J. Cent. South Univ. (2012) 19: 2179-2186

DOI: 10.1007/s11771-012-1262-4

Acid-pickling plates and strips speed control system by microwave heating based on self-adaptive fuzzy PID algorithm

YANG Biao(杨彪)^{1, 2, 3}, PENG Jin-hui(彭金辉)^{2, 3}, GUO Sheng-hui(郭胜惠)^{2, 3},

ZHANG Shi-min(张世敏)^{2, 3}, LI Wei(李玮)^{2, 3}, HE Tao(何涛)⁴

1. Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China;

2. Key Laboratory of Unconventional Metallurgy of Ministry of Education

(Kunming University of Science and Technology), Kunming 650093, China;

3. Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China;

4. WISDRI (Wuhan Iron & Steel Design & Research Institute) Engineering & Researching Inc. Ltd.,Wuhan 430223, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: Double self-adaptive fuzzy PID algorithm-based control strategy was proposed to construct quasi-cascade control system to control the speed of the acid-pickling process of titanium plates and strips. It is very useful in overcoming non-linear dynamic behavior, uncertain and time-varying parameters, un-modeled dynamics, and couples between the automatic turbulence control (ATC) and the automatic acid temperature control (AATC) with varying parameters during the operation process. The quasi-cascade control system of inner and outer loop self-adaptive fuzzy PID controller was built, which could effectively control the pickling speed of plates and strips. The simulated results and real application indicate that the plates and strips acid pickling speed control system has good performances of adaptively tracking the parameter variations and anti-disturbances, which ensures the match of acid pickling temperature and turbulence of flowing with acid pickling speed, improving the surface quality of plates and strips acid pickling, and energy efficiency.

Key words: self-adaptive fuzzy PID algorithm; microwave heating; acid pickling; plates and strips; mixed-acid media

1 Introduction

The acid pickling process of plates and strips is an important pre-treatment step in metallurgical industry. Pickling step is essential to ensure high quality surface of plates and strips for further processing in which acid is used to remove scales from the surface containing oxides. Studies have been conducted on acid pickling technology, such as the choice of pickling technique type [1], various technologies of regeneration of pickling solutions and the methods with acid recovery [2], pickling technical process, instance, specific improving scheme of the turbulence pickling technical section [3-4], pickling line and equipments, for instance, review on existing equipments as well as improvements done within the recent years in the area [5], parameter control and operation experience [6-7]. Most of these developments are in the direction of better environmental compatibility of the pickling process, improving quality of product and energy efficiency.

Pickling, especially of plates and strips products, is normally done in a continuous way [6], by drawing the plates and strips from the rolls through a cascade of pickling tanks. In recent years, additional technologies were developed to enhance low cost alternatives, such as push-pull pickling or Ventrui tank pickling. The idea behind was to enforce turbulences in the acid bath to reduce the pickling time and to save chemical losses. New developments were done by the Andritz Ruthner group especially in advancements in tank design, which contains the acid, and further advances in rinsing controls to gain a better plates and strips surface after pickling. Around the world, about three quarters of hot strip rolling coils were processed in the continuous strip pickling process [5]. In Japan, in the largest producer of titanium, about 80% of titanium was rolled to     sheets, while in China about 50% of titanium was rolled. Pickling technologies for mild and high alloyed steel are basically similar, and only the pickling media are different. However, the speed control of pickling process was seldom investigated. Recently, WACHIRA et al [8] used neural network to directly inverse model-based control strategy which controls the pH of effluent streams to be maintained at the optimum value and obtains the maximum reaction rate. In addition, PAISAN et al [9] introduced the model predictive control (MPC), which utilized the neural network to predict the future process response, for controlling the concentrations of pickling in a steel pickling process.

Double self-adaptive fuzzy PID algorithm-based control strategy was presented for the mixed acid (HNO₃ and HF) pickling speed of a titanium plates and strips pickling process. The process involves removing of surface oxides and other contaminants out of titanium metals by immersing the metals into an acid solution, which consists of three low concentration mixed acid pre-rinsing baths, three acid baths and four pure water baths in series. Due to the highly non-linear dynamic behavior, multivariable interaction between baths cause that the pickling process speed is difficult to be controlled by conventional controllers. Therefore, the aim of this work is to apply double self-adaptive fuzzy PID algorithm for establishing optimum turbulence intensity for the best convective heat transfer at different speeds of plates and strips, and then choose the pickling temperature to provide the required heat by microwave heating to match with the turbulence intensity. In such scheme, the pickling line can be operated at a desired speed with high energy efficiency.

2 Problem description

2.1 Process characteristics of acid pickling plates and strips

The acid pickling process of plates and strips has two purposes: 1) removing the scale and oxides on the surface of the plates and strips produced during the hot rolling process; 2) leaching out the adsorbed impurities. For example, when temperature reaches above 250 ℃, the titanium oxide will adsorb carbon, oxygen, nitrogen, and hydrogen, and impurities will be removed from the surface during pickling. This is especially important for the continuous pickling line coupled tandem mill process because high quality plates and strips can keep the tandem mill process to operate continuously. Otherwise, it has to stop due to the cracks derived from un-removed impurities [3].

The pickling process for the plates and strips is realized through the pre-rinsing, pickling, and rinsing system by an immersion in an acid solution in a sequential order. The line has a number of baths for pre-rinsing, pickling and rinsing, respectively, and the baths are connected to the tanks for storing the acid solutions for pre-rinsing, pickling and rinsing, respectively. The plates and strips move counter current to the acid stream. The acid from the pre-pickling tank can be regenerated and recycled.

For the pickling operations, there are many studies having been investigated; for example, YE and PAN [10] studied the substitution of deep baths with shallow baths, turbulent pickling, in order to probe the basic principles of pickling, such as chemical thermodynamics, surface properties (oxides and scales), acid-exchange and heat and mass transfer characteristics. DING and JIN [3] concluded that only the turbulent intensity could improve the pickling effect, whereas pickling speed could be enhanced by increasing the length of the chemical segment [11].

2.2 Microwave heating mixed-acid media

For decades, studies of pickling line have been mostly focused on the equipment design, material compositions, and process parameters design. Because the performance of the usual block pore type of graphite heat exchangers is poor, researchers have been using the microwave energy for direct heating of mixed-acid media, instead of indirect heating through graphite heat exchanger [12-13]. Microwave heating overcomes the disadvantage of the traditional fuel heating methods, resulting in better temperature control due to the elimination of lag time, and the general issues in control fields. The transfer of thermal energy to acid is rapid through microwave heating, because heat is generated inside (the electromagnetic energy is transferred to thermal energy and it is a energy conversion process, rather than heat transfer process of conventional heating). In addition, the conversion efficiency of microwave energy to heat energy is very high, almost 95%, while stream heating is merely 12% [14].

2.3 Pickling speed control strategy

The concept of using microwave to directly heat mixed-acid media controls the speed in pickling which has been seldom studied. It will be possible to develop a new control strategy based on three parameters, namely, pickling temperature, pickling speed, and turbulence intensity. The conventional control strategy is to choose a pickling temperature, which establishes a pickling speed based on the relation between the speed of pickling and pickling temperature, and then set the turbulence intensity, which is compatible with the temperature. In such a system, the speed of pickling is ultimately controlled by turbulence intensity, because the variation in temperature within (±1-2) ℃ has no distinct effect on the pickling according to the experiments. In this work, it was proposed to establish the optimum turbulence intensity for the best convective heat transfer at different speeds of plates and strips, and then decide the pickling temperature to provide the required heat by the function of the turbulence intensity and pickling temperature. In such a scheme, the pickling line could be operated at a desired speed with high energy efficiency.

The acid pickling process of plates and strips is a non-linear dynamic behavior, containing multivariable interactions between manipulated (such as, turbulence intensity and pickling temperature) and controlled variables (namely, the speed of the plates and strips, high-order and distributed, uncertain and time-varying parameters, un-modeled dynamics, and dead time on inputs and measurements process). As for the traditional manual control, the conventional PID control, and even the fuzzy control, is difficult to obtain quality indicators to achieve optimal range. This work combined the advantages of comprehensive utilization of both conventional PID control and fuzzy control, based on adaptive fuzzy PID, and achieved the best online of PID parameters adjustment. Using turbulence intensity as slave regulation variable and temperature as the master regulation variable, the quasi-cascade control system realized speed control of pickling plates and strips by microwave heating based on self-adaptive fuzzy PID algorithm.

3 Self-adaptive fuzzy PID control algorithm

Self-adaptive fuzzy control [15-16] PID algorithm is based on the error of the system, e, and change rate of error, e_c, as measured values, namely, the system input. According to this algorithm, the output is   and  which are the variations of three parameters of PID controller, namely, K_p, K_i and K_d [8, 17-18]. The outputs of the system satisfy PID parameters of self-setting demands according to e and e_c at different time, and then manipulated variables of the systems are adjusted to update the controlled variables, and finally dynamic and static performance of the systems is improved.

Step 1: Define fuzzy linguistic variable of input error as E^~, fuzzy universe E={a₁, a₂, …, a_m}, linguistic variable value (fuzzy subset) E^~={  …, }, change rate of error  and its universe and value E_c={e_c1, e_c2, …, e_cn},   …,  respectively; fuzzy linguistic variable of output  its fuzzy universe {c₁, c₂, …, c_l} and linguistic variable value   …,  j={p, i, d}.

Specifically, as for the definition of the fuzzy universe of input, it is always divided into N intervals [19]. Each interval is homologous with a fuzzy linguistic variable value. The membership functions of the fuzzy linguistic variable values are 1 within the intervals; it is a straight line where the membership functions of the fuzzy linguistic variable values of adjacent interval boundary is 1, and adjacent interval midpoint of value is 0. Definition of five fuzzy subsets is shown in Fig. 1. Solid and dashed lines correspond to the membership functions of different fuzzy linguistic variables. Obviously, the membership function of fuzzy linguistic variable corresponding to the middle point of each interval in fuzzy universe is 1, otherwise, the membership function of the other linguistic variable is 0. These points are called the precise linguistic values of input fuzzy linguistic variables, marked as e_s, which is numbered as n. This definition of input linguistic variable value has two advantages; 1) n fuzzy linguistic values are determined by n+1 parameters; 2) It can be applied in engineering easily. In engineering practice, the real physical universe can be divided into several interval scales according to manual operation and experience. Each interval scale corresponds to a fuzzy linguistic variable value.

Step 2: Define output linguistic variable values. In the engineering application, each output linguistic variable is defined to map a linguistic value. Assuming that the number of linguistic variable value is s, as shown in Fig. 1, s={1, 2, 3, 4, 5} corresponding to “too small”, “smaller”, “appropriate” and “bigger”, “too bigger”, respectively. Then, s points are selected, according to operation experience, in the output fuzzy universe {c₁, c₂, …, c_s|c_i j={p, i, d}}, corresponding to the fuzzy linguistic variable values, namely {C₁, C₂, …, C_s}. The definition of the membership function output of fuzzy linguistic variable corresponding to output universe can be expressed as

       (1)

Fig. 1 Input language variable value and its membership definition

The relationship between output fuzzy linguistic variables and their values is a single mapping by such design shown as Eq. (1). It has advantages to identify the system fuzzy variables easily, to define a corresponding certain output fuzzy linguistic variable with single precision value for each fuzzy state of the system probably, and to realize an engineering application similar to the input fuzzy linguistic variable feasibly. The value c_i, in practice, is corresponding with the value of manipulated variable of the precise linguistic value of input fuzzy variable e_s. Similarly, c_i is called the precise linguistic value point of output fuzzy variables. The input and output precise linguistic points and construct pairs, (e_s, c_i), are supported by the input and output spaces of precise linguistic points. All (e_s, c_i) pairs are the characteristic equations of controlled objects that the control strategy is expected when operating controller.

Step 3: The kernel of fuzzy logic control algorithm is control rule, and it is in the form of “if-then”. The control rules of two-dimensional fuzzy control algorithm can be written in the form of conditional statements as follows:

if  and  then  

(i=1, 2, …, m; l=1, 2, …, n; j={p, i, d})

All such control rules comprise the control rule sets. Among them,  is the fuzzy linguistic variable value in fuzzy universe E, while E_{c, l}, the fuzzy linguistic variable value in the fuzzy universe  C_{i, l} the fuzzy linguistic variable in fuzzy universe Every fuzzy rule determines a fuzzy implication relationship, marked as  where

                         (2)

The multiple fuzzy reasoning was done by compositional operation, as for unique fuzzy input  and  obtaining fuzzy control output

           (3)

The fuzzy implication operators are defined using the Mamdani minimum operation [20], and thus the control output value of any fuzzy input within the above fuzzy universe is represented as

                                                        (4)

Step 4: The precise value of output control  can be obtained by using the anti-fuzzy weighted average method as weight coefficient [21], expressed as

                                                     (5)

Step 5: The PID parameters K_p, K_i and K_d can be calculated by  (j=p, i, d) according to the Eqs. (6)- (8) which is self-tuning formulation of PID parameters. At initial control stage, conventional PID control and pre-tuning parameters method are adopted to initialize PID parameters, and then self-adaptive fuzzy PID control comes into service; values of three PID parameters are updated by self- adaptive fuzzy algorithm ultimately. The PID parameters can be tuned on-line according to    Eqs. (6)-(8), where   and  are the pre-tuning values of K_p, K_i and K_d, respectively.

                                                             (6)

                               (7)

                              (8)

Step 6: Three PID control parameters can be obtained according to dynamic characteristics of the object at different sampling time. The current control increment of the system can be calculated using the incremental PID. This increment value is added to the control value of preceding time, and then the output control values at current time are obtained. Thus, the process is to be self-adaptively controlled by running the algorithm Steps 3-6, recursively.

4 Acid-pickling plates and strips speed control system based on self-adaptive fuzzy PID algorithm

The acid-pickling quality of the plates and strips surface is closely related to the speed of acid-pickling process. But the speed is inevitably affected by the factors such as looper, tension, and product specifications. When acid-pickling speed changes, the turbulence intensity is adjusted through self-adaptive fuzzy PID algorithm designed in this work. This makes the turbulence intensity of acid-pickling match the pickling speed. And then the temperature of the acid is adjusted with self-adaptive fuzzy PID algorithm again, so that the temperature matches the current turbulence intensity. The schematic diagram of the acid-pickling plates and strips speed with quasi-cascade control system by microwave heating based on self-adaptive fuzzy PID algorithm is shown in Fig. 2. In Fig. 2, R(x) is the relation of the optimum value of pickling temperature and acid-pickling speed; e is the acid-pickling speed error adjusted by the optimal turbulence intensity through the inner loop, and by pickling temperature in the external loop; de/dt is the change rate of error e; e_T is the relationship error of optimal turbulence intensity and acid-picking speed, and de_T/dt the change rate of e_T; self-adaptive adjusted values of three PID parameters    corresponding to the turbulent intensity value after the current plates and strips speed are adjusted. The PID parameters in the inner loop are derived through fuzzy reasoning; self-adaptive adjusted values of three PID parameters in the external loop,    corresponding to the temperature value after the current best turbulent intensity are tuned in the inner loop. The PID parameters in the external loop are obtained through fuzzy reasoning similarly. G₂(S) is the controlled acid-pickling line equipment consisting of the pipeline, and instruments from the pressure sensor, passing by internal PID controller 2 and pickling tank, ultimately to pneumatic valve; G₁(S) is the remaining acid-pickling line equipment; Y(S) is the current speed value of the acid-pickling plates and strips.

Fig. 2 Schematic diagram of acid-pickling plates and strips speed control system

5 Simulation and analysis

The self-adaptive fuzzy PID algorithm in the aforementioned work was used to control the acid-pickling plates and strips speed. This algorithm includes double self-adaptive fuzzy PID control system similar to the quasi-cascade control, as shown in Fig. 2. Pressure representing turbulence intensity in the inner loop system impacts acid-pickling plates and strips greatly, so that the fuzzy linguistic interval is divided into smaller one compared with the acid temperature in the external loop. The self-adaptive fuzzy algorithm for the inner loop was designed as, error (E_T) and change rate of error (E_CT) which both have eleven fuzzy linguistic values {NB, NMB, NM, NMS, NS, ZE, PS, PMS, PM, PMB, PB}, where NB means negative big, NMB means negative medium big, NM means negative medium, NMS means negative medium small, NS means negative small, ZE means zero, PS means positive small, PMS means positive medium small, PM means positive medium, PMB means positive medium big, and PB means positive big, corresponding to the fuzzy universe E=E_CT={-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}, then NB[-6, -5], NMB[-5, -4], NM[-4, -3], NMS[-3, -2], NS[-2, -1], ZE[-1, 1], PS[1, 2], PMS[2, 3], PM[3, 4], PMB[4, 5], PB[5, 6]. The output fuzzy linguistic variables and   also have eleven values,  {NB, NMB, NM, NMS, NS, ZE, PS, PMS, PM,

PMB, PB}, that is, NB=-1, NMB=-0.8, NM=-0.6, NMS=-0.4, NS=-0.2, ZE=0, PS=0.2, PMS=0.4, PM= 0.6, PMB=0.8, PB=1. According to the PID parameters, K_p, K_i and K_d for the influence of the system output and PID controller design experience, combining with operation experience of the workers and Matlab simulation [21] revision, the control rules were obtained, as listed in Tables 1 and 2 (The method of getting Table 2 is the same as Table 1).

The turbulence intensity of acid was adjusted to match with the current acid-pickling speed, according to self-adaptive fuzzy PID algorithm presented in this work. Also, the acid-pickling temperature of the external loop was adjusted by the same tuning algorithm as the best to match with turbulence intensity, which had already been adjusted to the optimum value by the self-adaptive fuzzy PID algorithm in the inner loop. According to the design method of inner loop, external loop was designed as error (E) and change rate of error (E_c), which both have seven fuzzy linguistic value {NB, NM, NS, ZE, PS, PM, PB}, and the corresponding fuzzy universe E=E_CT={-4, -3, -2, -1, 0, 1, 2, 3, 4}, with NB[-4,  -3], NM[-3, -2], NS[-2, -1], ZE[-1, 1], PS[1, 2], PM[2, 3], PB[3, 4]. The output fuzzy linguistic variables   and  also have seven values {NB, NM, NS, ZE, PS, PM, PB}, NB=-6, NM=-4, NS=-2, ZE =0, PS=2, PM=4, PB=6. Control rules are listed in Table 2.

In Matlab Simulink module, a group of appropriate values were selected as the parameters of the conventional PID controller for inner and external loop, respectively. Simultaneously, these values also acted as self-adaptive fuzzy PID inner and external loop controller preset parameters. The speed of acid-pickling plates and strips was set as normal speed value (10 m/s), acid stream pressure (turbulence intensity) value    (0.25 MPa) was set as the ideal turbulence intensity of acid-pickling speed and microwave heating fluid temperature was 50 ℃. Simulation time was 300 s; when time was equal to 200 s, the disturbance was added in the pickling process in a simulation experiment. Step response of self-adaptive fuzzy PID controller system error e, change rate of error e_c, and time characteristic curve of incremental values  {j=p, i, d} for three PID parameters are shown in the Fig. 3.

Table 1 Fuzzy control rules of PID parameters  (j=p, i, d) for internal loop

Table 2 Fuzzy control rules of PID parameters  (j=p, i, d) for external loop

From Fig. 3, it can be seen that the vales of  and  increase with the increase of the error e, and the change rate of error e_c according to the Eqs. (6)-(8); and then the values of K_p, K_i become big; the system response of pickling process can be accelerated due to these much bigger values of K_p and K_i while pickling process is disturbed by disturbances, model mismatch, noise effect and nonlinear dynamic, and the time required to eliminate deviation can be reduced, respectively.

Fig. 3 Dynamic characteristics of e, e_c and  (j=p, i, d): (a) Time characteristic of e; (b) Time characteristic of e_c; (c) Time characteristic of  (d) Time characteristic of  (e) Time characteristic of
 

As shown in Fig. 4, the overshoots of self-adaptive fuzzy PID algorithm proposed was about half that of traditional PID, response time was shorter (shown no oscillation) and steady-state error was smaller. The characteristic indexes are optimal obviously. Step response performance represented smooth stability of the beginning of pickling process and accuracy of reaching set speed of acid-pickling plates and strips. The smooth step response and rapid response speed of the self- adaptive fuzzy PID algorithm were due to the advantages both dynamic performance of fuzzy controller and static performance of conventional PID controller.

Turbulence intensity was adjusted to the optimum value matching with the current speed of acid-pickling plates and strips by the self-adaptive fuzzy PID algorithm at present time. Using this proposed algorithm again, the acid temperature of external loop was adjusted to the optimum value matching acid-pickling turbulence intensity which had already been adjusted to the best value by the self-adaptive fuzzy PID algorithm in the inner loop. The simulation result of the external loop was similar to Figs. 3 and 4 which were not shown considering the succinctness of this article.

Fig. 4 Step response of PID and self-adaptive fuzzy PID

6 Conclusions

1) The mixed-acid pickling temperature and turbulence intensity, and their relations with acid-pickling speed in the pickling of plates and strips are analyzed. Based on the analyses, a double self-adaptive fuzzy PID quasi-cascade control system is designed to control the pickling speed, being a hardly modeled and coupled process.

2) The simulation results show that double self-adaptive fuzzy PID control algorithm controls the pickling speed effectively by adjusting turbulence intensity in the internal loop matching with the move speed of mixed-acid pickling plates and strips, and then adjusting mixed-acid temperature in the external loop matching with the turbulence intensity.

3) Control of mixed-acid pickling temperature and turbulence intensity ensures the optimum pickling conditions in baths. In addition, the self adaptive fuzzy PID algorithm ensures that any change in pickling speed can be responded during microwave heating quickly. Meanwhile, the control effect of self-adaptive fuzzy PID control is better than that of pure PID controller; the enhancement of self-adaptive tracking object parameter variations and anti-jamming performance can reduce the system overshoots, improving the control precision of the system, and the surface quality of acid-pickling plates and strips roll.

Acknowledgement

We are grateful to thank the help of Mr R.P. Das in English writing.

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(Edited by DENG Lü-xiang)

Foundation item: Project(51090385) supported by the National Natural Science Foundation of China; Project(2001IB001) supported by Yunnan Provincial Science and Technology Fund, China

Received date: 2011-05-31; Accepted date: 2011-09-26

Corresponding author: PENG Jin-hui, Professor, PhD; Tel: +86-871-5192076; E-mail: jhpeng_ok@yeah.net