Microcontroller-based Data Acquisition/Control Applications and Synchronization of Sampled-data Chaotic Systems

1. 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

2. 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

3. 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 Motivation

4. 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

5. 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

6. 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 Hardware Components–PIC 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

7. 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 Board of Education BS2

8. 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 Male DB-9 Connector

9. 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

10. 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

11. 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

12. 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

13. 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

14. Coupled Two-Tank System Model

15. 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

16. 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

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

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

19. 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

20. 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

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

22. … 0 1 p+1 2 p p-1 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 , • Pulse synchronization • Pulse control: K(k) is a periodic gain matrix

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

24. 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

25. Illustrative Example: Chua’s Circuit State-space model:

26. 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

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

28. 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