting Cart Position and Link 1 and Link 2 Angles 0. 3450 -0. 2390 0. 3654 0. 6288 0. 0234 3. 8054 Variable Values

Plant Rigidity Analysis m kt lh 1 l b 1 x fin M Rigid Inverted Pendulum d 2 m 2 l 2 b 2 l 1 m 1 xc mc bc Flexible Inverted Pendulum

Rigidity Analysis: Pole Locations Varying b 2 and kt As b 2 Increases, Flexible Mode Damping Increases As kt Increases, Natural Bending Frequency Increases

Rigidity Analysis: Rigid Inverted Pendulum Linear Model Inputs, up Outputs, yp States, xp = Link angle (rad) d = Link angular velocity (rad/sec) x = Cart position (m) dx = Cart speed (m/sec) = Link Angle (rad) x = Cart Position (m) m l x s=0, 0, fin M

Rigidity Analysis: Transfer function comparison: Rigid vs Flexible Pendulums Flexible Inverted Pendulum Plant Rigid Inverted Pendulum Plant Low Frequency Poles of Both Systems Are the Same High Frequency Peak Due to the Imaginary Poles

H Controller design di r e K u Controller do y P Plant n • 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 w 1 w 2

No Steady State Error Fast Response H Design Sensitivity Good Low Frequency Command Following 2 Small Oscillations 1 Small Overshoot Small Control Force Complementary Sensitivity

Controller Comparison Classical LQG/LTR Pole Placement H (design 1) H (design 2) Command Following (Cart Position) for a Unit Step Input

Command Following (Link 1 Angle) for a Unit Step Input Controller Comparison Sensitivity Transfer Functions (S) Control Force Complementary Sensitivity Transfer Functions (T)

Controller Comparison: Robustness to Flexibility Uncertainty. Varying kt a Little Would Result in an Unstable Closed Loop System, for the H Controller kt kt

Controller Comparison: Robustness to Flexibility Uncertainty. Varying b 2 When Using H (2) Controller, b 2 Can Be Increased 3000% From Its Nominal Value Before Getting The System Unstable b 2 b 2

Simulation of Closed-Loop System Response for a Step Command Input (LQG/LTR Controller) Closing the Loop and Selecting the LQG/LTR Controller Selecting a Unit Step Command Input to The System The Mo. SART FIP Environment Plots Agree With The MATLAB Plots

Controller Comparison

Summary • Versatile system-specific interactive Mo. SART 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

Future Directions -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 Active. X Compatible -Integrated design & analysis environment -Develop Additional Environments … development of VISIT: Facility http: //www. eas. asu. edu/~aar/research/mosart/Presentations/