Closed-loop transfer functionIn control theory, a closed-loop transfer function is a mathematical function describing the net result of the effects of a feedback control loop on the input signal to the plant under control.
Linear time-invariant systemMathematical model which is both linear and time-invariantBlock diagram illustrating the superposition principle and time invariance for a deterministic continuous-time single-input single-output system. The system satisfies the superposition principle and is time-invariant if and only if y3(t) = a1y1(t – t0) + a2y2(t – t0) for all time t, for all real constants a1, a2, t0 and for all inputs x1(t), x2(t).
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems. The aim is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.Stable polynomialA polynomial is defined to be stable in two different ways. Hurwitz-stable: In the context of a differential equation (continuous-time) the characteristic polynomial is stable if all its roots lie in the open left complex half-plane. Schur-stable: In the context of a difference equation (discrete-time), its characteristic polynomial is stable if all its roots lie in the open complex unit disk.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle.
FeedbackFeedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems: Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument.
ParameterA parameter (from Ancient Greek (pará)'beside, subsidiary' and (métron)'measure'), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.).Stability criterionIn control theory, and especially stability theory, a stability criterion establishes when a system is stable. A number of stability criteria are in common use: Circle criterion Jury stability criterion Liénard–Chipart criterion Nyquist stability criterion Routh–Hurwitz stability criterion Vakhitov–Kolokolov stability criterion Barkhausen stability criterion Stability may also be determined by means of root locus analysis.Zeros and polesIn complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function (see essential singularity). Technically, a point z0 is a pole of a function f if it is a zero of the function 1/f and 1/f is holomorphic (i.e. complex differentiable) in some neighbourhood of z0.
Walter R. EvansWalter Richard Evans (15 January 1920 – 10 July 1999) was a noted American control theorist and the inventor of the root locus method and the Spirule device in 1948. He was the recipient of the 1987 American Society of Mechanical EngineersRufus Oldenburger Medal and the 1988 AACC's Richard E. Bellman Control Heritage Award.
Closed-loop controllerA closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system.
Linear time-invariant systemMathematical model which is both linear and time-invariantBlock diagram illustrating the superposition principle and time invariance for a deterministic continuous-time single-input single-output system. The system satisfies the superposition principle and is time-invariant if and only if y3(t) = a1y1(t – t0) + a2y2(t – t0) for all time t, for all real constants a1, a2, t0 and for all inputs x1(t), x2(t).Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems. The aim is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.Stable polynomialA polynomial is defined to be stable in two different ways. Hurwitz-stable: In the context of a differential equation (continuous-time) the characteristic polynomial is stable if all its roots lie in the open left complex half-plane. Schur-stable: In the context of a difference equation (discrete-time), its characteristic polynomial is stable if all its roots lie in the open complex unit disk.Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle.FeedbackFeedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems: Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument.ParameterA parameter (from Ancient Greek (pará)'beside, subsidiary' and (métron)'measure'), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.).Stability criterionIn control theory, and especially stability theory, a stability criterion establishes when a system is stable. A number of stability criteria are in common use: Circle criterion Jury stability criterion Liénard–Chipart criterion Nyquist stability criterion Routh–Hurwitz stability criterion Vakhitov–Kolokolov stability criterion Barkhausen stability criterion Stability may also be determined by means of root locus analysis.Zeros and polesIn complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function (see essential singularity). Technically, a point z0 is a pole of a function f if it is a zero of the function 1/f and 1/f is holomorphic (i.e. complex differentiable) in some neighbourhood of z0.Walter R. EvansWalter Richard Evans (15 January 1920 – 10 July 1999) was a noted American control theorist and the inventor of the root locus method and the Spirule device in 1948. He was the recipient of the 1987 American Society of Mechanical EngineersRufus Oldenburger Medal and the 1988 AACC's Richard E. Bellman Control Heritage Award.Closed-loop controllerA closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system.*As an Amazon Associate I earn from qualifying purchases.