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基于S7-200PLC的连铸结晶器液位控制(无源码).rar

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    Journal of Process Control 21 (2011) 1022– 1029Contents lists available at ScienceDirectJournal of Process Controlj ourna l ho me pag e: www.elsevier.com/locate/jprocontControl of mold level in continuous castingMinsung Kima,∗, SungWoong Moona, Changheum Naaabof KoreaaArticleReceivedReceivedAcceptedAvailable online 13 July 2011Keywords:AdaptiveAdaptiveBulgingContinuousTime-delayindisturbancelagdelay,fuzzythat the1.tantregulating molten steel level is difficult, because it suffers from var-ious disturbances, including variations in casting speed and tundishweight, clogging and unclogging of the nozzle, and bulging dis-turbances [10]. Among these, the bulging disturbance is the mostsevere [11]. It is created when the supporting rollers push the liquidsteelsoidalTherefore,fromturbancecontrollerPIDbasedaspeed[5]turbancesand(S.yskueon@posco.comfunction, whereas in reality the dynamics are more complicatedmainly due to time delay in the molten steel level system. Inthe past, the casting speed and the bulging frequency were rel-atively low, so the effect of system delays, which consist mainlyof actuator delays and sensor delays, were not so serious. How-0959-1524/$doi:upward periodically. The bulging disturbance is almost sinu-in shape and degrades the quality of the molten steel level.we focus on removing the bulging disturbance effectthe molten steel level.Various control strategies have been proposed, including a dis-observer to remove disturbances [1], a master-slave PIDin which a slave PID control loop is used inside a mastercontrol loop to reduce sensitivity to disturbance [2], a model-controller for stable regulation of mold and tundish level [3],neural network model for stopper control to reduce the castingvariation [4], a fuzzy logic controller to remove disturbances, a notch filter, PID and a fuzzy logic controller to remove dis-[6], an H∞ controller to balance disturbance rejectionrobust stabilization [7], a notch filter and an H∞ controller to∗Corresponding author.E-mail addresses: redtoss@postech.ac.kr (M. Kim), midas321@postech.ac.krMoon), changheum@postech.ac.kr (C. Na), drdmlee@posco.com (D. Lee),(Y. Kueon), jsoo@postech.ac.kr (J.S. Lee).ever, as the demand for a high-speed casting process increases,the bulging frequency increases and the phase lag due to systemdelays also increases. For example, given the command sin(ωt),the mold response will be Am·sin(ω(t + td) + DC2) = Am·sin(ωt + ωtd+ DC2),where Amis mold response amplitude, and ωtdis the phase lagdue to system delay td. So, whenever the casting speed increases,ω increases, and the phase lag ωtdincreases even though the sys-tem delay tdis fixed. For this reason, the system delay has becomea crucial obstacle to stabilizing the molten steel level. An adaptivefuzzy estimator has been proposed to remove the bulging distur-bance taking the system delay into account [9], but its performancedegrades significantly when applied to a molten steel level systemwith a time-varying bulging disturbance. In this paper, we pro-pose an adaptive sine estimator based disturbance observer, whichis used to eliminate the time-varying bulging disturbance in thepresence of system delay. In addition, we supplement this observerwith a phase lead adaptive fuzzy controller to reject the remainingdisturbance.This paper is organized as follows. In Section 2, the system mod-eling is derived. In Section 3, the proposed controller is presented.– see front matter © 2011 Elsevier Ltd. All rights reserved.10.1016/j.jprocont.2011.06.003Department of Electrical Engineering, Pohang University of Science and Technology, 790-784Technical Research Laboratories, Pohang Iron dotted line: estimated sinusoidwith 0.3 ˆω (rad) phase lead.∂yse(k)∂hatwideω(k)= ˇkTs·parenleftbigghatwidea∂yse(k)∂hatwideb(k)−hatwideb∂yse(k)∂hatwidea(k)parenrightbigg, (24)∂yse(k)∂hatwideDC2(k)= CR ·parenleftbigghatwidea∂yse(k)∂hatwideb(k)−hatwideb∂yse(k)∂hatwidea(k)parenrightbigg, (25)Fig. 7. Molten steel level under time-varying bulging disturbance within0.25–0.35 Hz range. Solid line: molten steel level; dotted line: estimated sinusoidwith 1.1 ˆω (rad) phase lead.the Q-filter. However, the time advance term, e , is notrealizable. To overcome the problem, we implement theinverse using the adaptive sine estimator (ASE).When the molten steel level passes the band pass Q-filter, itmostly the sinusoidal part in the disturbance frequencyWe then estimate this sinusoidal part of the molten steelthe ASE. Then, we are able to implement the plant inverse bythe phase lead of the sinusoidal input. In fact, when the sinu-input is applied to the plant inverse, its output will also besinusoid with the same frequency, but with adjusted amplitudethe phase lead. The output can be represented asprimese(k) = Kpi·hatwidea sin(hatwideω(kTs+ Tpi) +hatwideDC2) + Kpi·hatwideb cos(hatwideω(kTs+ Tpi) +hatwideDC2),(15)Kpi= |P−1n(hatwideω)|, and TPi= ∠P−1n(j ˆω)/ ˆω.The ASE based DOB is described as in Fig. 5. Mathematically,is almost the same as the ideal DOB that implements Pn−1(s) inoriginal form, because the Q-filter output is almost sinusoidal.the proposed DOB is physically implementable, because theadvance term is replaced with the phase lead of the sinusoidalAdaptive sine estimatorWe now introduce the adaptive sine estimator, which estimatessinusoid that represents the periodic fluctuation of the moltenlevel. The estimated sinusoid can be described asse(k) =hatwidea sin(hatwideωkTs+hatwideDC2) +hatwideb cos(hatwideωkTs+hatwideDC2), (16)hatwidea is the estimated sine amplitude,ˆb is the estimated cosineˆω is the estimated frequency,hatwideDC2 is the estimated phase,= 0,1,2,3,. . . is the discrete time index, and Tsis the sampling time.The ASE updates its parameters ˆa,ˆb, ˆω andˆDC2 so as to minimizecost functionse(k) =12(y(k) − yse(k))2, (17)y(k) and yse(k) are the plant output and the ASE outputWe use the gradient descent method to minimizese(k), and then update ˆa,ˆb, ˆω andˆDC2 as(k + 1) =hatwidea(k) + ˛ · (y(k) − yse(k)) ·∂yse(k)∂hatwidea(k), (18)(k + 1) =hatwideb(k) + ˛ · (y(k) − yse(k)) ·∂yse(k)∂hatwideb(k), (19)hatwide(k + 1) = hatwideω(k) + ˛ · (y(k) − yse(k)) ·∂yse(k)∂hatwideω(k), (20)(k + 1) =hatwideDC2(k) + ˛ · (y(k) − yse(k)) ·∂yse(k)∂hatwideDC2(k), (21)∂yse(k)/∂hatwidea(k), ∂yse(k)/∂hatwideb(k), ∂yse(k)/∂hatwideω(k) and ∂yse(k)/∂hatwideDC2(k)respectively computed as∂yse(k)∂hatwidea(k)= sin(hatwideωkTs+hatwideDC2), (22)∂yse(k)∂hatwideb(k)= cos(hatwideωkTs+hatwideDC2), (23)Note here that ˛, ˇ, and CR are adaptation parameters: ˛determines the adaptation rate of all adaptation parameters, ˇdetermines the adaptation rate ofhatwideDC2, and CR determines the adap-tation rate ofhatwideDC2. The sinusoidal part of molten steel level is wellestimated as the sinusoid with phase lead (Figs. 6 and 7).3.3. Phase lead adaptive fuzzy controllerThe ASE based DOB can reduce a significant portion of thebulging disturbance, but not all of it. Additional measurements willhelp improve the control quality of the molten steel level. We pro-pose to use the phase lead adaptive fuzzy controller (PLAFC) whichworks with the PID controller to eliminate the remaining moltensteel error. The adaptive fuzzy control technique has been usedto estimate and cancel the outgoing flow variance in [14], but theproposed PLAFC aims to reduce the remaining disturbance on themolten steel level.We first construct the AFC using the singleton fuzzifier, the prod-uct inference rule, and the center average defuzzifier. The AFC isrepresented asyfc(k) =summationtextMl=1wl(k) ·parenleftBigproducttextNi=1trimf (uli(k), ali, bli, cli)parenrightBigsummationtextMl=1producttextNi=1trimf (uli(k), ali, bli, cli), (26)1026 M. Kim et al. / Journal of Process Control 21 (2011) 1022– 1029where k = 0,1,2,. . .is the discrete time index; yfc(k) is the fuzzy con-troller output; M is the number of linguistic rules; N is the numberof input; wlis weight of the lth rule; uiis the ith input; trimf is thetriangular membership function where ail, bil, cilare the left feet,peak and right feet of the triangular membership function for thelth rule and ith input. trimf is represented astrimf (uli, ali, bli, cli) =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0, uli≤ ali,uli− alibli− ali, ali3 mm(35)wherefilteredTable 1The input values at which the left feet (A), peak (B) and right feet (C) of the triangularmembership functions occur. NB represents negative big, NM represents negativemedium, NS represents negative small, Z represents zero, PS represents positivesmall, PM represents positive medium, PB represents positive big.Fuzzy rules for errorNB NM NS Z PS PM PBA −4 −3 −2 −1 0 1 2B −3 −2 −1 0 1 2 3C −2 −1 0 1 2 3 4The PID controller is used for C(s) in Fig. 7, and its gains areobtained experimentally:C(s) = 0.12 +0.04s+ 0.00024s, (36)In this experiment, we set ˛ = 0.2, ˇ = 30, CR = 3, and SYN = 0.004. Weused only the level error as the input and seven rules for the PLAFC.The error rate was not used because it did not have a significanteffect on the molten steel level in the hardware simulator. Underone input and seven rules, the left feet, the peak, and the right feet ofthe triangular membership functions are chosen to cover the entireinput range (Table 1). In each rule, initial weights are set to zero.Other parameters (Table 2) were chosen based on actual mea-surement and system identification (see Fig. 10).4.2. Experimental resultWe applied the developed DOB to the molten steel levelsimulator connected with the bulging disturbance generator(Figs. 11 and 12). Under the above parameter settings and 0.3 Hzbulging disturbance, the molten steel level fluctuates withina ± 6 mm range from the reference level with the PID controller, butyuf(k) is the averaged unfiltered molten steel level, y(k) is themolten steel level, and a = 0.03.Fig. 10. The overview of moltenonly a ± 3.5 mm range with the PID controller plus the ASE basedDOB (Fig. 11a). When we add the PLAFC to the PID controller plusthe ASE based DOB, the level falls mostly within ±2.5 mm (Fig. 11b).steel level system.1028 M. Kim et al. / Journal of Process Control 21 (2011) 1022– 1029Fig. 11. PID controller is used when time ≤ 55 s; the ASE based DOB or the ASE based DOBhorizontal lines indicate ± 3 mm from the 100 mm reference level: (a) molten steel levelASE based DOB plus the PLAFC.Fig. DOB plus the PLAFC afterward. The frequency of bulging disturbance is 0.25–0.35 Hz.The steel level performance of the ASE based DOB and (b) molten steel level performanceofMoreover,range,weSTRwhererangesofWeofsteellevel.thetheTableTheTable 3Strike rates (%) of molten steel level.Controller Within ± 2 mm Within ± 3 mm Within ± 5 mm(a) 0.3 Hz bulging frequencyPID 63.00 68.00 87.00PID + ASE based DOB 69.65 82.76 100.00PID + ASE basedDOB + PLAFC85.86 96.21 100.0012. PID controller is used when time ≤ 55 s; the ASE based DOB or the ASE basedfine horizontal lines indicate ± 3 mm from the 100 mm reference level: (a) moltenthe ASE based DOB plus the PLAFC.as the bulging frequency varies within 0.25–0.35 Hzthe controller performance is maintained (Fig. 12).To compare the performance of various controllers numerically,define the strike rate as=nstrikentotal· 100, (37)n is the number of samples that are within the specifiedstrike(±2 mm, ±3 mm, and ±5 mm), and ntotalis the total numbersamples.We examined the strike rates of various controllers as in Table 3.usually recommend ±3 mm range, because the surface qualitythe slabs is considered good in practical systems when the moltenlevel fluctuation is within ±3 mm range from the referenceWe also used ±2 mm range because it is useful to compareperformances of the ASE based DOB to the ASE based DOB plusPLAFC. The ASE based DOB plus the PLAFC achieves the highest2identified parameters of the process.The identified parameters ValueCross sectional area of the mold A (mm2) 125,000Cross sectional area of the mold exit Aout(mm2) 31,400Loss factor SUB 0.7Acceleration of gravity g (mm s−2) 9800Height of molten steel in the tundish H (mm) 2060Stopper gain Ks156Amplitude of bulging disturbance Ad(mm) 6Frequency of the bulging disturbance Wd(rad s−1) 1.88, 1.57–2.20Phase of the bulging disturbance DC2d(rad) 0Casting speed V0(mm s−1) 106.15Actuator time constant FSac0.1Actuator delay Tac(s) 0.20Sensor delay Tsn(s) 0.04plus the PLAFC afterward. The frequency of bulging disturbance is 0.3 Hz. The fineperformance of the ASE based DOB and (b) molten steel level performance of the(b) 0.25–0.35 Hz bulging frequencyPID 60.00 69.00 82.00PID + ASE based DOB 69.31 83.10 99.52PID + ASE basedDOB + PLAFC81.72 95.52 100.00strike rates within the ±2 mm and ±3 mm range among the threecontrollers and therefore qualifies as a good controller candidate.5. ConclusionIn this paper, we introduced an adaptive sine estimator baseddisturbance observer and a phase lead adaptive fuzzy controller toreduce the bulging disturbance effect on molten steel level in thecontinuous casting process. As the processing speed in continuouscasting increases, the time-delay in the mold level system becomesserious, but it is effectively compensated for with a time-delay com-pensation mechanism built into the ASE based DOB. In addition, weadded the PLAFC in conjunction with the PID controller to reject theremaining bulging disturbance. The performance of the proposedcontroller was tested using a 1:1 hardware simulator. The simula-tion test showed that the bulging disturbance effect on the moltensteel level was significantly reduced.M. Kim et al. / Journal of Process Control 21 (2011) 1022– 1029 1029AcknowledgementsThe authors would like to thank Hsiao-Ping Huang, the editorand anonymous reviewers at JPC for many helpful comments andsuggestion on previous draft of this paper. This research was sup-ported by POSCO. Also, this work was supported by the Brain Korea21 Project in 2011.References[1] K. Asano, T. Kaji, H. Aoki, M. Ibaraki, S. Moriwaki, Robust molten steel level con-trol for continuous casting, in: Proceedings of the 35th Conference on Decisionand Control, Kobe, Japan, 1996.[2] R. Keyser, Improved mould-level control in a continuous steel casting line,Control Eng. Practice 5 (1991) 231–237.[3] M.A. Barron, R. Aguilar, J. Gonzalez, E. Melendez, Model-based control of moldlevel in a continuous steel caster under model uncertainties, Control Eng. Prac-tice 6 (1998) 191–196.[4] T. Watanabe, K. OMURA, M. Konishi, S. Watanabe, Furukawa, Mold level controlin continuous caster by neural network model, ISIJ Int. 39 (1999) 1053–1060.[5] M. Dussud, S. Galichet, L.P. Foulloy, Application of fuzzy logic control for con-tinuous casting mold level control, IEEE Trans. Control Syst. Technol. 6 (1998)246–256.[6] D. Lee, Y.S. Kueon, S.H. Lee, High performance hybrid mold level controller forthin slab caster, Control Eng. Practice 12 (2003) 275–281.[7] H. Kitada, O. Kondo, H. Kusachi, K. Sasame, H∞control of molten steel level incontinuous caster, IEEE Trans. Control Syst. Technol. 6 (1998) 200–207.[8] J. Schuurmans, A. K
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