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.