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Two Interesting Papers Introduction at ICFDA 2014

Two Interesting Papers Introduction at ICFDA 2014. Xiaobao Jia MESA (Mechatronics, Embedded Systems and Automation) Lab School of Engineering, University of California, Merced E : xjia3@ucmerced.edu Phone: 13925273161 Lab : CAS Eng 820 ( T : 228-4398). Jun. 30 , 2014. Monday 4:00-6:00 PM

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Two Interesting Papers Introduction at ICFDA 2014

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  1. Two Interesting Papers Introductionat ICFDA 2014 Xiaobao Jia MESA (Mechatronics, Embedded Systems and Automation)Lab School of Engineering, University of California, Merced E: xjia3@ucmerced.edu Phone: 13925273161 Lab: CAS Eng 820 (T: 228-4398) Jun. 30, 2014. Monday 4:00-6:00 PM Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

  2. Slide-2/1024 Two papers 1. Hybrid Systems and Control With Fractional Dynamics (I): Modeling and Analysis 2. Hybrid Systems and Control With Fractional Dynamics (II): Control AFC Workshop Series @ MESALAB @ UCMerced

  3. Slide-3/1024 Outline 1. Hybrid Systems Conception 2. Hybrid Systems layers 3. Fractional-order Switching System 4. Fractional-order reset control systems 5. Stability of Fractional-Order Hybrid Systems 6. Robust Fractional-Order Control of Switching System 7. Summa AFC Workshop Series @ MESALAB @ UCMerced

  4. Slide-4/1024 1. Hybrid Systems Conception A hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior – a system that can both flow and jump. Often, the term "hybrid dynamic system" is used, to distinguish over hybrid systems such as those that combine neural nets and fuzzy logic, or electrical and mechanical drivelines. AFC Workshop Series @ MESALAB @ UCMerced

  5. Slide-5/1024 2. Hybrid Systems layers The control of a continuous state dynamical plant is often divided into two layers. At the lower or servo layer is a controller that regulates the plant in the traditional manner. At the upper layer the supervisor issues symbolic commands. Some time after a command is issued the supervisor receives a symbolic response indicating either that the command has been executed or that an error condition occurred. AFC Workshop Series @ MESALAB @ UCMerced

  6. Slide-6/1024 2. Hybrid Systems layers Mathematically, the servo layer and plant are modeled together as a differential equation evolving in real time. The supervisor, however, views the lower layer as a discrete event system whose behavior is described by sequences of events that unfold in logical time. AFC Workshop Series @ MESALAB @ UCMerced

  7. Slide-7/1024 3. Fractional-orderSwitching System Switching system is a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching among them. A general formulation of the switching systems with fractional-order is: AFC Workshop Series @ MESALAB @ UCMerced

  8. Slide-8/1024 3. Fractional-orderSwitching System a first-order system with two different dynamics Function fractional-order PI controllers the closed-loop transfer function of the system AFC Workshop Series @ MESALAB @ UCMerced

  9. Slide-9/1024 4. Fractional-order Reset Control Systems Reset controllers are linear controllers that reset some of their states to zero when their input is zero. A general Block diagram of a reset control is: AFC Workshop Series @ MESALAB @ UCMerced

  10. Slide-10/1024 4. Fractional-order Reset Control Systems The dynamics of the reset controller FDI equation The linear controller C(s) state space representations AFC Workshop Series @ MESALAB @ UCMerced

  11. Slide-11/1024 4. Fractional-order Reset Control Systems The plant P(s) state space representations The closed-loop reset control system can be then described by the following FDI as follows: AFC Workshop Series @ MESALAB @ UCMerced

  12. Slide-12/1024 5. Stability of Fractional-Order Hybrid Systems the stability of fractional-order switching systems by common Lyapunov functions and its equivalence in frequency domain. AFC Workshop Series @ MESALAB @ UCMerced

  13. Slide-13/1024 5. Stability of Fractional-Order Hybrid Systems Example: AFC Workshop Series @ MESALAB @ UCMerced

  14. Slide-14/1024 5. Stability of Fractional-Order Hybrid Systems Example: AFC Workshop Series @ MESALAB @ UCMerced

  15. Slide-15/1024 6. Robust Fractional-Order Control of Switching System A scheme of the strategy is shown in Fig. 1 for a general system with subsystems Gi(s), with i = 1;2; :::;L subsystems. AFC Workshop Series @ MESALAB @ UCMerced

  16. Slide-16/1024 6. Robust Fractional-Order Control of Switching System Controller Type: AFC Workshop Series @ MESALAB @ UCMerced

  17. Slide-17/1024 6. Robust Fractional-Order Control of Switching System Example: AFC Workshop Series @ MESALAB @ UCMerced

  18. Slide-18/1024 6. Robust Fractional-Order Control of Switching System Result: AFC Workshop Series @ MESALAB @ UCMerced

  19. Slide-19/1024 6. Robust Fractional-Order Control of Switching System Result: AFC Workshop Series @ MESALAB @ UCMerced

  20. Slide-20/1024 7 Summa • Additional flexibility to the Hybrid system • More stability to the Hybrid system • Strong robustness to the Hybrid system AFC Workshop Series @ MESALAB @ UCMerced

  21. Slide-21/1024 Thank You! AFC Workshop Series @ MESALAB @ UCMerced

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