Lecture

Loop Shaping: Goals

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In course

ME-321: Control systems + TP

Provides the students with basic notions and tools for the analysis and control of dynamic systems. Shows them how to design controllers and analyze the performance of controlled systems. ...

Description

This lecture covers the design of a controller to meet specific requirements by shaping the response of the closed-loop transfer functions, focusing on sensitivity and complementary sensitivity functions, frequency response, bandwidth, and PID coefficients. It explains the relationship between time-domain behaviors, robustness margins, and the impact of noise and reference on the system's output. The lecture also discusses the tradeoff between tracking and noise rejection, the resonance peak, and the closed-loop bandwidth approximating the crossover frequency.

Instructors (2)

Christophe Salzmann

Expertise Real-time Internet ServicesReal-time controlQuality of Service and Bandwidth adaptationLabVIEW Education PhD | Remote experimentation, Network 2005 – 2005 EPFL Directed by Denis Gillet MS. Degree | Computer Science 1999 – 1999 University of Florida Directed by Prof. H. Latchman Teaching & PhD Past EPFL PhD Students as codirector Damien Perritaz, Evgeny Bogdanov, Wissam Halimi Courses Control systems + TP ME

Colin Neil Jones

Colin Jones is an Associate Professor in the Automatic Control Laboratory at the Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland. He was a Senior Researcher at the Automatic Control Lab at ETH Zurich until 2011 and obtained a PhD in 2005 from the University of Cambridge for his work on polyhedral computational methods for constrained control. Prior to that, he was at the University of British Columbia in Canada, where he took a BASc and MASc in Electrical Engineering and Mathematics. Colin has worked in a variety of industrial roles, ranging from commercial building control to the development of custom optimization tools focusing on retail human resource scheduling. His current research interests are in the theory and computation of predictive control and optimization, and their application to green energy generation, distribution and management.

Official source

Ontological neighbourhood

Information engineering

Control theory and engineering: Control theory

Related concepts (32)

Closed-loop controller

A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g., voltage applied to an electric motor) have an effect on the process outputs (e.g., speed or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop.

Control theory

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective 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. To do this, a controller with the requisite corrective behavior is required.

Impulse response

In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (δ(t)). More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).

Principal ideal domain

In mathematics, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element. More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors (e.g., Bourbaki) refer to PIDs as principal rings. The distinction is that a principal ideal ring may have zero divisors whereas a principal ideal domain cannot.

Bézout's identity

In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout, is the following theorem: Here the greatest common divisor of 0 and 0 is taken to be 0. The integers x and y are called Bézout coefficients for (a, b); they are not unique. A pair of Bézout coefficients can be computed by the extended Euclidean algorithm, and this pair is, in the case of integers one of the two pairs such that and equality occurs only if one of a and b is a multiple of the other.

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