ENGINE SPEED CONTROL Peter Westead and Mark Readman, contro systems principes.co.uk ABSTRACT: This is one of a series of white papers on systems modeing, anaysis and contro, prepared by Contro Systems Principes.co.uk to give insights into important principes and processes in contro. In contro systems there are a number of generic systems and methods which are encountered in a areas of industry and technoogy. These white papers aim to expain these important systems and methods in straightforward terms. The white papers describe what makes a particuar type of system/method important, how it works and then demonstrates how to contro it. The contro demonstrations are performed using modes of rea systems that Contro Systems Principes partners designed to teach contro ideas and that are now manufactured by TQ Education and Training Ltd in their CE range of equipment. This white paper is about one of the most historicay important contro probems - engine speed contro and reguation.. Why is Important?.. Some History The speed contro of engines is intimatey associated with the origins of contro theory. There are many exampes in the ancient times [] of devices that coud be said to incorporate feedback or reguation, and most basic contro textbooks [e.g.] wi have some discussion of the ancient origins of feedback mechanisms. However, for the true beginnings of modern feedback contro anaysis we must ook to the practica probem of reguating the speed of engines and the centifuga governor (Figure ). Figure. A Simpe Centrifuga Governor. In the beginning of mechanisation, the engine power was suppied by water whees and wind mis but the reay big change occurred when the steam engine arrived in the eary 8 th century. The deveopment of the steam engine in a usefu form was crucia to the success of the Industria Revoution. Equay important for the success of the steam engine was the deveopment of the fy-ba or centrifuga speed governor in the ast quarter of the 8 th century. James Watt is normay associated with this invention, but as so often happens, Watt s innovation was buit upon the work of many other engineers and inventors,[3]. In fact there had been many forms of speed governer before Watt, but the simpicity and
effectiveness of his design, combined with new steam engine deveopments, gave a centrifuga device that coud reguate speed reiaby. It did this via a steam vave connected to a pair of rotating weights. As the engine speed increased, the centrifuga force on the weights increased, and ifted a coar on the reguator shaft. The coar was connected to a vave in a way that reduced steam fow into the cyinders of a steam engine when the speed increased, and increased the steam fow as the engine speed decreased. Figure shows a picture of a very simpe centrifuga governor from our deveopment workshop. The centrifuga governor and the inkage to the steam vave gave a negative feedback oop with which to contro the engine speed. Watt s centrifuga speed governer gave factory and mi owners a reiabe and practica way in which to reguate the speed of a forms of rotating machines, ranging from water whees to steam engines and in a forms of industry that required a constancy of operating conditions. The deveopment of the centrifuga governor was in fact a sideshow to the Industria Revoution, Nevertheess, its invention foowed by its mathematica anaysis - is at the heart of much of today s contro engineering theory and practice. This was enabed by the Industria Revoution, when a group of highy inteigent men who mixed scientific curiosity with commercia energy came into being and formed a conduit between new practica engineering probems and mathematica toos of anaysis [4]. During the 8 th century many scientists and engineers contributed to the improvement of the centrifuga governer with exceent resuts and amazing anaysis. However these peope were outside the British educationa estabishment represented by Oxford, London and Cambridge, and so it waited unti a centrifuga governor found its way to Cambridge in the ate 9 th century before its dynamica anaysis gained scientific respectabiity and wide pubicity in Britain through Maxwe s paper On Governors for the Roya Society of London. The 8 th century deveopments in the industria midands of Engand attracted wide attention from other countries. Vistors from continenta Europe - incuding many important scientists from France and Germany - woud by-pass the stagnant South East of Engand and trave direct to centres of industry such as Birmingham and Manchester where they were wecomed by the Dissenter scientists and engineers. Through this route knowedge of the centrifuga governor and its practica deveopment spread. Its anaysis was widey taken up, with the most we known work being from the Russian, Wischnegradski, but with other important and exceent technica deveopments from Germany and France. However, if we ay aside questions of who did what, where and first, the important fact is that the centrifuga speed governor for engines ed to the important theoretica step that showed that the dynamic behaviour of a system is associated with the roots of a poynomia equation. We now ca this the characteristic equation of a system, the roots of the equation are caed the poes of the system transfer function or the eigenvaues of the system. These concepts ie at the heart of a inear contro systems anaysis and design... The Reevance of Today To see why engine speed contro remains an important issue, we fast forward from the reguation of steam engine speed to the contro of the automobie engine. The petro (gasoine if you are from the USA) and diese motor for cars and orries are the most important engines of our age. For the contro engineer they are intensey interesting to work with and chaenging to contro. In addition to speed, the petro engine has a number of other contro aspects, starting from ignition timing contro, through fue-air ratio contro to the growing number of emissions and efficiency requirements that a require yet more compex contro strategies. The modern car is in fact controed by eectronic contro units (ECU s), Figure, which contains more computing power than was used to take man to the Moon and back.
Figure. An Engine Contro Unit (ECU) photograph by permission of Lucas Industries. The contro of diese engines has foowed a simiar trend with the historica connection that unti quite recenty centrifuga governers were used to imit the maximum and contro the minimum speeds of diese engines. The modern automotive diese engine has an ECU of simiar compexity to the petro engine device. And a this compexity to contro engines. This is why engine speed contro remains reevant today it is the appication that gave rise to the theoretica anaysis and design of contro systems. Moreover, engine speed contro sti ies at the heart of some of the most sophisticated contro systems in the word. Now read on.. A Standard System The basic eements of an engine contro system of the kind that ed to the deveopment of reguators are: A vave with which to change the suppy rate of the fue source A reciprocating engine An output shaft with fywhee and the engine oad. In a standard system, especiay one which students might use, a safe fue source is compressed air. This gives simiar resuts to steam but without the extremes of temperature or energy. A standard engine speed contro system using compressed air is shown in Figure 3. The inet vave is a very important part of this system the vave is non-inear with a dead-zone in its input characteristics. This is important because the input vave dead-zone, usuay caused by static friction, was a significant feature in the design of centrifuga speed governers. Actuator dead-zone remains a probematic feature of engine contro and to emphasize this probem, a arge amount of deadzone is designed into the standard system. The input vave in the standard system is aso motorized so that a constant contro input to the vave motor causes a constant rate of change of the vave position. The airfow rate/ vave position characteristic is aso non-inear so that the contro of the air fow into the engine is itsef a probem. The design and ayout of the engine is typica of a four cyinder steam engine with an inertia oad in the form of a fywhee, and variabe oad in the form of an eectrica generator. To vary the eectrica oad a oad contro votage is used. The appendix shows a more detaied schematic ayout for a standard engine speed contro system. 3
Figure 3. A Standard System 3. Modeing. The components of the standard engine contro system are the air contro vave, the engine and the oad. The air contro vave in turn has two parts, the drive motor and the vave. The drive motor gives a rate of change of vave position y& ( proportiona to the motor input signa u(, so it can be modeed as an integrator with gain g. The vave output pressure P ( is proportiona to the vave position y( so it can be modeed as a gain. m g v dy( dt = g u(, P( g y( () m = v The engine torque τ ( is proportiona to the air pressure. e τ ( g P( () e = e The engine torque is used to suppy the engine oad, frictiona osses and to acceerate the engine fywhee inertia I. If the engine speed is ω then we can write; Rate of change of Engine Frictiona Load = Fywhee Momentum Torque Torque Torque dω( I dt = τ τ e f τ (3) The torque required to overcome friction is τ = bω(, where b is the friction coefficient. The oad torque τ is proportiona to the oad demand votage equations gives: f d ( such that; τ g d ( =.Combining these dω( I + bω( = g dt e g y( g d v ( (4) 4
Equations () and (4) are the differentia equation mode of the standard engine speed contro system. In transfer function form these are: y( s) = ω( s) = g m u( s) s g e g v y( s) b + Is g d( s) b + Is (5) Because the input vave has a dead-zone, the gain g v is non-inear with a characteristic as shown in Figure 4. The air fow gain is aso non-inear but with a smooth characteristic, usuay power aw. In norma operation the vave characteristic is ocay inearised about the norma operating speed of the engine, and the dead-zone is compensated for as described in section 4.. beow. g m dy ( dt D D g m u( Figure 4. Dead-zone Characteristic. 4. Contro Probems for a Standard Engine System. The standard engine contro probem as shown in Figure 3 has two main components that are found in many engine contro situations. They are: The requirement to contro a non-inear input actuator (the air fow contro vave) The requirement to reguate the speed of the engine when the oad on its output shaft changes The soution to these contro probems requires some standard and important contro techniques: Compensation for dead-zone in the actuator. A oca feedback oop is used, together with some noninear compensating mechanism to reduce the actuator dead-zone and to give direct contro over the vave position. The use of cascade contro. An inner feedback oop gives contro over the position of the air fow vave and an outer feedback oop does the speed reguation. The use of feed forward of the oad demand. When a signa is avaiabe which is proportiona to the oad, then the signa (the oad generator demand votage in this case) can be fed forward to the input of the contro system to anticipate changes in oad. 5
4.. Dead-zone Compensation A typica actuator dead-zone characteristic is shown in Figure 4. For input signas smaer than the deadzone width, D, the actuator output response is zero and no actuation signa is sent to the system. This can be compensated for in severa ways. If the actuator position is measured (as in the standard engine speed contro system) then high gain feedback around the actuator can reduce the effective dead-zone by a factor equa to the feedback gain. A further common procedure is to use a technique caed dither. In this a periodic signa is added to the actuator input signa. The frequency of the dither signa shoud be higher than the bandwith of the system dynamics, and the ampitude shoud be approximatey D. The effect of this is to give an effective gain characteristic as shown in Figure 5. dy ( dt g m D D u( g sope m Figure 5. Dither Compensated Dead-zone Characteristic. g m The probem caused by dead-zone is that when the contro signa fas within the dead-zone band, then no contro signa is fed to the system. This causes a servo tracking error proportiona to the size of the deadzone. The advantage of dither is that the vave dead-zone as shown in Figure 4 is repaced by the nonzero gain of. In this case there is aways a corrective contro signa being fed to the system and the servo tracking error can be contro by norma means. There are other dead-zone compensation methods, (see the Servo Systems white paper for detais of this). 4.. Cascade Contro The engine speed contro system is an exampe of a process in which we must first contro the actuator (the air vave) before the main system (the engine) can be controed. This is a common ocurence in industry and eads to what is known as cascade contro. Figure 6 iustrates a cascade contro system for the engine speed contro system. The cascade contro system consists of an inner oop (or save controer) which contros the vave position y ( to a reference vave position y r (. The outer oop (or master controer) contros the engine speed ω ( The outer oop is termed the master contro oop because it suppies the reference vave position which the inner (save) oop must foow. Cascade contro systems are widey used in industria systems, where it is important to proceed step by step through a compex system. The aim is to start with the inner most bocks of a system, pace them 6
under contro and then work outwards to the next eve of contro. In the engine speed contro system the procedure is to cose the vave position contro oop using non-inear compensation, (e.g. dither), and obtain good accurate vave position contro. The vave reference position then becomes the system input for the master controer design. The master controer design woud use three-term contro as described in Eke s white paper (see the down oad page at www.contro-systems-principes.co.uk). K K Figure 6. Cascade Contro Structure for the Standard System. 4.3. Feed Forward Contro An externa oad wi infuence the quaity of contro when it changes. A good feedback controer with integra action can compensate for this externa disturbance. However, if the disturbance can be measured, then better contro can be achieved by using the measured disturbance in the contro system. This is caed Feedforward Contro. In the standard engine speed contro system the disturbance signa, d (, can be measured. This measurement is used to assist the feedback controer action. The signa d ( is fed through a feedforward controer F(s) and added (or subtracted as appropriate) from the output of the feedback controer. By correct choice of F(s) the feedforward signa wi exacty compensate for the infuence of the disturbance. 5. An System Figure 7 shows a commercia version of the standard engine contro probem produced by TQ Education and Training Ltd. It uses compressed air to drive the system and the engine is a scae mode of a steam engine. A other aspects of the system foow the standard mode that was described in Section of this white paper. We wi use a mode of this hardware to iustrate the contro experiments in a ater white paper we wi use the rea system and compare resuts. 7
Figure 7. The TQ CE7 System. 6. Contro Exampes for the Standard System In this section we use simuation to demonstrate dead-zone compensation using dither and cascade compensation. Feedforward compensation is used to demonstrate oad disturbance rejection. The simuation mode is shown beow where the motor dynamics are represented by a simpe st order ag. The actuator incudes an integrator as described above. The inputs are the reference, dither and disturbance signas. DIther SIgna Gain Contro Disturbance Gain4 Reference Gain PID Controer Gain Dead Zone s Integrator s+ Motor Cascad feedback gain Steam engine speed contro Figure 8. Simuation of System. 8
6.. Dead-zone Compensation In this section we compare speed contro of the steam engine with and without dither compensation of the actuator. The dither signa is inserted into the feedback oop just before the input to the actuator. The ampitude of the dither signa shoud exceed the dead-zone and the frequency of the dither shoud be higher than the cosed oop bandwidth of the system. Because the actuator aready contains an integrator, ony proportiona contro is required to track a step change in speed. The simuation resuts shown beow compares contro of the shaft speed with and without dither. The ony difference between these signas is the presence of dither on the ower trace. The dither signa has an ampitude of vot and a frequency of Hz. This is we above the cosed oop bandwidth of the system. Notice the improvement in steady steady state error and dynamic response when the dither signa is added. Aso note that the dither signa has no visibe effect on the contro signa. This is important. The dither signa shoud inearize the system but have as itte effect a possibe on the controed variabes. An accessibe contro orientated dicussion on the use of dither can be found in reference [9]. - - 3 4 5 6 7 8 9 - - 3 4 5 6 7 8 9 Time (Sec) Figure 9. Dead-zone Compensation Using A Dither Signa. 6.. Cascade Contro In this section the dead-zone is compensated for by using feedback. Feedback can have a strong inearizing effect. To demonstrate this in the simuation the dither signa is turned off by reducing the gain in the dither channe to zero. Feedback is now introduced around the actuator. This has the efffect of inearizing the actuator dynamics but aso resuts in a type system. Therefore the PID controer for the shaft speed now has to incude integra action to compensate for the steady state error. The type of a system tes us how many integrators there are in the cosed oop. A type system has none, a type system has one, and so on. The type of a servo system is important because it tes the designer with what input signa he/she can hope to have zero steady state errors. 9
- - 3 4 5 6 7 8 9 - - 3 4 5 6 7 8 9 Time (Sec) Figure. Dead-zone Compensation Using Cascade Contro. 6.3. Load Feed Forward A soution to disturbance rejection is to use feedforward contro. With feedforward contro it is assumed that a signa reated to (ideay proportiona to) the disturbance is avaiabe. For exampe with a steam engine a generator connected to the output might suppy eectrica power to a oad. Measuring the oad current as the oad varies gives a measure of the disturbance signa. This signa can the be used to generate a contro signa that wi cance or reduce the effect of the disturbance. In the simuation beow a trianguar oad disturbance is injected into the feedback oop. The effect of feedforward is ceary seen in Figure. Without compensation this oad disturbance causes a arge steady-state error (bue po. With feedforward compensation this error is ceary reduced (red po. Disturbance s Integrator.5 Dgain Contro Gain s.5s+ Feed Forward Constant PID Controer Dead Zone s Integrator s+ Motor Contro Steam engine speed contro: Feed Forward Disturbance Rejection Figure. Feed Forward Simuation
.8.6.4. -. -.4 -.6 -.8-3 4 5 6 7 8 9 Time (Seconds) Figure. Feed Forward Disturbance Rejection. 7. A Fina Word We are sorry to say that it is not possibe to answer genera questions about the contents of our white papers, uness we have a contract with your organisation. For more information about speed contro of engines and the CE7 System go to the TQ Education and Training web site using the inks on our web site www.contro-systems-principes.co.uk or use the emai info@tq.com. The history of contro systems is a rich one in the area of engine speed contro. For exampe, ook at references [, 3] for the detais of how speed controers were deveoped in the industria revoution. Contro Systems Principes have especiay enjoyed Jenny Ugow s book [4] because it paints a picture of the compex socia and scientific changes that were occuring at the time and gives a wider understanding of the atmosphere in which engine contro was born. For IEEE members the specia issue of the IEEE Contro Systems Magazine [5] is a good read. We aso recommends the web sites [6,7] and industria museum web sites in genera. The Manchester Museum of Science and Industry [8] is especiay good. References.Mayr, O. The Origins of Feedback Contro, MIT Press, 97.. Dorf, R C and Bishop, R H, Modern Contro Systems, (9 th Ed) Prentice Ha. 3. Bennett, S. A History of Contro Engineering, Peregrinus, 979. 4. Ugow, J, The Lunar Men: The Friends that Made the Future, Faber and Faber,. 5. IEEE Contro Systems Magazine, Vo., No., Apri. 6. A mathematica anaysis of the centrifuga governor http://www.nsm.buffao.edu/~hassard/ 7. A exceent site for od engines http://odenginehouse.users.btopenword.com/oeh.htm 8. The Manchester Museum of Industry and Science http://www.msim.org.uk/ 9. Cook, P. Non-inear Dynamica Systems', ( nd ed.) Prentice-Ha Internationa, 994
Appendix Schematic of the Standard Contro System