Control Theory Glossary

A device that converts a control signal into physical action, such as a motor, valve, or heater, to influence the plant.

The range of frequencies over which a system responds effectively, typically defined as the frequency where the gain drops to -3 dB from its maximum value.

A graphical representation of a control system showing the interconnection of components using blocks, summing junctions, and signal flow lines.

The polynomial equation obtained by setting the denominator of the closed-loop transfer function to zero. Its roots (the poles) determine system stability.

A control system that uses feedback from the output to adjust the control input, enabling error correction and disturbance rejection.

A controller component designed to reshape the system's frequency response or root locus to achieve desired performance, such as lead, lag, or lead-lag compensators.

The ability to drive a system from any initial state to any desired state in finite time using admissible control inputs.

A dimensionless measure describing how oscillations in a second-order system decay over time. Values less than 1 indicate underdamped behavior.

An unwanted signal or input that affects the system output, which the controller must reject or minimize.

A scalar associated with the system matrix A in state-space representation. The eigenvalues of A are the system poles and determine stability and dynamic behavior.

The steady-state response of a system to sinusoidal inputs of varying frequency, characterized by gain and phase shift as functions of frequency.

The ratio of output magnitude to input magnitude in a system, often expressed in decibels (dB). In a controller, it determines the strength of the corrective action.

The output of a system when the input is a Dirac delta function. For LTI systems, the impulse response completely characterizes the system's behavior.

An integral transform converting time-domain functions into complex-frequency-domain functions, enabling algebraic manipulation of differential equations.

A stability framework where a positive-definite energy-like function (Lyapunov function) is shown to decrease along system trajectories, proving convergence to equilibrium.

Multiple-Input Multiple-Output: a system with more than one input and more than one output, requiring matrix-based analysis methods.

The frequency at which a second-order system oscillates in the absence of damping, denoted omega_n.

A polar plot of the open-loop transfer function G(jw)H(jw) as frequency varies from zero to infinity, used with the Nyquist criterion to assess closed-loop stability.

The ability to determine the complete internal state of a system from its output measurements over a finite interval.

The amount by which the system output exceeds the desired final value during a transient response, typically expressed as a percentage of the steady-state value.

The physical system or process being controlled, such as a motor, chemical reactor, aircraft, or thermal system.

The values of s that make the denominator of the transfer function zero. Pole locations in the complex plane determine system stability and transient characteristics.

The time required for the system output to rise from 10% to 90% of its final steady-state value in response to a step input.

The time required for the system output to reach and remain within a specified percentage (typically 2% or 5%) of the final steady-state value.

The values of s that make the numerator of the transfer function zero. Zeros affect the transient response shape and the system's frequency response.