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Lecture

Dynamical Systems: Transfer Functions

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 the Bode form of transfer functions, filter design, block diagrams, examples of transfer functions, Nyquist plots for stability assessment, and guidelines for quick sketches. It also explores Nyquist diagrams, polar representations, and examples with time delays.

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Instructor

Mahmut Selman Sakar

Official source

Ontological neighbourhood

Information engineering

Control theory and engineering: Control theory

Related concepts (32)

Nyquist stability criterion

In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability of a dynamical system.

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 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.

Nichols plot

The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols. Given a transfer function, with the closed-loop transfer function defined as, the Nichols plots displays versus . Loci of constant and are overlaid to allow the designer to obtain the closed loop transfer function directly from the open loop transfer function. Thus, the frequency is the parameter along the curve. This plot may be compared to the Bode plot in which the two inter-related graphs - versus and versus ) - are plotted.

Filter design

Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful. The filter design process can be described as an optimization problem where each requirement contributes to an error function that should be minimized. Certain parts of the design process can be automated, but normally an experienced electrical engineer is needed to get a good result.

Related lectures (33)

Bode Diagram Synthesis

Covers the synthesis in the Bode diagram, dynamic controls, and the link between the Bode and Nyquist diagrams.

Frequency Response Analysis: Bode and Nyquist Diagrams

Explores frequency response analysis through Bode and Nyquist diagrams, emphasizing controller synthesis and system stability.

Nyquist Stability Criteria

Explains Nyquist stability criteria and loop shaping for system performance and robustness.

Frequency Sampling

Explores the frequency sampling method to approximate ideal filters, useful for quick prototyping but lacking fine control over errors.

Nyquist Criterion: Stability Analysis