英文翻译19880903原文.pdf

Non linear Christian Doppler Control in Rolling Mills A new Perspective A Kugi R Novak and K Schlacher Department of Automatic Control Altenbergerstr 69 4040 Linz Austria Europe kugi mechatronik uni 1inz ac at Altenbergerstr 69 4040 Linz Austria Europe Laboratory Automatic Control of Mechatronic Systems in Steel Industries Abstract This paper is concerned with the application of modern non linear control techniques to the thickness con trol in rolling mills It turns out that the performance of the closed loop can be significantly improved by taking into account the essential non linearities of the to be controlled plant already in the controller design These non linear control strategies totally differ from the common approach of linearizing the non linear system around a nominal oper ating point because they are not limited to a more or less small neighborhood of the operating point but are valid all over the operating range Practically these non linear con trol concepts are a possible answer to the trend of modern rolling mills towards tighter thickness tolerances thinner final strip thicknesses faster production rates and shorter off gauge lengths However a straight forward application of the well established non linear control theory does not always lead to a control concept that is practically feasible It is rather unavoidable to consider all the special features and properties of the plant By means of the gap control of a mill stand with a hydraulic positioning system we will show in detail the advantages of a non linear control ap proach Finally sidulation and measurement results will demonstrate the feasibility and the excellent performance of the proposed design Keywords rolling mill hydraulic positioning system non linear control thickness control hydraulic gap control I INTRODUCTION It is a well known fact that rolling mills are highly com plex coupled non linear systems Nevertheless the classi cal control concepts are mostly based on a linear approach with several single loop controllers These concepts suf fer from two deficiencies namely at first the coupling phenomena are neglected and second it is assumed that the system can be described sufficiently accurate by its linearization around the nominal operating point How ever in recent publications concerning control strategies for rolling mills it is shown that the first deficiency can be overcome by a linear multivariable controller design see e g 5 SI 17 A successfully implemented robust linear MIMO multi input multi output H controller which in addition enables to take into account parame ter inaccuracies of the plant is presented e g in 5 6 It turns out that if the rolling mill is operating around a predefined nominal pass schedule the linearization as sumption is often no substantial restriction But considering the trend of modern rolling mills to wards tighter thickness tolerances thinner final strip thicknesses faster production rates and shorter off gauge lengths we are more and more confronted with the fact that the non linear nature of the rolling process can no longer be neglected in the controller design In this con text let us mention the flying gauge change in continuous rolling mills where in view of minimizing the off gauge lengths the demands on the thickness and tension control concept are very challenging see 14 for more details on this topic In particular in combination with the develop ment of continuous casting a strong trend to continuous hot rolling mills can be expected in the near future During the last decade there have been some signifi cant advances in the area of non linear control system design Apart from the progress in non linear control theory the practical use of these non linear control con cepts was only made possible on the one hand by the increasing availability of computer algebra programs for the symbolic computation and on the other hand by the increasing power of the automation hardware for the real time execution of the non linear control laws A software package in the computer algebra program MAPLEV for the analysis and synthesis of a special class of non linear systems the so called AI affine input systems see e g 7 HI 201 21 can be found e g on the webpage of the Maple Application Center lo Despite for all these advances in non linear control the number of realizations of non linear controllers in the industrial environment is not that wide spread as one might expect from the well established non linear control theory One possible ex planation for this is that a straight forward application of the non linear control methods often results in a closed loop system which is very sensitive to parameter variations and or transducer and quantization noise The control task is getting even more difficult since not all quantities are directly available through measurement and in con trast to linear systems the separation property see e g SI of an observer controller based control design proce dure is no longer valid in the non linear case Hence it is unavoidable to consider all these special features of the to be controlled plant already in the controller design Another important aspect which has to be taken into account is that the proposed control concept can easily 0 7803 6401 5 00 10 00 0 2000 IEEE 2613 Authorized licensed use limited to Central South University Downloaded on February 28 2010 at 23 37 30 EST from IEEE Xplore Restrictions apply be implemented and realized by the commissioning engi neer and that the start up time of the mill can be kept to a minimum This requires that the control concept is ex tensively tested in advance on a mill simulator which con tains a much more detailed model than the model which serves as a basis for the controller design In the mill simulator all the dirty effects like the dynamics of the sensors the quantization the transducer noise the sam pling process the stick slip friction effects between the mill stand and the chocks the parameter inaccuracies in the roll force model etc have to be included Our non linear control approach will only be practically feasible if we can show at least in simulation that the control concept can cope with all these dirty effects The paper is organized as follows In Section I1 the mathematical model of a four high mill stand configura tion with a hydraulic positioning system is derived as a basis for the controller design The next section Section 111 is devoted to the design of a non linear hydraulic gap controller which is in the commonly used thickness con trol concepts the most inner control loop of a cascaded structure Section IV presents some measurement results and in the last section Section V we give a short conclu sion 11 MATHEMATICAL MODEL Without restriction of generality we will base our subse quent considerations on a four high mill stand configura tion due to Fig 1 with the hydraulic adjustment system acting on the upper backup roll Thereby the work rolls are effectively used for the strip deformation whereas the backup rolls serve to support the work rolls in order to prevent too excessive bending of the work rolls The rolls are running in so called chocks which can move vertically in the mill housing and hence enable a change of the roll gap Generally the thickness of the rolled strip is deter mined by the gap between the two work rolls The actual position control is then performed by the exact and fast acting hydraulic adjustment system In the following we will give a detailed formulation of the different components of the four high mill stand of Fig 1 and we will always try to point out clearly the simplifications and neglects of the mathematical model A Hydraulic Adjustment System Let us assume that the hydraulic adjustment system consists of a double acting double ended hydraulic ram with a three land four way spool valve as shown in Fig 2 At this point it is worth mentioning that the con trol approach presented in Section I11 is not restricted to this special configuration but can be easily adapted to all hydraulic adjustment systems commonly used in rolling mills It is a well known fact that generally the mass density of servo valve hydraulic ram z lower work roll screwdown drive Fig 1 Schematic diagram of a four high mill stand with the hydraulic adjustment system acting on the upper backup roll oil pail changes with both pressure p and temperature T By assuming that the oil is isotropic and that the temper ature dependence is negligible we may use the definition of the so called isothermal bulk modulus Eoil see e g 1 1 1 Oil PI Eozl Poil T P L ConSt as a linearized constitutive law Hence the continuity equations written for the two chambers of the hydraulic r a m read as d b o i l 2 VO A x poi 2 qi qe 2 42 2 with the effective piston areas A1 and A2 the displace ment of the piston 2 the volumes V O and V O of the forward and the return chamber for z 0 the flow from the valve to the forward chamber q1 the flow from the return chamber to the valve q 2 the internal leakage flow pi and the external leakage flcows qe l and q Inserting 1 into 2 and using the fact that the leakage flows are laminar we get d EOil A2v 92 C i PI PZ C e 2 2 3 V0 2 A2x Z P 2 with v dx dt and the leakage coefficients Ci Ce l and Ce 2 Suppose that the spool valve is an ideal critical 2614 Authorized licensed use limited to Central South University Downloaded on February 28 2010 at 23 37 30 EST from IEEE Xplore Restrictions apply Fig 2 Schematic diagram of a double acting hydraulic ram with a three land four way spool valve center valve and that it is rigidly connected to a constant pressure pump then the flows from and to the valve q1 and q2 can be calculated by 41 K l time in s Fig 6 HGC with new non linear controller Piston position deviation Ax and spool valve displacement 2 for different offset pressures p ff and different initial positions xo of the piston but now for a singleacting piston configuration see 19 for details of the plant In order to get an impression of the dimension of this mill we will subsequently just give a few data concerning the hydraulic adjustment system The head side of the single acting piston is connected via rigid steel pipes with two three stage servo valves Be cause of the enormous dimension of the piston namely the effective piston area is 1 13 m2 and the maximum pis ton displacement is 0 7 m two valves with a rated flow of 800l min are driven synchronously in order to make the required oil flow available The rod side of the piston is filled with nitrogen at a constant pressure of 3 lo5 Pa and the volume of the connection lines is 0 02m3 With out going into the details here the non linear controller of Proposition 1 can also be applied to single acting piston configurations with some slight but rather easy modifica tions Figure 7 depicts the measured deviation of the pis ton displacement and the associated servo valve position for reference step inputs of 50 m around an operat ing point of approximately 7 8 m and no load in the roll gap with a traditional linear controller and with the non linear controller of Proposition 1 For comparison rea sons with the results of the linear controller and for testing the controller under extreme dynamic situations the pa 2619 Authorized licensed use limited to Central South University Downloaded on February 28 2010 at 23 37 30 EST from IEEE Xplore Restrictions apply rameter a of the non linear controller 16 was adjusted in such a way that the step responses of Fig 7 show an overshoot of approximately 15 As one can immediately see in contrast to the non linear control concept the tra ditional linear controller has a different dynamic behavior for steps in positive and negative directions Especially this fact may limit the achievable thickness tolerances and it badly influences the dynamics of the outer control loops in a cascaded thickness control concept in particular of the mill stretch compensation loop Of course for the nominal operation of the plant CY is decreased such that the overshoot of the step response vanishes 12 I 0 0 I 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 scaled time in s Fig 7 Comparison of the traditional linear with the new non linear controller measured in a reversing hot strip mill in the Czech Republic V CONCLUSION This paper presents a new perspective for designing controllers in rolling mills It turns out that by apply ing modern non linear control theory to control problems in rolling mills we can achieve a significant improvement of the existing control concepts Summarizing we think that this is a further step toward