^{1}

^{*}

^{1}

^{*}

In rolling mill, the accuracy and quality of the strip exit thickness are very important factors. To realize high accuracy in the strip exit thickness, the Automatic Gauge Control (AGC) system is used. Because of roll eccentricity in backup rolls, the exit thickness deviates periodically. In this paper, we design PI controller in outer loop for the strip exit thickness while PD controller is used in inner loop for the work roll actuator position. Also, in order to reduce the periodic thickness deviation, we propose roll eccentricity compensation by using Fuzzy Neural Network with online tuning. Simulink model for the overall system has been implemented using MATLAB/SIMULINK software. The simulation results show the effectiveness of the proposed control.

Rolling strip is widely used for automobile manufacturing, food packaging, household electric appliances, machinery, light industry, instruments, communications, military affairs and other fields [

Strip products thickness precision is an important quality parameter. But the export thickness appears as the periodical fluctuation in the practical production because of the roll eccentricity thermal expansion of rolls and the fluctuation of the entrance thickness and material stiffness. The mill can be composed of either a single stand or a number of stands where each stand is made up of two back-up rolls and two work rolls. A common problem is the back-up and work rolls are not perfectly circular in shape. In other words, the rolls are eccentric. The roll eccentricity effect will, under normal constant operating forces, result in steel strip with undesirable thickness deviations [

The tandem cold rolling of metal strip is one process in a sequence of processes performed to convert raw materials into a finished product [

The strip is passed through four pairs of independently driven work rolls, with each work roll supported by a backup roll of larger diameter. As the strip passes through the individual pairs of work rolls, the thickness is successively reduced. The reduction in thickness is caused by very high compression stress in a small region (denoted as the roll gap, or the roll bite) between the work rolls. In this region the metal is plastically deformed, and there is slipping between the strip and the work roll surface. The necessary compression force is applied by hydraulic rams, or in many older mills by a screw arrangement driven by an electric motor [

Define the theory for prediction of specific roll force is central to the development of a model for tandem cold rolling. Referring to

where d = draft, mm.

The rolling strip contact length can be approximated by [

The true strain experienced by the strip in rolling is based on before and after stock thickness. In equation form:

The true strain can be used to determine the average flow stress

where K = the strength coefficient, MPa; and n is the strain hardening exponent.

The force F required to maintain separation between the two rolls can be calculated based on the average flow stress experienced by the strip material in the roll gap [7,8]. That is,

where w = width of the strip, R is radius of work roll.

In the cold rolling process and the precision is strip thickness of cold rolled strips of key quality products. Conventional Automatic roll gap Control (where Gauge, AGC) system used for Automatic correction strip thickness accuracy [

where M is mill modulus The BISRA relationship is used to develop a thickness feedback signal for closed-loop control. To control the output thickness, the motion of hydraulic cylinder controlling the roll gap position is such that produces the desired output thickness [

When the entry strip is passed through the roll stand with the velocity

where

usually includes its effects. The eccentricity components remaining in the mill exit thickness after compensation. In the model, roll eccentricity modifies Equation (5) as [

where e is the roll eccentricity.

A promising approach to obtaining the benefits of both fuzzy systems and neural networks and solving their respective problems is to combine them into an integrated system. The integrated system will possess the advantages of both neural networks (e.g., learning abilities, optimization abilities, and connectionist structures) and fuzzy systems (e.g., humanlike IF-THEN rules thinking and ease of incorporating expert knowledge). In this way, we can bring the low-level learning and computational power of neural networks into fuzzy systems and also high-level, humanlike IF-THEN rule thinking and reasoning of fuzzy systems into neural networks. Thus, neural networks can improve their transparency, making them closer to fuzzy systems, while fuzzy systems can self-adapt, making them closer to neural networks. Integrated systems can learn and adapt [

The Architecture of FNN shown in

Input Layer I: Input layer transmits the input linguistic variables

Hidden Layer II: Membership layer represents the input values with the following Gaussian membership functions [

where

Hidden Layer III: Rule layer implements the fuzzy inference mechanism, and each node in this layer multiplies the input signals and outputs the result of the product. The output of this layer is given as [

where

Output Layer IV: Layer four is the output layer, and nodes in this layer represent output linguistic variables. Each node

where

The parameter of the FNN controller presented in

The goal of the learning algorithm is to minimize the error between the desired output thickness

where η is the learning rate for each parameter in the system,

The block diagram of exit thickness control with roll eccentricity compensation is shown in

used as APC.

The simulink model of force equation is shown in

A program written in Matlab code is used to simulate FNN using Matlab S-function programming. In the primes part, the number of membership functions for each input are five. So, the number of weights in the consequence part is also five. The mill and strip properties is shown in Table1Without roll eccentricity effect,

shows the exit thickness after cancellation the effect of roll eccentricity. The exit thickness with and without compensation is shown in

results, It is found that FNN is robust in that it eliminate the periodic thickness deviation considerably.

In this paper, the mathematical model of single-stand cold rolling mill is developed and PI controller has been used to control exit thickness of the strip. We propose FNN in order to reduce the effect of roll eccentricity. The error between the reference exit thickness and output thickness of stand is used as trajectory to adapt the primes part and the consequence part of the FNN so that the error goes toward zero. The output of FNN is added to the desired position roll gap to reduce periodic deviation in the output thickness. As we have shown in the simulation results, the performance of proposed method is good.