Microcontroller-based Data Acquisition/Control Applications and

Synchronization of Sampled-data Chaotic Systems

Sang-Hoon LeeDepartment of Mechanical and Aerospace Engineering

Polytechnic University, Brooklyn, NY 11201

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• Motivation

• Goals

• Prior research

• Hardware components

• Software components

• Coupled two-tank system

• System model & ID

• Proposed research—I

Outline

• Chaos and Synchronization

• Motivation and goals

• Master-slave synchronization

• Problem formulation

• Control design objective

• Chua’s system

• Experimental setup

• Proposed research—II

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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 sampli

ng 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

Motivation

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• 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

Goals

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• 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

Prior Research

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• 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

Hardware Components–PIC

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• 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

Board of Education

Hardware Components–BS2

BS2

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• 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

Pin # Label Signal Name Signal Type

1 CD Carrier detect Control

2 RD Received data Data

3 TD Transmitted data Data

4 DTR Data terminal ready Control

5 GND Signal ground Ground

6 DSR Data set ready Control

7 RTS Request to send Control

8 CTS Clear to send Control

9 RI Ring indicator Control

1

9876

5432

Male DB-9 Connector

• A DB-9 serial cable facilitates data

communication between BS2 and PC

Hardware Components–Serial Communication

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• 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

Software Components–PIC Assembly and PBASIC

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• 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

Software Components–MATLAB

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• 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

Software Components–Simulink

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• 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

Software Components–Dials and Gauges Blockset

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• 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

Coupled Two-Tank System

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Coupled Two-Tank System Model

)()()( 11 tBVtLAtL p

)()()( 212 tLDtLCtL

parameters system - ,,, DCBA

2 and 1 tank of levels liquid - , 21 LL

voltagepump - pV

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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

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• 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 GU

I 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

Proposed Research—I

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• Mostly described as a deterministic system that exhibits aperiodic behavior depe

nding on the initial conditions

Chaos

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“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

Synchronization

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• 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

Motivation

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• 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

Goals

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• Assumption: nonlinear vector function g(·) satisfies

where

Master

+-

Slave

( )x t

( )u t

( )x t( )Ke t

( )e t

KVast literature!

lim ( ) ( )tx t x t

Synchronization

Master-Slave Synchronization—C.T. Case

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• 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 ,

• Pulse synchronization

– Pulse control: K(k) is a periodic gain matrix

0

…1 2 p-1 p p+1

Master-Slave Synchronization—Sampled-data Case

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• Design control gains so that

• Error system for pulse synchronization

• Error system formulation

where we have used

,

Problem Formulation

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• 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

Control Design Objective

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1 1 2 1

2 1 2 3

3 2

( ( ))x x x f x

x x x x

x x

State-space model:

22 2

1

,C C R

C L

Illustrative Example: Chua’s Circuit

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• Plots of double scroll attractors of the sample-data master Chua’s circuit

• Parameters of sample-data master Chua’s circuit and nonlinear function

Chua’s System—Sampled Data Representation

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Propeller demoboard

32-bit processor

912MHz RF transciever

Experimental Setup

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• Develop a state feedback controller for the pulse synchronization of a master-slave ch

aotic 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 in

itial conditions

– Use a discrete-time Lyapunov stability theory

– Use a linear matrix inequality

• Develop an experimental setup to validate our research by performing Synchronizatio

n of a sampled-data master-slave chaotic system based on Chua's circuit

– Using Propeller microcontroller

– RF wireless communication

Proposed Research—II