Construction Process Control of Large Extra Caissons

TSINGHUA SCIENCE AND TECHNOLOGYISSN 1007-0214 13/21 pp359-363Volume 10, Number 3, June 2005Construction Process Control of Large Extra CaissonsHU Shaowei (胡少伟+)"*, WANG Hongxia (王红霞), FAN Jiansheng (樊建生)1. Department of Materials and Structural Engineering, Nanjing Hydraulic Research Institute,Nanjing 210024, China;2. Schoo of Naval Architecture and Ocean Engineering, Shanghai Jiao Tong University,Shanghai 200030, China;3. Department of Civi Engineering, Tsinghua University, Bejing 100084, ChinaAbstract: The complexity of geotechnical engineering and varability in construction circumstances of largeextra caissons make the problem of maintaining appropriate sink attitude quite dificult, especially in keepingsink uniformity and achieving the expected final sink depth. A new construction control method is presentedusing H。theory, considering uncertainties in the mechanics model and external noise in the constructionsite parameters. The design method of an H_ controller has consequently been obtained for large extracaissons. Control results using only constructor experiences are compared with simulation results using theH.. contollr ftor a practical engineering sitution, which indicates that the H。contoller is successful inmaintaining sink uniformity, avoiding sink as well as in achieving the expected final sink depth.Key words: large extra caissons; construction process; atitude control; H_ controlwithout sink attitude analysis from the principle of aIntroductionsink mechanics model. Hu and Niel-l did not considerThe extra caisson is a structure with an open top andthat uncertainties might occur in the process of con-bottom, while the lateral surface is a closed-loop. Thisstruction, and consequently one of the extra caissonsstructure is applied to foundation engineering ofdeflected severely. To solve this kind of control prob-bridges, pump stations, underground plants, under-lem involving uncertainty of the model and statisticalground storages, and foundations of buildings. Sincecharacters of parameter noise, a suitable controlextra caissons are often built in complex soil, in ordermethod should be developed to handle all these com-to keep sink uniformity, to prevent sink sharp, and toplications. In this paper, attitude control of a large ex-achieve the expected final sink depth, the constructiontra caisson is studied using H。。 control theory, takingcontrol of an extra caisson is very important. Althoughinto account uncertainties of the mechanics model andmuch experience has been obtained in constructionexternal noise around the construction site.control, there is still a lack of a mature theory and a1 Equation of Sink Statecredible numerical simulation stable for practical application. Abesener' adjusts excavation in terms ofWithe中国煤化工say, when there is no .observed information; this is a rather passive approachexcava caisson is subjectedReceived: 2003-12-24to itsYH. C N M H Grection on the blade.* * To whom correspondence should be addressed.It also suffers a floating force while undrained. TheE-mail: hushaowei@ nhri.cn; Tel: 86 25- 85829601sink equation under these conditions is'1360Tsinghua Science and Technology, June 2005, 10(3): 359 - 363mh=G-(Ufn-2.5U.f)-K.Kmp.considered when examining control methods for Eq.(3), i.e, a suitable controller based on parameter uncer-| cN. +zrbN, |Ub+rN.Ubh |-N =tainties and external noise must be designed for largeextra caissons.-(U,J +KmpyN、Ub)h+G+2.5U.f-2 Design Problem for H_ ControllerK_Kmp[ cN。+;ybN, Ub-N.(|)The most important thing for sink attitude control of anwhere U， is the external perimeter of the extraextra caisson is to let the extra caisson reach the de-caisson; U2 the internal perimeter of the caisson; Usigned elevation in the designated construction periodthe mean perimeter of the extra caisson, U=(U1+U2)/2;, tatis ()="m alanFurthermore, thef the sidefrictionper unitarea:Nq=0(1+ sinp)e*m1-sin psin(2η+φ)N.=(N。-1)cotp; N,= (N-controller must maintain uniform sinkage, i.e, make1) tan1.4p; c cohesion for unit soil; φ the internaly,()=s°t. The control objective is, therefore, to .t,friction angle; γ gravity of the soil; b the thicknessmake output near y,(t) during the construction pe-of the sidewall;G the dead load and additional loadriod, but without using too much control energy.helping sinkage of the extra caisson (kN); N theSuppose the error vector isweight of outlet water from the sidewall (kN);e(t)= y,(t)-y(t)(4)N =0 (when sink drained); m the mass of the extraand the performance index is given bycaisson; K a factor influenced by the cross sectionJm= ['[e" ()Qe()+ u" ()Ru(t)Jdr(5)and blade reaction; K。a factor influencing reactionof the blade considering disturbance of soil;where Q (positive definite) is the weighting matrix ofgravitational acceleration; and h the sink depth ofthe error vector and R > 0 is a weighting factor of thecaisson. .control vector.Equation (1) can be simplified asFor large extra caisson, the state equation ish=ah+az(2)x=Ax+B,u，x(0)=x。(6)K_K1To minimize Eq. (5), and to ensure a closed-loop sys-wherea=-_γN,Ub--Uf，tem that is continuously stable, a state feedback con-nmtroller is designed，2.5K_KmpNa=g+-( cN。+=ybN,Ub--u= Kx(7)The controller which makes Jmine can be obtainedWe introduce a control force u. The equation ofthrough solving the relevant Riccati equations. So farsink state is then given bythe design problem does not consider the influence of[x=Ax+B,u,extermal noise. That is to say, optimality of perform-l y=Cxx(3)ance index can be achieved only when the controlledobject is described accurately by Eq. (6). The optimal-ity cannot be realized due to noise in real systems. Towhere A =la 0_B.=」C2=[1 0]，include this effect, we introduce noise w . The con-trolled model is then given byx, x=h+岁, x=j.x=(A+OA)x+ Bw+ B,u(8)a中国煤化工al.Because there are many uncertainties in construction,:MYHC N M H G the singularity valuethe influence of model uncertainties (here indicated asanalysis theorem,parameter uncertainties) and external noise must beMA=E EF(9)HU Shaowei (胡少佛) et al: Construction Process Control of Large Extra Caissons361where E∈∩ is arbitraryunknown matrix,[(,-Cx) Q(y. -C,x)+ Ru"()]d<2={EIE"E≤l}.Considering a state feedback contolled system thate["w()d，Vw∈L2(16)makes the performance given by Eq. (5) a minimum,tenable to all noises w which satisfy Eq. (14), wherewe defined an auxiliary signal,ε>0 is given constant.Q"0Now discuss controller design problems that satisfyZ=[(x+.e"(10)robust stable performance and interference suppressionwhen uncertainties exist in the system.where Q"2 is the square root of the matrix, andWhile M=0,if A+B,K is a stable matrix andQ=Q"Q42.satisfies closed-loop system.Then J in Eq. (5) is given by(C+D2K)(sI-A-B,K)" B| <1. .J= [~"()2()d= 5h" (1)h(t)dt(11)where h(t) is pulse response of closed-loop systemTo solve the state feedback controller satisfying Eq.constituted by Eqs. (7), (8), and (10).(1) and Eq. (2), supposeIn terms of Parseval identityl4, Eq. (1) can be given_[w7z|的=，i=(17)」° [2」byJ=，C "r'(jo)T(jo)do=The augmented contolled plant is then'71，L ur{r(ja)rT (jo)}dw(12)[y_=G(s)的(18)u」where T() is a closed-loop transfer function fromwtoz.A一B、EB2Equation (12) is the definition of the H2 norm ofrational number T(s)，G(s)=|[C]「D.2](19)|(])L=ζ+_([r[()*(io)]do} (3)[F」[0C2Therefore, the design mentioned above is able tosolve the feedback controller K so as to make the Controllers that satisfy design indexes (1) and (2) canclosed-loop system stable and | T(s)|，a minimum.be used to obtain K(s) by solving H__ , the standardInterference suppression of the sink system isdesign problem of augmented controlled plant G(s).discussed next. Noise sets of a large extra caisson areThe controller is then givenby u= K(s)x.defined5I as(14)3 Practical Engineering Example4=05 w()u0certain pump station. The caisson is round with theto represent the interference suppression level. For aexternal diameter of 52.4 m, the intermal well is astepped structure, the wall thickness is from 1.0 m to .dynamic feedback contollerf),1.92 m. The designed elevation of the blade is 14.1 m,u=Kx(15)the start sink elevation of the blade is 1.2 m, and the .consider the design index as follows:nf the. oytra. raicconn is 15.9 m. The1) The closed-loop system is quadratic stable whenconst中国煤化工: an ancient channelw=0.2) The closed-loop system satifies the interferencedepos:rYHC N M H Gyers are distributedunevenly. Soil layers that the extra caisson cross aresuppression performance index when 0A=0 asalty clay, mud salty clay, and mud clay in turn. Winitial state x(0) = 0, to arbitrary t, >0, there is362Tsinghua Science and Technology, June 2005, 10(3): 359 - 363designthe controller considering interferencecontroller. To maintain sink uniformity and arrive atsuppression with the aim of sink uniformity and obtainhe final sink depth， the designed excavation isthe final sink depth.compared with a practical excavation without :The state equation of the extra caisson is given bycontroller as shown in Fig. I. A significant difference01].0 ... 0]is seen between the two cases in Fig. 1. .i=x+y+u(20)[- -3.6558+8 0_| 0.0001」14厂12-where x=[x x]",x=h+a/q =h-0.9211, x2=h, and h is sink depth. The range of parameterObserved datauncertainties is taken as |8| ≤3.6558x0.3= 1.0967 ;stthis denotes that there is a 30% uncertainty in a. The'4-H。designdesign state feedback controllers that make the closed-loop system must satisfy.1) For parameter uncertaintiesδ ，the system is5507509501150quadric stable;1/2) For arbitrary givent, >0,Fig. 1 Time history of excavation depth with H.design and observed data without controller5[(s,-C:x)" Q(y, -Cx)+ Ru"(c]d<“w2()drFigures 2 and 3 give the time history of sink depth(21)under H。controller together with observed resultsConsider any δ satisfying 8|≤ 1.0967 . Supposewithout a controller. It can be seen that the sink curvethat the weighting function is given as:under H_ controller is nearly a straight line, denoting「72 0that sink of the extra caisson is uniform, and that theQ=R=1，E=|1,)0controller achieved the expected results. Figures 2 and83 also present the H_ controller suppression interfer-F=[1.0967 0]，E=1.0967ence affecting sink depth.Define the evaluation signal z =Cx + D2u such that6[70]「0]2C|=D2=|0，√Vε=1.| 1.0967 CHoo controllerThe state feedback controller (u = Kx ) that satisfies首the mentioned conditions can be obtained throughsolving H_ as in a standard design problem of G(s)0.21.01.52.0 2. sfor Eq. (19). By subtituting the data mentioned aboveExcavation (10'm)for Eq. (19), the positive solution satisfying the RiccatiFig. 2 Sink depth varying with excavation with H.equation is given bycontroller and observed data without controller「17.3472 3.2070x=3.2070 2.4346 JTo find out the effect on the sink depth of parameteruncertainties, we make a perturbation analysis on pa-The expected controller is thus given byrameter a (Ref. [9]). Assume the nominal value in theK=[-3.2070 -2.4346].range of 30%. thatis. a. =-3.0591, -3.5591, - 4.0591,中国煤化工of -3.6558 The timeSince the start mark of measurement is 343 h, theexcavation time is also taken from 343 h so as to allowhistHC N M H Glationship between thea comparison in the relationship between excavationexcavation and sink depth with the H_ feedbacktime and sink depth using the H_ controller and nocontroller for the different a are shown in Figs. 4 and 5.HU Shaowei (胡少伟) et al: Construction Process Control of Large Extra Caissons363164 Conclusions2-To maintain sink uniformity and to obtain the finalObserved datarequired sink depth in construction of large extra85caissons，construction control must consider twoH.o contollerimportant factors which affect the sink attitude4severely. One is the geotechnical uncertainty; the otheris interference associated with the construction6008001200circumstances. The important contribution of the/hcontrol method presented in this paper is the ability toFig. 3 Time history of sink depth with H。controller andconsider uncertainties and to suppress interference.observed data without controllerThe numerical results presented show that the H_18ra= -3.0591controller is successful in attitude control ina- 3.6558construction of a large extra caisson, especially inmaintaining sink uniformity and in arriving at the final吉官!2a=-4.5591sink depth'References6[1] Abesener Joe. Automatic construction techniques for largeextra caisson. Construction of Civil Engineering, 1999,400100040(2): 9-15.[2] Yang Qihai. The method of righting and correcting inclina-Fig. 4 Time history of sink depth with perturbationtion for large extra caisson of Yuanjiang bridge. Consrruc-of parameter a in system matrixtion of Bridge, 2000, (1): 51-53. (in Chinese)a- -3.0591[3] Hu shaowei, Nie Jianguo. Dynamic behaviour of oilfielda=-3.5591A' form derricks. Tsinghua Science and Technology,an=-3.65582001, 6(1): 57-62.食12-a--4.0591= -4.55914] Meyerhof G G. Bearing capacity and sttlement of pilefoundation. Journal of the Geotechrical EngineeringDivision, Proc. ASCE, 1965, 12(1): 88-96.5-[5] Hu Shaowei, Nie Jianguo, Wang Wei. Dynamic asessmentof the carrying capacity of olfeld derricks. Tsinghua Sci-ence and Technology, 2001, 6(1): 63-66.0.51.01.52.02.5[6] Sun Gengsheng. Zheng Datong. Soft Soil Foundations andExcavation (10'm')Substructure Works. Beijing: China Building Press, 1984.Fig.5 Sink depth varying with excavation with(in Chinese)perturbation of parameter a, in system matrix[7] Lin Guoxiong, Fang Qinhan. Study on design and keytechnology of Wuhu Yangtse Bridge. Construction 0fIt can be seen from Figs. 4 and 5 that although theBridge, 1998, (4): 1-8. (in Chinese)interference explicitly affects the model of the extra[8] Williams M L. Stress singularities resulting from variouscaisson, the output is nevertheless quite similar for aboundary conditions in angular comers of plates in extension.certain input under the H。controller. That is to say,Joumal of Applied Mechanics, 1952, 5(4): 526-528.the robustness of the controller to parameter[9] Xu Zilun. Elastic Mechanics. Beijing; Tsinghua Universityuncertainties is good; and the influence of modeluncertainties affecting sink depth is quite small under中国煤化工merical Recipes - Thethe H_ controller. The designed H。 controllerTYHC N M H Gmbridge, London, Newtherefore had a good application value in constructionYork: Cambridge University Press, 1986.control of this large extra caisson.