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.
Harry NyquistHarry Theodor Nyquist (, Swedish:; February 7, 1889 – April 4, 1976) was a Swedish-American physicist and electronic engineer who made important contributions to communication theory and feedback control systems. Early life and educationHarry Theodor Nykvist was born on 7 February 1889 in the village of Nilsby, in the , Värmland, Sweden. He was the fourth of eight children born to Lars Jonsson Nyqvist (1847–1930) and Catarina (or Katrina) Eriksdotter (1857–1920).
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.
Bode plotIn electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptoticapproximation of the frequency response, using straight line segments.
Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake.
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.
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.Rational functionIn mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.Singularity (mathematics)In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the reciprocal function f ( x ) = 1 / x {\displaystyle f(x)=1/x} has a singularity at x = 0 {\displaystyle x=0} , where the value of the function is not defined, as involving a division by zero.Open-loop controllerIn control theory, an open-loop controller, also called a non-feedback controller, is a control loop part of a control system in which the control action ("input" to the system) is independent of the "process output", which is the process variable that is being controlled. It does not use feedback to determine if its output has achieved the desired goal of the input command or process setpoint.
SiemensGerman multinational conglomerateSiemens AG (German pronunciation:or) is a German multinational company. It is focused on industrial automation, building automation, rail transport and health technology. Siemens is the largest engineering company in Europe, and holds the position of global market leader in industrial AI, automation, and industrial software.
Bell LabsResearch and scientific development companyNokia Bell Labs, commonly referred to as Bell Labs, is an American industrial research and development company owned by the Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world.
Harry NyquistHarry Theodor Nyquist (, Swedish:; February 7, 1889 – April 4, 1976) was a Swedish-American physicist and electronic engineer who made important contributions to communication theory and feedback control systems. Early life and educationHarry Theodor Nykvist was born on 7 February 1889 in the village of Nilsby, in the , Värmland, Sweden. He was the fourth of eight children born to Lars Jonsson Nyqvist (1847–1930) and Catarina (or Katrina) Eriksdotter (1857–1920).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.Bode plotIn electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptoticapproximation of the frequency response, using straight line segments.Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake.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.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.Rational functionIn mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.Singularity (mathematics)In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the reciprocal function f ( x ) = 1 / x {\displaystyle f(x)=1/x} has a singularity at x = 0 {\displaystyle x=0} , where the value of the function is not defined, as involving a division by zero.Open-loop controllerIn control theory, an open-loop controller, also called a non-feedback controller, is a control loop part of a control system in which the control action ("input" to the system) is independent of the "process output", which is the process variable that is being controlled. It does not use feedback to determine if its output has achieved the desired goal of the input command or process setpoint.SiemensGerman multinational conglomerateSiemens AG (German pronunciation:or) is a German multinational company. It is focused on industrial automation, building automation, rail transport and health technology. Siemens is the largest engineering company in Europe, and holds the position of global market leader in industrial AI, automation, and industrial software.Bell LabsResearch and scientific development companyNokia Bell Labs, commonly referred to as Bell Labs, is an American industrial research and development company owned by the Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world.*As an Amazon Associate I earn from qualifying purchases.