Outline of the presentation An Introduction to Feedback ...

An Introduction toFeedback Control

Control Automático III-Ing. Industriales

Escuela Superior de IngenierosUniversidad de Sevilla

Course 2008-092

Outline of the presentation

Motivation for control engineeringFeedback as a universal paradigmHistorical perspective

Empirical control Classic controlModern control

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Motivation for Control Engineering

Feedback control has a long history which began with the early desire of humans to harness the materials and forces of nature to their advantage.

Early examples of control devices include clock regulating systems and mechanisms for keeping wind-mills pointed into the wind.

Modern industrial plants have sophisticated control systems which are crucial to their successful operation.

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A modern industrial plant: A section of the OMV Oil Refinery in Austria

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Relevance of Control Engineering

Control Engineering has a major impact on society (although it is a sort of hidden technology)

Indeed, most modern systems (aircraft, high speed trains, CD players, … ) could not operate without the aid of sophisticated control systems.

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Improved control is a key enabling technology for:

enhanced product quality higher productivitywaste minimization energy savingsenvironmental protection greater throughput for a given installed capacity deferring costly plant upgrades, and higher safety margins

Motivation for improved control

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Process schematic of an ammonia plant

All of the aforementioned issues are relevant to the control of an integrated plant such as that shown below.

Motivation for improved control

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Types of control system design

Control system design also takes several different forms and each requires a slightly different approach.

Continuos time control Discrete events control(Automata)

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System Integration

Success in control engineering depends on taking a holistic viewpoint. Some of the issues are:

plant, i.e. the process to be controlled objectives sensors actuators communications computing and algorithmsarchitectures and interfacing accounting for disturbances and uncertainty

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Plant

The physical layout of a plant is an intrinsic part of control problems.

Thus a control engineer needs to be familiar with the "physics" of the process under study.

This includes a rudimentary knowledge of the basic energy balance, mass balance and material flows in the system.

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Objectives

Before designing sensors, actuators or control architectures, it is important to know the goal, that is, to formulate the control objectives. This includes

what do we want to achieve (energy reduction, yield increase,...)

what variables need to be controlled to achieve these objectives

what level of performance is necessary (accuracy, speed,...)

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Sensors and actuators

Sensors are the eyes of control enabling one to see what is going on. Indeed, one statement that is sometimes made about control is:

If you can measure it, you can control it.Once sensors are in place to report on the state

of a process, then the next issue is the ability to affect, or actuate, the system in order to move the process from the current state to a desired state. This is achieved by means of the actuators.

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A typical industrial control problem will usually involve many different actuators:

Typical flatness control set-up for rolling mill

Example

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A modern rolling mill

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Communications

Interconnecting sensors to actuators, involves the use of communication systems.

A typical plant can have many thousands of separate signals to be sent over long distances.

Thus the design of communication systems and their associated protocols is an increasingly important aspect of modern control engineering.

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Computing

In modern control systems, the connection between sensors and actuators is invariably made via a computer of some sort.

Thus, computer issues are necessarily part of the overall design.

Current control systems use a variety of computational devices including DCS's (Distributed Control Systems), PLC's (Programmable Logic Controllers), PC's (Personal Computers), etc.

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Architectures and interfacing

The issue of what to connect to what is a non-trivial one in control system design.

One may feel that the best solution would always be to bring all signals to a central point so that each control action would be based on complete information (leading to so called, centralized control).

However, this is rarely (if ever) the best solution in practice. Indeed, there are very good reasons why one may not wish to bring all signals to a common point. Obvious objections to this include complexity, cost, time constraints in computation, maintainability, reliability, etc.

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Algorithms

Finally, we come to the real heart of control engineering i.e. the algorithms that connect the sensors to the actuators. It is all to easy to underestimate this final aspect of the problem.

As a simple example from our everyday experience, consider the problem of playing tennis at top international level.

One can readily accept that one needs good eye sight (sensors) and strong muscles (actuators) to play tennis at this level, but these attributes are not sufficient. Indeed eye-hand coordination (i.e. control) is also crucial to success.

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Better ControlProvides more finesse by combining sensors and actuators in more intelligent ways

Better ActuatorsProvide more Muscle

Better SensorsProvide betterVision

Algorithms

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Disturbances and Uncertainty

One of the things that makes control science interesting is that all real life systems are acted on by noise and external disturbances.

These factors can have a significant impact on the performance of the system.

As a simple example, aircraft are subject to disturbances in the form of wind-gusts, and cruise controllers in cars have to cope with different road gradients and different car loadings.

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Homogeneity

A final point is that all interconnected systems, including control systems, are only as good as their weakest element.

The implications of this in control system design are that one should aim to have all components (plant, sensors, actuators, communications, computing, interfaces, algorithms, etc) of roughly comparable accuracy and performance.

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Control previous to the 20th centuryClassic controlModern control

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We will see that feedback is a key tool that can be used to modify the behaviour of a system.

What is feedback system ? a system that uses a measurement of the output and compares it with the desired output in order to obtain the desired behaviour.

Feedback

A’

ym(t)

+

−y(t)u(t)r(t)

Measurement and signaltransmission system

PlantController

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Other Examples of FeedbackBiological Systems

Physiological regulation (homeostasis)Bio-molecular regulatory networks

Environmental SystemsMicrobial ecosystemsGlobal carbon cycle

Financial SystemsMarkets and exchangesSupply and service chains

ESE

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Feedback example

Control based on feedback

TankValve

flow

level

FloatControl device

position

FeedbackFeedback

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Control of linear systems

Controller

G(s)C(s)

Gs(s)

Ga(s)

Actuator Plant

Sensor

-

+R E U Y

Ym

V

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Empirical control Classic controlModern control

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Main historical facts involved in the development of Control Theory:

Greeks and Arabs concern for measuring time in a precise manner. Several feedback applications were developed between 300 B.C. and 1200 A.D.

The Industrial Revolution was a period in the late 18th and early 19th centuries when major changes in agriculture, manufacturing, and transportation had a profound effect on socioeconomic and cultural conditions.

During World War I and World War II (1914-1945) numerous technical advances were developed.

The Space Race, which lasted roughly from 1957 to 1975, and thedevelopment of computers.

History of Control Theory

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The First Control Applications

A water clock or clepsydra is any timekeeper operated by means of a regulated flow of liquid into (inflow type) or out from (outflow type) a vessel where it is measured.

Water inflow

HoleWater inflow

Constant flow

Water level is proportional to time

Controlled level

Floating valve

Floating device

Output valve

Objetive: Regulate the level of thefirst vessel to obtain a constant flowto the second vessel.

Floating valve = Feedback

Relay based control

Level high Close water inflowLevel low Open water inflow

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The First Control Applications

The notion of feedback that gave rise to the Greek water clock was applied in several other inventions, however, the development of the mechanical clock in the 14th century stopped the invention of new feedback based designs until the Industrial Revolution.

The mechanical clock has no feedbackBall-and-cock float-valve (Feedback)

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The Industrial Revolution

The onset of the Industrial Revolution marked a major turning point in human social history (late 18th and early 19th centuries)

A Watt steam, engine, the steam engine that propelled the Industrial Revolution in Britain and the world

Based on the development of windmills, furnaces, boilers and at last the steam engine.

Could not be regulatedby an operator

Automatic Control

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Edmund Lee's "Fantail"

Fantail: A little windmill mounted at right angles to the sails, at the rear of the windmill, and which turns the cap automatically to bring it into the wind.

Patented in 1745 by Edmund Lee, a blacksmith working at Brockmill Forge in Wigan England.

No movement

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The Float Valve

Same idea of feedback used in the water clock

Boiler of steam machinesWater supply systemsFlush toiletProportional control action

The ballcock (also balltap or fill valve). Invented by Thomas Crapper is a float valve used in flush toilets (WC).

Relay control action

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The Steam Engine

Automatic control systems:• Boiler pressure regulation (safety valve)• Centrifugal governor (Throttle regulation)

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Actuator

Sensor

Controller

Centrifugal "flyball" governor

System

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Symbol of the Industrial Engineers

The Centrifugal "flyball" governor becomea symbol of the new era ofThe Industrial Revolution

Feedback Control:Classic Approach

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Classic Approach

The design of feedback control systems up through the IndustrialRevolution was by trial-and-error together with a great deal of engineering intuition. Thus, it was more of an art than a science.

In the mid 1800's mathematics was first used to analyze the stability of feedback control systems. Since mathematics is the formal language of automatic control theory, we could call the period before this time the prehistory of control theory

The early work in the mathematical analysis of control systems was in terms of differential equations

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Classic Approach(1840) British Astronomer G.B. Airy, developed a feedback device for pointing a telescope. His device was a speed control system which turned the telescope automatically to compensate for the earth's rotation, affording the ability to study a given star for an extended time.Airy discovered that by improper design of the feedback control loop, wild oscillations were introduced into the system. He was the first to discuss the instability of closed-loop systems, and the first to use differential equations in their analysis

Key Issue: STABILITY

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Classic Approach

(1868) J.C.Maxwell formulated a mathematical theory related to control theory using a differential equation model of Watt’s flyballgovernor.He studied the effect of the system parameters on stability and showed that the system is stable if the roots of the characteristic equation have negative real parts. With the work of Maxwell we can say that the theory of control systems was firmly established The Birth of Mathematical

Control Theory

Routh (1884); Hurwitz (1895), algebra stability criterion. Numerical technique for determining when a characteristic equation has stable roots

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Classic Approach

1920's and 1930's . At Bell Telephone Laboratories the frequency domain approaches - P.S. de Laplace(1749-1827), J. Fourier (1768-1830), A.L. Cauchy (1789-1857) , and others - were explored and used in communication systems

Problem: extending voice signals over long distances needs periodical amplification. Unfortunately, unless care is exercised, not only the information but also the noise is amplified.

(1934) H.S. Black demonstrated the usefulness of negative feedback in the design of amplifiers. The design problem was to introduce a phase shift at the correct frequencies in the system.

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Classic Approach

By this time fundamental groundings of the theory of automatic control were well established.

(1932 ) H. Nyquist. Derived his Nyquist stability criterion based on the polar plot of a complex function.

(1938) H.W. Bode. Used the magnitude and phase frequency response plots of a complex function. He investigated closed-loop stability using the notions of gain and phase margin

Mathematical modeling (Transfer function)Stability AnalysisControl design (SISO systems)

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Classic Approach

During the war feedback control systems became a matter of survival

Control and the World War II

Ship Control

Gun Pointing Devices

RADAR

War plane

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Classic Approach

The V-1 guidance system used a simple autopilot to regulate height and speedWeighted pendulum system provided fore-and-aft attitude measurement to control pitchGyromagnetic compass (set by swinging in a hangar before launch) gave feedback to control each of pitch and rollTarget range was estimated ( accurate enough for area bombing ) and the determination of when it had been reached was by a countdown timer.

Example: The V-1 "Buzz Bomb"

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Classic ApproachAfter WW2 boost in control, knowledge was “recycled” for civil applications

(1947) Theory of Servomechanisms [James, Nichols, and Phillips].

(1948) W.R. Evans presented his root locus technique(1949) N. Wiener analyzed information processing systems using models of stochastic processes. Stochastic Analisys

Other developments

Industry Home appliances Civil aviation

Sensor

Actuador

Controlador

Referencia

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Classic Approach

Limitations of classical controlThe frequency-domain approach is appropriate for linear time-invariant systems and single-input/single-output systemsLimitations to deal with nonlinearitiesMore appropriate descriptions are necessary for complex multivariable control problems

Feedback Control:Modern Approach

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Modern Control

(1957) USSR launches first earth-orbiting satelliteAlso in Soviet Union relevant advances in nonlinear control

(1893 -> 1960) Lyapunov – characterization of stability for nonlinear systems(1948), Ivachenko - principles of relay control(1960), Popov – Stability for hybrid linear-nonlinear systems (Circle criterion)

Differential equation are reintroduced as mathematical tool

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Modern Control

60’s – Different approaches to control theoryOptimal Control (Bellman, Pontryagin)Estimation theory (Kalman, Bleltram)

Matrix description is introduced(State Space)

A Kalman filter is used to provide navigational data for the first lunar

landing

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Modern Control

60’s – Extensions of nonlinear controlZames, Narendra, DesoerExtensive application of these results in the study of nonlinear distortion in bandlimitedfeedback loops, nonlinear process control, aircraft controls design, and eventually in robotics

The advent of the computer era

Late 60’s – 70’s First Microprocessor

(1969) W. Hoff

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Modern Control

Theory of sampled data systems adapted for these new devices

J.R. Ragazzini, G. Franklin, and L.A. Zadeh

70’s – till nowControl Theory keeps growing. New problems and challenges

Robust ControlAdaptive ControlNetworked and distributed control, etc

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Modern Control

Nowadays Control Technology is fundamental

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What do these two have in common?

Tornado Boeing 777

• Highly nonlinear, complicated dynamics!• Both are capable of transporting goods and people over long distances

BUT• One is controlled, and the other is not.• Control is “the hidden technology that you meet every day”• It heavily relies on the notion of “feedback”

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