luokai0 Control Theory Expert
Before Starting
- Linear or nonlinear system?
- Continuous or discrete time?
- Single input single output or multi-input multi-output?
Core Expertise Areas
Classical Control
Transfer function: Laplace domain representation of linear time-invariant systems. PID controller: proportional, integral, derivative terms, most widely deployed controller. Root locus: how closed-loop poles move as gain varies. Bode plot: frequency response magnitude and phase vs frequency. Gain and phase margin: stability margins from Bode plot.
State-Space Methods
State equation: x-dot = Ax + Bu, y = Cx + Du. Controllability: can reach any state from any initial state with appropriate input. Observability: can infer state from output measurements. Pole placement: choose control gain K so eigenvalues of A minus BK are desired. Kalman filter: optimal state estimator for linear systems with Gaussian noise.
Stability Analysis
Lyapunov stability: find positive definite V such that V-dot is negative semi-definite. LaSalle invariance: extends Lyapunov for asymptotic stability proof. Input-output stability: BIBO stability, bounded input gives bounded output. Robust stability: system remains stable under bounded model uncertainty.
Optimal Control
LQR: linear quadratic regulator, minimizes quadratic cost on state and input. Pontryagin minimum principle: necessary conditions for optimal control. Dynamic programming: Bellman equation, value function approach. MPC: model predictive control, optimize over receding horizon with constraints.
Nonlinear Control
Feedback linearization: cancel nonlinearities, apply linear control to linearized system. Sliding mode: drive state to manifold, robust to disturbances and uncertainty. Adaptive control: update controller parameters online as system changes. Backstepping: systematic design for cascaded nonlinear systems.
Best Practices
- Always verify stability before deploying controller on hardware
- Tune PID with systematic methods not random trial and error
- Validate model before designing model-based controllers
- Test controller robustness to parameter variations and disturbances
Common Pitfalls
| Pitfall | Fix |
|---|---|
| Integral windup | Implement anti-windup in all PID controllers |
| Ignoring actuator saturation | Include saturation in stability analysis |
| Model mismatch in MPC | Robustify MPC or use adaptive approach |
| Derivative kick on setpoint change | Apply derivative on measurement not error |
Related Skills
- robot-dynamics-expert
- robot-kinematics-expert
- mathematics/optimization-expert