实机变结构实验.doc

Research on the Governor of Diesel Engine with Discrete Sliding Mode Variable Structure TheoryXiao-Bing Mao School of Energy and Power Engineering, Wuhan University of Technology, Wuhan, China 430063 E-mail: Abstract-The speed control system of diesel engine is one typical nonlinear system. In order to control speed of the engine, in the paper, the nonlinear model of the 2135 engine governor is established. And the discrete sliding mode variable structure controller is designed. In-ring simulation of MATLAB has proved that when controlling a nonlinear system, the sliding mode variable structure control (VSC) has characteristics such as strong adaptive ability, fine static and dynamic qualities, good robustness, etc. Repeated bench tests also verify that the sliding mode variable structure control is able to solve problems that for the conventional PID controller, the overshoot is too big, regulating time is too long and resistibility to external disturbances are bad. I. IntroductionBecause only ideal continuous sliding mode variable structure control has equivalent control in theory produced by switching logic variable structure control, sliding mode variable structure control is mostly for continuous system model. As to discrete system, sliding mode variable structure control which couldnt produce ideal sliding mode only produces the quasi- sliding mode variable structure control. However, in the actual engineering, real-time computer control system is a discrete system, therefore, study on the sliding mode variable structure control of discrete system has becomes an important part of sliding mode variable structure control theory and application. On later 80s of the 20th century, the discrete sliding mode variable structure control developed rapidly, and has got a series of application in the engineering field 1. For a discrete-time system (1)conditions of existence, accessibility and stability are stated as:orChoosing linear switching functions when system is doing sliding mode motion, its state should meetsTherefore, equivalent control could be reduced as:where matrix should not be oddity singular.Correspondingly, the sliding mode equation of discrete-time is as followswhich is dimensions. If the sliding mode parameter matrix is selected appropriately, sliding mode motion could be stable asymptotically.II. GOVRENOR MODELA. The Digital Electronic GovernorWith the development of single-chip computer technology and control technology, the governor of diesel engine begins to be developed toward digital electronic governor from the traditional mechanical governor too. Development of the digital electronic governor passed though three generations. For the first generation of position control system, the electronic governor is used to replace mechanical or hydraulic governor on the basis of injection device that already exists. For the second generation of time controlled system, injection timing is determined by energize time of electromagnetic valve and the fuel-injection amount is determined by energize duration time of electromagnetic valve. The third generation of common rail system gets rid of constraint of cam, whose injection pressure is a kind of flexible control according to different diesel engine working modes 2.All digital electronic governors of different generations have mature products abroad, but no matter which generation product, its speed control algorithms are all PID and fuzzy- PID 35. In the paper, at first, a simulation software of the digital electronic governor which adopts discrete sliding mode variable structure control algorithm is developed in MATLAB environment. Then, under experiment conditions which already exist, bench tests of the first generation digital electronic governor are carried out to prove that the sliding mode variable structure control algorithm is adopted to control the speed of diesel engine better than PID.B. The Nonlinear Model of the Governor The main function of the governor is to regulate speed. Deviation of the speed of the diesel engine depends on the difference of its power torque and load torque directly. According to dAlembert principle, we can get the following equation (2)where is equivalent moment of inertia of total running parts including the diesel engine itself and mechanical parts driven by the engine.Analyzing measured values of 2135 diesel engine, we can get that when the speed is a constant, relation between mean indicated pressure (M.I.P.) and the fuel injected every cycle can be considered to be linear. Therefore, M.I.P. can be written as: (3) where is M.I.P.(KPa), is the fuel injected every cycle(g), and -are constants.Choosing the speed data as follows:=400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 r/min,we can get: 7418.9；7762.4；8148.4；8435.5；8729.4； 8993.6；9608.8；9799.9；9941.9；10035；10080；10070；9997.8；9862.9 -109.5；-116.8；-123.7；-129.5；-133.7；-140.5；-147.2；-149.1；-151.3；-154；-155；-158；-156.5；-156.4Fitting and with degree-2 polynomial form of speed , as shown in Fig. 1 and Fig. 2, we can get: (4) (5)Fig. 1. Fitting result of Fig. 2. Fitting result of In this paper, the vehicles road characteristic is chose as the characteristic of in (2), i.e., (6)where =0.00007 is a constant.Substituting (6) into (2) together with following equations (7) (8) (9)where is mean friction pressure(M.F.P.)(KPa), is mean effective pressure (M.E.P.) (KPa), is the speed of diesel engine(r/min),we have the mathematical model of the diesel engine as the following format: (10)whereChoosing the state variables as follows: where is the target speed of diesel engine, is the actual speed, is the error of speedthen the state equation of the original system can be written as: (11)where III. DISCRETE SLIDING MODE VSC A. Nonlinear State Transformation of the SystemSubstituting into (11), we can get: (12)whereFirstly, sincewhen, the rank of matrix is 2. Secondly, according to involutive distribution theorem, one-dimension distribution must be involutive. Therefore, there must be exist one solvable function which meets i.e.,so as that (12) could be transformed into the followingformat as (13) though nonlinear state transformation: (13)Also, could be easily solved by .Letting transition matrix because latent roots of (13) are , we haveTherefore, we getSince when choosing 0.1s as sampling period , the state equation of the discrete system on the new coordinate is (14)where Correspondingly, relation between the control of the original system and that of the discrete system on the new coordinate is (15)So, the controllability matrix can be written as follows:which demonstrates that the discrete system is completely controllable when sampling period .B. Structure of the ControllerChoosing linear switching functions, (16)writing matrixes and of (1) as(14) and (16) could be transformed into the following standard form though nonlinear state transformation: (17) where Consequently, (17) becomes: Choosing sliding mode parameter matrix by using the method of sliding mode pole assignment, we can separately get the equivalent control and the sliding mode motion equation Letting , the sliding mode motion equation could be written as follows:In order to make the sliding mode motion stable asymptotically, the pole should be allocated to meetChoosing , we can getTherefore, the sliding mode motion equation isSince , we haveConsequently, the sliding mode motion equation and the equivalent control are separately written as follows:To simple structure of the controller, the variable structure control strategy put forward by K.Furuta is adoptedIn order to estimate the max amplitude of original system state variables, letTherefore, max state amplitudes of variables which are educated by the nonlinear coordinate transformation equation are estimated as follows:Consequently, we haveAccording to simulation result, choose . And since we can getTherefore, according to we havefor which the controller is According to (12) and (15), we can getSo structure of the discrete variable structure controller is shown in Fig. 3.Fig. 3. Structure of the discrete variable structure controllerIV. SIMULATION IN-RING OF SOFTWAREIn order to prove the nonlinear model of the diesel engine and the discrete sliding mode variable structure controller to be correct, simulation in-ring of the virtual diesel engine is done.The whole process and the global construction of simulation are shown in Fig.4 which include working processes of the digital electronic governor and the diesel engine. For the former, in order to control the diesel engine speed, continuous servo-regulation of the rack position is done to control indirectly the injection process, where the electric actuating device which installs near the high lift pump to drive the rack is essentially a stepping motor which carries an inner stopper. Therefore, the MAP which represents relation among different speed of the diesel engine, the rack position and fuel injection amount should be included in the working process of the digital electronic governor. For the latter, an actual 2135 diesel engine carries the rack is selected as the subject for research. In order to simulate in-ring, we should obtain measured data of fuel injection amount and the mean indicated pressure (M.I.P.) that correspond with different speed at first. Then, establish the MAP which represents relation among different speed of the diesel engine, fuel injection amount and M.I.P. by using Model-Based Calibration Toolbox and CAGE in MATLAB software. Thirdly, log it in the simulation working module of the diesel engine. Fourthly, regarding speed and fuel injection amount as inputs, inquire the MAP to get the datum of M.I.P. that is the output. Lastly, employ dAlembert principle in simulation to get the actual speed which is a feedback for many blocks in Fig.4. Fig. 4. Structure of the VSC speed control systemAs shown in Fig.5, for the nonlinear system, simulation result of the discrete variable structure controller shows that it has characteristics that good tracking performance, small overshoot, good robustness and so on.Fig. 5. Simulation result of the discrete VSCTo further prove the ascendancy of the discrete variable structure control, replacing the discrete variable structure controller with the PID controller, we could obtain simulation result as shown in Fig.6 which is not good. Fig. 6. Simulation result of the PID controlV. BENCH TESTSTo prove the discrete sliding mode controller to be correct, bench tests for 2135 diesel engine are carried out where a step motor which is the actuating device of the electronic governor is deciding the rack position of the oil pump, as shown in Fig.7 which is experiments result. Fig.8 shows bench tests result with the PID algorithm. All experiments of VSC and PID whose processes respectively include increasing and decreasing suddenly 100% load choose 0.1s as sampling period and gather about 9500 data. From two following Figs, it can be concluded that for the discrete VSC, resistibility to external disturbances are good. Furthermore, there are big error and overshoot in the PID simulation result. However, the upper and lower fluctuation of 15rpm range in Fig.7 is because that on the one hand, speed of the diesel engine is instantaneous speed, on the other hand, the step motor could only advance or recede round figures steps but not decimal steps which induces chattering. Fig. 7. Ben