Control Theory and Autonomous Systems

Introduction

Goal: Understand how to control autonomous systems (e.g., cars, buildings, distillation columns).
Control Theory: A mathematical framework for developing these systems.

Dynamical System: The system we want to control.
- Can be anything (car, building, distillation column).
- Affected by:
  - Control Inputs (U): Intentional actions (e.g., steering, braking).
  - Disturbances (D): Unintentional effects (e.g., wind, bumps).
State (X): Changes over time based on inputs and dynamics.

Feed Forward Control: Algorithm generates control signals based only on desired outcomes (reference R) without measuring current state.
- Example: Steering straight and maintaining speed.
- Limitations: Requires thorough knowledge of the system dynamics and predictable environment.

Closed Loop Control: Uses both reference and current state to adjust control inputs.
- Self-correcting mechanism: If the state deviates, it recognizes and adjusts.
- Important to understand system dynamics as it can change stability.
- Types of feedback controllers:
  - Linear Controllers: PID, Full State Feedback.
  - Non-linear Controllers: On-off, Sliding Mode, Gain Scheduling.
  - Robust Controllers: handle uncertainty.
  - Adaptive Controllers: adjust to changes in the system.
  - Optimal Controllers: minimize cost functions.
  - Predictive Controllers: forecast future states to optimize control inputs.
  - Intelligent Controllers: Lean on data for better control (e.g., fuzzy logic, reinforcement learning).

Essential step in designing control systems.
- Determines path to destination, avoids obstacles, adheres to rules, considers Comfort and safety.
- Examples of planning algorithms: Rapidly expanding random trees (RRT), A*.

Measurement Noise: Affects accurate state representation.
Observability: Requires sufficient sensor placement to observe every state (e.g., using speedometer to derive acceleration).
State estimation techniques: Kalman filter, particle filter, moving averages.

Ensures system meets requirements through:
- Stability checking: Body diagrams, Nyquist diagrams.
- Simulations: Matlab, Simulink.

All parts of control theory interlinked: Controller design, state estimation, planning, analysis.
Models: Crucial in all aspects of control theory.
Additional resources available for further learning on each topic mentioned.