Introduction to Control Theory Concepts

Aug 22, 2024

Control Theory Overview

Introduction

  • Importance of control theory in autonomous systems
    • Examples: self-driving cars, building temperature control, distillation processes
  • Presenter: Brian, Matlab Tech talk

Basic Concepts

  • Dynamical System: The system we want to control (e.g., a car)
  • Inputs:
    • Control Inputs (U): Intentional effects (e.g., steering, braking)
    • Disturbances (D): Unintentional effects (e.g., wind, road bumps)
  • System State (X): Changes over time based on inputs and dynamics

Control Strategies

Open Loop Control (Feed Forward Control)

  • Definition: Generates control inputs based on desired reference without measuring the system state.
  • Example: Driving straight at a constant speed by keeping steering fixed and pressing the accelerator.
  • Limitations:
    • Requires a good understanding of system dynamics
    • Vulnerable to disturbances and uncertainties

Closed Loop Control (Feedback Control)

  • Definition: Uses both reference and current state to determine control inputs.
  • Functionality: Adjusts control inputs based on deviations from the reference.
  • Advantages: Self-correcting mechanism, improves stability
  • Risks: Can change system dynamics, potentially making systems unstable.

Types of Feedback Controllers

  • Linear Controllers: Assume linear behavior (e.g., PID controllers)
  • Non-linear Controllers: Handle non-linear behaviors (e.g., sliding mode control)
  • Robust Controllers: Ensure performance under uncertainty
  • Adaptive Controllers: Adjust to changes over time
  • Optimal Controllers: Minimize cost functions to balance performance and effort
  • Predictive Controllers: Use models to simulate future states
  • Intelligent Controllers: Learn from data (e.g., reinforcement learning)

Planning in Control Systems

  • Importance of planning for the control system to follow a reference.
  • Example: Self-driving cars must plan paths, avoid obstacles, and comply with traffic rules.
  • Planning ensures that the system can physically follow the desired commands.

State Estimation

  • Challenges:
    • Noise in sensor measurements
    • Observability: being able to measure necessary states
  • Techniques:
    • Kalman filter, particle filter, and running averages

Analysis and Validation

  • Ensuring the control system meets design requirements through:
    • Stability checks
    • Performance margins
    • Simulation (e.g., using Matlab, Simulink)

Conclusion

  • Key aspects of control theory:
    • Different control methods (feed forward and feedback)
    • State estimation
    • Planning
    • System analysis
    • Importance of mathematical modeling

Additional Resources

  • Brian provides links to further reading and resources on various control theory topics.
  • Mention of organized resources on resourcium.org
  • Encouragement to subscribe for future tech talks and explore control system lectures.