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Automatic rolling process is a high-speed system which always requires high-speed control and communication capabilities. Meanwhile, it is also a typical complex electromechanical system; distributed control has become the mainstream of computer control system for rolling mill. Generally, the control system adopts the 2-level control structure—basic automation (Level 1) and process control (Level 2)—to achieve the automatic gauge control. In Level 1, there is always a certain distance between the roll gap of each stand and the thickness testing point, leading to the time delay of gauge control. Smith predictor is a method to cope with time-delay system, but the practical feedback control based on traditional Smith predictor cannot get the ideal control result, because the time delay is hard to be measured precisely and in some situations it may vary in a certain range. In this paper, based on adaptive Smith predictor, we employ multiple models to cover the uncertainties of time delay. The optimal model will be selected by the proposed switch mechanism. Simulations show that the proposed multiple Smith model method exhibits excellent performance in improving the control result even for system with jumping time delay.

Because the control objects are electromechanical and hydraulic systems with small inertia and fast response, automatic rolling is a fast process which requires high-speed control and communication capabilities. With the technological and industrial development, requirements for high-quality strips and high-level automation are becoming critical. Distributed control has become the mainstream of computer control system for rolling mill which is a typical complex electromechanical system [

Ethernet network structure in a tandem rolling line.

RM fiber optic network in a tandem rolling line.

In practical AGC thickness control process, two main factors will lead to the uncertain time delay for controlled system. One is the certain distance between the thickness gauge and rolling gap of each stand, and the other is the essentially existing time delay in network transmission. Smith predictor is a method to deal with above problem, but as the value of system time delay is hard to be measured precisely, the Smith predictor method always cannot be carried out effectively in practice. Adaptive Smith predictor model can cope with partial model mismatch [

In this paper, we introduce MMAC into adaptive Smith predictor to form the multiple model adaptive Smith predictor control method, so as to improve the control performance. According to the possible varying range of the controlled plant’s time delay, multiple fixed and adaptive models are established to cover the plant’s uncertainties; corresponding controllers are also set up; the switch index function is proposed based on model error to decide the most appropriate controller for the system at every moment and select it as the current controller. Ultimately, multiple adaptive Smith controllers are composed to improve the system’s control performance.

The following paper is organized as follows. Section

AGC thickness control of rolling mill is a control system with time delay; traditional AGC control methods cannot get satisfying control performance [

According to control theory, to cope with the time-delay problem, we can take the Smith predictor scheme. A prediction model is added into the AGC process as the feedback loop, which can predict the change of system output and give feedback signal in advance, so as to offset the original system delay and make the characteristic equation of the whole closed loop system without time delay [

AGC control process based on Smith predictor.

In Figure

When Smith predictor is not used, the system transfer function is

Corresponding characteristic equation is

As the pure time-delay part

Corresponding characteristic equation becomes

Practically, condition

AGC control process based on adaptive Smith predictor.

Consider

Corresponding state equations can be got as

For given generalized error

Lynaponov function is set up as

An adaptive control law

The adaptive parameter identification mechanism can be viewed as a kind of data-driven strategy [

From Figure

Consider the rolling system in Figure

AGC control process based on multiple adaptive Smith prediction model.

Define

Consider the character of first order system; we assume that a first order system with small delay can be approximated by a first order process with different parameters [

Further, we have the multiple model adaptive control system (see Figure

As in Figure

Based on the possible parameters variation range of

Define the switch index function

At time

In practical AGC control process,

For multiple adaptive Smith prediction model controller, parallel computation of multiple adaptive processes will lead to the increase of calculation amount.

If all the

With enough fixed models, take (

Multiple fixed models as in Section

The existence of multiple fixed models reduces the amount of calculation, and the adaptive model guarantees the system stability, so the control performance can be improved as the case of multiple adaptive models.

If the adaptive Smith controller in Section

From [

Consider

From (

For

Consider

Take (

(1) For multiple model control composed of multiple adaptive Smith predictors, since each Smith model has its own adaptive mechanism, so for each model we have

Though there is model switching among multiple models based on the switch index function, it finally comes to

(2) For multiple model control composed of multiple fixed Smith predictors and one adaptive Smith predictor, as to the adaptive Smith predictor

For each fixed model

If

If there is a fixed model

Multiple model control based on multiple fixed Smith models can improve the transient response, but as it lacks the adaptive parameter regulation, system stability can hardly be guaranteed.

The existence of multiple models covering the parameter uncertain range of the controlled plant can improve the system’s transient response and improve the control quality for system with jumping parameter.

A first order time delay system as follows will be simulated for rolling AGC system:

The same PID controller as in [

The compensation Smith predictor will be designed as

For single adaptive Smith prediction model, let the feedforward and feedback adaptive initial parameters be

Single model adaptive Smith predictor.

Multiple model adaptive Smith predictor.

It can be seen in Figures

When four fixed Smith prediction models with initial adaptive feedback parameters

Multiple fixed Smith prediction model.

Multiple fixed and single adaptive Smith prediction model.

System output

Switching sequence

Compared with multiple adaptive Smith predictor model, the computing time can be reduced by using multiple fixed Smith predictor models, but the stability cannot be guaranteed because of the absence of adaptive adjustment. From Figure

The rolling AGC system with jumping time delay can be described as

Take the single adaptive Smith prediction model, multiple adaptive Smith prediction model, and the multiple mixed fixed-adaptive Smith prediction model with the same initial feedback and feedforward parameters as in Section

Multiple Smith prediction model for system with jumping time delay.

When system time delay jumps, the present multiple adaptive Smith prediction model and multiple mixed fixed-adaptive Smith prediction model can both guarantee the system stability. Meanwhile, compared with single adaptive Smith prediction model, system transient response of multiple adaptive Smith prediction model has been improved obviously no matter before or after the time delay change point.

In the rolling AGC control process, control systems under complex network condition are generally used. Consider the time delay of network transmission and thickness gauge is usually far away from the roll gap, the transfer function model of the controlled plant will always be described by a first order system with uncertain time delay. Generally, fixed and adaptive Smith predictors are the effective methods to solve this problem, but they all need the precisely known time delay value which is hard to be obtained. This paper approximates the variation of time delay and the parameters in system model by a first order process with different parameters. Multiple Smith prediction model for AGC will be used to set up a MMAC to cope with the change range of time delay in rolling process. The problem of regular Smith predictor is solved and the transient response of adaptive Smith predictor is improved.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supposed by the Fundamental Research Funds for the Central Universities under Grant FRF-TP-12-005B; the Program for New Century Excellent Talents in Universities under Grant NCET-11-0578; and the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) under Grant 20130006110008.