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  1. Ubiquitous Fractional Order Controls? YangQuan Chen Center for Self-Organizing and Intelligent Systems (CSOIS), Dept. of Electrical and Computer Engineering Utah State University E: yqchen@ieee.org; T: 1(435)797-0148; F: 1(435)797-3054 W: http://mechatronics.ece.usu.edu/foc/ 14:30-15:30, July 21, 2006,Auditório E 2nd IFAC Workshop on Fractional Differentiation and its Applications (IFAC FDA’06), July 19-21, 2006, Porto, Portugal.

  2. Outline • Introduction - CSOIS and Research Strength • Fractional Order Control – Better? • Fractional Order Systems Control – Ubiquitous? • Concluding Remarks Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  3. Utah State University Located in Logan, Utah, USA 80 miles North of Salt Lake City 22,000 students study at USU’s Logan campus, nestled in the Rocky Mountains of the inter-mountain west CSOIS is a research center in the Department of Electrical and Computer Engineering Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  4. Outline • Introduction - CSOIS and Research Strength • Fractional Order Control – Better? • Fractional Order Systems Control – Ubiquitous? • Concluding Remarks Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  5. CSOIS research impacts (1998-2004) • Educational • 2 PhD graduated with 2 others expected this year • 38 MS and ME students graduated • Numerous ECE and MAE Senior Design Projects • Scholarly • Five faculty collaborating between three different departments • Four books • Over 100 refereed journal and conference publications • 18 visiting research scholars from 7 countries (3 month to 1 year visits) • Economic • 14 full-time staff employed (average of 7 FTE per year) • 8 PhD students employed • 64 MS and ME students employed • 31 Undergraduate students employed • 12 Other staff employed • A payroll of over $5 million in salaries paid to students, faculty, and staff • Purchases of over $1.5M in the U.S. economy Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  6. CSRA Research:Center for Self-Organizing and Intelligent Systems • CSOIS is a research center in USU’s Department of Electrical and Computer Engineering that coordinates most CSRA (Control Systems, Robotics and Automation) research • Officially Organized 1992 - Funded for 7 (seven) years by the State of Utah’s Center of Excellence Program (COEP) • Horizontally-Integrated (multi-disciplinary) • Electrical and Computer Engineering (Home dept.) • Mechanical Engineering • Computer Science • Vertically-integrated staff (20-40) of faculty, postdocs, engineers, grad students and undergrads • Average over $2.0M in funding per year since 1998 • Three spin-off companies since 1994. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  7. CSOIS Core Capabilitiesand Expertise • Control System Engineering • Algorithms (Intelligent Control) • Actuators and Sensors • Hardware and Software Implementation • Intelligent Planning and Optimization • Real-Time Programming • Electronics Design and Implementation • Mechanical Engineering Design and Implementation • System Integration We make real systems that WORK! Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  8. CSOIS Projects • Since 1992: Approximately • 15 automation and control projects • 15 robotics/autonomous vehicle projects • Funding from both private industry and government • Current focus on vehicle automation and robotics • Major US Army Tank-Automotive Command (TACOM) program, 1998-present Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  9. CSRA/CSOIS Courses • Undergraduate Courses • MAE3340 (Instrumentation, Measurements); ECE3620/40 (Laplace, Fourier) • MAE5310/ECE4310 Control I (classical, state space, continuous time) • MAE5620 Manufacturing Automation • ECE/MAE5320 Mechatronics (4cr, lab intensive) • ECE/MAE5330 Mobile Robots (4cr, lab intensive) • Basic Graduate Courses • MAE/ECE6340 Spacecraft attitude control • ECE/MAE6320 Linear multivariable control • ECE/MAE6350 Robotics • Advanced Graduate Courses • ECE/MAE7330 Nonlinear and Adaptive control • ECE/MAE7350 Intelligent Control Systems • ECE/MAE7360 Robust and Optimal Control <<== FOC • ECE/MAE7750 Distributed Control Systems <<== FOC Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  10. CSOIS Research Strengths • ODV (omni-directional vehicle) Robotics • MAS-net (mobile actuator and sensor networks) • Fractional Dynamic Systems and Control • Iterative Learning Control Techniques • Smart Mechatronics, Computer Vision. • Unmanned Autonomous Vehicles (UAVs) • Formation Control and Information Consensus Building Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  11. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  12. USU ODV Technology • USU has worked on a mobility capability called the “smart wheel” • Each “smart wheel” has two or three independent degrees of freedom: • Drive • Steering (infinite rotation) • Height • Multiple smart wheels on a chassis creates a “nearly-holonomic” or omni-directional (ODV) vehicle Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  13. T1 Omni Directional Vehicle (ODV) Mobility enhancements achieved by ODV design Maneuverability of the ODV design concept Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  14. ODIS On Duty in Baghdad “Putting Robots in Harm’s Way, So People Aren’t” Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  15. Ten ODIS Manufactured “Putting Robots in Harm’s Way, So People Aren’t” Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  16. ODIS On Duty in Baghdad “Putting Robots in Harm’s Way, So People Aren’t” Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  17. CSOIS Research Strengths • ODV (omni-directional vehicle) Robotics • MAS-net (mobile actuator and sensor networks) • Fractional Dynamic Systems and Control • Iterative Learning Control Techniques • Smart Mechatronics, Computer Vision. • Unmanned Autonomous Vehicles (UAVs) • Formation Control and Information Consensus Building Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  18. Outline • Introduction - CSOIS and Research Strength • Fractional Order Control – Better? • Fractional order calculus, systems, controls • Example-1: FO PID • Example-2: FO Boundary Control • Fractional Order System Controls – Ubiquitous? • Concluding Remarks Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  19. What Is Non-Integer Order Calculus? • “In-between” thinking, e.g., • Between integers there are non-integers; • Between logic 0 and logic 1, there is the fuzzy logic; • Between integer order splines, there are “fractional order splines” • Between integer high order moments, there are noninteger order moments • Between “integer dimensions”, there are fractal dimensions • Fractional Fourier transform (FrFT) • Non-Integer order calculus (fractional order calculus – abuse of terminology.) (FOC) Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  20. Slide credit: Igor Podlubny Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  21. Slide credit: Igor Podlubny Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  22. Slide credit: Igor Podlubny Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  23. Why and How and When • Why – Many reasons. Dynamic systems modeling and controlsHow – Analog versus digital realization methods. Many.When – Now. Ubiquitous. Take a try since we have the new tool. Slide credit: Igor Podlubny Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  24. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  25. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  26. FO Controller + IO Plant Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  27. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  28. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  29. Fractional order PID control (Ubiquitous) • 90% are PI/PID type in industry. Igor Podlubny. “Fractional-order systems and PIlDµ-controllers”. IEEE Trans. Automatic Control,44(1): 208–214, 1999. YangQuan Chen, Dingyu Xue, and Huifang Dou. "Fractional Calculus and Biomimetic Control". IEEE Int. Conf. on Robotics and Biomimetics (RoBio04), August 22-25, 2004, Shengyang, China. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  30. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  31. Fractional Order Controls • IO Controller + IO Plant • FO Controller + IO Plant (Example 1) • FO Controller + FO Plant (Example 2) • IO Controller + FO Plant D. Xue and Y. Chen*, “A Comparative Introduction of Four Fractional Order Controllers”. Proc. of The 4th IEEE World Congress on Intelligent Control and Automation (WCICA02), June 10-14, 2002, Shanghai, China. pp. 3228-3235. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  32. Realizations: Analog I. Petras, I. Podlubny, P. O’Leary, L. Dorcak, and Vinagre B. “Analogue Realization of Fractional Order Controllers”. FBERG, Technical University of Kosice, Kosice, Slovak, ISBN 8070996277 edition, 2002. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  33. Photo credit: Igor Podlubny Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  34. Realizations: CT (Oustaloup) Approx. A modified Oustaloup’s approximation method A new approximate realization method for fractional derivative in the frequency range of interest where the zeros, poles and the gain can be Dingy¨u Xue, Chunna Zhao and YangQuan Chen. “A Modified Approximation Method of Fractional Order System”. IEEE ICMA’06, Luoyang, China, pp. 1043-1048. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  35. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  36. Realizations: DT Approx. (fo_c2d.m) YangQuan Chen, Blas M. Vinagre, and IgorPodlubny. “Continued fraction expansion approaches to discretizing fractional order derivatives - an expository review”. Nonlinear Dynamics (Kluwer), 38(1-4): 155-170. Dec. 2004. Missing:Joint time-frequency domain approximation Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  37. Example-1: FO Controller + IO Plant Dingy¨u Xue, Chunna Zhao and YangQuan Chen. “Fractional Order PID Control of a DC-Motor with Elastic Shaft: A Case Study”. American Control Conference’06, Minneapolis, USA, June 13-15, 2006, pp. 3182-7. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  38. LTI state-space form of system Servomechanism System's Parameters The Benchmark Position Servo System Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  39. Best IO PID • For the optimally searched IO PID using ITAE • For the optimally searched IO PID using ISE Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  40. Best FO PID • Optimal FO PID using ITAE • Optimal FO PID using ISE Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  41. How to Decide and ? we build two tables of optimal ITAE and ISE, respectively, with respect to and which are enumerated from 0.5 to 1.5 with step of 0.1 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  42. Which N Is Good Enough? Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  43. Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  44. Robustness Against Load Variations Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  45. Best IO PI • The optimal IO PI using ITAE • The optimal IO PI using ISE Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  46. Decide Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  47. Best FO PI • Optimal FO PI using ITAE • Optimal FO PI using ISE Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  48. Robustness Against Load Variations Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  49. Robustness to Mechanical Nonlinearities A: Using square wave as the reference input signal (period T=40 sec.) and adding Coulomb friction 0.1 Plenary Lecture #5. IFAC FDA'06, Porto, Portugal

  50. B: with the deadband width of 0.5 Robustness to Mechanical Nonlinearities Plenary Lecture #5. IFAC FDA'06, Porto, Portugal