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Outline Motivation Chaos and Synchronization Goals

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0 Microcontroller-based Data Acquisition/Control Applications and Synchronization of Sampled-data Chaotic Systems Sang-Hoon Lee Department of Mechanical and Aerospace Engineering Polytechnic University, Brooklyn, NY 11201

1 Outline Motivation Chaos and Synchronization Goals
Prior research Hardware components Software components Coupled two-tank system System model & ID Proposed research—I Chaos and Synchronization Motivation and goals Master-slave synchronization Problem formulation Control design objective Chua’s system Experimental setup Proposed research—II

2 Motivation PC-based data acquisition and control (DAC) boards
High-end DAC boards (e.g., Quanser and National Instruments) Advanced hardware capabilities and sophisticated software environment Drawback: cost! (hundreds to few thousand dollars) DAC boards supported by MATLAB Costly and usually include additional hardware features that may not be fully used (e.g., high sampling rates and high resolution analog to digital converter) Low-end DAC boards Relatively low cost Drawback: use proprietary software Graphical User Interface (GUI) capabilities are nonexistent for microcontrollers Microcontrollers are not designed to directly interact with human beings Microcontrollers are directly embedded into automated products/processes

3 Goals Develop a low-cost MATLAB-based DAC systems by exploiting
Microcontrollers MATLAB Simulink (Dials and Gauges Blockset) Serial communication capabilities of MATLAB and microcontrollers The GUIs which will be designed using our framework allow the user to Vary control commands Acquire sensory data Perform data processing Visualize and control data using realistic looking virtual instruments Use the MATLAB DAC toolbox to facilitate Automatic generation of proper program codes for a variety of sensors and actuators Automatic programming of the microcontrollers Data communication between the microcontrollers and MATLAB

4 Prior Research BASIC Stamp 2 (BS2) microcontroller to LabVIEW interface by Radcliffe, 2001 An approach to endow BS2 microcontroller with GUI capabilities by interfacing it with MATLAB by Li, Harari, Wong, and Kapila, 2004

5 Hardware Components–PIC
Microcontrollers are designed to interface to and interact with electrical/electronic devices, sensors and actuators, and high-tech gadgets to automate systems Directly embedded into the product or process for automated decision making Do not have GUI capabilities that are common in many PC applications Peripheral Interface Controllers (PICs) Inexpensive microcontroller units (few dollars) that include Central processing unit Peripherals: memory, timers, and I/O functions PIC Assembly language 35 single-word instruction set Various selection

6 Hardware Components–BS2
BS2 Microcontroller is a 24-pin DIP IC based on Microchip Inc.’s PIC 16C57 microcontroller 32 bytes of RAM and 2 kilobytes of EEPROM of memory 16 general-purpose digital input/output (I/O) pins that are user defined BS2 processing speed is approximately 4000 instructions/sec Board of Education (BOE) is a carrier board interfacing BS2 to additional hardware Provides DB9 connector for BS2 Provides connectivity to BS2’s general purpose I/O pins BS2 installed on BOE transmits/receives data to/from the PC via serial communication BS2 Board of Education

7 Hardware Components–Serial Communication
BS2 and PC communicate through a RS-232 serial communication link Allows user program to be sent to the BS2 Allows data exchange between BS2 and PC BS2 maximum data exchange rate (Baud rate): 9600 kilobytes per second PC identifies serial ports as COM ports Pin assignments for a DB-9 serial cable A DB-9 serial cable facilitates data communication between BS2 and PC Pin # Label Signal Name Signal Type 1 CD Carrier detect Control 2 RD Received data Data 3 TD Transmitted data 4 DTR Data terminal ready 5 GND Signal ground Ground 6 DSR Data set ready 7 RTS Request to send 8 CTS Clear to send 9 RI Ring indicator Male DB-9 Connector

8 Software Components–PIC Assembly and PBASIC
PIC assembly language is a primitive programming language consisting of a 35 single- word instruction set Parallax Beginner's all-purpose symbolic instruction code (PBASIC) is a high level programming language similar to BASIC PBasic includes many of the same functions found in BASIC, plus microcontroller specific functions (e.g., serial communication, PWM, I/O pin monitoring/ control, etc.) Key benefits of utilizing PBASIC as a microcontroller programming language: Simple, high-level programming language to implement and debug microcontroller programs Intuitive commands used for interacting with BS2 hardware

9 Software Components–MATLAB
MATLAB is an interactive technical computing software MATLAB versions 6.1 and higher support serial communication Custom designed m-file functions provide serial communication functionality

10 Software Components–Simulink
Simulink is a model-based, system-level, visual programming environment Used to simulate and analyze dynamic systems using icon-based tools User can design Simulink diagrams by: Dragging and dropping Simulink blocks into a Simulink diagram Connecting I/O ports of Simulink blocks Changing Simulink block parameters

11 Software Components–Dials and Gauges Blockset
Dials and Gauges Blockset provides a library of Simulink blocks that are in the form of visual, realistic-looking, virtual instruments Transforms Simulink block diagrams into virtual control panels Small subset of Dials and Gauges blocks

12 Coupled Two-Tank System
Two-tank system consists of: Two liquid level tanks with orifices Liquid level sensors at the bottom of each tank Voltage controlled pump Liquid basin Pump provides the liquid infeed into Tank 1 Outflow of Tank 1 becomes the liquid infeed to Tank 2 Outflow of Tank 2 is emptied into the liquid basin Two tanks have the same diameters and can be fitted with differing diameter outflow orifices

13 Coupled Two-Tank System Model

14 System Identification
Provide a fixed pump voltage to allow for steady state conditions to occur Obtain system parameter ratios A/B and C/D Fill Tank 1 with a fixed amount of water and let it drain out to Tank 2 Compute the system parameters A and B using the transient response data Fill Tank 2 with a fixed amount of water and let it drain out to the basin Compute the system parameters C and D using the transient response data

15 Proposed Research—I Develop MATLAB and Simulink-based DAC toolbox by
Using BS2 and PIC microcontrollers Utilizing MATLAB, Simulink, and Dials/Gauges Blockset Exploiting the serial communication functionality of MATLAB and the microcontrollers Develop user-defined microcontroller libraries that allow The generation of proper microcontroller codes for a variety of sensors and actuators Programming of the microcontroller Data communication between the microcontroller and MATLAB Develop an experimental setup to show the effectiveness of our MATLAB-based GUI environment by performing liquid-level control of a coupled, two-tank system and Design a classical PI controller for the system Determine the system parameters by an experimental system identification study

16 Chaos Mostly described as a deterministic system that exhibits aperiodic behavior depending on the initial conditions

17 but for a proper parameter choice
Synchronization “Two oscillators” with a coupling may give rise to chaos but for a proper parameter choice they may synchronize School of fish Flock of birds Team of robots

18 Motivation Synchronization of chaotic oscillators: Secure communication systems Use chaos to mask a transmitted signal Recover the signal securely in reception using chaos synchronization Sampled-data: improve robustness of secure communication Noise corruption in analog signal transmission is a severe drawback Pulse synchronization: particularly more realistic for real communication systems Reduce power load Reduce time delay Sampled-data: design of robust and effective cooperative control algorithms for spatially distributed robots

19 Goals Design a periodic state feedback control law for global pulse synchronization of sampled-data chaotic system Perform experimental validation of a sampled-data representation of Chua's oscillators implemented using microcontrollers and RF communication

20 Master-Slave Synchronization—C.T. Case
+ - Slave Vast literature! Synchronization Assumption: nonlinear vector function g(·) satisfies where

21 Master-Slave Synchronization—Sampled-data Case
Euler approximation of continuous-time master and slave systems Let u(t)=0, no loss of generality, and let h be the step-size for Euler approximation Master system Slave system using unidirectional coupling where , 1 2 p-1 p p+1 Pulse synchronization Pulse control: K(k) is a periodic gain matrix

22 Problem Formulation where we have used , Design control gains so that
Error system formulation Error system for pulse synchronization where we have used ,

23 Control Design Objective
Sampled-data master-slave system need to be asymptotically synchronized for arbitrary initial conditions Error system dynamics need to asymptotically converge to zero for arbitrary initial conditions

24 Illustrative Example: Chua’s Circuit
State-space model:

25 Chua’s System—Sampled Data Representation
Parameters of sample-data master Chua’s circuit and nonlinear function Plots of double scroll attractors of the sample-data master Chua’s circuit

26 Experimental Setup Propeller demoboard 32-bit processor
912MHz RF transciever

27 Proposed Research—II Develop a state feedback controller for the pulse synchronization of a master-slave chaotic system in the sampled-data setting Use the Euler approximation technique to discretize the system Formulate the problem of global asymptotic synchronization of the system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions Use a discrete-time Lyapunov stability theory Use a linear matrix inequality Develop an experimental setup to validate our research by performing Synchronization of a sampled-data master-slave chaotic system based on Chua's circuit Using Propeller microcontroller RF wireless communication

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