Feedback
Control

Dynamics

Intro

Frequency
domain

1st order

2nd order

  • step response
  • time constant
  • equation
  • step response
  • rise time
  • overshoot
  • settling time
  • natural frequency
  • damping ratio

Tools

Why feedback?

Block-diagrams

Modeling

Black's formula

Modeling

  • Electromagnetic
  • Mechanisms
  • Electronic circuits
  • Continuous
  • Switching

Control Loop

  • Return Ratio (- L.T.)
    vs. Closed Loop
  • Characteristic Equation
  • Loop shaping

Tools

  • Spring-mass-damper
  • Impedances
  • Admittances
    -Bond-graph
  • On/Off control
  • PID control

Linear Time Invariant systems

Implementation

Issues

Frequency responses

  • Return ratio
  • Controller
  • Closed Loop
  • Sensitivity

Performance
Specs

Time-domain

  • Rise time
  • Time to peak magnitude
  • Peak magnitude / overshoot
  • Settling time (within 1% of set-point)
  • Steady-state tracking error

Frequency-domain

  • Tracking error with frequency
  • Disturbance rejection
  • Stability through Gang of 6 / 4

Stability-Robustness

  • Phase-margin
  • Gain-margin
  • Cross-over
    frequency
  • Continuous vs. Discrete time
  • Quantization
  • Saturation
  • Non-linearities
  • Simulation vs. experiments

What is feedback?

Fundamental Limits

  • Bode's integral formula
  • Gain Crossover Frequency Inequality
  • The Maximum Modulus Principle

Advanced
Topics

Feed-forward

Reference shaping

State-Space

  • MIMO systems
  • Computation
  • Block-diagrams
  • Transfer functions
  • State-space
  • Pole-zero map
  • Bode plots
  • Root Locus
  • Nyquist

Gain Scheduling

Iterative Learning Control

Adaptive feed-forward