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Controls Bootcamp - Steve Brunton

Overview

  • Controls are of two types:
    • Passive Control: Control introduced in system due to design. Does not need additional energy to function. e.g. Truck shape introducing drag to keep it from lifting
    • Active Control: Control introduced in system by use of external energy. Types:
      • Open Loop: No feedback in system which results in continuous inputs.
      • Closed Loop: Introduces feedback system using sensors which can be used for minute control which varies based on output of the system.

  • Why Feedback is needed?
    • Uncertainity: System often has uncertainity which renders preplanned input useless.
    • Instability: System might be unstable due to external noise. Feedback can result in better control.
    • Disturbance tends to pass through system dynamics and can be measured to improve control over it.
    • Efficient: Introducing feedback results in overall lower energy consumption due to applied force being proportional to present error, thus reduces overall lower energy.

Important Topics

  • Linear Systems
  • Stability and Eigen Values
  • Linearizing Around a Fixed Point
  • Controllability
  • Controllabiltiy, Reachability and Eigen Value Placement
  • Controllability and the Discrete-Time Impulse Response
  • Degree of Controllability and Gramians
  • Controllability and PBH Test
  • Cayley-Hamilton Theorem
  • Reachability and Controllabilty with Cayley Hamilton
  • Inverted Pendulum on a Cart
  • Pole Placement for the Inverted Pendulum on a Cart
  • Linear Quadratic Regulator(LQR) Control for the Inverted Pendulum on a Cart
  • Motivation for Full-State Estimation
  • Observability
  • Full-State Estimation
  • The Kalman Filter
  • Linear Quadratic Gaussian (LQG)
  • Robust Control
  • Equivalent Representations of Linear Systems

Resources