Lecture

System Analysis in Frequency Domain

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In course

ME-221: Dynamical systems

Provides the students with basic notions and tools for the analysis of dynamic systems. Shows them how to develop mathematical models of dynamic systems and perform analysis in time and frequency domains. ...

Description

This lecture covers system analysis in the frequency domain, focusing on dynamical systems. Topics include input-output models, step response of LTI systems, underdamped systems, frequency response, first and second-order systems, integrators, differentiators, sinusoidal transfer functions, complex numbers, Bode plots, and examples illustrating the concepts discussed.

Instructor

Mahmut Selman Sakar

Expertise robotics, mechanobiology, microtechnology, smart materials, biomedical devices Teaching & PhD PhD Students Lorenzo Francesco John Noseda, Nikita Norkin, Elif Ezgi Inan, Houman Javaheri, Mehdi Ali Gadiri, Julian Leon Raub, Junsun Hwang Past EPFL PhD Students Erik Mailand, Raquel Filipa Penacho Parreira, Murat Kaynak, Lucio Pancaldi-Giubbini, Fazil Emre Uslu, Matthias Rüegg, Ece Özelçi, Emilie Vuille-Dit-Bille Past EPFL PhD Students as codirector Laura Joan Hermans, Sourabh Monnappa Kuppanda Jafri

Official source

Ontological neighbourhood

Information engineering

Control theory and engineering: Control theory

Related concepts (32)

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.

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.

Transfer function

In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. They are widely used in electronic engineering tools like circuit simulators and control systems. In some simple cases, this function can be represented as two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve.

Bode plot

In electrical engineering and control theory, a Bode plot ˈboʊdi 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 asymptotic approximation of the frequency response, using straight line segments.

Frequency domain

In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal.

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