Daniel M. Lofaro, Tony Truong Giang Le, Dr. Paul Oh Presented By Daniel M. Lofaro

Transcription

1 Daniel M. Lofaro, Tony Truong Giang Le, Dr. Paul Oh Presented By Daniel M. Lofaro

2 Overview Getting people excited about controls Attract new talent to the field Retain students 2

3 Overview Issues with Control Systems Courses Fear of too much math Lack of accessible hands on learning Teaching techniques antiquated 3

4 Proposed Class Real World Design Required task Required performance Budget Real World (Pre-existing) Tools CAD Control/Simulation Software Hardware Control System Low Cost Small Modifiable 4

5 Quanser Control Solutions The Good Accurate Well Designed Compatible with Matlab, Simulink and LabVIEW The Bad Large Expensive Black Box Un-Modifiable 5

6 Modifiable Control System (Lego NXT) The Good Inexpensive (Commercial Product) Powerful Arm7 Processor Compatible with Matlab, Simulink and LabVIEW Small Reconfigurable Open Source The Bad Not as accurate as Quanser 6

7 Class Outline Hardware design (Lego (MLCAD) Itemized Software parts tutorial list Virtual Sensor Reality integration Model Virtual Reality model Design Simulation Dynamic model Control theory MATLAB Simulink Construction Programming (Simulink LEGO ECRobot) [1] LEGO MINDSTORMS MINDSTORMS NXT NXT Prototype and Experimentation Experimentation 7

8 Class WILL Work If: Pre-Existing Tools Exist Lego CAD ECRobot MATLAB/Simulink Reconfigurable Platform Exits Lego NXT Kit IF ANY DOES NOT EXIST WILL NOT WORK 8

9 9

10 Case Study Objective Make a two (2) wheeled balancing robot Minimum forward speed 0.1m/s Minimum turning speed π/4 rad/sec Minimum floor angle ±15 o Segway [7] 10

11 Case Study: Design 11

12 Case Study: Simulation and Test PID Balance Control Minimizes angular pitch rate Gains manually tuned to balance, peak between ±15º & 2 sec. settling time Difficult to tune Moving average to smooth calculation Pitch Angle, θ p [deg] Simulation Experimental Time [sec] 12

13 Case Study: Simulation and Test State Variable Feedback State feedback control using linear quadratic regulator Weight matrices Q & R are manually tuned Emphasis on wheel angle and pitch angle Pitch Angle, θ p [deg] Simulation Experimental Time [sec] 13

14 Case Study: Simulation and Test 14

15 Recap Class Designed to be Fun Interactive Educational Uses Pre-Existing Tools Lego NXT Lego CAD MATLAB/Simulink Use Reconfigurable Small Low Cost Used for Multiple Design Problems 15

16 References 1. Yamamoto, Yorihisa: NXTway-GS Model-Based Design Control of selfbalancing two-wheeled robot built with LEGO Mindstorm NXT. First Edition, 29 February Nise, Norman S.: Control Systems Engineering Fourth Edition. John Wiley and Sons INC, Lofaro, Daniel M.: Control Design to Reduce the Effects of Torsional Resonance in Coupled Systems. Master s Thesis, Drexel University Department of Electrical and Computer Engineering, May Kwatny, Harry G. Blankenship Gilmer L. Nonlinear Control and Analytical Mechanics A Computational Approach. Birkhauser, Boston Erkkinen, Tom: Embedded Coder Robot NXT Demo. Updated 18 December Yamamoto, Yorihisa: NXTway-GS Model-Based Design Control of self-balancing two-wheeled robot built with LEGO Mindstorm NXT. First Edition, 29 February Le, Tony: NXT-WhIP: NXT Wheeled Inverted Pendulum. Master s Thesis, Drexel University Department of Electrical and Computer Engineering, May Greenwood, Donald T.: Principles Of Dynamics Second Edition. Prentice Hall, Upper Saddle River, New Jersey Le Tony, Oh Paul: IDETC Presentation: System Integration Case Study: NXT-WhIP NXT Wheeled Inverted Pendulum. New York City, NY,

17 17

18 Motor Controller Motor Controller Friction Compensator Rotation, k δ Wheel sync, k sync Motor velocity, k ϕ Worked to balance, rotate, and keep wheels synchronized 18

19 Motor Model Motors represented as rigid body Electrical & mechanical constants determined by Hurbain & Watanabe trusted and validated 19

20 Prototype and Simulation MathWorks MATLAB Simulink ECRobot NXT 20

21 21