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- •1. TABLE OF CONTENTS
- •2. OVERVIEW
- •3. PROCESS CONTROL
- •3.1 INTRODUCTION
- •3.2 CONTROL SYSTEM CHARACTERISTICS
- •3.3 CONTROLLER TYPES
- •3.4 PROCESS DIAGRAMS AND SYMBOLS
- •3.5 PRACTICE QUESTIONS
- •4. DISCRETE CONTROLLER DESIGN
- •4.1 POSITIONING CONTROLLERS
- •4.1.1 Dead Beat Control
- •4.1.2 Programming Examples
- •4.1.2.1 - BASIC
- •4.1.2.3 - Pascal
- •4.1.2.4 - 6811 Assembler
- •4.1.3 First Order Response
- •4.2 TRACKING
- •4.2.1 Minimum Error
- •4.3 DISTURBANCE RESISTANT
- •4.3.1 Disturbance Minimization
- •4.4 MULTI-CONTROLLER SYSTEMS
- •4.4.1 Disturbance Feedforward
- •4.4.2 Command Feedforward
- •4.4.3 Cascade
- •4.5 SAMPLE TIME
- •4.6 SUMMARY
- •4.7 PRACTICE PROBLEMS
- •5. DISCRETE SYSTEMS
- •5.1 DISCRETE SYSTEM MODELLING WITH EQUATIONS
- •5.1.1 Getting a Discrete Equation
- •5.1.2 First Order System Example
- •5.1.3 Second Order System Example
- •5.1.4 Example of Dead (Delay) Time
- •5.2 DISCRETE CONTROLLERS
- •5.2.1 A Proportional Controller
- •5.2.2 Integral Control
- •5.2.3 Differential Control
- •5.2.4 Proportional, Integral, Derivative (PID) Control
- •5.3 BLOCK DIAGRAMS AND TRANSFER FUNCTIONS
- •5.3.1 The Backward-Shift ‘B’ Operator
- •5.3.2 Reducing Block Diagrams
- •5.3.3 Back-Shift Transform Table
- •5.3.3.1 - A Summary of Differential Equation Solutions
- •5.3.4 Stability
- •5.4 SAMPLING FUNCTIONS
- •5.5 SYSTEM RESPONSE
- •5.6 STEADY STATE ERROR
- •5.7 PRACTICE PROBLEMS
- •6. PETRI NETS
- •6.1 INTRODUCTION
- •6.2 IMPLEMENTATION FOR A PLC
- •6.3 PRACTICE PROBLEMS
- •7. CONTINUOUS CONTROL SYSTEMS
- •7.1 CONTROL SYSTEMS
- •7.1.1 PID Control Systems
- •7.1.2 Analysis of PID Controlled Systems With Laplace Transforms
- •7.1.3 Manipulating Block Diagrams
- •7.1.3.1 - Commercial PID Tuners
- •7.1.4 Finding The System Response To An Input
- •7.1.5 System Response
- •7.1.6 A Motor Control System Example
- •7.1.7 System Error
- •7.1.8 Controller Transfer Functions
- •7.2 ROOT-LOCUS PLOTS
- •7.2.1 Approximate Plotting Techniques
- •7.2.2 State Variable Control Systems
- •7.3 DESIGN OF CONTINUOUS CONTROLLERS
- •7.4 PRACTICE PROBLEMS
- •8. FUZZY LOGIC
- •8.1 COMMERCIAL CONTROLLERS
- •8.2 REFERENCES
- •8.3 PRACTICE PROBLEMS
- •9. MECHATRONICS CIRCUITS
- •9.1 POWER SWITCHING
- •9.2 USER INPUT/OUTPUT
- •9.2.1 Multiplexing
- •10. HARDWARE BASED CONTROLLERS
- •10.1 CIRCUITS
- •10.2 FLUIDICS
- •10.3 PNEUMATICS
- •10.4 PRACTICE PROBLEMS
- •11. EMBEDDED CONTROLLERS
- •11.1 TYPES
- •11.1.1 Micro Controllers
- •11.1.2 DSPs
- •11.1.3 CPUs
- •11.2 CONTROLLER DESIGN EXAMPLE
- •11.3 PRACTICE PROBLEMS
- •12. DISCRETE SENSORS
- •12.1 INTRODUCTION
- •12.2 SENSOR WIRING
- •12.2.1 Switches
- •12.2.2 Transistor Transistor Logic (TTL)
- •12.2.3 Sinking/Sourcing
- •12.2.4 Solid State Relays
- •12.3 CONTACT DETECTION
- •12.3.1 Contact Switches
- •12.3.2 Reed Switches
- •12.4 PROXIMITY DETECTION
- •12.4.1 Optical (Photoelectric) Sensors
- •12.4.2 Capacitive Sensors
- •12.4.3 Inductive Sensors
- •12.4.4 Ultrasonic
- •12.4.5 Hall Effect
- •12.4.6 Fluid Flow
- •12.4.7 Other Types
- •12.5 PRACTICE PROBLEMS
- •13. CONTINUOUS SENSORS
- •13.1 INPUT ISSUES
- •13.2 SENSOR TYPES
- •13.3 ANGULAR POSITION
- •13.3.1 Potentiometers
- •13.3.2 Encoders
- •13.3.3 Resolvers
- •13.3.4 Practice Problems
- •13.4 LINEAR POSITION
- •13.4.1 Potentiometers
- •13.4.2 Linear Variable Differential Transformers (LVDT)
- •13.4.3 Moire Fringes
- •13.4.4 Interferometers
- •13.5 VELOCITY
- •13.5.1 Velocity Pickups
- •13.5.2 Tachometers
- •13.6 ACCELERATION
- •13.6.1 Accelerometers
- •13.7 FORCE/MOMENT
- •13.7.1 Strain Gages
- •13.7.2 Piezoelectric
- •13.8 FLOW RATE
- •13.8.1 Venturi
- •13.9 TEMPERATURE
- •13.9.1 Resistive Temperature Detectors (RTDs)
- •13.9.2 Thermocouples
- •13.9.3 Thermistors
- •13.10 SOUND
- •13.10.1 Microphones
- •13.11 LIGHT INTENSITY
- •13.11.1 Light Dependant Resistors (LDR)
- •13.12 PRESSURE
- •13.12.1 Bourdon Tubes
- •13.13 PRACTICE PROBLEMS
- •13.14 REFERENCES
- •14. ACTUATORS
- •14.1 ACTUATOR TYPES
- •15. DISCRETE ACTUATORS
- •15.1 INTRODUCTION
- •15.1.1 Interfacing
- •15.1.1.1 - Relays
- •15.1.1.2 - Transistors
- •15.1.1.3 - Triacs
- •15.2 TYPES
- •15.2.1 Solenoids
- •15.2.2 Hydraulic
- •15.2.3 Hydraulics
- •15.2.4 Electric
- •15.2.5 Pneumatic
- •15.2.6 Others
- •15.3 PRACTICE PROBLEMS
- •16. CONTINUOUS ACTUATORS
- •16.1 ACTUATOR CONTROL
- •16.1.1 Block Diagrams
- •16.1.2 Linear Control Systems
- •16.1.3 Motor Controllers
- •16.1.3.1 - DC Motors
- •16.1.3.2 - Stepper Motors
- •16.1.3.3 - Separately Excited DC Motor
- •16.1.3.4 - AC Motors
- •16.1.3.4.1 - Synchronous
- •16.1.4 Hydraulic
- •16.2 PRACTICE PROBLEMS
- •17. PROGRAMMABLE LOGIC CONTROLLERS
- •17.1 BASIC PLCs
- •17.1.1 PLC Connections
- •17.1.2 Ladder Logic
- •17.1.3 Ladder Logic Outputs
- •17.1.4 Ladder Logic Inputs
- •17.2 A SIMPLE EXAMPLE
- •17.3 PRACTICE PROBLEMS
- •18. PLC CONNECTION
- •18.1 SWITCHED INPUTS AND OUTPUTS
- •18.1.1 Input Modules
- •18.1.2 Output Modules
- •18.1.2.1 - Relays
- •18.2 PRACTICE PROBLEMS
- •19. PLC OPERATION
- •19.1 PLC ORGANIZATION
- •19.2 PLC STATUS
- •19.3 MEMORY TYPES
- •19.4 SOFTWARE BASED PLCS
- •19.5 PROGRAMMING STANDARDS
- •19.5.2 The Future of Open Architecture Controllers
- •19.6 PRACTICE PROBLEMS
- •20. SWITCHING LOGIC
- •20.1 BOOLEAN ALGEBRA
- •20.2 DISCRETE LOGIC
- •20.2.1 Boolean Algebra for Circuit and Ladder Logic Design
- •20.2.2 Boolean Forms
- •20.3 SIMPLIFYING BOOLEAN EQUATIONS
- •20.3.1 Karnaugh Maps for Combinatorial Design
- •20.4 ADDITIONAL TOPICS
- •20.4.1 Negative Logic
- •20.4.2 Common Logic Forms
- •20.4.2.1 - NAND/NOR Forms
- •20.4.2.2 - Multiplexers
- •20.4.2.3 - Seal-in Circuits
- •20.5 DESIGN CASES
- •20.5.1 Logic Functions
- •20.5.2 Car Safety System
- •20.5.3 Motor Forward/Reverse
- •20.6 PRACTICE PROBLEMS
- •21. NUMBERING
- •21.1 INTRODUCTION
- •21.2 DATA VALUES
- •21.2.1 Binary
- •21.2.2 Boolean Operations
- •21.2.3 Binary Mathematics
- •21.2.4 BCD (Binary Coded Decimal)
- •21.2.5 Number Conversions
- •21.2.6 ASCII (American Standard Code for Information Interchange)
- •21.3 DATA CHARACTERIZATION
- •21.3.1 Parity
- •21.3.2 Gray Code
- •21.3.3 Checksums
- •21.4 PRACTICE PROBLEMS
- •22. EVENT BASED LOGIC
- •22.1 INTRODUCTION
- •22.2 TIMERS, COUNTERS, FLIP-FLOPS, LATCHES
- •22.2.1 Latches
- •22.2.2 Flip-Flops
- •22.2.3 Timers
- •22.2.4 Counters
- •22.3 PROGRAM DESIGN METHODS
- •22.3.1 Process Sequence Bits
- •22.3.2 Timing Diagrams
- •22.4 DESIGN CASES
- •22.4.1 Counters And Timers
- •22.4.2 More Timers And Counters
- •22.4.3 Oscillator
- •22.4.4 More Timers
- •22.4.5 Cascaded Timers
- •22.4.6 Deadman Switch
- •22.4.7 Conveyor
- •22.4.8 Accept/Reject Sorting
- •22.4.9 Shear Press
- •22.4.10 Actuator Failure
- •22.4.11 Palm Button Detection
- •22.5 PRACTICE PROBLEMS
- •23. SEQUENTIAL LOGIC DESIGN
- •23.1 SCRIPTS
- •23.2 FLOW CHARTS
- •23.3 STATE BASED MODELLING
- •23.3.1 State Diagrams Example
- •23.3.1.1 - Block Logic Conversion
- •23.3.1.2 - Single State Equations
- •23.3.1.3 - Entry and Exit State Equations
- •23.3.1.4 - State Transition Equations
- •23.4 PARALLEL PROCESS FLOWCHARTS
- •23.4.1 Implementation with Microcontroller
- •23.5 SEQUENTIAL LOGIC CIRCUITS
- •23.5.1 Latches and Seal-in
- •23.5.2 Shift Registers
- •23.6 PRACTICE PROBLEMS
- •24. ADVANCED LADDER LOGIC FUNCTIONS
- •24.1 ADDRESSING
- •24.1.1 Data Files
- •24.1.1.1 - Inputs and Outputs
- •24.1.1.2 - User Bit Memory
- •24.1.1.3 - Timer Counter Memory
- •24.1.1.4 - PLC Status Bits (for PLC-5s and Micrologix)
- •24.1.1.5 - User Function Control Memory
- •24.1.1.6 - Integer Memory
- •24.1.1.7 - Floating Point Memory
- •24.2 INSTRUCTION TYPES
- •24.2.1 Basic Data Handling
- •24.2.1.1 - Move Functions
- •24.2.1.2 - Mathematical Functions
- •24.2.2 Logical Functions
- •24.2.2.1 - Comparison of Values
- •24.2.2.2 - Binary Functions
- •24.2.3 Boolean Operations
- •24.2.4 Binary Mathematics
- •24.2.5 BCD (Binary Coded Decimal)
- •24.2.6 Advanced Data Handling
- •24.2.6.1 - Multiple Data Value Functions
- •24.2.7 Complex Functions
- •24.2.7.1 - Shift Registers
- •24.2.7.2 - Stacks
- •24.2.7.3 - Sequencers
- •24.2.8 Program Control Structures
- •24.2.8.1 - Branching and Looping
- •24.2.8.2 - Immediate I/O Instructions
- •24.2.8.3 - Fault Detection and Interrupts
- •24.2.9 Block Transfer Functions
- •24.3 DESIGN TECHNIQUES
- •24.3.1 State Diagrams
- •24.4 DESIGN CASES
- •24.4.1 If-Then
- •24.4.2 For-Next
- •24.4.3 Conveyor
- •24.5 FUNCTION REFERENCE
- •24.6 PRACTICE PROBLEMS
- •25. PLC PROGRAMMING
- •25.1 PROGRAMMING STANDARDS
- •25.1.2 The Future of Open Architecture Controllers
- •25.2 PRACTICE PROBLEMS
- •26. STRUCTURED TEXT PROGRAMMING
- •26.1 INTRODUCTION
- •26.2 THE LANGUAGE
- •26.3 PRACTICE PROBLEMS
- •27. INSTRUCTION LIST PROGRAMMING
- •27.1 INTRODUCTION
- •27.2 PRACTICE PROBLEMS
- •28. FUNCTION BLOCK PROGRAMMING
- •28.1 INTRODUCTION
- •28.2 PRACTICE PROBLEMS
- •29. ANALOG INPUTS AND OUTPUTS
- •29.1 ANALOG INPUTS
- •29.1.1 Analog To Digital Conversions
- •29.1.2 Analog Inputs With a PLC
- •29.2 ANALOG OUTPUTS
- •29.2.1 Analog Outputs With A PLC
- •29.3 DESIGN CASES
- •29.3.1 Oven Temperature Control
- •29.3.2 Statistical Process Control (SPC)
- •29.4 PRACTICE PROBLEMS
- •30. CONTINUOUS CONTROL
- •30.1 CONTROLLING CONTINUOUS SYSTEMS
- •30.2 CONTROLLING DISCRETE SYSTEMS
- •30.3 CONTROL SYSTEMS
- •30.3.1 PID Control Systems
- •30.3.1.1 - PID Control With a PLC
- •30.4 DESIGN CASES
- •30.4.1 Temperature Controller
- •30.5 PRACTICE PROBLEMS
- •31. PLC DATA COMMUNICATION
- •31.1 COMPUTER COMMUNICATIONS CATEGORIES
- •31.2 THE HISTORY
- •31.3 WITH PLCs
- •31.4 SERIAL COMMUNICATIONS
- •31.4.1.1 - ASCII Functions
- •31.4.2 ASCII (American Standard Code for Information Interchange)
- •31.5 PARALLEL
- •31.6 NETWORKS
- •31.6.1 Introduction
- •31.6.2 OSI Network Model
- •31.6.2.1 - Physical Layer
- •31.6.2.2 - Data Link Layer
- •31.6.2.3 - Network Layer
- •31.6.2.4 - Transport Layer
- •31.6.2.5 - Session Layer
- •31.6.2.6 - Presentation Layer
- •31.6.2.7 - Application Layer
- •31.6.2.8 - Open Systems
- •31.6.2.9 - Networking Hardware
- •31.7 BUS TYPES
- •31.7.1 Devicenet
- •31.7.2 CANbus
- •31.7.3 Controlnet
- •31.7.4 Profibus
- •31.7.5 Ethernet
- •31.7.6 Proprietary Networks
- •31.7.6.1 - Data Highway
- •31.7.7 Other Network Types
- •31.8 DESIGN CASES
- •31.8.1 PLC Interface To Robots And NC Machines
- •31.9 PRACTICE PROBLEMS
- •32. HUMAN MACHINE INTERFACES (HMI)
- •32.1 INTRODUCTION
- •32.2 HMI/MMI DESIGN
- •32.3 DESIGN CASES
- •32.4 PRACTICE PROBLEMS
- •33. DESIGNING LARGE SYSTEMS
- •33.1 PROGRAMMING
- •33.2 DOCUMENTATION
- •33.3 PLC PROGRAM DESIGN FORMS
- •33.4 PRACTICE PROBLEMS
- •34. IMPLEMENTATION
- •34.1 ELECTRICAL
- •34.1.1 Electrical Wiring Diagrams
- •34.1.1.1 - JIC Wiring Symbols
- •34.1.2 Wiring
- •34.1.3 Shielding and Grounding
- •34.2 SAFETY
- •34.2.1 Troubleshooting
- •34.2.2 Forcing Outputs
- •34.2.3 PLC Environment
- •34.2.3.1 - Enclosures
- •35. PROCESS MODELLING
- •35.1 REFERENCES
- •35.2 PRACTICE PROBLEMS
- •36. SELECTING A PLC
- •36.1 SPECIAL I/O MODULES
- •36.2 PLC PROGRAMMING LANGUAGES
- •36.3 ISSUES
- •36.4 PRACTICE PROBLEMS
- •37. PLC REFERENCES
- •37.1 SUPPLIERS
- •37.2 PROFESSIONAL INTEREST GROUPS
- •37.3 PLC/DISCRETE CONTROL REFERENCES
- •38. USING THE OMRON DEMO PACKAGE
- •38.1 OVERVIEW
- •38.1.1 Installation
- •38.1.2 Basic Use
- •38.1.3 Connecting to the PLC
- •38.2 REFERENCE GUIDE FOR OMRON PLC DEMO SOFTWARE
- •39. INDUSTRIAL ROBOTICS
- •39.1 INTRODUCTION
- •39.1.1 Basic Terms
- •39.1.2 Positioning Concepts
- •39.1.2.1 - Accuracy and Repeatability
- •39.1.2.2 - Control Resolution
- •39.1.2.3 - Payload
- •39.2 ROBOT TYPES
- •39.2.1 Basic Robotic Systems
- •39.2.2 Types of Robots
- •39.2.2.1 - Robotic Arms
- •39.2.2.2 - Autonomous/Mobile Robots
- •39.2.2.2.1 - Automatic Guided Vehicles (AGVs)
- •39.2.3 Commercial Robots
- •39.2.3.1 - Seiko RT 3000 Manipulator
- •39.2.3.2 - DARL Programs
- •39.2.3.2.1 - Language Examples
- •39.2.3.2.2 - Commands Summary
- •39.2.3.3 - Mitsubishi RV-M1 Manipulator
- •39.2.3.4 - Movemaster Programs
- •39.2.3.4.1 - Language Examples
- •39.2.3.4.2 - Command Summary
- •39.2.3.5 - IBM 7535 Manipulator
- •39.2.3.6 - AML Programs
- •39.2.3.7 - ASEA IRB-1000
- •39.2.4 Unimation Puma (360, 550, 560 Series)
- •39.3 ROBOT APPLICATIONS
- •39.3.1 Overview
- •39.3.2 Spray Painting and Finishing
- •39.3.3 Welding
- •39.3.4 Assembly
- •39.3.5 Belt Based Material Transfer
- •39.4 END OF ARM TOOLING (EOAT)
- •39.4.1 EOAT Design
- •39.4.2 Gripper Mechanisms
- •39.4.2.1 - Vacuum grippers
- •39.4.3 Magnetic Grippers
- •39.4.3.1 - Adhesive Grippers
- •39.4.4 Expanding Grippers
- •39.4.5 Other Types Of Grippers
- •39.5 ADVANCED TOPICS
- •39.5.1 Simulation/Off-line Programming
- •39.6 PRACTICE PROBLEMS
- •40. ROBOTIC PATH PLANNING METHODS
- •40.1 INTRODUCTION:
- •40.1.1 ROBOT APPLICATIONS
- •40.1.2 ROBOTIC CONSTRAINTS
- •40.1.3 THE OPTIMIZATION PROBLEM OF PATH PLANNERS
- •40.1.4 EVALUATION OF PATH PLANNERS
- •40.2 GENERAL REQUIREMENTS
- •40.2.1 PROBLEM DIMENSIONALITY
- •40.2.2 2D MOBILITY PROBLEM
- •40.2.2.1 - 2.5D HEIGHT PROBLEM
- •40.2.2.2 - 3D SPACE PROBLEM
- •40.2.3 COLLISION AVOIDANCE
- •40.2.4 MULTILINK
- •40.2.5 ROTATIONS
- •40.2.6 OBSTACLE MOTION PROBLEM
- •40.2.7 ROBOT COORDINATION
- •40.2.8 INTERACTIVE PROGRAMMING
- •40.3 SETUP EVALUATION CRITERIA
- •40.3.1 INFORMATION SOURCE
- •40.3.1.1 - KNOWLEDGE BASED PLANNING (A PRIORI)
- •40.3.1.2 - SENSOR BASED PLANNING (A POSTIERI)
- •40.3.2 WORLD MODELLING
- •40.4 METHOD EVALUATION CRITERIA
- •40.4.1 PATH PLANNING STRATEGIES
- •40.4.1.1 - BASIC PATH PLANNERS (A PRIORI)
- •40.4.1.2 - HYBRID PATH PLANNERS (A PRIORI)
- •40.4.1.3 - TRAJECTORY PATH PLANNING (A POSTIERI)
- •40.4.1.4 - HIERARCHICAL PLANNERS (A PRIORI & A POSTIERI)
- •40.4.1.5 - DYNAMIC PLANNERS (A PRIORI & A POSTIERI)
- •40.4.1.6 - OFF-LINE PROGRAMMING
- •40.4.1.7 - ON-LINE PROGRAMMING
- •40.4.2 PATH PLANNING METHODS
- •40.4.3 OPTIMIZATION TECHNIQUES
- •40.4.3.1 - SPATIAL PLANNING
- •40.4.3.2 - TRANSFORMED SPACE
- •40.4.3.3 - FIELD METHODS
- •40.4.3.4 - NEW AND ADVANCED TOPICS
- •40.4.4 INTERNAL REPRESENTATIONS
- •40.4.5 MINIMIZATION OF PATH COSTS
- •40.4.6 LIMITATIONS IN PATH PLANNING
- •40.4.7 RESULTS FROM PATH PLANNERS
- •40.5 IMPLEMENTATION EVALUATION CRITERIA
- •40.5.1 COMPUTATIONAL TIME
- •40.5.2 TESTING OF PATH PLANNERS
- •40.6 OTHER AREAS OF INTEREST
- •40.6.1 ERRORS
- •40.6.2 RESOLUTION OF ENVIRONMENT REPRESENTAION
- •40.7 COMPARISONS
- •40.8 CONCLUSIONS
- •40.9 APPENDIX A - OPTIMIZATION TECHNIQUES
- •40.9.1 OPTIMIZATION : VELOCITY
- •40.9.2 OPTIMIZATION : GEOMETRICAL
- •40.9.3 OPTIMIZATION : PATH REFINEMENT
- •40.9.4 OPTIMIZATION : MOVING OBSTACLES
- •40.9.5 OPTIMIZATION : SENSOR BASED
- •40.9.6 OPTIMIZATION : ENERGY
- •40.10 APPENDIX B - SPATIAL PLANNING
- •40.10.1 SPATIAL PLANNING : SWEPT VOLUME
- •40.10.2 SPATIAL PLANNING : OPTIMIZATION
- •40.10.3 SPATIAL PLANNING : GENERALIZED CONES
- •40.10.4 SPATIAL PLANNING : FREEWAYS
- •40.10.5 SPATIAL PLANNING : OCT-TREE
- •40.10.6 SPATIAL PLANNING : VORONOI DIAGRAMS
- •40.10.7 SPATIAL PLANNING : GENERAL INTEREST
- •40.10.8 SPATIAL PLANNING - VGRAPHS
- •40.11 APPENDIX C - TRANSFORMED SPACE
- •40.11.1 TRANSFORMED SPACE : CARTESIAN CONFIGURATION SPACE
- •40.11.1.1 - TRANSFORMED SPACE :
- •40.11.2 TRANSFORMED SPACE : JOINT CONFIGURATION SPACE
- •40.11.3 TRANSFORMED SPACE : OCT-TREES
- •40.11.4 TRANSFORMED SPACE : CONSTRAINT SPACE
- •40.11.5 TRANSFORMED SPACE : VISION BASED
- •40.11.6 TRANSFORMED SPACE : GENERAL INTEREST
- •40.12 APPENDIX D - FIELD METHODS
- •40.12.1 SPATIAL PLANNING : STEEPEST DESCENT
- •40.12.2 SPATIAL PLANNING : POTENTIAL FIELD METHOD
- •40.13 APPENDIX E - NEW AND ADVANCED TOPICS
- •40.13.1 ADVANCED TOPICS : DUAL MANIPULATOR COOPERATION
- •40.13.2 ADVANCED TOPICS : A POSTIERI PATH PLANNER
- •40.13.3 NEW TOPICS - SLACK VARIABLES
- •40.14 REFERENCES:
- •41. ROBOTIC MECHANISMS
- •41.1 KINEMATICS
- •41.1.1 Basic Terms
- •41.1.2 Kinematics
- •41.1.2.1 - Geometry Methods for Forward Kinematics
- •41.1.2.2 - Geometry Methods for Inverse Kinematics
- •41.2 MECHANISMS
- •41.3 ACTUATORS
- •41.3.1 Modeling the Robot
- •41.4 PATH PLANNING
- •41.4.1 Slew Motion
- •41.4.1.1 - Joint Interpolated Motion
- •41.4.1.2 - Straight-line motion
- •41.4.2 Computer Control of Robot Paths (Incremental Interpolation)
- •41.5 PRACTICE PROBLEMS
- •42. MOTION PLANNING AND TRAJECTORY CONTROL
- •42.1 TRAJECTORY CONTROL
- •42.1.1 Resolved Rate Motion Control
- •42.1.2 Cartesian Motion System
- •42.1.3 Model Reference Adaptive Control (MRAC)
- •42.1.4 Digital Control System
- •42.2 PATH PLANNING
- •42.2.1 Slew Motion
- •42.2.1.1 - Joint Interpolated Motion
- •42.2.1.2 - Straight-line motion
- •42.3 MOTION CONTROLLERS
- •42.3.1 Computer Control of Robot Paths (Incremental Interpolation)
- •42.4 SPECIAL ISSUES
- •42.4.1 Optimal Motion
- •42.4.2 Singularities
- •42.5 PRACTICE PROBLEMS
- •42.6 MICROBOT OVERVIEW
- •42.7 CRS PLUS ROBOT OVERVIEW
- •42.8 BASIC DEMONSTRATION STEPS
- •43. CNC MACHINES
- •43.1 MACHINE AXES
- •43.2 NUMERICAL CONTROL (NC)
- •43.2.1 NC Tapes
- •43.2.2 Computer Numerical Control (CNC)
- •43.2.3 Direct/Distributed Numerical Control (DNC)
- •43.3 EXAMPLES OF EQUIPMENT
- •43.3.1 EMCO PC Turn 50
- •43.3.2 Light Machines Corp. proLIGHT Mill
- •43.4 PRACTICE PROBLEMS
- •44. CNC PROGRAMMING
- •44.1 G-CODES
- •44.3 PROPRIETARY NC CODES
- •44.4 GRAPHICAL PART PROGRAMMING
- •44.5 NC CUTTER PATHS
- •44.6 NC CONTROLLERS
- •44.7 PRACTICE PROBLEMS
page 48
Calculate the position of a 5 Kg mass if a force of 2N is applied for 5 seconds and then removed. There is a one second delay between the time that the force is applied, and when the effects are apparent on the mass.
5.2 DISCRETE CONTROLLERS
•The system models we developed before allow us to predict how a system will behave. A separate, and important topic is computer control.
•With no controller we would set an input, and hope for an output. For example, push the gas pedal and hope for the right speed.
•A controller looks at the desired system condition, and the actual system condition, and then adjusts the input to bring the desired and actual closer. For example cruise control.
•The diagram below is a representation of a simple control system add to in the previous tank example,
page 49
hdesired |
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e |
Controller |
θ |
Process |
hactual |
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(valve/tank) |
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Feedback |
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To make notations more generic we will associate stock variables for desired and actual positions, as well as error, and controller output. We will also add the discrete timestep subscripts used before,
rn = hdesired
cn = hactual
en = rn – cn
mn = θ
•We have already dealt with deriving an equation for the process. In this case it was the valve tank combination discussed before. By itself the tank is an open loop system, we set the valve angle and hope for a liquid level.
•Next, we need to find an equation for the controller. This equation can be highly dependent upon the control method to be used. If we are to use a computer it is best to have a simple equation, as shown below, (NOTE: the form of the equation, and the values of the coefficients change the nature of the control problem).
The basic difference equation is,
mn – mn – 1 = K0en + K1en – 1 + K2en – 2 + K3en – 3 + K4en – 4 + …
The ‘output oriented’ form is shown below,
mn = mn – 1 + K0en + K1en – 1 + K2en – 2 + K3en – 3 + K4en – 4 + …
•The controllers (equations) that follow will be put in the above form. These controllers can also be used individually, or combined to get more complex properties.
•Keep in mind that the typical objective of a control system is to minimize the error between the input and output. Another common goal is to do this as quickly, or efficiently as possible. One constraint we must observe is that the system should not become unstable.
page 50
5.2.1 A Proportional Controller
• One of the simplest controllers is the proportional control,
The basic proportional equation is, m = Ke
This can be put in discrete form easily, mn = Ken
Finally this can be put into the general form seen before, mn – mn – 1 = Ken – Ken – 1
mn = mn – 1 + Ken – Ken – 1
Note: This form will be more useful when dealing with more complex controllers.
•The magnitude of K will determine how fast the system responds. If the value is too large the system will oscillate and/or become unstable (i.e. flood or go empty). If too small the system error will be very large. (ie, the tank will never reach the right height.)
•This type of controller will always have a small error between the actual and desired values.
•For the water tank (from before) add a controller, and try varying ‘K’ values.
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–T |
Ko |
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K |
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Ko |
K |
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A |
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A |
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e |
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+ θ |
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–T ----- |
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h |
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= h |
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– |
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n – 1 |
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n – 1 |
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Ko |
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Ko |
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page 51
• We could implement this controller using the Basic stamp chip. (Note: not a full implementation)
GND |
+5V |
+5V |
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23 |
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potentiometer |
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21 |
220 |
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20 |
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1uF |
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10K |
10K |
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10K |
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19 |
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+5V |
10K |
motor |
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10K |
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e_last=0 ‘set previous error to zero k=2 ‘ set multiplier
r=100 ‘desired water height m_last=0 ‘ last control output value loop:
high 15 ‘discharge the capacitor pause 1 ‘ wait for 1ms
rctime 15,1,c ‘measure charge time e_now=r-c ‘ calculate the error
m_now=m_last+k*e_now-k*e_last ‘ the controller equation e_last=e_now
m_last=m_now
pwm 14,m,100 ‘set the output voltage goto loop
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