Control Theory Expert

Before Starting

1. Linear or nonlinear system?
2. Continuous or discrete time?
3. 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