Teaching Feedback Systems with LEGO Mindstorms

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Teaching Feedback Systems with LEGO Mindstorms

• Trevor Ashley and Andrew Macrae

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Key Questions

• What are feedback systems?
• What are our goals?
• Summer 2008 What was accomplished?
• Fall 2008 Whats left?

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Intro to Feedback Systems

• Open Loop System
• No connection from output to input
• Examples
• Plant RLC circuit Input Voltage Output
  Current through inductor
• Plant Rigid body Input Force on body Output
  body displacement
• Plant DC motor Input Voltage Output Torque
• Nearly all systems seen in E59/E101

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Intro to Feedback Systems

• Closed Loop System
• Sensors measure output
• Error calculated by subtracting system output
  from reference input
• Controller used to alter behavior of entire
  system
• Typical Controllers Lead-Lag and PID
• Various methods exist for designing a controller

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Intro to Feedback Systems

• Closed Loop Considerations
• Stability
• Does the entire system exhibit controllable
  behavior?
• Performance
• How well does the system follow given commands
  (i.e. settling time, rise time and overshoot)?
• Robustness
• How well does the dynamic system perform and
  maintain stability given uncertainties (i.e.
  plant modeling errors, sensor noise and outside
  disturbances)?
• These considerations affect how we design a
  controller
• and controller selection is the main topic of
  E102!

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Project Goals

• Write six hands-on labs for Spring 2008 E102
  Course
• Labs should emphasize concepts taught in E102
  lectures
• Students should be able to bring equipment to
  their dorms and complete labs there
• Each lab should take approximately four hours to
  complete
• Controller design and system simulation should be
  emphasized programming (Java, C, etc.) should be
  deemphasized
• Have professors perform labs and provide comments
  before Spring 2008
• Act as lab assistants for Spring 2008
• Write conference paper for the ASEE

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Overview of Labs

• Students will
• Build a balancing robot (BOB) using LEGO
  Mindstorms
• Simulate BOBs dynamics using Simulink and MATLAB
• Upload their controllers from Simulink to the NXT

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Lab 1 Introduction to Simulink

• Lab Objectives
• Build the LEGO cart
• Check that MATLAB has the required toolboxes
  (Simulink, Realtime Workshop, Realtime Workshop
  Embedded Coder, Control Systems)
• Install the required third party software
  (Cygwin, Gnuarm, and the ECRobot block diagrams,
  LIBUSB)
• Install a third party firmware onto the NXT (NXT
  OSEK)
• Learn Simulink by building and simulating a
  continuous time, second order model of a
  pendulum.
• Build and simulate a discrete time and discrete
  valued Simulink model of a controller that drives
  the LEGO carts wheels forward 3 rotations.
• Download the controller to the Mindstorms NXT and
  test it

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Lab 2 Stationary Robot Control

• Lab Objectives
• Attach a pair of beams to the wheels of the cart
• Explain the utility of each element of a PID
  system
• Add each element of a PID to a simulated
  controller, observing their effects
• Download the controller to the NXT
• Set up Bluetooth in order to make a plot of the
  real arms performance
• Test the arm and compare its performance to
  simulation
• Remove the beams so that cart can be used in
  subsequent labs

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Lab 3 System ID of Balancing Robot

• Lab Objectives
• Derive the governing equations of the balancing
  robot model and a brushed DC motor
• Experimentally determine parameters used in the
  model
• DC motor armature resistance, inductance, rotor
  moment of inertia, coefficient of viscous
  friction, back emf constant and torque constant
• Robot mass and moment of inertia

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Lab 4 Classical Control of Balancing Robot

• Lab Objectives
• Detach the beams from the robots base
• Use classical feedback control design (root locus
  and Bode diagrams) to design a controller that
  stabilizes only the pendulums tilt
• Upload controller to the NXT
• Observe performance

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Lab 5 Modern Control of Balancing Robot

• Lab Objectives
• Use modern feedback control design (full-state
  feedback and pole placement) to design a
  controller that stabilizes both tilt and wheel
• Upload controller to the NXT
• Observe performance and compare to the
  classical method of controller design

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Lab 6 Race!

• Lab Objectives
• The robot competes in an open ended time trial in
  which robust control in previous steps will
  enable the robot to move faster
• Race has three portions
• After start button is pressed the robot must
  balance at the start line for 5 seconds
• It must drive 10 feet to the finish
• It must again balance for 5 seconds.

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Future Work

• Check legacy code for compatibility with MATLAB
  2008a
• Apply for Strategic Visions funding by September
  29
• Complete lab drafts by October 16
• Order classroom LEGO sets by November 13
• Final drafts of labs due by November 20
• Lab assistants during 2009 Semester
• Write conference paper for 2010 ASEE Conference
  and/or 2010 ACC

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Questions?