Transcript Fractional Order Motion Control - The MESA Lab

MESA Lab
Two Interesting Papers Introduction
at ICFDA 2014
Xiaobao Jia
MESA (Mechatronics, Embedded Systems and Automation)Lab
School of Engineering,
University of California, Merced
E: [email protected] Phone: 13925273161
Lab: CAS Eng 820 (T: 228-4398)
Jun. 30, 2014. Monday 4:00-6:00 PM
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Two papers
1. Hybrid Systems and Control With Fractional
Dynamics (I): Modeling and Analysis
2. Hybrid Systems and Control With Fractional
Dynamics (II): Control
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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
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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.
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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 that
regulates the plant in the traditional manner. At the upper layer th
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 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:
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3. Fractional-order Switching System
a 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 Systems
The 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 general
system with subsystems Gi(s), with i = 1;2; :::;L subsystems.
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6. Robust Fractional-Order Control of Switching
System
Controller Type:
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6. Robust Fractional-Order Control of Switching
Example:
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System
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6. Robust Fractional-Order Control of Switching
Result:
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System
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6. Robust Fractional-Order Control of Switching
Result:
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System
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7 Summa
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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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