Research on the Nonlinear Governor of Diesel Engine with Variable Structure Control Theory

Transcription

1 Research on the Noninear Governor of Diese Engine with Variabe Structure Contro Theory Xiao-Bing Mao schoo of energy and power engineering wuhan university of technoogy Wuhan, China Kai-Sheng Lu schoo of energy and power engineering wuhan university of technoogy Wuhan, China Abstract Diese engine speed contro syste is one typica noninear syste. In order to contro speed of the singe input noninear engine, the noninear ode of the 4 engine governor is estabished and the siding ode variabe structure controer is designed in the paper. Siuation in MATLAB has deonstrated that the siding ode variabe structure contro is abe to respond quicky, robust against syste paraeters and externa disturbances, and abe to keep the syste stabe, obtain strong robustness. This paper soves the probe that for the conventiona PID controer, the overshoot is too big, setting and rise ties are too ong. Keywords diese engine speed contro syste, siding ode variabe structure controer, noninear I. INTRODUCTION Variabe structure contro(vsc) is a synthesis ethod which beongs to the noninear contro theory on the basis of phase-pane. Its basis principe is that syste state variabes reaches soe switching surface firsty and then side to the origin ore and ore on this surface. When the siding oveent has good quaity, the purpose of contro is accopished[]. The ain characteristic of this kind of contro is extreey strong robustness. That is, it is insensitive to the ode error, syste paraeter variation and externa disturbance[]. For the genera contro syste, the equation is given as n x f ( x, u, t) x R, u R, t R Siding ode controer is designed by deterining switching function vector s (, s R, and seeking variabe structure contro u (, s( > u ( u ( u ( u (, s( < The foowing descriptions are required siding ode exists, that is, eets ds is ; s if the reaching condition is fufied, the phase-contour beyond the switching surface s wi reach switching surface in iit tie; switching surface is siding ode region, whose siding oveent is ore and ore steady, and the syste has good dynaic characteristic. Therefore, ain tasks of designing siding ode controer are deterining switching surface and designing contro aw. Above a, the structure of variabe structure controer or the figure of switching surfaces and the for of switching functions shoud be confired. Generay, we choose inear switching functions, whose figure eans the contro variabes count [], i.e., xn n s( cx, s R, c R, x R and choose unifor veocity convergence aw as the foowing for: s ε sgn( s), ( ε >, ε R ) or proportiona convergence aw S ε sgn( S ) ks ε, k > or acceerating convergence aw α S k S sgn( S ) k > < α < where, s > sgn( s ), s < Obviousy, for a VSC syste, the existence and the reaching conditions are stated as s s <. The fundaenta difference between VSC contro and the conventiona contro ies in the discontinuity of VSC contro which is a kind of switching characteristic of aking syste structure change at any tie[4]. The contro characteristic can force syste structure change purposefuy by the way of juping in the process of sudden changes according to syste state (deviation and a differentias)at that tie, and to do the upper an ower oveents(siding ode or siding ode oveent) of ow range, high frequency aong the fixed state orbit under certain condition. This kind of siding ode can be designed, and have nothing to do with syste paraeters and disturbances. The characteristic of contro is to ake the syste respond fast and to be robust extreey, i.e., to be not sensitive extreey to ode error, change of target paraeters and perturbations outside /8 /$. 8 IEEE RAM 8

2 II. DIESEL ENGINE SPEED CONTROL SYSTEM MODEL A. Eectronicay Controed Fue Syste of the Engine The speed of diese engine depends on the fue-injection aount. Deveopent of the eectronicay controed fue syste went though three generations. For the first generation of position contro syste, the eectronic governor is used to repace echanica or hydrauic governor on the basis of injection device that aready exists. Usuay, we get the inearized ode of diese engine at first. Then PID agorith is epoyed which coud be adjusted on ine as ong as the contro paraeter is confired. Especiay under the steady - state, when eeting externa strong disturbances, the contro syste overshoot is too big, setting and rise ties are too ong, which infuences the whoe dynaic and static perforance of contro syste to raise. In addition, the saturation phenoenon of the integrator takes pace in the process of starting up or the great dynaic reguation, at the sae tie, the overshoot of the contro syste is too big, recover tie of steady-state engthens. For the second generation of tie controed syste, injection tiing is deterined by energize tie of eectroagnetic vave and the fue-injection aount is deterined by energize duration tie of eectroagnetic vave. Eectronicay controed fue syste epoys the suppying fue principe of the traditiona array and the assign puping punger which is that fue is copressed by fue puping punger driven by the cashaft of fue injected pup which is driven by the diese crankshaft. Then, the high-pressure puse is produced which is conducted to the nozze in the for of pressure wave to raise the neede vave. Thus, this kind of tie controed type injection syste of the autoaticay controed diese engine, no atter which pup (eectronicay controed singe pup, or united pup-nozze), their injection pressures depend on speed of the engine excessivey. Then, when speed and oad are ow, its injection pressure is very ow, and injecting any ties is very difficut. The third generation of coon rai syste gets rid of constraint of ca, whose injection pressure is a kind of fexibe contro according to different diese engine working ode. The pressure-tie coon rai diese engine reaizes not ony precise contro and reguation of the fue-injection aount and the injection tiing, but aso precise reguation of injection pressure and fexibe contro of injection rue. However, no atter which generation production, its speed contro agoriths are a PID and fuzzy- PID. B. The Noninear Mode of the Speed Contro Syste The ain function of the diese engine speed contro syste is to reguate speed. Deviation of the speed of the diese engine depends on the difference of its power torque and oad torque directy. According to the power echanica equation dω J M M Where J is equivaent oent of inertia of tota running parts incuding the diese engine itsef and echanica parts driven by the engine. M and M are changeabe copicated function. The characteristic of the oad torque M is either a function reated to speed such as propeer characteristic in the stabe rivers, vehice characteristic on the steady road, etc., or a kind of quantity with very strong rando factor such as propeer oad in heavy story waves, vehice oad on copicated road, etc. In order to ake the controer eet the appication in genera condition, oad can be regarded as a rando disturbances. So, we can concentrate on discussing the characteristic of the output torque M of the diese engine in the controer design. The output torque M is torque of diese engine in dynaic process. Considering that the output torque of dynaic process coud be approxiate to a series of quasi-steady state, we can oit detais in working process of the diese engine when studying the contro strategy. Then through substituting the torque characteristic of the dynaic process with torque characteristic under the steady state of the diese engine, we get the function for of the power characteristic: p e f ( n, q) where p e is ean effective pressure (M.E.P.), n is the speed of diese engine, q is the fue-injection aount every cyce. So, the output torque M can be expressed as: M M () M M ( n, q ) dn dq M n q If we inearize dynaic characteristics of the diese engine near a certain baanced working point, i.e., M / n and M / q are both constants, () approxiates good near soe point. But if we inearize in a arge scope, the error at the oent is quite big. Thus, the noninear characteristic of the diese engine s dynaic characteristic shoud be sufficienty considered. Oitting interna detais of the diese engine s working process, dynaic characteristic of diese engine can epoy noninear fitting, i.e., M / n and M / q are both considered variabes, and are functions of n and q. Generay speaking, indicated thera efficiency of the diese engine η i is a function which varies according to the speed of engine and oad. But under the situation that speed is a constant(oad characteristic), indicated thera efficiency changes very tiny. Thus, we suppose that indicative thera efficiency is a function of the diese engine speed which is a constant when speed doesn t vary and estabish: kq p i p n const where k is a proportiona constant which reates to indicated efficiency, p is a constant. When the speed of diese engine doesn t change, echanica ost ean pressure can be regarded as a constant. Thus, M.E.P. is : p e pi p kq p p kq c n const () That is to say, reation between M.E.P. and the fue injected every cyce can be considered to be inear. Fig. ists the reation between fue injected every cyce and M.E.P. for severa speeds. However, for every speed, the sope of the fitting straight ine is different, and interception between the fitting with straight ine and coun is different, too, which are because that k andc in () are both paraeters reate to the

3 diese engine speed. And we find that k andc can expressed in degree- poynoia for of speed, i.e., the ethod is poynoia approxiation. Then its dynaic characteristic can be written in a poynoia of degree two as foows: p e bn q bn bnq b4n b q b where p e is M.E.P. (KPa), n is the speed of diese engine(r/in), q is the fue-injection aount every cyce(g), b is a constant. i According to reation between M.E.P. and the output torque, we can get: M a n q () an anq a4n aq a Figure. Reation between M.E.P. and the fue-injection aount Copared () with (), it shows that M / n and M / q are functions of speed n in (). M an a, M 4 an an a n q Then the diese engine dynaic characteristic forua is as foows when working condition varies in arge scope. dn πj an q an anq (4) a4n aq a M Equation(4) is not ony a typica poynoia noninear differentiating equation, but aso a typica singe input iitative noninear syste(reation between the state equation and u is inear). d n x f ( g( u x R u R Generay, we epoy the ean vaue ode which is the average of every cyce to describe engine working process when studying engine. Then regard the engine speed contro syste as a singe input noninear syste which is the sae as that the fue injected is input and speed n is state variabe. Thus, we can choose reasonabe switching surface and contro aw of VSC to get VSC contro ode of noninear engine speed contro syste. III. SIMULATION MODEL In this paper, the vehice s road characteristic is chose as the characteristic of M M ( r) kn Where k is a constant, r is a rando disturbances. If the boundaries of uncertainties [] r is known, etting r.sin(πt ), we can get the foowing atheatica ode as () according to (4): n { d [.sin(π k } n d4n d () ( dn dn d) q Choosing the state variabes as foows: x t e, x e n n, where n is the target speed of diese engine, n is the actua speed, e is the error of speed. then the state equation of the origina syste can be written as: x x x { d [.sin(πt )] k } n d 4n d () ( dn d n d ) u Choosing the foowing switching function for (): s cx x then it shoud eet the foowing siding ode equation as ong as the syste enters the siding ode: s cx x x cx which is soved by : ct x () t x ( ) e Obviousy, ony when c >, the aforesaid is steady. Thus, the VSC syste is steady too. At the sae tie, we can get the foowing equivaent contro according to ds /. { d [.sin(π k } n d4n d cx u eq ( dn dn d Choosing proportiona convergence aw: s ε sgn( s) ks, ε, k > we can confir the structure of the siding ode VSC controer: u u u { d [.sin(π k } n d4n d d n d n d { d [.sin(π k } n d4n d cx d n d n d { d [.sin(π k } n d4n d d n d n d cx ε ks cx ε ks s > s s < If paraeters are chose as foows for 4 diese engine, siuating () as Fig. and Fig., and choosing disturbances as r sin( πt ), we can get siuation resut as shown in Fig. 4:

4 d -.7 d -.4 d.484 d d 74. d c 4 ε k.8 k.7 Figure. VSC controer structure of noninear speed contro syste According to the siuation resut, it is cear that the controer s characteristic of VSC agorith for the noninear syste incudes: good tracing perforance, quick response, tiny overshoot. Especiay adding or subtracting % of the oad, the contro syste is robust. IV. SIMULATION RESULTS To prove the controer and the ode to be correct, the noninear ode is repaced by the actua diese engine. So, we shoud obtain the working MAP of the diese engine at first. Carrying out vast experients, we get data of the fueinjection aount and M.E.P. for different speed. Then, on the basis of supposing the injection fue ahead ange to be not changing, perfor inserting vaue operation by using Mode- Based Caibration Toobox and CAGE in MATLAB software, and obtain property data of the diese engine on other working points. Lasty, estabish MAP of the rea-tie siuation and og the in working odue of the diese engine. As shown in Fig., when siuating in-ring, the controer recognize the speed error and get the contro input u ( the fue injected every cyce q (g)) at first. Then, inquires the MAP together with feedback of the diese speed to obtain the ean indicated pressure(m.i.p.). M.I.P. subtracts ean friction pressure(m.f.p.) is M.E.P.. Mutipies M.E.P. by coefficient k is the power torque. Finay, according to the error that the power torque M subtracts the oad torque M, epoying the power echanica equation principe, we can get the actua speed. Figure. Mode of noninear speed contro syste Figure. VSC structure of siuation in-ring The siuation resuts are shown in Figs.-9: Figure 4. The siuation resut of the VSC

5 Figure. VSC siuation resut Figure. The siuation resut of the PID agorith When strengthening disturbances(increasing or decreasing % oad at rando), as shown in Fig., Figure 7. The output of controer(the fue injected) Figure. % disturbances variation siuation resuts of VSC and PID are respectivey shown in Fig. and Fig.. Figure 8. The output of the power torque Figure. VSC siuation resut of increasing oad Figure 9. The oad torque(disturbances) When appying traditiona PID agorith, the siuation resut is as Fig.: Figure. PID siuation resut of increasing oad Coparing two controers of the noninear engine, it shows that for VSC, overshoot is very tiny, reguating tie is shot.

6 Thus, VSC syste responds fast and has good dynaic and static quaity. V. SHELF TESTS To prove the siding ode controer to be correct, siuations for diese engine in ring are done, as shown in Fig.4 and Fig.. Finay, shef tests are carried out to test the responding abiity in rea-tie. In order to contro the oiinjection aount, a step-by-step eectrica device which is the executive organization of the eectronic governor to decide rack position of the oi pup. The whoe course incudes choosing.s as sape tie and gathering 4 data. And the upper and ower fuctuation of rp range in Fig. is because that speed of the diese engine is instantaneous speed. Test resuts of VSC and PID are respectivey shown in Fig. and Fig.7. Figure 4. VSC siuation resut of diese engine Figure. PID siuation resut of diese engine Figure 7. Shef tests of diese engine with PID agorith SUMMARY The paper proposes a robust contro syste for the diese engine by epoying VSC. The practica iitations of the conventiona PID approach for the speed contro syste are investigated and VSC ethod is proposed as an effective way of overcoing the probes in the conventiona PID approach. The distinctive resuts of this research are suarized. Unike the conventiona ethods, VSC is suitabe for noninear systes[], and is abe to respond quicky against disturbances without overshoot. These appications are being considered as our further research topics. REFERENCES [] V. Utkin, Variabe structure systes with siding odes, IEEE Trans. Autoat. Contr., vo. AC-. pp [] S. Sarpturk, S.Y. Istefanopuos, and O. Kaynak, On the stabiity of discrete-tie siding ode contro systes, IEEE Trans. Autoat. Contr., vo..pp. 9-9, 987. [] U.Kotta, Coents on On the stabiity of discrete-tie siding ode contro systes, IEEE Trans. Autoat. Contr., vo.4.pp. -, 989. [4] Lingfei Xiao, Hongye Su, and Xiaoyu Zhang, A new discrete variabe structure contro agorith based on siding ode prediction, in IEEE AC(Aerican Contro) Conf. Rec.,, pp. 44~449. [] E. Mehet Onder, and O. Ce, Variabe Structure Sontro of a Cass of Uncertain Systes. Autoation, V 4, n, January. 4: 9~4. [] Bouyoucef K., and Khorasani K., Variabe structure-based noninear congestion contro for networked controed systes, IEEE Physics and contro. : 8~8. Figure. Shef tests of diese engine with VSC agorith