Covering terminology and understanding the importance of robust control
Presenter: Brian from MATLAB Tech Talk
Key Definitions
Robust System: Can meet stability or performance requirements despite model or disturbance uncertainty.
Robust Control Theory: Method to design systems that handle uncertainty effectively.
Design of a Controller: Workflow Example
Process: Real system you aim to control (e.g., a drone's hover controller).
Model Development: Mathematical model mapping inputs (motor speeds) to outputs (position, velocity, orientation).
Controller Design: Mapping takes reference signal & system state as inputs, outputs control variables (e.g., PID, neural network).
Implementation: Controller implemented on real hardware.
Reality Check: Model inaccuracies affect the real system performance; thus, 'good enough' becomes a key point.
Why Models are Imperfect
Real systems are complex; certain dynamics might be poorly understood or unmeasured (e.g., high-frequency dynamics).
Intentionally simplified models (e.g., linear models) deviate from real physics for practicality.
Systems naturally vary over time due to stochastic events (noise, degradation).
Manufacturing variations create differences among systems.
Results: Models are approximations that introduce uncertainties.
Addressing Model Uncertainty
Adding Margins: e.g., stability margins (gain/phase margins) to ensure the system can handle deviations.
Margin Choices: Balancing act between conservative and cost-effective design.
Assessing Robustness: Classical gain and phase margins are traditional methods. They consider robustness to individual uncertainties (e.g., gain, phase anomalies).
Beyond Classical Margins: Disk Margins
Account for combined gain and phase perturbations.
Applicable for multi-input multi-output systems.
Practical example using MATLAB: Classical and disk margins comparison highlighting robustness insights.
Robust Control Theory: Analysis and Synthesis
Analysis: Determine how robust the system is to uncertainties.
Synthesis: Designing a system with robustness in mind, not tied to specific controller types (e.g., PID).
Classical vs. Advanced Robust Control Methods
Classical loop shaping with gain/phase margins for single-input single-output systems.
Advanced methods (e.g., H∞ loop shaping, μ synthesis) for complex systems (multi-input multi-output, nonlinear systems).
Major Steps in Robust Control
Understanding and representing system uncertainty.
Analyzing system robustness against uncertainties.
Making system changes to enhance robustness.
Conclusion
Emphasis on addressing uncertainty in control systems.
Preview of next videos covering deeper dives into robust control topics.