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