Control theory - Wikipedia

Wikipedia overview of control theory — the field of engineering and applied mathematics dealing with the control of dynamical systems. Covers the full arc from Maxwell’s 1868 analysis of the centrifugal governor through Minorsky’s PID theory (1922), Wiener’s cybernetics, Kalman’s state-space revolution, and modern robust/adaptive methods.

Key contributions to the knowledge base:

• Closed-loop definition: a controller monitors a process variable, compares it with a setpoint, and applies feedback to reduce the error to zero — continuously and despite disturbances.
• Stability: a system is stable when all poles have negative real parts. Practical concerns: overshoot, oscillation, settling time, steady-state error.
• PID control: the canonical industrial controller — proportional, integral, derivative components each address a different aspect of error correction.
• Controllability and observability: a state must be both controllable (steerable by inputs) and observable (measurable through outputs) for any controller to stabilize it.
• Robustness: no real system matches its model. Robust controllers tolerate parameter uncertainty and external disturbance.
• History: Watt’s governor (1788) → Maxwell’s analysis (1868) → Routh-Hurwitz stability criteria → Minorsky PID (1922) → WWII automation → Wiener cybernetics (1940s) → Kalman state-space (1960s) → modern optimal/robust/adaptive control.