Method and apparatus for controlling acid concentration for pickling in cold rolling

Abstract

The present invention discloses an acid concentration control method and device for cold rolling pickling production line. In the method, the acid circulating tank of the pickling production line are provided with three acid-filling tanks. And the three acid-filling tanks are interconnected with each other. An acid concentration measuring device is concatenated on the acid solution back-flow pipeline of each acid-filling tank and acid tank, through which the actual acid concentration of the acid solution in the acid tank of the production line may be measured. The measured acid concentration, after being analyzed by the analyzer, will be transmitted to the multi-variable controller where it is compared to the specified acid concentration as per process requirements. The difference between the measured acid concentration and the specified acid concentration will be used as the input value for the model of the multi-variable controller. As the acid concentrations of the three acid-filling tanks are affected by each other, the coupling relationship of the acid concentrations at the three measuring points must be found out to build the mathematical model for the acid circulating tank of the production line, and perform the multi-variable decoupling calculation. With the control method of the present invention, the close-loop control to the acid concentration can be achieved, thus to save the hydrochloric acid, reduce the regeneration amount of waste acid and decrease the environmental pollution.

Claims

1. An acid concentration control method for pickling a steel strip in a cold rolling process, comprising: providing three acid-filling tanks which are interconnected with each other and with an acid circulating tank of a pickling production line; concatenating three acid concentration measuring devices to three acid solution back-flow pipelines between each of the three interconnected acid-filling tanks and the acid circulating tank such that one acid concentration measuring device is concatenated to one respective acid solution back-flow pipeline; obtaining a respective actual acid concentration of acid solution in the acid circulating tank by each of the three acid concentration measuring devices; analyzing the actual acid concentrations by an analyzer and feedbacking to a multi-variable controller; comparing the actual acid concentrations, by the multi-variable controller, with a specific acid concentration, and setting a difference between the actual acid concentrations and the specific acid concentration as an input value for a model of the multi-variable controller; performing, via the multi-variable controller, a multi-variable decoupling calculation to convert a multi-variable control system into a single-variable control system; adjusting, based on the multi-variable decoupling calculation, an actuator to control a liquid feed into each of the three acid-filling tanks; and processing a steel strip by introducing the steel strip into the acid circulating tank for pickling during the cold rolling process; wherein the multi-variable controller performs the following steps: Step 1, implementing a multi-variable mathematical model for the acid circulating tank, wherein a formula of a transfer function matrix G(s) for the three acid-filling tanks comprises: $G\left(s\right)=\frac{1}{\begin{array}{c}\left(a_1{a}_2{a}_{3}s+a_3{}_1\left(a_1+a_2\right)\right)s^2+\\ \left({}_2+{}_3\right)\left(a_1{a}_{2}s+{}_1\left(a_1+a_2\right)\right)s\end{array}}{G}^{-1}\left(s\right)$ and a formula of an inverse function G.sup.1(s) of the transfer function matrix G(s) for the three acid-filling tanks comprises: $G^{-1}\left(s\right)=\left(\begin{array}{ccc}{a}_{1}s+{}_1& -{}_1& 0\\ -{}_1& a_{2}s+{}_1+{}_2& -{}_2\\ 0& -{}_2& a_{3}s+{}_2+{}_3\end{array}\right)$ wherein a.sub.1, a.sub.2, a.sub.3 are respectively the cross-sectional areas of the three acid-filling tanks, and the three acid-filling tanks have a same volume; and .sub.1, .sub.2, .sub.3 are allowable deviations of acid-filling amount; Step 2, implementing a transfer function matrix K.sub.p(s) for a pre-compensator based on the transfer function matrix G(s) obtained in Step 1, such that K.sub.p(s) G(s) comprises a diagonally dominant matrix, including: plotting a Gussie-Collins belt of the transfer function G(s), implementing the transfer function G(s), and obtaining a Nyquist plot with the Gussie-Collins belt, in which K.sub.p(s) G(s) comprises a diagonally dominant matrix; and calculating the transfer function matrix K.sub.p(s) for the pre-compensator, plotting a Gussie-Collins belt of Q(s), and reaching a diagonal dominance for an open-loop system compensated; Step 3, implementing a single-loop compensation for the transfer function matrix G(s) of the three acid-filling tanks, applying a single-variable design method to complete a compensation design for three single loops, taking K.sub.ci(i=1,2,3) as a PI adjuster, and obtaining a value of a transfer function matrix K.sub.c(s) of a dynamic compensator; and Step 4, implementing a Nyquist plot attached with a Gussie-Collins belt for G(s)K.sub.c(s)K.sub.p(s), ensuring a close-loop system to be stable according to a Nyquist stability criterion and obtaining a feedback gain value F(s) of the acid concentration; and wherein the cross-sectional areas of the three acid-filling tanks are a.sub.1=a.sub.2=a.sub.3=1.8 m.sup.2, the allowable deviations of acid-filling amounts are .sub.1=0.6; .sub.2=0.5; .sub.3=0.36, the transfer function matrix G(s) comprises: $G\left(s\right)=\frac{1}{\left(5.832s+3.88\right)s^2+\left(2.78s+1.856\right)s}\left[\begin{array}{ccc}1.8s+0.6& -0.6& 0\\ -0.6& 1.8s+1.1& -0.5\\ 0& -0.5& 1.8s+0.86\end{array}\right]$ wherein the inverse function G.sup.1(s) comprises: $G^{-1}\left(s\right)=\left[\begin{array}{ccc}1.8s+0.6& -0.6& 0\\ -0.6& 1.8s+1.1& -0.5\\ 0& -0.5& 1.8s+0.86\end{array}\right]$ wherein the transfer function matrix K.sub.p(s) of the pre-compensator is calculated as: $K_p=\left(\begin{array}{ccc}-82.0325& 67.2212& 0\\ 66.3421& -18.2674& 55.9562\\ 0& 57.3965& -17.5638\end{array}\right)$ wherein the transfer function matrix K.sub.c(s) of the dynamic compensator comprises: $K_c\left(s\right)=\mathrm{diag}\left[\begin{array}{ccc}1+\frac{0.0078}{s}& 1+\frac{0.0021}{s}& 1+\frac{0.0038}{s}\end{array}\right]$ wherein the feedback gain value F(s) comprises: F(s)=diag[1.5 1.5 1.5].

2. The acid concentration control method according to claim 1, further comprising: adjusting the feedback gain value F(s) of the acid concentration, and using it as a step imitation curve of the close-loop system; and adjusting the feedback gain value F(s) of the acid concentration to complete design of multi-variable close-loop control system.

3. The acid concentration control method according to claim 2, further comprising: simulating the close-loop control system, wherein a unit step response curve of the system is obtained, and system parameters are adjusted, including: inputting parameter setting values, the transfer function matrix K.sub.p(s) of the pre-compensator, the transfer function matrix K.sub.c(s) of the dynamic compensator and the feedback gain value F(s) of the acid concentration, wherein there is no overshoot in each main channel, and steady state error and response speed requirements of the system are met.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 shows the schematic diagram of concentration control process for cold rolling pickling production line;

(2) FIG. 2 shows the schematic diagram of the concentration control device for cold rolling pickling production line in the present invention;

(3) FIG. 3 shows the schematic diagram of modeling of the acid concentration multi-variable controller in the present invention;

(4) FIG. 4 shows the schematic diagram of the acid concentration multi-variable controller in the present invention;

(5) FIG. 5 shows the schematic diagram of the design process of the Nyquist array method in the present invention;

(6) FIG. 6 shows a system block diagram of the acid concentration multi-variable close-loop controller in the present invention.

(7) In figures: 11-117 valves, 21-23 heaters, 31-311 flowmeters, 41-411 pumps, 5, 51-53 acid-filling tanks; 1 roller, 2 acid sprayer, 3 overflow pipe, 4 strip steel; 6 sensor (acid concentration measuring device), 7 acid concentration analyzer, 8 actuator, 9 pre-compensation controller, 10 dynamic compensation controller, 100 production line acid circulating tank (acid tank, pickling tank).

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(8) Next, drawings and preferred embodiments are combined to further explain the present invention.

(9) As shown in FIGS. 1 and 2, the concentration control device for cold rolling pickling production line includes acid concentration analyzer 7, sensors 6, instrument setting and display system, multi-variable controller, and actuator 8; sensors 6 includes an electric conductivity sensor and a temperature sensor. The conductivity sensor measures the solution conductivity at the outlet of acid circulating tank 100 (referred to as the acid tank), and the temperature sensor measures the temperature of the acid solution at the outlet of the acid tank. The signals of the temperature sensor and conductivity sensor are output to acid concentration analyzer 7; and acid concentration analyzer 7 analyzes and calculates the concentration of the solution in acid tank 100. The concentration is fed to the multi-variable controller, which includes a dynamic compensation controller 10 and a pre-compensation controller 9. The production operator can set the parameters of multi-variable controller through the instrument setting and display system. The multi-variable controller implements multi-variable decoupling calculations according to the acid concentration signal input by the operator and the actual value of the acid concentration measured by the sensors, and outputs the calculated control variables to actuator 8; actuator 8 controls the liquid feed pumps and valves on each one of the acid-filling tanks 5 that are interconnected with each other to control the acid concentration of the acid to be transported in acid circulating tank 100.

(10) As shown in FIG. 1, in the cold rolling pickling production line, the device typically controls the acid concentrations at three points of acid circulating tank 100 in the production line to ensure that the concentration of the solution in the acid tank of the whole production line meets the requirements of the production process. Therefore, three acid-filling tanks 51, 52 and 53 are provided in the pickling production line; an acid concentration measuring device 6 (i.e. sensors) is connected in series in the pipe (i.e. overflow pipe 3) for reflux of acid solution between each one of the acid-filling tanks 51, 52, and 53 and the pickling tank 100 in the production line; this acid concentration measuring device 6 is used to measure the actual acid concentration value of the internal acid solution in acid tank 100 in the production line which is fed to the multi-variable controller after acid concentration analyzer 7. The controller compares this value with the concentration value given by the process. This difference is taken as the input value to the controller model. The measuring points are usually chosen as the positions at the inlet where the strip steel 4 enters the pickling tank 100, outlet, and middle of pickling tank. Since strip steel 4 enters pickling tank 100 from the inlet, and exits from the outlet at a certain speed, the acid solution inside acid tank 100 flows from inlet to outlet. Three acid-filling tanks 51, 52, and 53 are interconnected with each other; the raw acid flows into No. 3 acid-filling tank 53, flows into the inlet of acid tank 100 and No. 2 acid-filling tank 52 respectively after being diluted in No. 3 acid-filling tank 53, flows into the middle position of acid tank 100 and No. 1 acid-filling tank 51 respectively after being diluted in No. 2 acid-filling tank 52 again, and flows into pickling acid tank 100 and the waste acid tank respectively after being diluted in No. 1 acid-filling tank 51 again. Therefore, the acid concentrations in three acid-adding tanks 51, 52, and 53 are mutually interacted, namely, the measured acid concentration values are associated with each other, indicating that the acid concentration controller is a multi-variable controller, as shown in FIG. 4.

(11) In order to precisely control the acid concentration inside the acid circulating tank 100 in the production line, this invention establishes a mathematical model of the acid circulating tank in the production line by finding out the coupling relationship between the acid concentrations of three measurement points, and implements multi-variable decoupling calculations to convert the multi-variable control system into a single-variable control system. In order to establish the mathematical model, the present invention combines the flow diagram of cold rolling pickling acid concentration control process in FIG. 1 with the schematic diagram of the concentration control device for cold rolling pickling production line in FIG. 2, makes them equivalent to the modeling schematic diagram of the acid concentration multi-variable controller in FIG. 3. The mathematical model G(s) of the controlled objects is obtained based on FIG. 3. G(s) is used to design the multi-variable controller. The Nyquist array method is used during the designing of the multi-variable controller. Its basic design idea is: first introduce a pre-compensator K.sub.p(s) before the controlled objects to weaken the coupling effect between each loop, thus making the system's open-loop transfer function matrix become diagonal dominance matrix, and simplifying the design of the entire multi-variable system to a compensation design of a group of single-variable system; secondly design a dynamic compensator K.sub.c(s) using the single-variable design method. As shown in FIG. 4, FIG. 4 is a schematic diagram of the acid concentration multi-variable controller. After being calculated and processed by the multi-variable controller, the calculated control variables are output to the actuator, and the actuator controls the liquid feed pumps and the valves on each acid-filling tank respectively so as to control the acid concentrations of the acid circulating tank.

(12) A cold rolling pickling acid concentration control method comprises the following steps:

(13) Step 1: build a multi-variable mathematical model of the controlled object (i.e., the acid tank) in the pickling line

(14) As shown in FIG. 3. FIG. 3 is a schematic diagram of modeling of the acid concentration multi-variable controller, wherein: a.sub.i is the sectional area of the i.sup.th acid-filling tank. The cross-sectional area of acid-filling tank is known as uniform; h.sub.i(t) is the liquid level of the i.sup.th acid-filling tank at time t; f.sub.i(t) is the flow from the i.sup.th acid-filling tank to the (i+1).sup.th acid-filling tank i+1 at time t; d.sub.i(t) is the flow of the liquid output from the i.sup.th acid-filling tank at time t; and q (t) is the flow of liquid input to the i.sup.th acid-filling tank at time t;

(15) It is assumed that the velocity q.sub.i(t)(1im) of the flow into the acid-filling tank is taken as the input value of the system;

(16) the liquid level h.sub.i(t)(1im) of the acid-filling tank is taken as the output value of the system;

(17) the flow d.sub.i(t)(1im) of the liquid output from the acid-filling tank is taken as the amount of external disturbance of the system.

(18) Thus, based on the basic laws of physics, it can be deduced that the general expression of the differential equation that describes the system is as follows:
a.sub.i{dot over (h)}.sub.i(t)=q.sub.i(t)d.sub.i(t)f.sub.i(t)+f.sub.i1(t)(1im)(1)
wherein:
f.sub.0(t)=f.sub.m(t)=0
it is assumed that
h.sub.i(t)=h.sub.i0+x.sub.i(t)(1im)
q.sub.i(t)=q.sub.i0+u.sub.i(t)(1im)
d.sub.i(t)=d.sub.i0+l.sub.i(t)(1im)
f.sub.i(t)=f.sub.i0+.sub.i[x.sub.i(t)x.sub.i+1(t)](1im)
wherein: h.sub.i0, q.sub.i0, d.sub.i0, and f.sub.i0 are the rated steady-state values of h.sub.i(t), q.sub.i(t), d.sub.i(t), and f.sub.i(t), respectively; x.sub.i(t), u.sub.i(t), l.sub.i(t), and [x.sub.i(t)x.sub.i1(t)], are the change amounts of h.sub.i(t), q.sub.i(t), d.sub.i(t) and f.sub.i(t) relative to the rated steady-state values, respectively; .sub.i>0, (1im);

(19) Thus, it can be obtained that the differential equation with smaller deviation relative to the rated steady state values is as follows:
a.sub.1{dot over (x)}.sub.1(t)=u.sub.1(t)l.sub.1(t).sub.1[x.sub.1(t)x.sub.2(t)](2)
a.sub.i{dot over (x)}.sub.i(t)=u.sub.i(t)l.sub.i(t).sub.i[x.sub.i(t)x.sub.i+1(t)]+.sub.i1[x.sub.i1(t)x.sub.i(t)](2im1)
a.sub.m{dot over (x)}.sub.m(t)=u.sub.m(t)l.sub.m(t)+.sub.m1[x.sub.m1(t)x.sub.m(t)]

(20) For convenience, it is assumed that the disturbance l.sub.i(t)(1im) equals to zero. The differential equation with small deviation relative to the rated steady state values can be expressed as:

(21) $\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)\\ y\left(t\right)=\mathrm{Cx}\left(t\right)\end{array}& \left(3\right)\end{array}$
wherein:

(22) $\begin{array}{cc}A=\left[\begin{array}{ccccccc}-\frac{{}_1}{a_1}& \frac{{}_1}{a_1}& 0& 0& \mathrm{.Math.}& \mathrm{.Math.}& 0\\ \frac{{}_1}{a_2}& \frac{-\left({}_1+{}_2\right)}{a_2}& \frac{{}_2}{a_2}& 0& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& \frac{{}_2}{a_3}& \frac{-\left({}_2+{}_3\right)}{a_3}& \frac{{}_3}{a_3}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& 0\\ 0& 0& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \frac{{}_{m-1}}{a_m}& \frac{-{}_{m-1}}{a_m}\end{array}\right]& \\ B=\left[\begin{array}{ccccc}\frac{1}{a_1}& 0& 0& \mathrm{.Math.}& 0\\ 0& \frac{1}{a_2}& 0& \mathrm{.Math.}& 0\\ 0& 0& \frac{1}{a_3}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& 0& 0& \mathrm{.Math.}& \frac{1}{a_m}\end{array}\right]& \\ C=\left[\begin{array}{cccc}1& & & 0\\ & 1& & \\ & & & \\ 0& & & 1\end{array}\right]x\left(t\right)={\left[x_1\left(t\right)x_2\left(t\right)\mathrm{.Math.}{x}_m\left(t\right)\right]}^{T}y\left(t\right)={\left[y_1\left(t\right)y_2\left(t\right)\mathrm{.Math.}{y}_m\left(t\right)\right]}^{T}u\left(t\right)={\left[u_1\left(t\right)u\left(t\right)\mathrm{.Math.}{u}_{m\left(t\right)}\right]}^T& \end{array}$

(23) The system's transfer function matrix is:
G(s)=C[sIA].sup.1B(4)

(24) Its inverse function is:
G.sup.1(s)=B.sup.1[sIA]C.sup.1(5)
wherein:

(25) $B^{-1}=\left(\begin{array}{cccc}{a}_1& & & 0\\ & a_2& & \\ & & & \\ 0& & & a_m\end{array}\right)$

(26) Apply B.sup.1, A and C.sup.1 into Formula (5) to obtain the general expression:

(27) $\begin{array}{cc}{G}^{-1}\left(s\right)=\left(\begin{array}{cccccc}{a}_{1}s+{}_1& -{}_1& 0& 0& \mathrm{.Math.}& 0\\ -{}_1& a_{2}s+{}_1+{}_2& -{}_2& 0& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& -{}_2& a_{3}s+{}_2+{}_3& -{}_3& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& 0& -{}_3& a_{4}s+{}_3+{}_4& \mathrm{.Math.}& \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& -{}_{m-1}\\ 0& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& -{}_{m-1}& a_{m}s+{}_{m-1}\end{array}\right)& \left(6\right)\end{array}$

(28) G.sup.1 (s) describes the dynamic characteristics of the open-loop system of the acid-filling tank.

(29) When m=3:

(30) 0$G^{-1}\left(s\right)=\left(\begin{array}{ccc}{a}_{1}s+{}_1& -{}_1& 0\\ -{}_1& a_{2}s+{}_1+{}_2& -{}_2\\ 0& -{}_2& a_{3}s+{}_2+{}_3\end{array}\right)$
it can be obtained that the transfer function of the acid-filling tank is as follows:

(31) $\begin{array}{cc}G\left(s\right)=\frac{1}{\begin{array}{c}\left(a_1{a}_2{a}_{3}s+a_3{}_1\left(a_1+a_2\right)\right)s^2+\\ \left({}_2+{}_3\right)\left(a_1{a}_{2}s+{}_1\left(a_1+a_2\right)\right)s\end{array}}{G}^{-1}\left(s\right)& \left(7\right)\end{array}$
wherein: a.sub.1, a.sub.2, a.sub.3 are cross-sectional areas of three acid-filling tanks The three acid adding volumes are the same. a.sub.1=a.sub.2=a.sub.3=1.8 m.sup.2. .sub.1=0.6; .sub.2=0.5; .sub.3=0.36 are the deviation amount values of the acid adding flow allowed by the process. Apply them into Formula (7), and then

(32) $\begin{array}{cc}{G}^{-1}\left(s\right)=\left[\begin{array}{ccc}1.8s+0.6& -0.6& 0\\ -0.6& 1.8s+1.1& -0.5\\ 0& -0.5& 1.8s+0.86\end{array}\right]G\left(s\right)=\frac{1}{\left(5.832s+3.88\right)s^2+\left(2.78s+1.856\right)s}\left[\begin{array}{ccc}1.8s+0.6& -0.6& 0\\ -0.6& 1.8s+1.1& 0\\ 0& -0.5& 1.8s+0.86\end{array}\right]& \left(8\right)\end{array}$

(33) Step 2: design a transfer function matrix K.sub.p(s) for a pre-compensator based on the transfer function matrix G(s) for the acid-filling tank obtained in Step 1, to make K.sub.p(s) and G(s) become the diagonally dominant matrix. As shown in FIGS. 4 and 5. FIG. 4 is a schematic diagram of the acid concentration multi-variable controller. FIG. 5 is a schematic diagram of the design process of the Nyquist array method. The step is as follows: 1) operate existing software (which is available in the software market, is an existing technology) to plot Gussie-Collins belt of the transfer function G(s), input the mathematical model G(s) into a pop-up interface, and click to operation after completion of input, a Nyquist plot attached with Gussie-Collins belt is displayed on the interface, in which K.sub.p(s) and G(s) become diagonally dominant matrix; 2) calculate the transfer function matrix K.sub.p(s) for a pre-compensator using existing diagonal dominance software (which is available in the software market, is an existing technology):

(34) $\begin{array}{cc}{K}_p=\left(\begin{array}{ccc}-82.0325& 67.2212& 0\\ 66.3421& -18.2674& 55.9562\\ 0& 57.3965& -17.5638\end{array}\right)& \left(9\right)\end{array}$

(35) plot Gussie-Collins belt of K.sub.p(s) G(s) and then an open-loop system compensated has reached diagonal dominance;

(36) Step 3: design of single-loop compensation for G(s), since K.sub.p(s) G(s) has reached the diagonal dominance, a single-variable design method may be used to complete compensation design for three single loops. According to the requirements of production process, the overshoot of acid concentration should be small, the transient response procedure should be short, and the close-loop steady-state error should be zero. Therefore, take K.sub.ci(i=1,2,3) as PI adjuster. Through several parameter trials, obtain that:

(37) $\begin{array}{cc}{K}_c\left(s\right)=\mathrm{diag}\left[\begin{array}{ccc}1+\frac{0.0078}{s}& 1+\frac{0.0021}{s}& 1+\frac{0.0038}{s}\end{array}\right]& \left(10\right)\end{array}$

(38) Step 4: plot Nyquist plot attached with Gussie-Collins belt for G(s)K.sub.c(s)K.sub.p(s), ensure close-loop system to be stable according to Nyquist stability criterion and obtain feedback gain value F(s) of the acid concentration as
F(s)=diag[1.5 1.5 1.5].(11)

(39) Step 5: adjust the feedback gain value F(s) of the acid concentration, and use it as a step imitation curve of the close-loop system, adjust the feedback gain value F(s) of the acid concentration to complete design of multi-variable close-loop control system. Upon completion of the close-loop control system, the block diagram is shown in FIG. 6.

(40) Step 6: simulate the close-loop control system, a unit step response curve of the system can be obtained through existing simulation software, adjust system parameters, including input parameter setting values, the transfer function matrix K.sub.p(s) of the pre-compensator, the transfer function matrix K.sub.c(s) of the dynamic compensator and the feedback gain value F(s) of the acid concentration so that there is no overshoot in each main channel, meeting steady state error and response speed requirements of the system.

(41) The main inventive ideas of the cold rolling pickling acid concentration control method of the present invention focus on the determining of various parameters in the acid concentration multi-variable controller model. The parameters include the transfer function matrix G(s) of the acid-filling tanks (the controlled objects), transfer function matrix K.sub.p(s) of pre-compensator, transfer function matrix K.sub.c(s) of dynamic compensator and feedback gain F(s) of acid concentration. The block diagram of the closed-loop control system after the parameters of the multi-variable controller arithmetic unit and the acid concentration multi-variable controller are determined is as shown in FIG. 6.

(42) The actual values of acid concentration of the acid solution inside the acid tank of the production line are obtained through three acid concentration measuring devices, and fed to the multi-variable controller through the acid concentration analyzer. The multi-variable controller compares the actual values with the acid concentration values given by the process. The differences are taken as the input values of the multi-variable controller model; after being calculated and processed by the multi-variable controller, the control variables are calculated and output to the actuator. The actuator controls the liquid feed pumps and the valves on each oen of the acid-filling tanks respectively, so as to control the acid concentrations of the acid circulating tank.

(43) Provided above are only preferred embodiments of the present invention, which is in no way used to limit the scope of protection of the present invention. Thus, any modification, equivalent substitution, improvement or other changes made in the spirit and principle of the present invention shall fall within the scope of protection of the present invention.