Mathematics and Physics from the Ground Up
PLEN

Control engineering

From feedback seen in the time domain, before any transforms, through the frequency domain and the PID controller in practice, to state space, LQR and the Kalman filter. Running example: a drone that has to hold its altitude. Part V is a bridge to A. Tewari's book “Advanced Control of Aircraft, Spacecraft and Rockets”. Continued in the Flight dynamics and Astronautics courses. In control engineering the imaginary unit is written j.

I Feedback in the time domain

  1. 1.1Why feedback? Open and closed loops draft requires: Mathematics 0.2, Physics 1
  2. 1.2How systems respond: basic elements and the step response draft requires: Mathematics 4.1, Mathematics 5.2, Physics 6, 1.1
  3. 1.3P and PI control in the loop: why the integral removes the error draft requires: Mathematics 6.2, 1.2

II The s and frequency domains: tools for the loop

  1. 2.1Block diagrams and the loop transfer function draft requires: Mathematics 4.4, 1.3
  2. 2.2Closed-loop poles and zeros, root locus draft requires: 2.1
  3. 2.3Frequency response and Bode plots draft requires: Mathematics 1.7, Physics 6, 2.1
  4. 2.4Loop stability: the −1 point, margins and delay draft requires: 2.2, 2.3
  5. 2.5Disturbances, noise and sensitivity: S, T and loop shaping draft requires: 2.4

III The PID controller in practice

  1. 3.1The PID controller: P, I and D action and steady-state error planned requires: 2.5
  2. 3.2Tuning: a model from a test, tuning rules and cascade control planned requires: 3.1
  3. 3.3Nonlinear reality: saturation, windup, feedforward and gain scheduling planned requires: 3.2
  4. 3.4Digital control: sampling, the Z-transform and the controller in code planned requires: Mathematics 1.6, Mathematics 6.2, 3.3

IV State space, estimation and optimal control

  1. 4.1State feedback, pole placement and controllability planned requires: Mathematics 2.3, Mathematics 4.5, 3.1
  2. 4.2State observers and observability planned requires: 4.1
  3. 4.3LQR: a cost instead of poles planned requires: Mathematics 6.1, 4.1
  4. 4.4The Kalman filter planned requires: Mathematics 5.2, 3.4, 4.2
  5. 4.5The extended Kalman filter and single-axis sensor fusion planned requires: Mathematics 4.6, 4.4
  6. 4.6Lyapunov stability and nonlinear control planned requires: Mathematics 4.6, 3.3, 4.3

V A bridge to Tewari

  1. 5.1Pontryagin's maximum principle, time-optimal control and the shooting method planned requires: Mathematics 6.1, Mathematics 6.2, 4.3
  2. 5.2LQG and robustness planned requires: 2.5, 4.3, 4.4