In this paper, an iterative learning control (ILC) method is introduced to control molten steel level in a continuous casting process, in the presence of disturbance, noise and initial errors. The general ILC method was originally developed for processes that perform tasks repetitively but it can also be applied to periodic time-domain signals. To propose a more realistic algorithm, an ILC algorithm that consists of a P-type learning rule with a forgetting factor and a switching mechanism is introduced. Then it is proved that the input signal error, the state error and the output error are ultimately bounded in the presence of model uncertainties, periodic bulging disturbances, measurement noises and initial state errors. Computer simulation and experimental results establish the validity of the proposed control method.
In continuous casting of steel, controlling the molten steel level is very important because a consistent level increases the surface quality of the final products. However, the level of molten steel in continuous casters is affected by disturbances, time delays and nonlinearities. In a continuous caster, one of the most severe disturbances is bulging, which disturbs the level periodically. Normally, bulging is similar in shape to a superposition of sinusoidal waves and causes molten steel level to oscillate periodically. This paper focuses mainly on eliminating bulging disturbance.
Many strategies have been proposed to control the level of molten steel during continuous casting (Barron, Aguilar, Gonzalez, & Melendez, 1998; Dussud, Galichet, & Foulloy, 1998; Keyser, 1991; Lee, Kueon, & Lee, 2003; Watanabe, Omura, Konishi, Watanabe, & Furukawa, 1999), but none of these attempts to eliminate bulging disturbance directly. Furtmueller and Gruenbacher (2006) modeled the bulging effect and applied it to his control strategy, but this method requires measurement of the current signal of the roller motor under the mold, but this is difficult to obtain in the field and does not properly reflect mold level disturbance due to bulging. Therefore, an iterative learning controller is proposed that can be applied easily to controlling molten steel level.
In a system that is subject to periodic disturbance, the repetitive control method (Doh, Ryoo, & Chung, 2006; Moon, Lee, & Chung, 1998) is often useful. However the repetitive controller needs precise plant information for stability, and large time delay significantly degrades its performance. In contrast, ILC method does not need any plant information, and is easy to implement even in systems that experience large time delay. The proposed ILC technique is responsible for eliminating bulging disturbance while the PID controller mainly stabilizes molten steel level.
This paper is organized as follows. Section 2 derives a mathematical model for molten steel level system; Section 3 describes the proposed controller and the resulting control system; Section 4 shows computer simulation results and Section 5 shows experimental results on 1/4 scale hardware (H/W) simulator; the conclusion is given in Section 6; the stability analysis on the control system is given in the Appendix.
In this paper, the following notations and definitions will be used. RnRn is the n -dimensional Euclidean space with norm ∥z∥=(zTz)1/2∥z∥=(zTz)1/2 for z∈Rnz∈Rn. C∈Rp×mC∈Rp×m is a (p ×m )-dimensional matrix with real elements and View the MathML source∥C∥=λmax(CTC) represents the induced matrix norm where λmax(·)λmax(·) denotes the maximum eigenvalue. Let NN be the set of positive integers 1,2,…,n . Finally, the α-normα-norm is defined for a positive real function z:N→Rz:N→R as
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In this paper, an iterative learning control technique was proposed and applied to a continuous casting simulator. Treating one period of bulging disturbance as one iteration, it is developed an iterative learning controller that performs well in reducing the periodic bulging disturbance. In the presence of model uncertainties, disturbances, noises and initial errors, it is proved that the state signal error, the output signal error and the input signal error of the control system are ultimately bounded. The proposed control method was implemented on a 1/4 scale H/W simulator but it will soon be applied to a full scale H/W simulator in an active steel mill.
