Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Convolution and Laplace Transform

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 control of dynamic systems, linear systems, impulse response, step response, piecewise constant functions, neutral identity, convolution product, Laplace transform, and Fourier transform. It explains the properties of the convolution product, the concept of an integrated ring, and the utility of these tools for solving differential equations.

Instructor

Philippe Müllhaupt

Official source

Ontological neighbourhood

Information engineering

Signal processing: Fourier analysis

Control theory and engineering: Control theory

Related concepts (32)

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.

Step response

The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter.

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.

Frequency response

In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations.

Linear system

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.

Related lectures (47)

Electric Motors: Principles and Applications

Explores electric motor principles, linearity, control systems, active suspensions, and Laplace transforms.

Discrete Systems Analysis: Z-Transform and System Properties

Explores Z-transform, system properties, and analysis of discrete systems, focusing on stability and transfer functions.

Discrete Systems Theory

Covers difference equations, dynamic systems, linearity, and impulse response in discrete systems.

Modeling Dynamic Systems: Definitions and Examples

Covers the modeling of dynamic systems, including definitions, examples, and linearization processes for easier analysis.

Applications of Laplace Transform: State Space Modeling