Control theory

Control theory studies how to regulate dynamic systems through inputs, especially feedback, so their behavior follows desired goals despite disturbances and uncertainty.

Feedback: A process in which a system’s output influences its subsequent input or operation. Feedback lets a controller correct deviations using measurements of the system’s output.
Dynamical system: A system whose state changes over time according to rules involving its current state and inputs. Control theory targets systems whose behavior evolves over time.
Automatic flight control system: An aircraft system that automatically controls flight variables such as attitude, heading, or altitude. Aircraft use feedback to maintain commanded flight conditions and counter disturbances.
Open-loop control: Control that applies inputs without using measurements of the resulting output. It lacks feedback’s ability to correct errors caused by disturbances or model mismatch.
State-space representation: A mathematical description of a dynamic system using internal state variables, inputs, and outputs. State-space models represent interacting variables and support modern controller design.
Ordinary differential equation: An equation relating a function of one variable to its derivatives. Continuous-time system models often express how state variables change through differential equations.
Industrial control system: Hardware and software that monitor and regulate industrial processes. Factories and infrastructure use controllers to keep processes within target operating ranges.
Adaptive control: Control methods that adjust controller parameters as system behavior or conditions change. Adaptive control addresses systems whose dynamics are uncertain or vary over time.
Transfer function: A ratio describing a linear time-invariant system’s output to input in the Laplace domain, under zero initial conditions. Transfer functions reveal how a system responds across frequencies and simplify classical analysis.
Linear system: A system whose response to combined inputs equals the corresponding combination of individual responses. Linearity enables powerful analytical tools for modeling and controller design.

Linked from 40 pages