Lecture

Stability: Poles, Zeros, and Control

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In course

ME-273: Introduction to control of dynamical systems

Cours introductif à la commande des systèmes dynamiques. On part de quatre exemples concrets et on introduit au fur et à mesure un haut niveau d'abstraction permettant de résoudre de manière unifiée les problèmes d'asservissement et de régulation, en parti ...

Description

This lecture covers the concept of stability in dynamic systems, focusing on poles and zeros of transfer functions. It discusses the calculation of residuals, configuration of simple elements, and the control of dynamic systems. The instructor explains the parameterization of multiple complex poles, the relationship between eigenvalues and the transfer function, and the importance of observability in state systems.

Instructor

Philippe Müllhaupt

Expertise Nonlinear Control (Geometry and Algebra)Classical DynamicsRoboticsStatistics Mission Provide rigorous technical and scientific training in nonlinear control, classical mechanics, and statistical theory Current Work Research and teaching in the fields of control theory, statistics, dynamical systems, and general mechanics. Philippe Mullhaupt received his Diplôme d Education Ingï¿½nieur | Electricitï¿½ 1993 – 1993 EPFL DEA | Automatique et Traitement du Signal 199

Official source

Ontological neighbourhood

Information engineering

Control theory and engineering: Control theory

Related concepts (32)

Zeros and poles

In 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. A function f is meromorphic in an open set U if for every point z of U there is a neighborhood of z in which either f or 1/f is holomorphic.

Dynamical system

In 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. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.

Dynamical systems theory

Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.

Dynamic linker

In computing, a dynamic linker is the part of an operating system that loads and links the shared libraries needed by an executable when it is executed (at "run time"), by copying the content of libraries from persistent storage to RAM, filling jump tables and relocating pointers. The specific operating system and executable format determine how the dynamic linker functions and how it is implemented.

Chaos theory

Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization.

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