Advanced Control Method of Steering on the Hot Rolling Mill

Copyright @ IFAC Automation in Mining, Mineral and Metal Processing, Tokyo, Japan, 2001

ADVANCED CONTROL METHOD OF STEERlNG ON THE HOT ROLLING MILL Yoshihiro Marushita· Hidetoshi Ikeda * Kentaro Yano ** Seiichi Shindo *

Industrial Electronics fj Systems Laboratory, Mitsubishi Electric Corporation, 1-1, Tsukaguchi-honmachi 8-chome, Amagasaki, Hyogo 661-8661, Japan ** Enegy fj Industrial Systems Center, Mitsubishi Electric Corporation, 1-1-2, Wadamisaki-cho, Hyogo-ku, Kobe 652-8555, Japan

*

Abstract: During the hot strip operation, the strip is often driven rapidly to one side. The phenomenon is caused by the horizontally asymmetrical factors of the strip or Hot rolling mills. As the result, the accuracy of the products decrease, and the work rolls are damaged, that causes of product ability. This paper propose an advanced control method of steering to prevent this ploblem. Copyright© 2001 IFAC Keywords: Steel industry, Unstable, PD controllers, Filter, Frequency responses

Traditional measure to prevent the steering and narrowed down are to perform pressure rolling under crowning condition. Accuracy requirements on the sheet thickness have become increasingly severe and accordingly, tolerance on crown has also become small. Improvement of mechanical accuracy of rolling mills and establishment of controlling technology are desired.

1. INTRODUCTION

During the hot strip operation, end of hot rolled material is often driven to one side and narrowed downdue to lack of backward tension. Many studies focused on this problem have been conducted. This phenomenon is often seen as the material being rolled is pulled crosswise toward one side continuously and rapidly and will not be returned back to its original path.

To minimize steering, roll gap must be reduced at the deviating side. One way to do so is to install load cells on the rolling mills through which the load difference between left and right sides can be sensed (load difference method), as figure 1. desucribe, the other way is to directly sense horizontal positional deviations through steering sensors (sensor method). Otherwise, loop er load cell can be used as the sensor to perceive the deviation of exit tension.

As the material is largely deflected, it hits the left and right sideguides and folds up. If the folding work is rolled, it will damage the pressure roll, leadingto a narrow down accident. The damaged pressure roll must be replaced with new one to avoiddetrimental effects on the subsequent production. Discontinued production line decreases productivity and precision of theproduct and increases the cost. Other detrimental effects include horizontal asymmetry at the end ofrolled works. Pressure is concentrated on one side which causes sheet fracture and may heavily damage the rolling mills.

The load difference method is popular because it is easier to sense load balance. But, it cannot clearly distinguish between load deviation caused by steering and the deviation produced by controlling, resulting in insufficient control. In contrast,

113

Mill

t--_OT_ 8P

Load cell {

' SensOr .. ..w.,,;..

~;ao.

Steering sensor

Looper load cell

~.

r"- .

(a)

L....:

Fig. 1. Phenomenon of the strip steering and steering control system when steering sensors are installed at the entry of the rolling mills, degree and change in deviation can be measured, helping to distinguish between above-mentioned deviations for effective control. Because the sensors are to be located close to the rolling mills, in hostile environment, special consideration must be given to durability and reliability of the sensors.

(b)

Fig. 2. Block diagram of the steering process including characteristics of rolling mills (a) Mathmatical model (b) Equivalent conversion

Recently reported studies handle steering width and changes in deviation as state variables and control the state feedback by estimating changes in variables through observer. These methods can measure width and changes in deviation without using sensors but require complicated control configuration. In addition, location of the observer and state feedback control pole are unclear, making adjustment difficult.

y~ = kbV2(CyYc

+ CsoS - CHoH) 6P = LyYc - L s 6S + LH6H

(1) (2)

The C y, Cs , CH , Ly, Ls, LH in the equations above are positive numbers determined by the mechanical characteristics of rolling mills and rolling condition . If the target of control is expressed in the transfer function from input oS to output OP, then the following equation can be applied .

None of these studies use techniques designed to secure robust stability. This paper proposes a control method of steering on rolling mills, which gives special consideration to robust stability and easily controls the steering.

(3)

2. TARGET TO BE CONTROLLED

2.2 Analysis of steering model

This paper describes a control of steering by detecting load deviation that causes steering. In contrast to this method, the sensor method requires a wider mounting space and causes time lag.

From equations (1) and (2), it is clear that the target controlled in this paper has poles and zeros on the complex right hemihedry. (4)

2.1 Mathematical model of steering phenomenon

(5)

Based on previous studies, physical model of steering process is discribed in figure 2(a). This is including both steering process and characteristics of rolling mills Figure 2(b) is obtained from figure 2(a) easily (refer to appendix in last page of this paper to know parameters in figure 2).

Figure 3 plots the frequency responses of transfer function expressed in the equation (3). Figure 3 shows that the pole and zero point are close to each other and remain 180 out of phase with each other. These facts suggest that the steering phenomenon is very unstable and the system is difficult to control. Suppose that a proportional control is applied to this target. Since the target 0

From figure 2(b), steering phenomenon and characteristics of rolling mills are expressed as follows :

114

~ :I -~0~-- j

!:I:'' : -10

' .. d.

-

- .5 10.

1

10'

101

101

-100'

~

:~.!;~.-..... _. . . . .

~

~

_ ... . .

"'~..:'

-_

~

... ~

~

""A

~.

_

"_

_

~

~

~

-

~

freqlacncy(radls)

~1rW"1

(a)

Fig. 3. Frequency responses of steering model

'"

!»

Fig. 4. Frequency responses of open loop transfer function in case of application PD controller. Time constant of roll gap control system is equal to 1 (ideal PD controller) (a), fast (b), appropriate (c).

(b)

has unstable pole and unstable point, it further becomes unstable if the transfer function is too high or too low. For example, if the open loop gain is lower than 0 dB in a lower frequency range or higher than 0 dB in a higher frequency range, it is unstable and cannot control steering. The proportional gain must be adjusted so that the open loop gain always traverses the 0 dB line. However, since the gain curve within the cross frequency range is -40 dB, the response of the system will be oscillatory.

Fig. 5. Frequency responses of open loop transfer function in case of application observer and state feedback control. poles in closed loop is plased suitably (a), too large (b) . the first (or second) order lag, then we can obtain uniform differential gain at the higher frequency range as shown in Figure 4, line (b), assuring stability. It is, however, difficult to change the time constant of the rolling mills.

If the rolling mills has an appropriate time constant as shown in Figure 4, line (c), and the gain at higher frequency range is lower than 0 dB , then the steering can be corrected. However, if the rolling mills has a small time constant , the gain will be higher than 0 dB and system becomes unstable. As shown is Figure 4, line (b) .

3. TRADTIONAL CONTROL METHOD

3.1 PD Control One of steering control methods studied for load difference system is the proportional plus differential (PD) control method. Figure 4 shows the frequency response characteristic of an open loop transfer function configurated by plant and PD controller.

The stable region of the control gain can be determined by using Routh or Hurwitz method but clear design guide cannot be obtained.

3.2 State Feedback Control and Observer

As can be seen from Figure 4, line(a), the gain becomes infinite at higher frequency range due to effects of differential control, and the phase shifts by 180 degrees, causing the entire system to be unstable. If we approximate the rolling mills with

Figure 5 shows the frequency response of the open loop transfer funct ion of the state feedback control system using Ye and Ye as state variables and state variables estimated by the observer. With appro-

115

priate pole, relatively good frequency response is obtained as shown in Figure 5(a). Larger pole degrades robust stability. Especailly, stability in the range between 101 and 104 rad/s will be lost by small noise. In addition, characteristic will not change greatly around at 0 dB level even if poles of closed loop are moved. This means that good response may not be obtained even if larger pole is used . Changing pole leads to a complicated frequency response change, making adjustment difficult.

5 j i

CS

!

0

~

; i p=~0

~

.;c 0

,

p=35

-17

·5

ii·

!:

!

11:

i!:i

.10 L-~.L..L.LL..l..LL--'-~...J...L.iJ..lJ.._.L....i--L.l.J:l::o"':"~-'--'-............u ·120

4. PROPOSED CONTROL METHOD

'180~""",,~e1::rr:;.--'---,-..L:..l.w..,.---,-~c.:::::±±t:?~~;;;d 10-' 10' Frequency [rad /sec]

4.1 PD Control with LPF

Fig. 6. Influences by change of P

This paper reviews the preceding control systems and proposes new steering control method designed based on the following policy.

5

• Simple control system configuration • Robust stability • Easier control parameter adjustment

CS ~

.;c

0

0

-5

Considering the result shown in Figure 5(a) , the control system (observer plus state feedback) described in Section 3 can be expressed using transfer function as shown below. C(s)=K

s+z

(s

+ pd(s + 112)

(6)

ill

J! -1601r---+-+++

c.

-1801~~~±EJt;::L...l.Jjlili~Uiliilli:~~bi.l.i.J.U

Equation (6) can be regarded as a combination of PD control and secondary filter.

10-'

Equation (6) contains 4 adjustable parameters. For field adjustments, fewer parameters are helpful. Assuming that PI « 112 and ignoring a pole that will not affect the stability, the PD control and linear filter (LPF) are combined. C(s) = K s + z 112 (s + PI)

10' Frequency [rad/sec]

103

Fig. 7. Influences by change of z Note that, K/(P1 . P2) is replaced with K, and PI is replaced with p . Figures 6, 7, and 8 show frequency responses against changes in K, P and z , respectively_

(7)

Here, pole and zero point to be controlled are, Po(=6 rad/s), zo(=17 rad/s) .

The above-mentioned assumption is appropriate because the pole P2 does not affect the control range.

First, effects of changes in p are ' described. As can be seen from Figure 6, the gain of the loop increases as the frequency increases, above 0 dB at p=35 rad/s, causing the loop to become unstable. At p=30 rad/s, the gain does not exceed 0 dB but the robust stability is degraded and then further becomes unstable with slight change in a parameter value. The robust stability increases if P is smaller than Zo but degree of its slope increases in the cross frequency zone, causing oscillatory response, a detrimental effect. For stable operation, it is desirable to set the p close to the zero point Zo of the target.

4·2 Effects on robust stability

Changes in the control parameters affect the robust stability of the control system described in the preceding section. In equation (7) , changing parameter value will affect the open loop frequency range. Therefore, the equation is modified as follows: s+z C(s)=K(/ s p+ 1)

Same considerations must be given to z , that is, the robust stability decreases in lower frequency range if z is smaller than Po. The robust stability

(8)

116

increases if z is larger than pO but it leads to oscillatory response. Therefore, it is desirable to set z value close to pole Po of the controlled target.

5

iXi" ~

Once p and z are set as described above, the pattern of gain diagram of the open loop transfer function becomes uniqueness. The gain slope in the cross frequency range is -20 dB and no oscillation occurs in the response curve.

0

c

'OJ 0

·5

~ . 15,~-+~-+mr~-+Tri~~~~rin~~hh~

The level of gain pattern goes high or low as the k is changed as shown in Figure 8. We then determine the steering steady-state deviation after the steering has been corrected. The transfer function G y• from 6S to Ye is obtained from the equation below.

~

~ . 1~~-++HTm--~~~r-~~~+--rTT~

ll: co

f

.17'~-~-~~~+~~- TrnTIIT--r~T·~hcl·'--~·r·t~~m

Frequency [radlsec]

Fig. 8. Influences by change of K Ca)

(9)

0.1 SO.05 .§.

..!'

~ .

0 .0.05 ' - - - - - - - - ' - - - - - - ' - - - - - - - '

While the depression system is under stepwise disturbance , the steady-state deviation is expressed in the following equation according to the terminal theory.

Ye(t -t 00)

= 8-+0 lim s G y •

'"' I

::.[C

'0'1

]c

'~l

':f\ I '-----------------1

s 6 S

K z (GsLy

Gs 8Sd + GyLa) - Gy (10)

From equation (10) it is clear that the steady-state deviation decreases as K is increases.


According to Figure 8 and the associated description, K must reside in a certain range to maintain the control system stable. The range can be determined by Hurwitz stability judging method.

·0.1

·0.2 ' - - - - - - - - ' - - - - - - ' - - - - - - - ' o 2 3 Time [s]

Fig. 9. Simulation results Step disturbance as leveling error(6Sd) is added at 0.1 [s]

Po) and the gain K is set to a value so that the steering steady-state deviation is limited below 30 mm. This is proven in Figure 9(b) . Figures 9(c) and (d) show inverse response curves, implying existence of zero in the control target.

From equation (11), determine the value of K so that the steering steady-state deviation can meet the specification.

6. CONCLUSION This paper offers idea of a steering control system for the hot rolling mills. The system can take into account the robust stability and can definitely determine the control parameters. The performance of the system has been verified through the simulation.

5. RESULTS OF SIMULATION This section reports results of the simulation performed using the control system and method described in earlier sections of this paper (Figure 9) . Disturbance to the depression system is assumed to be 50 J.L m stepwise. Control parameters P and z are set to match the control targets zero (zo and

The system is combined PD control and LFP which can assure stability without depending on

117

the response of the rolling mills and will be more practical than conventional control systems. With this system, control parameters are easily adjusted because the steering can be stably corrected by simply adjusting gain K when target pole and approx. zero point are known.

APPENDIX Symbols in figure 2(a) are expressed as follow: Table 1 Model Parameters

Kw REFERENCES Nakajima Hand Kajiwara T (1980). Study of Steering Control in Hot Strip Rolling. The Proceedings of the 31th Japanese Joint Conference for the Technology of Plasticity. p.471-474. Okamura Y. and Hoshino 1. (1995). State Feedback Control for Steering Process of Aluminum Hot Rolling Mills. Transactions of the Society of Instrument and Control Engineering, Vo!. 36, pp.1686-1694. The Iron and Steel Institute of Japan(1985). Theory and Plactice of Flat Rolling, The Iron and Steel Institute of Japan, Japn. Yamashita M and Yoshida H Other(1997) . Advanced Snaking Control by Transverse Differential Load in Hot Strip Finishing Mills. Current Advances in Materials and Processes bf Vol. 10., p. 1101. '

b h H

P BP/Bh

oP/oH v Ye

6S 6P 6p

6h Yeo

oH s

ll8

Spring constant of housing and chock Spring constant between WR and BUR Spring constant of Flattering in roll bite Chock distance Barrel length Width Entry thickness Exit thickness Rolling force Influence factor Influence factor Entry rolling speed Steering wedge ratio Leveling deviation of rolling force deviation of rolling force per unit width deviation of exit thickness Initial steering deviation of entry thickness Difference of gap between WS and DS Laplace operator