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Pt.1: Negative Feedback and Control Systems WHAT IS NEGXI1VE Have you had trouble understanding the concept of feedback? This article tells the story of feedback irr simple everyday terms. By BRYAN MAHER Negative feedback systems are part of our everyday experience. They may be electronic, mechanical, hydraulic, pneumatic, nuclear, chemical, economic, logical, biological - almost any type. We are born with them, they control our bodies, the Sun and the stars, our domestic appliances, our motor cars, virtually everything. So we ought to have a simple description, an explanation, which is expressed in a language which every body can understand. This short series of articles aims to do just that. Once upon a time there was a little girl and her dog, a lovable mischievous hound, playful but quite adverse to washing. One day, after being all soaped up, the dog took off and jumped over the back fence at the sight of the rinsing hose spouting cold water. The little girl decided to hose down that squirming, frothy animal by squirting hose water high over the fence. Trouble was, she couldn't hit her moving target because the fence blocked her view. Then she hit on a solution. She enlisted the aid of her big brother to sit on the top of the fence and feed back directions to her. "Swing hose to left ... no, more left! ... too much! ... back some! ... a bit to the right ... lift hose higher ... too much! ... down a bit..." The farce went on as the dog, out of the little girl's line-of-sight, dodged back and forth in attempts to avoid the freezing hose water. At the same time, big brother found that both he and little sister had to be quick or · the dog could move Without negative feedback, modern amplifiers would not be able to give the superb performance that we routinely expect from hifi equipment. 10 SILICON CHIP away faster than the information could be fed back to hose-toting little sister! While it would never be referred to as such in a child's bedtime story, here was a negative feedback system in violent action. • The Input or Demand was the little girl's desire to hit the soapydog with hose-water. The Desired Output would be an image of the input demand; ie, a clean, wet dog. • The Actual Output was the hosewater missing the dog and landing on the ground (ie, the feedback system was not fast enough). • The hose itself and the water it carried was the dumb power or energy input. • The Negative Feedback was the information fed back by big brother sitting on that fence. • The Error was the difference between the spot where the hosewater landed, and the spot where it should have landed. That last statement could be stated concisely as: Error = (Desired Output Actual Output) Now the Desired Output is an image of the Input Demand. And the Feedback Information is an image of the Actual output. The Actual Output cannot be "seen" by the system. Feedback becomes the only indication to the system of what's happening at the output end. So, best results come when the system is working to make the Feedback and the Input Demand coincide (which implies that the Actual Output and Desired Output also coincide). In other words: Error = (Input Demand Feedback) = Zero Now, because Feedback appears in that equation as a negative, we call it a Negative Feedback System. We say that the "forward Autopilot In a Yeppoon fishing boat, the auto-pilot control system may be instructed to keep the boat heading east to reach Keppel Island fishing reefs. Here the input is "Direction East'', the controller is the direction sensing and correction circuitry, the actuator is the hydraulic ram system pushing the rudder into position, and the output is the direction the boat is actually heading. In an Ft 11 fighter airplane, the pilot may insert an input instruction "fly to Keppel Island coordinates" into his Inertial Navigational System, a remarkable electromechanical-hydraulic control system. Here the first input is the pair of co-ordinates which describe the position of Keppel Island (the pilot inserts these numbers using digital switches). Other inputs include: (a) Reference position coordinates before he starts. (b) Inputs automatically inserted to describe the Earth's pear-shape; (ie, it is · bigger in the southern hemisphere). (c) Inputs automatically inserted to describe the Earth's bulge around the equator. (d) Inputs automatically inserted to de.s cribe the effect on the plane of Coriolis force. (e) Inertial references to the "fixed" stars of the universe by way of electrically-driven captured gyroscopes. The controller in this case is an electronic analog computer, while the actuators are the hydraulic rams controlling the wing, tail and FEEDBACK? system" from the Input to the Output, plus the "returning feedback information pathway" from the output back to the "front end" makes a "closed loop". Thus, Negative Feedback Systems are known as Closed Loop Systems. Later, when big brother tired of the game and departed to ride his skateboard, little sister could only squirt the hose in a hope-for-thebest sort of action, simply applying the Input but not being able to correct to bring the error to zero. Naturally, the results were pretty awful. This last condition, without any feedback path closing the loop, is (not surprisingly} known as an Open Loop System. Our wet-dog story vividly illustrates all the features of every Closed Loop Negative Feedback System. Alternative names used are "Automatic Control System", "Feedback Control System", or just "Control System". All mean the same thing. These days, electro-mechanical and electro-mechanical-hydraulic control systems are everywhere. If the Feedback Control System is purely electronic, and all components and actions linear, we would simply call it a "Negative Feedback Amplifier". All hifi audio amplifiers fit into this description. Essential parts The Feedback Control systems we meet may be fairly simple, or they may be extremely complicated but usually we will be able to identify the essential parts as in Fig.1: (1} Input. Sometimes called the command or demand, there may be more than one input. Sometimes we must be careful to define exactly what is the input. The input is the definition of what we want done. (2} Controller. The brains of the system, the controller may be anything from a simple electronic amplifier to a complex electrohydraulic system controlled by a computer. (3} Actuator. The muscle of the system, the part that actually does the work. It may be a single output transistor, or the power output stage of your hifi amplifier, a hydraulic ram, a 20MW electric motor or even a two-gigawatt power station. (4) Output. Supposed to be the obedient servant of the input. Hence the common name Servo System (the word servo is a Latin word meaning slave). Sometimes the term MasterSlave System is also used. As with the input, sometimes it is not quite obvious exactly what is the output. And there may be more than one output. If one of the inputs is a carefully maintained constant it is often called a reference. If the input command is to keep the output quantity level always, the whole feedback system is usually called a regulator. Let's have a look at a few examples of Negative Feedback Control Systems. INPUT CONTROLLER - ACTUATOR -- OUTPUT Fig.1: the essential elements of an open loop control system. There is no feedback path from output to input. - INPUT- CONTROLLER ACTUATOR OUTPUT FEEDBACK TO CONTROLLER OF INFORMATION ABOUT OUTPUT Fig.2: a closed loop control system. In this system, information is fed back from the output to modify the controller action. Al'HIL 1988 11 BUILDING UNDER CONSTRUCTION BUILDERS SCAFFOLD Builders and bystanders GEAR WHEEL ----, MOTOR WINDING DRUM H01ST AT GROUND LEVEL I I Fig.3: a simple motor-driven hoist. With this scheme, it's difficult to operate the on/off switch to stop the hoist in the correct position. table, the Input is the instruction "keep the turntable speed exactly 33-1/3 RPM". The controller is a complex electronic circuit which includes frequency to voltage converters. The Reference is the frequency of a crystal oscillator, the Actuator is a DC motor mounted directly on the turntable shaft, the Output is the actual rotational speed of the turntable. As we want the output to be a constant always, we might call this control system a "speed regulator". rudder surfaces. The output is the aircraft's arrival position. The result is remarkably accurate the plane will pass over the island and if further instructions are not given, the plane will automatically fly in a circle with the island coordinates as the centre. Should strong side winds prevail during the flight the controller will sense that the direction of heading is incorrect and automatically insert compensation aimed at successful arrival at the desired coordinates. This is a very different system from the autopilot on the fishing boat. On the boat it is the heading direction which is controlled; on the Fl 11 it is the arrival position (coordinates) which is controlled. System types To summarise, systems can be divided into two types: [a) Open Loop Systems in which the input or command is inserted into the controller and we hope the correct result app13ars as the output. as in Fig, 1. That's all there is to it· you might call them "hope for th~ Speed regulator In a direct drive record turn- LIMIT SWITCH ON COLUMN WORKED BY RISING HOIST \ J_ __ , -------j r ___ I I I I HOIST I ==S=CA=F::::F/=LD=ING=L=·Ev=EL====:::::1 Fig.4: a limit switch can be used to stop the hoist automatically. Motor over-run after switch-off is the problem here. 12 best" systems. Such systems are simple, stable, inaccurate, not automatically error-correcting, and are often under human control. [b) Closed Loop Systems in which the input command is inserted into the controller, an output occurs, and something is fed back from the output to tell the controller how accurately the input command was obeyed. The controller is capable of correcting the output if it is not right, as in Fig.2. SILICON Cllll' This is a fantasy, with a theoretical message. A group of young electronics enthusiasts were standing on the footpath watching the construction of a multi-storey building. Being "of enquiring mind" they watched, fascinated, the electro-mechanical feedback control problem which unfolded before them. In Fig.3 we see a hoist used in a building under construction. Workmen wheel barrows of wet cement onto the hoist, then switch on a motor to lift the hoist and barrow of cement up to the level of the scaffolding. Another workman wheels the barrow off the hoist onto the scaffolding platform to the worksite. The difficulty is that if the man working the motor switch is not good at it, he will stop the motor with the hoist platform not quite level with the scaffolding, leaving a step up to the scaffolding. If you have ever tried to wheel a builder's barrow of wet cement up even a small step, you will be very enthusiastic a bout improving the whole system. An improvement was suggested to the electrician on the site. A switch was mounted on the hoist to stop the motor when it reached the right level, as is done in many lifts [see Fig.4). This was a failure as motors take time to stop after being switched off and some "over-run" was bound to occur, varying with different weight loads. Something better was needed. Somehow any over-run must be automatically corrected. Closed loop system As shown in Fig.5, a method was devised to generate a voltage, Fig.5: in this scheme, a potentiometer provides an output voltage that's proportional to the hoist's vertical position. This voltage is then fed to the control circuitry. r----- ,I I HOIST I I I [b) Error Voltage = [A - BJ = positive when the hoist is lower than it should be; and (c) Error Voltage = (A - B) = negative when the hoist is higher than it should be. Clearly, the feedback voltage B subtracts from the input voltage A, and tends to make the output smaller, so it is called negative SCAFFOLDING LEVEL I b====== d======== POTENTIOMETER - - REPRESENTS VERTICAL POSITNJN OF HOIST which we will call B, proportional to the hoist's actual vertical position. Our intrepid electrician was really being innovative here. Tests showed that a voltage B = 5.1234 volts was generated when the hoist was actually level with the scaffolding, more when the hoist was higher, less when the hoist was lower. And the voltage B = 0 was generated when the hoist was down on ground level. At any position, the voltage was a linear function of the hoist's vertical position. As this voltage represents information about the output, it is called the feedback. The controller was an amplifier with a gain of 10 and powerful enough to drive the 50V 30 amp DC hoist motor directly. The input A was switched to zero when the hoist was wanted down on ground level. Similarly, input A was switched to + 5.1234 volts when the hoist was required to go up to the scaffolding. Finally, a difference amplifier was added between the input and the controller; ie, an amplifier whose output E is equal to the difference between two input points A and B. Thus: Error E = (A - B) As shown in Fig. 6, the switched input A and the feedback voltage B (which indicates hoist position) are the two inputs to the difference amplifier. The difference (A - B) was called the error voltage because the difference (A - B) truly represents the error in the position of the hoist. We note that: (a) Error Voltage = (A - B) = zero when the hoist is in the correct position; feedback. Errors apparent Then someone noticed a funny thing: the hoist never reached quite high enough, always stopping a little lower than the scaffolding. Always the motor stopped when the feedback voltage B was about 4.8 volts, the input voltage A being of course 5.1234 volts. That is, it stopped when the Error Voltage was (5.1234 - 4.8) = 0.3234 volts. This being amplified by 10 meant that the motor came to a stop when the voltage supplied to it fell to 3.234 volts. This is not surprising after all (even though it would have been nice if the motor could continue to run until the voltage supplied came right down to zero). No-one could expect a motor to give enough torque with only 3.234 volts applied, so it stopped. One of the observers then made the obvious suggestion: "Why not raise the amplifier gain to 100 instead of 10?" To quell any fears of overvoltage being applied to the motor the electrician raised the amplifier gain to 100 but arranged it so that the amplifier output would always be limited and never exceed ± 50 volts [to protect the motor). +5.1234VOLTS REFERENCE DIFFERENCE AMPLIFIER ZERO «;) SWITCH VOLTU,_ ERROR VOLTAGE E = (A-8) .,. CONTROLLER AMPLIFIER ACTUATOR = OUTPUT = POWER AMPLIFIER .,__ _ HOIST POSITION AND MOTOR I = I TURN SWITCH UP TO +5.1234V WHEN HOIST REQUIRED TO GO UP TURN SWITCH DOWN TO ZERO VOLTS WHEN HOIST REQUIRED TO GO DOWN MECHANICAL ___ CONNECTION NEGATIVE FEEDBACK VOLTAGE IS A _ _ _ _ _ _F_uN...c_Tm_N_OF_H_OI_ST_V_ER_nc_A_LP_o,.s1T_1o_N 1 1 +6V I -------'--,-s POTENTIOMETER VFB VFB = OV AT BOTTOM = +5.1234V WHEN HOIST IS UP AT SCAFFOLD ZERO VOLTS Fig.6: control circuit for a motor-driven hoist. The difference amplifier compares a reference voltage (either + 5.1234V or OV) with the voltage from the potentiometer. This gives an error voltage which is amplified and used to drive the motor. J\l'HIL HW8 13 HOIST VERTICAL POSITION UNLOADED HOIST VERTICAL POSITION I VOLTAGE A UNDERSHOOT LOADED HOIST VERTICAL POSITION f= O TIME TIME SWITCHED FROM OV TO +5.1234V Fig.7: the hoist position as a function of time. If the hoist is unloaded, it will tend to oscillate about the desired stopping point. Now the hoist went up like a charm with a full barrow of cement in it. stopping much closer to correct position. This was because at the point where it used to stop, the error voltage of 0.3234 volts was being multiplied by 100 to 32.34 volts and of course the motor kept running up until the error in position was only about 1110th as much as before. One of the bystanders observed that the error in position appeared to be reduced by the same factor that the gain was increased. She guessed that perhaps the error in position of the hoist might be inversely proportional to the gain of the amplifier. and wondered, "Would the error be nearly zero if the gain were increased to 1000 or 1,000,000? Can the gain be increased indefinitely?" The answer to the silent question came when the builder sent the hoist up empty with no load at all. What happened gave everyone a fright! With no load at all the hoist went up quite quickly. The big gear wheel on the hoist winding drum got up to quite a speed and, of course, stored up considerable rotational momentum and rotational energy because of its moment of inertia. When the hoist got close to the scaffolding height the voltage applied to the motor reduced towards zero, but with no load the rotational stored energy in the gearwheel [and 14 SIUCON Cl/IP in the motor and winding drum too) just kept the hoist running. It shot right past the point where it should have stopped, eventually coming to rest 400mm too high. Of course, the feedback voltage up here was higher than 5.1234 volts, actually 5.32 volts. This made the error voltage E = (5.1234 - 5.32) = - 0.2 volts. This, when multiplied by 100 in the amplifier, produced - 20 volts [note that negative sign) at the motor, which thus reversed direction, sending the hoist plummeting downwards! It went right past the scaffolding position where E = zero, down at least 200mm too low before it stopped, where the amplified error voltage [now positive) measuring about + 15 volts sent the hoist up too high again! This went on for a few minutes until finally the hoist came to rest quite close to the correct height while the builders stood and watched with their mouths wide open. Clearly they had to know something about the dynamics of the system, whether mechanical, electrical or anything else! Someone drew a rough sketch of the vertical path of the hoist as a function of time, reproduced here as Fig.7. One bystander thought that this sketch looked just like the response of a second order differential equation when disturbed by a step function [ie, something just switched on). Someone said that the gain of the amplifier would have to be reduced and the error in the hoist position tolerated, but another observed that if the moment of inertia J of that big gearwheel could be reduced, they might not have to reduce the amplifier gain and could thus keep the error small. It then occurred to the onlookers, more or less simultaneously, that it ought to be possible to develop a theory to describe the antics of this hoist. Obviously, such a theory would be of enormous benefit to anyone who wanted to design elecronic amplifiers or machines, as then they could choose how much error, if any, whether it would overshoot the landing or not, and how stable the thing would be - and all this before it was ever built! It wasn't hard to see that such a theory would have a little mathematics in it, but that would serve to make it an elegant theory. Also it was pretty clear that this theory would include a few equations containing symbols representing things like Moment of Inertia (J), the Rotational Spring Constant of shafts [K) and something to describe any form of loss such as Bearing Friction or Brakes [B). Then of course all the electronic bods would want their C for capacitance in Farads, L for inductance in Henries, and G for conductance in Siemens [G Siemens = 1/R ohms). Naturally the variables would be volts [the "across" variable) and amps [the "through" variable). Someone quietly observed that all these constants J, K, B, C, L and G all represented quantities that were always positive, real and constant. So they would be nice things to have as coefficients of the equations. Remembering that graph of the overshooting and undershooting of the hoist we showed before as Fig.7, and the observation at the time that it just looked like the solution to a differential equation they had seen somewhere, they excontinued on page 96 T CEli'I' Cash in your surplus gear. Advertise it here in Silicon Chip. Advertising rates for this page: Classified ads - $7.00 for up to 15 words plus 40 cents for each additional word; Display ads (casual rate) - $20 per column centimetre (max. 10cm). Closing date: five weeks prior to month of sale. If you use a PO Box number, you must include your permanent address and phone number for our files. We cannot accept ads submitted without this information. To run your own classified ad, put one word on each of the lines below and send this form with your payment to: Silicon Chip Classifieds, PO Box 139, Collaroy Beach , NSW 2097. 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IBM compatible . Australian designed and manufactured. Ideal project for user groups or students. For a free catalog send a 37c stamp to : Don McKenzie, 29 Ellesmere Crescent, Tullamarine 3043. SHACK CLEAROUT . R1000 Kenwood Receiver with box and instructions. As new- $300 . HX 2000 Regency scan ner $200; Ranger AR3300 HF transceiver, 26-30MHz, 25W PEP, AM-SSB-CW-FM, $250; Marconi signal generator TF995 with spares $100; 2 x UHF CB Uniden Sundowner with CTCSS modules fitted , $200 each; 9dB base station antenna $90; 6dB base station antenna $60; Ratcliff 96 SILI CON Cl-Ill' signal generator Model 205 (45 - 180MHz) $50. All prices negotiable. Ring (02) 487 1439 after 8pm evenings and weekends . Garry VK2YBX. FOR SALE: ETI SERIES 5000 preamplifier, $320. 1/3-octave graphic equalisers, $160 each . Phone (02) 542 3628 after 5pm . Amateur Radio continued from page 69 which is wrapped around the top of the loading coil. Figs.1 & 2 show the details. This construction technique must be followed exactly, otherwise the resonant frequency will be other than that which is desired. In any case, a GDO (grid dip oscillator) should be used to verify the correct frequency of operation, after the antenna is mounted on the vehicle. After the coil has been wound .and the coupling "capacitor" installed, the PVC shroud can be glued in place and the top of the coil soldered to the top metal fitting. As the 1/2-wave whip mounting technique is quite strong, it is suitable for either VHF or UHF antennas. ~ Negative Feedback continued from page 14 pected to have the theory as a set of differential equations. Let's leave our young enthusiasts before they get too far ahead of us. Clearly they must be the brightest building site observers ever. One point is clear though. When they have fully developed their theory of feedback systems, it will be a truly general set of equations. Next month, we will show you more of this fascinating stuff, but we will naturally accent the electronic side of this beaut story. And we will be very down-to-earth and practical to boot. ~