Nonlinear Hydraulic Gap Control: A Practical Approach

Copyright @ IFAC Control Systems Design, Bratislava, Slovak Republic, 2000

NONLINEAR HYDRAULIC GAP CONTROL: A PRACTICAL APPROACH Rainer Novak * Kurt Schlacher * Andreas Kugi ** Helge Frank ***

* Christian Doppler Laboratory for Automatic Control of Mechatronic Systems in Steel Industries, Altenbergerstrasse 69, A-4040 Linz, Austria ** Johannes Kepler University, Department for Automatic Control, Altenbergerstrasse 69, A-4040 Linz, Austria *** VOEST-ALPINE Industrieanlagenbau, Turmstrasse 44, P. o. Box 4, A-4031 Linz, Austria

Abstract: This paper presents measurements and evaluates the results of a new nonlinear hydraulic gap controller (HGC) implemented in a reversing hot strip mill. Modern rolling mills contain several feedback loops and the roll gap is usually adjusted by a hydraulic system. Since the HGC is part of the most inner control loop in this cascaded structure, the use of a controller with high dynamics for the hydraulic positioning system is essential due to performance considerations. In order to fulfill the constantly rising demands on the quality as well as on the minimal strip thickness tolerances of the rolled products, it is unavoidable to improve existing control algorithms. Up today, linear design techniques are used for the HGC in most cases, although the nonlinear nature of the hydraulic system can be taken into account by means of modern nonlinear control concepts. Furthermore, the controller must be robust against friction forces, leakage flows, transducer and quantization noise in all possible operating conditions. This paper compares measured step responses of a recently proposed nonlinear controller with conventional linear ones. Copyright @20001FAC Keywords: Geometric approaches, Hydraulic actuators, Nonlinear control, Servo hydraulics

1. INTRODUCTION

ware or by new control concepts that take into account the nonlinear nature of the plant. A thickness reduction of the rolled products is achieved in each pass by an adequate positioning of the work rolls. Usually, the work rolls are adjusted in combination with the backup rolls by a hydraulic positioning system, the so called Hydraulic Gap Control (HGC), or by the screws. The screws are used for a rough placement of the rolls while the hydraulic system makes an exact positioning during the passes possible. Modern rolling mills operate at a very high level of automation. The HGC is the most inner loop in a cascaded con-

Rolling is one of the most important processes in metal forming. This process involves several stages normally. Details of metal forming are not within the scope of this paper, however, a brief description of the subject is needed to understand the system. Fig. 2 illustrates the major components of a "four-high" mill stand and introduces the terminology used in the rest of the paper. Apart from the mill productivity the quality of the products is of supreme importance and this can be obtained either by improving the hard-

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Hydraulic gap control (HGC)

Automatic gauge control (AGC)

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automation system Fig. 1. Block diagramm of the control concept of a rolling mill. screw stand

the whole operating range. The implemented controller is used for both position and force control. Because force control is in our case of less interest, it only works during the calibration process, we will not show any results concerning force control in this paper.

upper backup roll

suip

lower backup roll

2. MATHEMATICAL MODEL hydraulic adjustment system

A system as it is shown in fig. 2 can be split into three subsystems:

Fig. 2. Scheme of the plant.

• the roll gap model, • the stand model, • the hydraulic positioning system.

trol structure that receives reference values from different feedback loops. Therefore, the dynamics of the positioning system highly influences the quality of the rolled products. Traditionally, linear design methods are used for the Hydraulic Gap Controller despite the nonlinearities of the hydraulic subsystem. But these controllers do not meet the requirements of new systems and applications. Additionally, there are several limitations in the plant, e.g., the maximum amount of energy. of the actuator is limited by the supply pressure, there are force limitations for the work rolls and the stand, etc.. The presented measured results refer to a nonlinear controller for hydraulic systems which was presented in (Kugi et al., 1999) and is based on a physical model of the plant. This approach differs from other methods, because it takes into account the nonlinearities of the hydraulic system as well as the corruption of the measured signals by noise. Furthermore, it guarantees the same dynamic performance over

Basic mathematical strip models see, e.g., (Roberts, 1983); (Ford et al., 1951); (Ford et al., 1952); (Weber, 1965) for the roll gap are usually given by nonlinear equations which contain several parameters. The evaluated nonlinear controller is designed for several hydraulic systems of a stand. Therefore, a material model is not included in the controller. Traditional mathematical stand models see, e.g., (Pedersen, 1999) are either given by a system of lumped parameters or by partial differential equations. In the investigated mill, the dynamic influence of the stand can be neglected. The stationary influence, modeled by a nonlinear spring is compensated (see fig. 1) by the standard Automatic Gauge Control concept (AGC). Therefore, the nonlinear controller is restricted to the hydraulic positioning system.

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The measured data show that the dynamics of the valve can be neglected, so we can use the spool position X s as the input of the system. The valve flow can be calculated, see, e.g., (Murrenhoff, 1998); (Merritt, 1967) for regular operating conditions by

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(5)

<0 Qv = KdxsVPI - Pt Xs

with the valve coefficient Kd and Qv = Qv,l + Qv,2' For the controller the two valves are considered as one valve with doubled rated flow. Measured data show that the valves contain different offset values in the spool position and, therefore, in simulation both valves must be used. Unfortunately, the standard approach of the InputOutput-Linearization see, e.g., (Isidori, 1989); (Nijmeijer and der Schaft, 1991) for the system due to eq. (1), with the piston position x p as the plant output and the spool position X s as the plant input, leads to a control law that contains the velocity signal v p ' The velocity of the piston cannot be measured directly and an observer for the velocity that is based on the position signal fails due to the transducer and quantization noise. In (Kugi et al., 1999) a modified approach is proposed such that the linearization method can be applied with a new output z. This output z contains the essential nonlinearities of eq. (1). Performing the Input-Output-Linearization for the artificial output z

Fig. 3. Hydraulic ram with 2 servovalves. 2.1 Hydraulic positioning system

In this section, we derive the mathematical model for a hydraulic system due to fig. 3. The head side of the single acting piston is connected via rigid steel pipes with 2 three-stage-servovalves. Because of the enormous dimension of the piston, two valves are necessary to obtain the required flow rates and they are driven synchronously Xs,l = X s 2. The rod side of the piston is at a constant pr~ssure of 3 x 105 Pa. The valves are connected via the supply line with a pressure pump that generates the supply pressure Ps and via the return line with the tame The supply pressure is. a measured value whereas the immeasurable tank pressure is assumed to be constant Pt = O. The mathematical model takes the form dP1

E (-vpA

dt

+ Qv,l + Qv,2 VD + xpA

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dx p

(1)

- - =vp dt dv p

_

((PI -

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dt

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m

we get the nonlinear state feedback for positive valve displacement X s ~ 0

with the isothermal bulk modulus of the oil E the pressure PI in the forward chamber, the pressure P2 in the return chamber, the volume of the connection line Vo , the piston position x p , the piston velocity v p , the pressure surface head side A, the pressure surface rod side A r , the roll force Frail, the friction force F j ric and the mass of moving parts m. The isothermal bulk modulus see, (Truckenbrodt, 1989); (Johnson, 1999), defined by

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(7)

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gives the pressure in the chamber as

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(6)

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(3)

(9)

For the artificial output z, eqs. (3) and (6), one can find a nice physical interpretation. If we assume

with the mass density p. The leakage flow is assumed to be laminar, i.e.,

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(4)

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(14)

3. EXPERlMENTAL SETUP but in reality the mass flow is

The measurements were made at a reversing hot strip mill in the Czech republic in cooperation with VOEST-ALPINE Industrieanlagenbau Gmbh. The head side of the piston is 1.13 m 2 , the rated flow of one servovalve is 800 l/ min. The system works with a supply pressure of 320105 Pa, the maximum displacement of the piston xp,max = 70 mm. The rod side of the piston is filled with nitrogen at a constant pressure of 3105 Pa to avoid oxidation. The volume of the connection lines Vo = 0.02 m 3 . Fig. 4 shows a 100 J.Lm step response with the controller gain adapted to the existing operating conditions. Fig. 5 shows measured step responses to 50 J.Lm with a traditional P-controller and no load in the roll gap. Obviously, the dynamics for positive or negative steps are different, which shows that one should take the nonlinearities into account. FUrthermore, they show the difference between two valves with a certain controller gain and a single valve with doubled controller gain. Fig. 6 shows 50 J.Lm steps with the new nonlinear controller due to eqs. (6), (7) and (8) with an overshoot of 15 %. This overshoot was intended to make the measurements comparable with the measured results of the linear controller and to show that the used model also works in this extreme situation. For the transformed linear system eq. (9) we also used a P-controller. For

(15)

Because of this fact eq. (13) depends only on the initial volume Vo and not on the actual volume V = Vo + xpA. Nevertheless, eq. (14) is a very good approximation as E is about 1.6109 Pa, i.e. oil is a very "stiff" fluid. The analysis of the system, taking into account eq. (15) is more costly, but the stability can be guaranteed at the whole operating range as it is shown in (Kugi et al., 1999). The simulation has shown that this approach is more robust than the direct solution of. the Input-Output-Linearization based on eq. (1) which needs the velocity signal. A linear controller for this simplified system has been designed by standard techniques. Note that the controller due to eqs. (6), (7), (8) and (9) works with measured signals only and guarantees equal dynamics in the whole operating range. In particular, the velocity signal is not needed any more. The new input v was determined by a P-controller

with the reference position xp,re! and the measured piston position x p .

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both directions the dynamics is equal and the nonlinear behavior can be seen in the actuator signal, the valve position.

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4. CONCLUSIONS

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This paper evaluates measured results of a nonlinear hydraulic gap controller (HGC) implemented in a reversing hot strip mill. The measurements show that it is possible to improve the dynamics of existing hydraulic systems by means of nonlinear control concepts. Even in high automated plants like rolling mills modern control theory can be used to improve the product quality.

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5. REFERENCES Ford, H., F. Ellis and D. R. Bland (1951). Cold rolling with strip tension. Journal of the Iron and Steel Institute. Ford, H., F. Ellis and D. R. Bland (1952). Cold rolling with strip tension. Journal of the Iron and Steel Institute. Isidori, A. (1989). Nonlinear Control Systems. Johnson, R. W. (1999). The Handbook of Fluid Dynamics. Kugi, A., K. Schlacher and G. Keintzel (1999). Position control and active eccentricity compensation in rolling mills. atAutomatisierungstechnik 8/99, Special Issue 8/99,342-349. Merritt, H. E. (1967). Hydraulic Control Systems. Murrenhoff, H. (1998). Servohydraulik. Nijmeijer, H. and A. J. Van der Schaft (1991). Nonlinear Dynamical Control Systems. Pedersen, L. M. (1999). Modeling and Control of Plate Mill Processes. Roberts, W. L. (1983). Hot Rolling of Steel - Manufacturing Engineering and Materials Processing. Vol. 10. 'Iruckenbrodt, E. (1989). Fluidmechanik Band 1. Vol. 1. Weber, K. H. (1965). Hydrodynamic theory of rolling. Journal of the Iron and Steel Institute.

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