16-299: Introduction to Feedback Control Systems
Spring 2023
Instructor: Chris Atkeson, cga@cmu.edu
Class time: TR 2-3:20PM
Place: NSH 3002
Units: 12

Last year's course

Course administration and policies

Lab

Events

Video of the day

• SpaceX landings, Feedback control is cool Does this make a good project?
• Atlas, Behind the scenes,
• Older Atlas video, Older Behind the scenes, Writeup
• Robot learning pole balancing, Robot learning swingup

Of Interest

Textbook

There is a second book I urge you to read and the PDF is available from the CMU library: Feedback Control for Everyone

Schedule

• Jan 17: Atkeson introduction. Atkeson Youtube channel.
  Go over class web page
  Introduction to the course:
  How would you program the SpaceX rockets?
  Intuition and a useful mental model: Springs and dampers, natural frequency, damping ratio
  Examples: Thermostat, body temperature, breathing, blood pressure, gaze, driving (direction, cruise control), rockets (including landing), game-playing (alpha-zero), ...
  Assignment 0
  Assignment 1
  CGA Lecture 1
  Read Textbook: Chapter 1 - Introduction
  
• Jan 19: Models, states, actions/controls, continuous and discrete time dynamics functions, goals/optimization_functions/rewards, and control laws/policies.
  CGA Lecture 2
• Jan 24: Simulation, Numerical integration: Euler integration, Fancier numerical integration.
  Matlab example.
  CGA Lecture 3
  How to do Assignment 2.
  Read Textbook: Chapter 3 - System Modeling
  
• Jan 26: Build A Robot Day.
  We are going to give out and build the robots during class.
  Bring a laptop if possible.
  Tips on building the robot, and using an Arduino computer will be provided.
  
• Jan 31: The state space approach:
  CGA Lecture 4
  Read Textbook: Chapter 6 - Linear Systems
  
• Feb 2: Linear State Feedback: Eigenvalues;
  CGA Lecture 5
  Read Textbook: Chapter 7 - State Feedback
  
• Feb 7: Linear Quadratic Regulators (LQR)
  CGA Lecture 5
  Read Textbook: Chapter 7 - State Feedback
  
• Feb 9: State-estimation, Linear State Observers: Observability; Observer derivation and design.
  CGA Lecture 6
  Read Textbook: Chapter 8 - Output Feedback
  
• Feb 14: Previous lecture continued.
• Feb 16: PID control, Feedforward, robot arm modeling and system identification Read Textbook: Chapter 11 - PID Control
  PID section
  
• Feb 21: Robot arm control, computed torque, clocks, ...
  CGA Lecture 8
  
• Feb 24: Previous lecture continued.
• Feb 28: Optimization Video
  kinematics example.
  Redundant inverse kinematics:
  Unconstrained optimization: Using Matlab's fminsearch and fminunc.
  Unconstrained optimization with soft constraints: Using Matlab's fminsearch and fminunc, with desired posture.
  Constrained optimization: Using Matlab's fmincon.
  
• March 2: Discussion of lab robot
  Video
  
• Spring Vacation!
• March 14: Thinking in the frequency domain,
  More discussion of lab robot
  Video
  
• March 16: Nonlinear stability, Introduction to nonlinear control, local linearization of smooth nonlinearities. Divergence of KF, Extended Kalman Filter, Unscented Kalman Filter, MPC.
  
• March 21: Nonlinear continued.
• March 23: Dynamic Programming and Value Functions.
• March 28: Dynamic Programming: Random sampling of actions and other approaches to ameliorating the curse of dimensionality.
• March 30: Dynamic Programming: Random sampling of states. Differential Dynamic Programming.
• April 4: A*, game tree search, AlphaX
• April 6: Reinforcement Learning
• April 11: "AI" style planning (preconditions, postconditions), Motion planning, Graph planning
• April 13: Carnival, no class
• April 18: Application: Legged locomotion
• April 20: Application: Driving
• April 25: Project presentations
• April 27: Project presentations
• May 9 - Graduating students have to have turned everything in.
• May 15 - All students have to have turned everything in.

Topics

• UNDER CONSTRUCTION
  What you see are last year's topics.
  
  
• Unit 0: Intuition
• Unit I: State Space
  • Plans and feedforward control, clocks, phases, and internal states.
  • Output Feedback
    Read Textbook: Chapter 8 - Output Feedback
    
  • Learning: Optimization, Optimal control, and Reinforcement learning.
    
• Unit II: Frequency Domain Last year's notes
  • Read Textbook: Chapter 2 - Feedback Principles
    
  • Mathematical models: ODEs, diff. equations, and transfer functions. Last year's notes.
  • Conceptual overview, complex variables
  • Transfer Functions: Laplace transforms, frequency response, linearity
    Read Textbook: Chapter 9 - Transfer Functions
    
  • Complex Plane Intuition: 2nd order systems, moving poles with P and D
    Read Textbook: Chapter 10 - Frequency Domain Analysis
    
  • Frequency Domain Design
    Read Textbook: Chapter 12 - Frequency Domain Design
    
  • Integral Control: steady state error rejection, benefits of added state
• Unit III: Nonlinear Systems
  Nonlinear EOMs, eq. points, and linearization.
  • Revisit ODE models, attractors (equilibrium points), saddle points, repellers, and stability;
  • Dynamic programming
  • Nonlinear Stability: Lyapunov methods: introduction and simple cases.
    Read Textbook: Chapter 5 - Dynamic Behavior
    Last year's notes
  • Trajectory Following: pure pursuit, tubes: linearization about a trajectory;
• Unit IV: Additional topics: class suggests more and decides which to talk about.
  • System identification
  • Adaptive control
  • Optimal control and reinforcement learning, dynamic programming
  • Robust control
    Read Textbook: Chapter 13 - Robust Performance
    
  • Fundamental limits
    Read Textbook: Chapter 14 - Fundamental Limits
    
  • Architecture (top-down, bottom-up), system, and control design, interaction
    Adaptation, Learning and Cognition
    Textbook: Chapter 15 - Architecture and System Design
    
  • Hybrid systems (Discrete and continuous states)
• Case studies: class suggests more and decides which to talk about.
  • Textbook: Chapter 3, 4, and 15
    
  • scribbled models from last year
  • Inverted pendulums: the ballbot, rocket control and landing
  • Vehicle Modeling: kinematic models, nonholonomic constraints;
  • UAVs - equations of motion, decomposition, differential flatness, architecture, trajectory planning, controller design
  • Running and walking

Assignments

• Assignment 0: Due Jan 23. Send email to Chris: Who are you? Why are you here? Done any control (in simulation or on physical machines)? Any ideas about the project you want to do? ("I don't know what project I want to do." is okay.) What topics would you like the course to cover? Google and send us some interesting URLs. What example of control really impressed you (Boston Dynamics Atlas jumping around, SpaceX landing rockets on a barge, ...; send URLs of web pages or videos)? Are there other versions of this course at other places or useful web pages we should look at (send URLs)?
  Be sure your name is obvious in the email, and you mention the course name or number in the subject line. I teach more than one course, and a random email from robotlover@cs.cmu.edu is hard for us to process.
• Assignment 1: Due Jan 24. Get access to MATLAB.. Nothing to turn in.
• Assignment 2: Due Feb 6. Assignment 2 Nothing to turn in.
• Assignment 3: Due Feb 27. Assignment 3
  Code for assignment
  Please turn in your assignment by sending it in email to cga@cmu.edu
  Linearization and LQR examples
  
• Assignment 4: Due April 3. Lab assignment involving controlling a single wheel.
• Assignment 5: Due April 24. Lab assignment 2.

Project

We will work out the project topics together. The ideal project would involve modeling and controlling a real physical system. It would be cool to have a learning component. Second best is doing everything in simulation. You can do a project taking what we do in the balancing robot lab further. We can help you buy a real physical system, if we don't have what you want already. We can help you get access to robots.

See the deadlines in the schedule (above). You can work in groups or alone. The "deliverables" include a web page along the lines of an instructables web page explaining how others could do your project and improve on your results. You will also present your project, and ideally the presentation should be made public as part of your web page. There will be intermediate deliverables including draft web pages and practice presentations.

More Resources

• Wikipedia
• Introduction to feedback control systems: course notes