An Introduction to Feedback Control

Transcription

1 An Introduction to Feedback Control Control Automático III-Ing. Industriales Escuela Superior de Ingenieros Universidad de Sevilla Outline of the presentation Motivation for control engineering Feedback as a universal paradigm Historical perspective Empirical control Classic control Modern control Course Motivation for Control Engineering A modern industrial plant: A section of the OMV Oil Refinery in Austria 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. 3 4

2 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. Motivation for improved control Improved control is a key enabling technology for: enhanced product quality higher productivity waste minimization energy savings environmental protection greater throughput for a given installed capacity deferring costly plant upgrades, and higher safety margins 5 6 Motivation for improved control All of the aforementioned issues are relevant to the control of an integrated plant such as that shown below. Types of control system design Control system design also takes several different forms and each requires a slightly different approach. Process schematic of an ammonia plant Continuos time control Discrete events control (Automata) 7 8

3 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 algorithms architectures and interfacing accounting for disturbances and uncertainty 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 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,...) 11 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. 12

4 Example A modern rolling mill A typical industrial control problem will usually involve many different actuators: Typical flatness control set-up for rolling mill Communications Computing 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. 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

5 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. 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 eyehand coordination (i.e. control) is also crucial to success Algorithms Disturbances and Uncertainty Better Sensors Provide bettervision Better Actuators Provide more Muscle Better Control Provides more finesse by combining sensors and actuators in more intelligent ways 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

6 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. Outline of the presentation Motivation for control engineering Feedback as a universal paradigm Historical perspective Control previous to the 20th century Classic control Modern control Feedback Other Examples of Feedback 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. r(t) + y m (t) Controller u(t) Measurement and signal transmission system Plant A y(t) Biological Systems Physiological regulation (homeostasis) Bio-molecular regulatory networks Environmental Systems Microbial ecosystems Global carbon cycle Financial Systems Markets and exchanges Supply and service chains ESE 23 24

7 Feedback example Control of linear systems Control based on feedback position Valve flow Tank level R + E U V Y C(s) G a (s) G(s) - Controller Actuator Plant Control device Float Ym G s (s) Feedback Sensor Outline of the presentation Motivation for control engineering Feedback as a universal paradigm Historical perspective Empirical control Classic control Modern control History of Control Theory 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 ( ) numerous technical advances were developed. The Space Race, which lasted roughly from 1957 to 1975, and the development of computers

8 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. 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. Objetive: Regulate the level of the first vessel to obtain a constant flow to the second vessel. Water inflow Floating valve Floating valve = Feedback Relay based control Level high Level low Close water inflow Open water inflow Controlled level Water inflow Hole Constant flow Water level is proportional to time Floating device Output valve Ball-and-cock float-valve (Feedback) The mechanical clock has no feedback The Industrial Revolution The Industrial Revolution The onset of the Industrial Revolution marked a major turning point in human social history (late 18th and early 19th centuries) Based on the development of windmills, furnaces, boilers and at last the steam engine. 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. Could not be regulated by an operator Automatic Control A Watt steam, engine, the steam engine that propelled the Industrial Revolution in Britain and the world No movement 31 32

9 The Industrial Revolution The Industrial Revolution The Float Valve The Steam Engine Same idea of feedback used in the water clock Boiler of steam machines Water supply systems Flush toilet Proportional 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 Automatic control systems: Boiler pressure regulation (safety valve) Centrifugal governor (Throttle regulation) The Industrial Revolution Centrifugal "flyball" governor The Industrial Revolution Symbol of the Industrial Engineers Controller Sensor Actuator System The Centrifugal "flyball" governor become a symbol of the new era of The Industrial Revolution 35 36

10 Feedback Control: The design of feedback control systems up through the Industrial Revolution 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 38 (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 (1868) J.C.Maxwell formulated a mathematical theory related to control theory using a differential equation model of Watt s flyball governor. 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 39 40

11 1920's and 1930's. At Bell Telephone Laboratories the frequency domain approaches - P.S. de Laplace ( ), J. Fourier ( ), A.L. Cauchy ( ), 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. (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 (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. By this time fundamental groundings of the theory of automatic control were well established. Mathematical modeling (Transfer function) Stability Analysis Control design (SISO systems) Control and the World War II During the war feedback control systems became a matter of survival Ship Control Gun Pointing Devices RADAR War plane Example: The V-1 "Buzz Bomb" The V-1 guidance system used a simple autopilot to regulate height and speed Weighted pendulum system provided fore-and-aft attitude measurement to control pitch Gyromagnetic compass (set by swinging in a hangar before launch) gave feedback to control each of pitch and roll Target range was estimated ( accurate enough for area bombing ) and the determination of when it had been reached was by a countdown timer

12 After WW2 boost in control, knowledge was recycled for civil applications Industry Home appliances Civil aviation Other developments (1947) Theory of Servomechanisms [James, Nichols, and Phillips]. Referencia Controlador Actuador Sensor Limitations of classical control The frequency-domain approach is appropriate for linear time-invariant systems and singleinput/single-output systems Limitations to deal with nonlinearities More appropriate descriptions are necessary for complex multivariable control problems (1948) W.R. Evans presented his root locus technique (1949) N. Wiener analyzed information processing systems using models of stochastic processes. Stochastic Analisys Feedback Control: Modern Approach Modern Control (1957) USSR launches first earth-orbiting satellite Also 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 48

13 Modern Control 60 s Different approaches to control theory Optimal 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 Modern Control 60 s Extensions of nonlinear control Zames, Narendra, Desoer Extensive application of these results in the study of nonlinear distortion in bandlimited feedback loops, nonlinear process control, aircraft controls design, and eventually in robotics Late 60 s 70 s First Microprocessor (1969) W. Hoff The advent of the computer era Modern Control Theory of sampled data systems adapted for these new devices J.R. Ragazzini, G. Franklin, and L.A. Zadeh Modern Control Nowadays Control Technology is fundamental 70 s till now Control Theory keeps growing. New problems and challenges Robust Control Adaptive Control Networked and distributed control, etc 51 52

14 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 53