MESA Lab

Two Interesting Papers Introductionat ICFDA 2014

Xiaobao JiaMESA (Mechatronics, Embedded Systems and Automation)Lab

School of Engineering,University of California, Merced

E: xjia3@ucmerced.edu Phone: 13925273161Lab: CAS Eng 820 (T: 228-4398)

Jun. 30, 2014. Monday 4:00-6:00 PMApplied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

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1. Hybrid Systems and Control With Fractional

Dynamics (I): Modeling and Analysis

2. Hybrid Systems and Control With Fractional

Dynamics (II): Control

Two papers

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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

Outline

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1. Hybrid Systems ConceptionA 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.

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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 thatregulates 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.

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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.

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3. Fractional-order Switching SystemSwitching 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:

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3. Fractional-order Switching Systema first-order system with two different dynamics Function

fractional-order PI controllers

the closed-loop transfer function of the system

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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:

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4. Fractional-order Reset Control SystemsThe dynamics of the reset controller FDI equation

The linear controller C(s) state space representations

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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:

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5. Stability of Fractional-Order Hybrid Systems

the stability of fractional-order switching systems by common Lyapunov functions and its equivalence in frequency domain.

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5. Stability of Fractional-Order Hybrid Systems

Example:

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5. Stability of Fractional-Order Hybrid Systems

Example:

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6. Robust Fractional-Order Control of Switching System

A scheme of the strategy is shown in Fig. 1 for a generalsystem with subsystems Gi(s), with i = 1;2; :::;L subsystems.

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Controller Type:

6. Robust Fractional-Order Control of Switching System

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Example:

6. Robust Fractional-Order Control of Switching System

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Result:

6. Robust Fractional-Order Control of Switching System

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Result:

6. Robust Fractional-Order Control of Switching System

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7 Summa

Additional flexibility to the Hybrid system

More stability to the Hybrid system

Strong robustness to the Hybrid system

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Thank You!

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