Fig. 3 Multiple interstand fuzzy tension control system

Shown in Fig. 3 is a schematic of the proposed fuzzy multiple interstand tension control system. To ensure a constant product speed, the upstream speed correction scheme is used. For each stand, there are 3 controllers of different type. They are cascade controller (CC), interval controller (IC) and fuzzy tension controller (FTC). All these controllers are implemented in the PLC based MCS. Instead, the automatic speed regulator (ASR) is built in the speed drive system of each stand. The process control is through the correction of the reference speed applied to each ASR.

Cascade controller (CC) and interval controller (IC)

The combination of cascade controller and interval controller is the means to physically decouple the multiple-stand interactions caused by the interstand tension.

The cascade controller is to apply proportionally a correction to the speed drive of its upstream stand while the speed of this stand is being corrected. The purpose is to eliminate the interaction between the regulated stand and its adjacent upstream stand by means of avoiding the introduction of an extra

m,

change to the backward tension of the regulated stand.

k e, i,

k D e, i, k v, i

------ Current error, change of error

The interval controller is to periodically control

and speed correction scaling factors

the switch-in and switch-out of the fuzzy tension

e

m

i, j

D e i, j

------- Input membership mappings

controller so as to remove the interaction caused by

the forward tension between the stand being regulated and its adjacent downstream stand.

 

Fuzzy tension controller

Interstand tension can be either sensed through installation of load cells or derived from other detected physical variables [11]. Therefore, tension control can be classified into direct and indirect schemes.

Due to physical limitations in most rolling mills, the interstand tension in the proposed system is indirectly inferred through detecting the motor armature current. That is, the indirect current comparison method [11] is

w j--------------- Output fuzzy singletons

 

Five triangular membership functions are selected for the current difference (Error), three membership functions for the change of difference (Change of Error) and seven symmetrical fuzzy singletons are chosen for the output speed correction (Output). These membership functions are defined as follows. Error: NB [-1, -1, -0.6, -0.3], NS [-

0.6, -0.3, 0], Z [-0.3, 0, 0.3], PS [0, 0.3, 0.6], PB [0.3, 0.6,

1, 1]; Change of Error: N [-1, -1, -0.5, 0], Z [-0.5, 0, 0.5],

P [0, 0.5, 1, 1]; Output: NB [-0.75], NM [-0.5], NS [-

0.25], Z [0], PS [0.25], PM [0.5], PB [0.75]. The rule base

contains fifteen rules as shown in Table 1. The scaling

employed for achieving tension control. The difference of the armature current between before and after the billet hits on the next downstream stand

factors are selected as

k v, i =0.1.

k e, i =0.4,

k D e, i =1.5, and

indicates the occurrence of a forward interstand tension. If the armature current is controlled to trace its value before the billet hits on the downstream stand, the forward tension will be brought to zero.

Fuzzy tension controller takes both the difference and the change in difference of the armature current between before and after the billet hits on the downstream stand as inputs. It emulates human operator and bases on a Mamdani and Sugeno-type fuzzy reasoning to generate a correction signal for the motor speed of the upstream stand.

Let e i stand for the current difference between the forward-tension-free current and the actual armature current of the i-th stand, D e i the change in the current difference and D v i the correction to the reference speed of the ASR of the i-th stand. The controller output for each stand can be expressed as

The control algorithms of Eq. (1) are digitally implemented in Modicon PLC programs.

 

Table 1 Rule base

Output		Error
		NB	NS	Z	PS	PB
Change Of Error	N	NB	NM	NS	PS	PB
	Z	NB	NM	Z	PM	PB
	P	NB	NS	PS	PM	PB

Virtual rolling test

An initial mill setup prescribing the reference speed of each roll stand is usually designed to establish a theoretically “perfect” speed-matching condition based on the Conservation of Mass principle and stand parameters for each production schedule. Such a mill setup is a necessity for the process startup although it cannot realize perfect speed matching in reality due to complicated deformation dynamics and other external disturbances.

k   w × m ^e (k

× e) × m ^{D e} (k

× D e)

Interstand tension results from speed mismatch. To

 

D v =

v, i å j

j

 

i, j

 

e, i     i

 

i, j

D e, i         i

evaluate on the virtual rolling mill the multiple-stand fuzzy tension control system, a speed mismatch is

i                 å  m ^e (k

× e) × m ^{D e} (k

× D e)

therefore generated for each interstand zone before

 

j

i = 1,........ 5

where

i, j

e, i     i

i, j

D e, i          i

(1)

rolling. This was done by bringing the motor speed of the upstream stand away from the selected initial mill setup.

The selected production schedule has a finishing speed of 800FPM (feet per minute). The initial billet size is 5.5 in² and the product size is 0.75 in². Table 2 shows the intentionally disturbed startup speed of each roughing stand and the tension at each interstand zone after the first billet has been rolled.