JP2016203180A - Controller parameter derivation method, controller parameter derivation device, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To systematically perform design of a controller for realizing control of a molten metal surface level in a continuous casting machine using a stopper with high accuracy by simple adaptive control.SOLUTION: PFC gain β is derived so as to satisfy a restriction requirement showing that an ASPR condition is theoretically satisfied. Then, upon fixing a tentative upper limit value K_of an adaptive gain K(t) and the PFC gain β, PFC poles α, αare changed, and the PFC poles α, αwhen difference in amplitude between sensitivity functions S(s) and S(s) becomes minimum are derived in a predetermined frequency range. Then, upon fixing the PFC poles α, αand the PFC gain β, the adaptive gain is changed, and an adaptive gain when the sensitivity functions S(s), S(s) coincide with each other is derived as an upper limit value Kof the adaptive gain K(t) at an upper limit and a lower limit of the predetermined frequency range.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a controller parameter derivation method, a controller parameter derivation device, and a program, and is particularly suitable for use in controlling the level of molten metal in a mold in a continuous casting machine.

  In a continuous casting machine such as steel, the molten metal is supplied and stored from a ladle to a tundish and then continuously supplied into a mold (mold) through an immersion nozzle. In parallel with the supply of molten metal into the mold, the molten metal in the mold is continuously drawn from the bottom of the mold by multiple pairs of pinch rolls while being cooled from the surface with a water-cooled mold to form a solidified shell. It is. Further, the solidification nuclei drawn out from the lower part of the mold are sprayed with water by cooling spray to advance the cooling of the solidification nuclei, thereby solidifying the inside of the solidification nuclei. In this way, slabs such as slabs, blooms and billets are formed.

  At this time, depending on the temperature and composition of the molten metal, disturbance such as unsteady bulging and clogging / peeling of the immersion nozzle occurs, and the molten metal level in the mold (the height position of the molten metal surface) varies. When the amount of fluctuation of the molten metal level is large, the growth of the solidified shell on the molten metal surface, which is the solidification start point, becomes unstable. As a result, the molten metal overflows from the mold and breaks out, which may hinder stable operation. Moreover, if the amount of fluctuation of the molten metal surface level is large, the powder, which is a lubricant dispersed on the molten metal surface, may be caught inside the molten metal, and the quality of the steel slab may be deteriorated.

  Therefore, in the continuous casting machine, the molten metal level is always detected by a level meter arranged above the molten metal surface in the mold, and the injection amount of the molten metal from the tundish into the mold is based on the detection result. Automatic control to maintain the molten metal surface level at a constant target level is performed by adjusting the sliding nozzle or stopper opening degree by feedback control. Such automatic control is called mold surface level control of a continuous casting machine.

  In mold level control of a continuous casting machine, PI control is generally used in many cases. However, PI control is vulnerable to changes in process (plant) characteristics, and it is difficult to increase the control gain. For this reason, when PI control is used for mold surface level control of a continuous casting machine, fluctuation of the surface level is likely to occur, which may hinder the improvement of the quality of the steel slab.

The vulnerability of hot water level control to such process characteristic changes has been addressed by applying advanced control theory. As techniques for taking such measures, there are techniques disclosed in Patent Documents 1 and 2.
In Patent Document 1, by applying SAC (Simple Adaptive Control) to mold surface level control of a continuous casting machine, the stopper opening speed is fast based on the adaptive gain calculated from the deviation of the surface level. Adjust.
In Patent Document 2, in order to quickly remove the fluctuation of the molten metal surface level due to disturbance that is difficult to remove by feedback control alone, a disturbance observer is configured, the estimated disturbance is calculated by the disturbance observer, and the calculated estimated disturbance is output to the SAC control output. to add.

Japanese Patent Laid-Open No. 9-174215 Japanese Patent Laid-Open No. 10-328801

  In the simple adaptive control (SAC: (Simple Adaptive Control)) described in Patent Document 1 and Patent Document 2, the algorithm is simple, and the input / output transfer function for the output feedback of an arbitrary gain is almost positive, that is, Control stability is assured under conditions satisfying ASPR (Almost Strictly Positive Real) The inventors have applied the control methods described in Patent Document 1 and Patent Document 2 to a plurality of continuous casting machines. As a result, the present inventors can easily adjust the control parameters in the field and automatically adjust the process parameters according to changes in the process characteristics, and realize a high gain and robust level control. It was confirmed.

  The simple adaptive control (SAC) has a great feature that the stability of the control is guaranteed if the existence of a gain that stabilizes the process can be confirmed. This represents that the process is stable even when the adaptive gain is increased. However, the present inventors have actually found that when the adaptive gain becomes excessive, the hot water level hunts and the process may become unstable. In particular, the present inventors have found that the tendency is remarkable in the stopper injection system in which the operation change amount is more severely limited than the sliding nozzle.

  The shape of the stopper changes depending on the clogging / melting of the immersion nozzle. For this reason, it is preferable to open and close the stopper not by a position signal that directly controls the opening degree of the stopper that adjusts the amount of molten metal flowing into the mold but by a pulse signal that represents the change in the opening degree of the stopper. In addition, since the rate of change of the flow rate with respect to the operation amount is larger in the stopper than in the sliding nozzle, a delicate operation is required for the stopper. In the following description, the rate of change of the flow rate with respect to the unit manipulated variable is referred to as a flow rate coefficient as necessary.

  In order to realize a delicate operation on the stopper, it is necessary to set the moving speed of the stopper small. Therefore, severe restrictions are imposed on the operation change amount of the stopper. This means that if the adaptive gain of the simple adaptive control (SAC) becomes excessive and the operation change amount is saturated, the feedback control does not function normally and the simple adaptive control (SAC) becomes unstable. In particular, the higher the casting speed, the more the hot water surface becomes more prominent and the adaptive gain becomes excessive, so that the simple adaptive control (SAC) tends to become unstable. Therefore, in order to apply the simple adaptive control (SAC) to the continuous casting machine of the stopper injection system and stabilize the mold surface level control of the continuous casting machine, it is necessary to take measures to prevent the adaptive gain from becoming excessive.

  In addition, the design of a conventional controller for simple adaptive control (SAC) is empirical, and trial and error design and adjustment have been performed. Therefore, for example, a guideline on how to design a controller for a change in process characteristics when the injection device is changed from a sliding nozzle to a stopper is unclear. There is a limit to analogy from the experience of designing and adjusting sliding nozzles so far, and a controller design method with good visibility is required.

  The present invention has been made in view of the above problems, and systematically designed a controller for realizing high-precision control of the molten metal surface level in a continuous casting machine using a stopper by simple adaptive control. It aims to be able to do it.

  The controller parameter setting method of the present invention is a reference model for outputting a target level of a molten metal level in a mold in a continuous casting machine as an input and outputting a molten metal level that the detected value of the molten metal level should follow, A variable adaptive gain with respect to the deviation between the output of the reference model and the detected value of the molten metal level, and a stopper for adjusting the inflow amount of the molten metal stored in the tundish of the continuous casting machine into the mold And a parallel forward compensator (PFC) that compensates the output of a process model that outputs a detected value of the molten metal level as an input to the opening degree command, and controls the molten metal level by simple adaptive control. A controller parameter derivation method for deriving a controller parameter, wherein the first function is a sensitivity function when PI level control is performed on the molten metal surface level. A PI controller design step of deriving the frequency characteristic of the amplitude of the degree function by the PI controller design means, an adaptive gain upper limit temporary determination step of determining the temporary upper limit value of the adaptive gain by the adaptive gain upper limit temporary determination means, The frequency characteristic of the amplitude of the first sensitivity function derived by the PI controller design process and the frequency characteristic of the amplitude of the second sensitivity function, which is a sensitivity function when performing control of the molten metal surface level by simple adaptive control. A PFC parameter determination step of determining a parameter of a transfer function of the parallel forward compensator by a PFC parameter determination means using the temporary upper limit value of the adaptive gain determined by the adaptive gain upper limit temporary determination step; The frequency characteristic of the amplitude of the first sensitivity function derived by the PI controller design process, and the frequency characteristic of the amplitude of the second sensitivity function; An adaptive gain upper limit determining step of determining an upper limit value of the adaptive gain by an adaptive gain upper limit determining means using the parameters of the transfer function of the parallel forward compensator determined by the PFC parameter determining step, In the PFC parameter determination step, the adaptive gain is assumed to be a temporary upper limit value of the adaptive gain determined in the adaptive gain upper limit temporary determination step, and at least one transfer function of the parallel forward compensator is determined. Based on the result of comparing a plurality of frequency characteristics of the amplitude of the second sensitivity function derived by different parameters and the frequency characteristics of the amplitude of the first sensitivity function, the first sensitivity function The difference between the amplitude of the first sensitivity function and the amplitude of the first sensitivity function is minimum under a predetermined condition in a predetermined frequency range lower than a frequency where the amplitude of the first frequency exceeds 0 [dB]. The frequency characteristic of the amplitude of the second sensitivity function is searched, the parameter of the transfer function of the parallel forward compensator used for deriving the frequency characteristic of the amplitude of the searched second sensitivity function is specified, The adaptive gain upper limit determining step is derived by assuming that the parameter of the transfer function of the parallel forward compensator is the parameter derived in the PFC parameter determining step and changing the value of the adaptive gain. Based on the result of comparing the plurality of frequency characteristics of the amplitude of the second sensitivity function with the frequency characteristics of the amplitude of the first sensitivity function, the amplitude of the first sensitivity function exceeds 0 [dB]. The amplitude of the second sensitivity function in which the values at the upper and lower limits of the predetermined frequency range on the lower frequency side than the frequency coincide with the frequency characteristics of the amplitude of the first sensitivity function. Searching the frequency characteristic, the adaptive gain used in the derivation of the amplitude of the frequency characteristic of the second sensitivity function that the search, and identifies as the upper limit of the adaptive gain.

  The controller parameter setting device of the present invention, the reference model for outputting the target level of the molten metal level in the mold in the continuous casting machine as an input, and outputting the molten metal level that the detected value of the molten metal level should follow, A variable adaptive gain with respect to the deviation between the output of the reference model and the detected value of the molten metal level, and a stopper for adjusting the inflow amount of the molten metal stored in the tundish of the continuous casting machine into the mold And a parallel forward compensator (PFC) that compensates the output of a process model that outputs a detected value of the molten metal level as an input to the opening degree command, and controls the molten metal level by simple adaptive control. A controller parameter deriving device for deriving a parameter of a controller to perform the control, wherein a first function that is a sensitivity function when performing control of the molten metal surface level by PI control is provided. PI controller design means for deriving frequency characteristics of amplitude of the degree function, adaptive gain upper limit tentative determination means for determining a temporary upper limit value of the adaptive gain, and the first controller derived by the PI controller design means The frequency characteristic of the amplitude of the sensitivity function, the frequency characteristic of the amplitude of the second sensitivity function, which is a sensitivity function when the level control is performed by simple adaptive control, and the adaptive gain upper limit tentative determination means PFC parameter determining means for determining a transfer function parameter of the parallel forward compensator using the provisional upper limit value of the adaptive gain, and the first sensitivity function derived by the PI controller designing means. A frequency characteristic of the amplitude, a frequency characteristic of the amplitude of the second sensitivity function, and a parameter of the transfer function of the parallel forward compensator determined by the PFC parameter determining means And an adaptive gain upper limit determining means for determining an upper limit value of the adaptive gain using the PFC parameter determining means, wherein the PFC parameter determining means determines the adaptive gain determined by the adaptive gain upper limit temporary determining means. A plurality of frequency characteristics of the amplitude of the second sensitivity function derived by making at least one parameter of the transfer function of the parallel forward compensator different from the provisional upper limit value, On the basis of the result of comparison with the frequency characteristic of the amplitude of the first sensitivity function, the first sensitivity in a predetermined frequency range lower than the frequency at which the amplitude of the first sensitivity function exceeds 0 [dB]. The frequency characteristic of the amplitude of the second sensitivity function that minimizes the difference from the amplitude of the function under a predetermined condition is searched, and is used for deriving the frequency characteristic of the amplitude of the searched second sensitivity function. The transfer function parameter of the parallel forward compensator is specified, and the adaptive gain upper limit determining means is such that the parameter of the transfer function of the parallel forward compensator is the parameter derived by the PFC parameter determining means In addition, based on a result of comparing a plurality of frequency characteristics of the amplitude of the second sensitivity function derived by varying the value of the adaptive gain and a frequency characteristic of the amplitude of the first sensitivity function. The values at the upper and lower limits of the predetermined frequency range on the lower frequency side than the frequency at which the amplitude of the first sensitivity function exceeds 0 [dB] are the frequency characteristics of the amplitude of the first sensitivity function. The frequency characteristic of the amplitude of the second sensitivity function that matches is searched, and the adaptive gain used for deriving the frequency characteristic of the amplitude of the searched second sensitivity function is set to the appropriate gain. And identifies as the upper limit of the gain.

  A program according to the present invention causes a computer to execute each step of the controller parameter setting method.

  According to the present invention, when the molten metal surface level control is performed by PI control / simple adaptive control, the transmission of the parallel forward compensator so that the difference in amplitude of the sensitivity function in a predetermined frequency range is minimized under a predetermined condition. Derive the function parameters. Then, assuming that the parameter of the transfer function of the parallel forward compensator is the derived parameter, the upper and lower limits of the predetermined frequency range of the amplitude of the sensitivity function when the molten metal surface level control is performed by PI control / simple adaptive control The adaptive gain is derived so that the values at are equal, and the derived adaptive gain is set as the upper limit value of the adaptive gain. Therefore, it is possible to systematically design a controller for realizing the control of the molten metal surface level in a continuous casting machine using a stopper with high accuracy by simple adaptive control.

It is a figure which shows an example of a structure of a continuous casting machine. It is a figure which shows an example of a structure of the hot_water | molten_metal surface level control apparatus. It is a figure which rewrites and shows the structure of the hot-water surface level control apparatus of FIG. It is a figure which shows an example of a functional structure of a controller parameter derivation | leading-out apparatus. It is a figure which shows an example of a structure of a process model. It is a figure which shows an example of the block diagram for derivation | leading-out the sensitivity function at the time of using a PI controller. It is a figure which shows an example of the Bode diagram of a sensitivity function at the time of using a PI controller. It is a figure which rewrites and shows the composition of the hot-water surface level control device of FIG. It is a figure which shows an example of the block diagram for derivation | leading-out the sensitivity function at the time of using a SAC controller. It is a figure which illustrates notionally an example of the process at the time of deriving a PFC pole. It is a figure which shows an example of the Bode diagram of a sensitivity function when the value of an evaluation function becomes the minimum. It is a figure which shows an example of the Bode diagram of a plurality of sensitivity functions from which a PFC pole differs. It is a figure which shows notionally an example of the process at the time of deriving the upper limit of an adaptive gain. It is a figure which shows the 1st example of the Bode diagram of several sensitivity functions from which an adaptive gain differs. It is a figure which shows the 2nd example of the Bode diagram of the several sensitivity function from which an adaptive gain differs. It is a figure which shows an example of the Bode diagram of the transfer function from disturbance to the opening degree command. It is a figure which shows an example of the relationship between a hot-water surface level and time.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a diagram illustrating an example of a configuration of a continuous casting machine.
In FIG. 1, the continuous casting machine includes a tundish 11, an immersion nozzle 12, a stopper 13, a mold (mold) 14, a pinch roll 15, and a cooling spray 16.

The tundish 11 temporarily stores molten metal (molten steel) 17 supplied from a ladle (not shown).
The mold 14 is disposed below the tundish 11 with a space from the tundish 11. The mold 14 has, for example, a cylindrical shape. The mold 14 is water cooled.
The immersion nozzle 12 injects the molten metal 17 stored in the tundish 11 into the mold 14. The immersion nozzle 12 is disposed such that its base end is located on the bottom surface of the tundish 11 and a predetermined region on the distal end side is located inside the mold 14. Moreover, the inside of the immersion nozzle 12 and the inside of the tundish 11 communicate with each other.

  The stopper 13 is for controlling the supply amount of the molten metal 17 supplied from the tundish 11 to the immersion nozzle 12, and is arranged at a connection portion between the tundish 11 and the immersion nozzle 12. The stopper 13 moves in the height direction (vertical direction in FIG. 1). When the stopper 13 is at the lowest position, the connecting portion between the tundish 11 and the immersion nozzle 12 is fully closed. The opening area of the connection part of the tundish 11 and the immersion nozzle 12 increases, so that the stopper 13 is located in a position higher than the said position. When the stopper 13 rises to a predetermined upper limit position, the supply amount of the molten metal 17 supplied from the tundish 11 to the immersion nozzle 12 becomes maximum.

A plurality of pairs of pinch rolls 15 are arranged along the conveying path of steel (the ends facing each other) drawn downward from the mold 14. A plurality of cooling sprays 16 for injecting cooling water for cooling the steel drawn downward from the mold 14 onto the steel are arranged outside the pinch roll 15.
As described above, the molten steel injected into the mold 14 is cooled by the mold 14, and a solidified shell 18 is formed from the surface to solidify. Steel whose surface is a solidified shell 18 but whose interior is not solidified is continuously drawn out from the lower end of the mold 14 while being sandwiched between pinch rolls 15. In the process of being drawn out from the mold 14 in this way, the steel is solidified to the inside by advancing cooling of the steel with the cooling water sprayed from the cooling spray 16. The solidified steel is cut into a predetermined size on the downstream side of a continuous casting machine (not shown), and slabs having different cross-sectional shapes such as slabs, blooms and billets are manufactured.

The level meter 19 is arranged above the mold 14 so as to face the surface of the molten steel staying inside the mold 14 of the continuous casting machine as described above. The level meter 19 detects the height position (the surface level) of the surface of the molten metal 17 staying inside the mold 14.
The molten metal level control device 100 inputs the molten steel height position detected by the level meter 19 as the molten metal level, and determines the opening degree of the stopper 13 based on the deviation between the target value and the actual value of the molten metal level. An open / close pulse signal, which is a pulse signal representing the change, is output. In the present embodiment, the hot water level control device 100 operates as a SAC controller that feedback-controls the hot water level by simple adaptive control (SAC). Details of the hot water level control device 100 will be described later.

  The ST control device 200 includes a pulse motor drive circuit for operating the hydraulic cylinder 300. The ST control device 200 receives the open / close pulse signal output from the molten metal level control device 100 and outputs the open / close pulse signal after processing by the drive circuit or the like to the hydraulic cylinder 300. The molten metal level control device 100 can output an analog signal representing information included in the opening / closing pulse signal to the ST control device 200 instead of the opening / closing pulse signal. In this case, the ST control device 200 generates an opening / closing pulse signal based on the analog signal output from the hot water surface level control device 100 and outputs it to the hydraulic cylinder 300. Since the ST control device 200 can be realized by a known technique, a detailed description thereof is omitted here.

  The hydraulic cylinder 300 includes a pulse motor. The pulse motor rotates based on the open / close pulse signal transmitted from the ST control device 200. With this rotation, the position of the rod of the hydraulic cylinder 300 is changed, and the height position of the stopper 13 is changed. Since the hydraulic cylinder 300 can be realized by a known technique, a detailed description thereof is omitted here.

  During continuous casting with the continuous casting machine having the above configuration, the level of the molten metal in the mold 14 may fluctuate due to disturbance such as clogging / peeling (melting damage) of the immersion nozzle 12. The molten metal level control device 100 applies simple adaptive control (SAC) to an extended process model in which a parallel feed forward compensator (PFC) is added in parallel to the process model (plant model). A control input is provided to the process model such that the level detection value follows the output of the reference model. By doing so, a high gain and robust feedback control calculation can be executed, and the opening command value (open / close pulse signal) of the stopper 13 is calculated so that the detected value of the molten metal surface level matches the target value. Is done.

  The opening amount of the stopper 13 is adjusted based on the opening command value of the stopper 13 calculated in this way. By doing in this way, even if the characteristic of a process changes, supply_amount | feed_rate to the mold 14 of the molten metal 17 in the tundish 11 can be controlled so that a hot_water | molten_metal surface level will be a target value in the shortest time. . Therefore, it is possible to quickly respond to fluctuations in the molten metal surface level caused by disturbance such as clogging / peeling (melting damage) of the immersion nozzle 12. As a result, a stable hot water level with little fluctuation is maintained. Therefore, breakout due to fluctuations in the molten metal level is less likely to occur, and the powder is less likely to enter the molten metal, so that a high quality steel slab can be cast.

FIG. 2 is a block diagram showing an example of the configuration of the hot water surface level control device 100.
In FIG. 2, the molten metal level control device 100 includes a reference model 201, subtracters 202 and 203, multipliers 204 a, 204 b and 204 c, a parallel forward compensator 205, and an adder 206.
Hereinafter, an example of these components 201 to 206 and the process model 207 included in the molten metal level control apparatus 100 will be described.

  As described above, in this embodiment, the simple adaptive control (SAC) is applied to the feedback control at the molten metal level. Simple adaptive control (SAC) is a type of adaptive control similar to model reference control (MRACS), self-tuning adaptive control (STR), and the like.

  Simple adaptive control (SAC) is a simple adaptation of the structure under the condition that the closed loop transfer function obtained when the output feedback gain is applied to the transfer function of the process model is Strictly Positive Real. The control system can be configured. Such a condition is referred to as an ASPR (Almost Strictly Positive Real) condition. Simple adaptive control (SAC) is a real process because the requirements for application are not strict and the algorithm is simple like model reference control (MRACS) and self-tuning adaptive control method (STR). Easy to apply to equipment.

However, since many actual process facilities (transfer functions of the process model to be controlled) do not satisfy the ASPR condition, simple adaptive control (SAC) cannot be applied as it is. Therefore, by introducing a parallel forward compensator that compensates for the output of the process model, and by making the apparent process (extended system process) viewed from the simple adaptive control (SAC) satisfy the ASPR condition, simple adaptive control is achieved. (SAC) can be applied to actual process equipment.
In simple adaptive control (SAC), as an input a target value r of the molten metal surface level, the output y _m of the reference model 201 is calculated by the following formula (1) and (2) (general form of state-space representation) .

In Equation (1), A _m is a state matrix and B _m is an input matrix. In Expression (2), C _m is an output matrix, and D _m is a direct matrix.
In the present embodiment, a transfer function corresponding to the state space expression is defined as the following equation (3).

In Expression (3), s is a Laplace operator, G _m (s) is a transfer function of the normative model 201, and T _m is a time constant [sec] of the normative model 201.

The output y _m of the reference model 201, extended system value obtained by subtracting the output y _a of the process, i.e., a deviation E _y of molten metal surface level is calculated by the following equation (4). Here, the deviation E _y of the molten metal level is a value obtained by adding the detected value y of the molten metal level and the parallel advance compensation amount (compensation value) y _h calculated by the parallel advance compensator (PFC) 205. .
_{E y = y m -y a =} y m - (y h + y) ··· (4)

Then, the SAC control output u ₀ as the opening degree command for the stopper 13 is calculated by the following equations (5) to (12).

However, normally, the target value r of the molten metal level is not changed in one control cycle, and even if the target value r of the molten metal level is changed, the detected value y of the molten metal level is changed to the molten metal level. It is not necessary to rapidly follow the target value r of (which should be followed gently). Therefore, in this embodiment, for the sake of simplicity, the control gain in the multiplier 204b (adaptive gain K _x (t) with respect to the target value r of the molten metal surface level) and the control gain in the multiplier 204c (the state quantity X of the reference model 201). _The adaptive gain K _u (t)) for _{m is set} to 0 (zero, K _x (t) = K _u (t) = 0). Therefore, the equations (5) to (12) are simplified as the following equations (13) to (18). Note that (t) represents a function of time. That is, the adaptive gains K _x (t), _Ku (t), and _Ke (t) are variable.

In the equation (14), K _emax is an upper limit value of the control gain in the multiplier 204a. Control gain in the multiplier 204a receives the output y _m of the reference model 201 is an adaptive for the deviation between the detection value of the molten metal surface level is the output of process model 207 y (feedback value) gain K _e (t).
In Equation (15), K _p (t) is a deviation proportional term of the adaptive gain K _e (t), and K _i (t) is a deviation integral term of the adaptive gain K _e (t).
In the equation (16), γ _p is a deviation proportional coefficient in the adaptive gain K _e (t).
In equation (17), γ _i is a deviation integral coefficient in the adaptive gain K _e (t), and α (t) is an integral correction term in the adaptive gain K _e (t). Note that the second term on the right side of the equation (17) is a divergence prevention term.
In the equation (18), σ is an integral correction coefficient in the adaptive gain K _e (t).

Therefore, the block diagram of the molten metal level control apparatus 100 shown in FIG. 2 can be rewritten as the block diagram shown in FIG.
The SAC control output u ₀ obtained by the above equations (13) to (18) is given as an input to the parallel forward compensator (PFC) 205, and the parallel forward compensation amount y _h is _expressed by the following equations (19) and ( 20) Calculate according to the equation (general form of state space representation).

In equation (19), A _h is a state matrix and B _h is an input matrix. In equation (20), _Ch is an output matrix and _Dh is a direct matrix.
In the present embodiment, a transfer function corresponding to the state space expression is defined as the following equation (21).

In Equation (21), PFC (s) is a transfer function of the parallel forward compensator (PFC) 205, and β is a gain of the parallel forward compensator (PFC) 205 (multiplying the Laplace operator of the highest order of the numerator). Α ₁ is the first pole of the transfer function PFC (s) of the parallel forward compensator (PFC) 205, and α ₂ is the transfer function PFC of the parallel forward compensator (PFC) 205. This is the second pole of (s). However, α ₁ > 0, α ₂ > 0, and β> 0.
In the following description, the parallel forward compensator (PFC) 205 first pole alpha ₁ and the second pole alpha ₂ of the transfer function PFC (s) of, PFC poles alpha ₁ optionally, alpha ₂ and Called. Further, the gain β of the parallel forward compensator (PFC) 205 is referred to as a PFC gain β as necessary.

The hot water surface level control device 100 repeatedly executes the calculation based on the calculation formulas of the formulas (3), (4), (13) to (18), and (21) shown above. Then, the SAC control output u ₀ as the opening command value for the stopper 13 is obtained.
A low-pass filter may be provided between the process model 207 and the subtractor 202, and the detection value y of the molten metal level may be output to the subtracter 202 after passing through the low-pass filter.

In this embodiment, robust and stable surface level control is possible even for a stopper injection system (a system in which the amount of inflow of the molten metal 17 into the mold 14 is adjusted by the stopper 13), which has a strict limit on the operation change amount. The purpose is to do. For this reason, the transfer function PFC (s) of the parallel forward compensator (PFC) 205 and the upper limit value K _emax of the adaptive gain K _e that constitute the simple adaptive control (SAC) are set as follows.

FIG. 4 is a diagram illustrating an example of a functional configuration of the controller parameter deriving device 400. Controller parameter derivation unit 400 is a device for deriving the parameters of the SAC controller (upper limit value K _emax transmission of parallel forward compensator (PFC) 205 function PFC (s) and adaptive gain K _e). The controller parameter deriving device 400 is realized by using, for example, an information processing device including a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware.
Below, an example of the function which each part of the controller parameter derivation | leading-out apparatus 400 has is demonstrated.

(Process model acquisition unit 401)
The process model acquisition unit 401 acquires information for specifying the process model 207. As an acquisition form of the process model 207, for example, operation of a user interface, communication with an external device, or reading from a portable storage medium can be cited.
In this embodiment, the transfer function P (s) of the process model 207 is expressed by the following equation (22).

In the equation (22), KK is a flow coefficient [m ² / sec] of the stopper 13. A is the horizontal cross-sectional area [m ² ] of the hollow portion of the mold 14. T _CYL is a time constant [sec] of the opening / closing actuator (hydraulic cylinder 300). T _S is the time constant [sec] of the level meter 19. _TN is a dead time [sec] required for hot water to drop inside the immersion nozzle 12.

(2 / T _N −s) / (2 / T _N + s) in the equation (22) is a first-order Padé approximation of the transfer function of the dead time element based on the dead time T _N.
Therefore, in the present embodiment, the process model 207 is represented by the block diagram shown in FIG. In addition, y 'shown in FIG. 5 is a raw value of the hot water level. In actual control, the process model 207 is replaced with an actual plant (continuous casting machine).
In the present embodiment, the process model acquisition unit 401 acquires the form of equation (22) and the value of each parameter in equation (22).

(PI controller design unit 402: STEP0)
The PI controller design unit 402 derives a sensitivity function S _PI (s) when the PI controller is used instead of the SAC controller.
FIG. 6 is a diagram illustrating an example of a block diagram for deriving the sensitivity function S _PI (s) when the PI controller is used.
The transfer function C _PI (s) of the PI controller 601 is expressed by the following equation (23).

In the equation (23), KP is a proportional gain, and TI is an integration time [sec].
The sensitivity function S _PI (s) when the PI controller is used is expressed by the following equation (24).

The sensitivity function S _PI (s) coincides with the detected value y ′ of the molten metal level from the disturbance d. Therefore, the sensitivity function S _PI (s) means how the disturbance d is amplified and appears in the detected value y ′ of the molten metal surface level.

An open loop design is performed for the transfer function of P (s) · C _PI (s), which is the product of Equation (22) and Equation (23). Empirically, the proportional gain KP and the integration time TI are designed so that the phase margin is about 50 [°] and the gain margin is 10 [dB] or more. Note that the design method of the proportional gain KP and the integration time TI can be realized by a known technique, and therefore detailed description thereof is omitted here.

FIG. 7 is a diagram illustrating an example of a Bode diagram (frequency response diagram) of the sensitivity function S _PI (s) when the PI controller is used. In FIG. 7, the illustration of the phase frequency characteristic is omitted (this is the same in the Bode diagrams of the other figures).
In FIG. 7, the disturbance d is amplified at a frequency in the range where the amplitude (gain) of the sensitivity function S _PI (s) exceeds 0 [dB] and appears in the detected value y ′ of the molten metal surface level. In the example shown in FIG. 7, the amplitude of the sensitivity function S _PI (s) exceeds 0 [dB] in the frequency range of about 0.08 [Hz] to 0.7 [Hz].

(ASPR conditions)
The local feedback of the parallel forward compensator 205 shown in FIG. 3 can be rewritten in the form of parallel forward addition for the process model 207 as shown in FIG. That is, the block diagram shown in FIG. 8 is configured to feed back a value obtained by adding the output of the process model 207 and the output of the parallel forward compensator 205 by the adder 208.
The block diagram shown in FIG. 3 is equivalent to the block diagram shown in FIG. Then, the transfer function P _a (s) of the extended process model is defined as in the following equation (25).
P _a (s) = P (s) + PFC (s) (25)
Thus, the adaptive gain K _e (t) can be regarded as a controller, and can be interpreted as the process model being expanded by the parallel forward compensator 205.

When the expressions (21) and (22) are substituted into the expression (25), the transfer function P _a (s) of the extended process model is expressed by the following expression (26).

As apparent from FIGS. 3 and 8, in the present embodiment, the hot water level control device 100 is a one-input one-output system. Therefore, the extended process model satisfies the ASPR condition by satisfying the following conditions (A) to (C).
(A) The transfer function P _a (s) of the extended process model is a minimum phase system (B) The relative order of the transfer function P _a (s) of the extended process model is 0 or 1
(C) The gain of the transfer function P _a (s) of the extended process model is positive

The condition (B) is automatically satisfied by making the transfer function PFC (s) of the parallel forward compensator (PFC) 205 as shown in equation (21). In addition, the condition (C) is satisfied if the PFC gain β exceeds 0 (β> 0). Regarding the condition (A), it is a necessary condition that both the PFC poles α ₁ and α ₂ exceed 0 (α ₁ > 0, α ₂ > 0). In order for the PFC poles α ₁ and α ₂ and the PFC gain β to satisfy the condition (A), it is necessary that the transfer function P _a (s) of the extended process model does not have an unstable zero.

When designing the transfer function PFC (s) of the parallel forward compensator (PFC) 205, there are restrictions due to the above ASPR conditions. Therefore, conventionally, combinations of the PFC poles α ₁ and α ₂ and the PFC gain β that satisfy the condition (A) are designed by trial and error. In contrast, in the present embodiment, a combination of the PFC poles α ₁ and α ₂ and the PFC gain β that satisfies the conditions (A) to (C) is derived according to the following procedure.

(First PFC parameter determination unit 403: STEP1)
The first PFC parameter determination unit 403 derives the PFC gain β shown in Equation (21).
Hereinafter, an example of a method for deriving the PFC gain β will be described.
Expression (26) is expressed as the following expression (27).

The numerator and denominator of Equation (27) are irreducible s polynomials. The s polynomial P _a num (s) of the numerator of the equation (27) is shown in the following equation (28).

(28) Expanding the equation can be obtained (27) of the s polynomials molecular P _a num (s) can be expressed as the following equation (29) the coefficients of s polynomial N _i.

From the condition (A), it is required for the expression (29) that “all real parts of the root of P _a num (s) = 0 are negative”. If the Hurwitz stability determination method is applied to the equation (29), “all the coefficients N _i of the s polynomial are positive” becomes a necessary condition (however, it is not a necessary and sufficient condition). Therefore, the following constraint equation (30) for the PFC gain β can be obtained from N ₃ > 0.

As a control design, it is preferable to perform stable operation even when the responsiveness of the level meter 19 as a sensor and the hydraulic cylinder 300 changes. Therefore, in this embodiment, the time constant T _S of the level meter 19 and the time constant T _CYL of the hydraulic cylinder 300 are both set to 0 (T _S = 0, T _CYL = 0). Therefore, the equation (30) is transformed into the following equation (31). Equation (31) corresponds to maximizing the lower limit value of the PFC gain β, resulting in a conservative design. Thus, the lower limit value of the PFC gain β is determined so as to theoretically satisfy the ASPR condition.

In the present embodiment, considering that the flow coefficient KK of the stopper 13 is increased due to the melting damage of the immersion nozzle 12, a margin is given to the PFC gain β.
From the above, the first PFC parameter determination unit 403 derives the PFC gain β by the following equation (32).

In the equation (32), KK _MAX is the maximum value [m ² / sec] of the flow coefficient of the stopper 13 and satisfies the following equation (33).
KK _MAX = D1 × KK> KK (33)

As is apparent from the equation (33), D1 is a real number exceeding 1 (D> 1). The coefficient D1, that is, the maximum value KK _MAX of the flow coefficient of the stopper 13 is set in advance based on, for example, the operation results.

(Adaptive gain upper limit tentative determination unit 404: STEP2)
The adaptive gain upper limit tentative determination unit 404 is a proportional gain when a P controller is used instead of the SAC controller, and is an oscillation limit (gain margin = 0) with respect to the transfer function P (s) of the process model 207. A proportional gain with phase margin = 0) is derived as a temporary upper limit value K _{emax — temp} of the adaptive gain K _e (t).

Actually, in the SAC controller, since the extended process model is converted to ASPR by the parallel advance compensator 205, the gain margin is larger than that in the normal PI control.
However, by tentatively determining the upper limit value of the adaptive gain K _e (t), it becomes possible to make a path to the design of the SAC controller that has to be designed through trial and error.

(Second PFC parameter determination unit 405: STEP3)
The present inventors examined whether or not it is necessary to provide a restriction on the search range of the PFC poles α ₁ and α ₂ . Before describing an example of the function of the second PFC parameter determination unit 405, the result will be described.
As described above, if the Hurwitz stability determination method is applied to the equation (29), “all the coefficients N _i of the s polynomial are positive” becomes a necessary condition (however, it is not a necessary and sufficient condition). ). Therefore, the following constraint equations for the PFC poles α ₁ and α ₂ can be obtained from N ₁ > 0 and N ₂ > 0.
First, the following constraint equation (34) can be obtained from N ₁ > 0.

  When the equation (34) is modified, the following equation (35) is obtained.

Next, the following constraint equation (36) can be obtained from N ₂ > 0.

  When the equation (36) is modified, the following equation (37) is obtained, and the equation (38) can be obtained.

From the constraints of the equations (34) to (38), the upper limit values of the PFC poles α ₁ and α ₂ are given. However, the upper limit value is very large compared to the optimum values of the PFC poles α ₁ and α ₂ obtained by optimizing the sensitivity function described later. In the first place, the ASPR condition is for ensuring the stability of control, and is not an index of control performance. From the above, it is considered that there is no need to provide restrictions on the search range of the PFC poles α ₁ and α ₂ .

Therefore, in the present embodiment, the second PFC parameter determination unit 405 derives the PFC poles α ₁ and α ₂ as follows.
The second PFC parameter determination unit 405 is a temporary provision of the PFC gain β derived by the first PFC parameter determination unit 403 and the adaptive gain K _e (t) derived by the adaptive gain upper limit temporary determination unit 404. A sensitivity function S _SAC (s) when the SAC controller is used is derived using the upper limit value K _{emax — temp} . Then, the second PFC parameter determination unit 405 uses the sensitivity function S _PI (s) derived from the PI controller design unit 402 when the PI controller is used and the sensitivity function when the SAC controller is used. The PFC poles α ₁ and α ₂ when the difference in a predetermined frequency range from S _SAC (s) is minimized are searched.

Here, the amplitude of the sensitivity function S _PI (s) when the PI controller is used is 0 so that the predetermined frequency range includes at least part of the frequency assumed as the fluctuation level of the molten metal surface level. [DB] It is set from the frequency range which becomes below. As such a frequency range, a constraint that the slope in the Bode diagram (frequency characteristic of amplitude) is within a predetermined range can be added.

PFC pole alpha _1, will be described an example of a specific method of searching for alpha _2, first, it is assumed that the PFC pole alpha _1, alpha ₂ satisfies the following equation (39) relationship.
α ₂ = D2 × α ₁ (39)
D2 is a real number (D2> 0) exceeding 0 (zero). The coefficient D2 is set in advance based on, for example, operation results.

FIG. 9 is a diagram showing an example of a block diagram for deriving the sensitivity function S _SAC (s) when the SAC controller is used.
By fixing the adaptive gain K _e (t) at the temporary upper limit value K _{emax — temp} , the SAC controller is handled as one controller including the local feedback mechanism of the parallel forward compensator 205. Is possible. Thus, the transfer function C _SAC (s) of the SAC controller including the parallel forward compensator 205 is expressed by the following equation (40).

However, as described above, α ₁ > 0, α ₂ > 0, and β> 0.
Further, the sensitivity function S _SAC (s) in the case of using the SAC controller (including the parallel forward compensator 205) is expressed by the following equation (41).

Second PFC parameter determination unit 405, the initial values of PFC pole alpha ₁ and 0 (zero), the value of the PFC pole alpha ₁ gradually increases from 0 (zero), in each of the PFC pole alpha ₁ , The sensitivity function S _SAC (s) when the SAC controller is used is derived from the equations (39) to (41).

Next, the second PFC parameter determination unit 405 uses the sensitivity function S _SAC (when the SAC controller is used in the frequency range of 0.005 [Hz] to 0.04 [Hz] as the predetermined frequency range. The PFC poles α ₁ and α ₂ when the difference between the sensitivity function S _PI (s) and the sensitivity function S _PI (s) using the PI controller is minimized are derived. Thus, in the present embodiment, the sensitivity function S _PI (s) when the PI controller is used is optimally designed, and the sensitivity function S _SAC (s) and PI when the SAC controller is used. The sensitivity function S _PI (s) when the controller is used is compared.

FIG. 10 is a diagram conceptually illustrating an example of processing when deriving the PFC poles α ₁ and α ₂ .
In FIG. 10, the amplitude is the amplitude of the sensitivity function. Further, the graph 1001, the amplitude of the sensitivity function S _PI (s) | shows a frequency characteristic graph 1002, the amplitude of the sensitivity function _{S SAC (s) | | S} PI (s) S SAC (s) | of the frequency Show properties.
In the present embodiment, the second PFC parameter determination unit 405 selects 0.005 [Hz] to 0.04 [Hz] from a plurality of sensitivity functions S _SAC (s) with different PFC pole α ₁ . in frequency, the amplitude of the sensitivity function _{S PI (s) | S PI} (s) | for the amplitude of the sensitivity function _{S SAC (s) | S SAC} (s) | of the sensitivity function integrated value of error is minimized S _SAC (S) is obtained. The integral value corresponds to the area of the hatched area in FIG. Then, the second PFC parameter determination unit 405 specifies the PFC pole α ₁ used when the obtained sensitivity function S _SAC (s) is derived.

Specifically, for example, the amplitudes of the sensitivity functions obtained as s = jω (j: imaginary unit, ω: angular frequency [rad / sec]) are expressed as | S _PI (jω) | and | S _SAC (jω) | In other words, the second PFC parameter determination unit 405 obtains the PFC pole α ₁ that minimizes the evaluation function J shown in the following equation (42).

However, ω2 and ω1 are angular frequencies [rad / sec] corresponding to the upper limit and the lower limit of the above-described frequency range (0.005 [Hz] to 0.04 [Hz]), respectively (43) It is represented by the formula (44).
ω2 = 2π × 0.040 (43)
ω1 = 2π × 0.005 (44)
Further, as described above, the PFC pole α ₁ is a value exceeding 0 (zero) (α ₁ > 0).
As described above, the second PFC parameter determination unit 405 determines the evaluation function J when the initial value of the PFC pole α ₁ is 0 (zero) and the evaluation function when the PFC pole α ₁ is gradually increased. J is derived, and the PFC pole α ₁ that minimizes the evaluation function J is searched.

FIG. 11 is a diagram illustrating an example of a Bode diagram (frequency response diagram) of the sensitivity functions S _PI (s) and S _SAC (s) when the value of the evaluation function J is minimum.
In FIG. 11, a graph 1101 shows the frequency characteristic of the amplitude | S _PI (s) | of the sensitivity function S _PI (s), and a graph 1102 shows the amplitude | S _SAC (s) | of the sensitivity function S _SAC (s). The frequency characteristics of are shown.

FIG. 12 shows an example of a Bode diagram (frequency response diagram) of a plurality of sensitivity functions S _SAC (s) having different PFC poles α ₁ and α ₂ , and a Bode diagram (frequency response) of the sensitivity function S _PI (s). It is a figure shown with an example of a diagram.
In FIG. 12, a graph 1201 shows the frequency characteristic of the amplitude | S _PI (s) | of the sensitivity function S _PI (s), and is the same as the graph 1101 shown in FIG.
Graphs 1202 to 1204 indicate the frequency characteristics of the amplitude | S _SAC (s) | of the sensitivity function S _SAC (s). A graph 1203 is the same as the graph 1102 illustrated in FIG. The graphs 1202 and 1204 are obtained by making the graph 1203 different from only the values of the PFC poles α ₁ and α ₂ . Specifically, graph 1202, PFC pole alpha _1, alpha ₂ is the amplitude of the PFC pole alpha ₁ when obtaining the graph 1201, sensitivity when alpha smaller than ₂ function _{S SAC (s) | S SAC} (s ) |. A graph 1204, PFC pole alpha _1, alpha ₂ is the amplitude of the PFC pole alpha ₁ when obtaining the graph 1201, the sensitivity function when larger than the size of the _{α 2 S SAC (s) |} S SAC (s ) |.

As shown in the graph 1202, if the PFC poles α ₁ and α ₂ are too small, the amplitude in the low frequency region becomes small, and the fluctuation of the molten metal surface level cannot be sufficiently suppressed. On the other hand, as shown in the graph 1204, if the PFC poles α ₁ and α ₂ are excessively increased, the amplitude in the low frequency region increases and fluctuations in the molten metal surface level can be sufficiently suppressed. The amplitude exceeds 0 [dB] at the frequency. Therefore, in many areas of 0.03 [Hz] ~0.3 [Hz] found many as the fluctuation frequency of the molten metal surface level, the amplitude of the sensitivity function _{S SAC (s) | S SAC} (s) | sufficiently It cannot be reduced. Therefore, the disturbance d is amplified and tends to appear at the hot water level. On the other hand, as shown in the graph 1203, by appropriately setting the PFC poles α ₁ and α ₂ , both the fluctuation of the molten metal level in the low frequency region and the fact that the disturbance is amplified and appear at the molten metal level. Can be suppressed.

(Adaptive gain upper limit determination unit 406: STEP4)
The adaptive gain upper limit determination unit 406 derives an upper limit value K _emax of the adaptive gain K _e (t).
A specific example of a method for deriving the upper limit value K _emax of the adaptive gain K _e (t) will be described below.

First, the adaptive gain upper limit determination unit 406 uses the PFC gain β derived by the first PFC parameter determination unit 403 and the PFC poles α ₁ and α ₂ derived by the second PFC parameter determination unit 405. Then, the sensitivity function S _SAC (s) in the case of using the SAC controller (including the parallel forward compensator 205) is derived by calculating the above-described equation (41). At this time, adaptive gain limit determining unit 406, adapted derived by the gain limit provisional determining unit 404, adaptive gain K _e the upper limit value K _emax _ _temp provisional (t), (41) K emax _ temp in formula The initial value of the adaptive gain given to. The adaptive gain limit determining section 406, gradually increasing the adaptive gain applied to the K _emax _ _temp in equation (41), in each of the adaptive gain, the sensitivity function in the case of using the SAC controller S _SAC ( s) is derived from equations (39) to (41).

The adaptive gain upper limit determination unit 406 is a frequency characteristic of the amplitude of the sensitivity function S _SAC (s) that is equal to or lower than the amplitude of the sensitivity function S _PI (s) in a predetermined frequency range, _emax _ give _temp) derives the amplitude of the frequency characteristic of the adaptive gain is minimum sensitivity function S _SAC (s), the adaptive gain to become such a minimum, the upper limit value K _emax adaptive gain K _e (t) . That is, the adaptive gain upper limit determination unit 406 determines the amplitude of the sensitivity function S _SAC (s) whose values at the upper and lower limits of the predetermined frequency range match the frequency characteristics of the amplitude of the sensitivity function S _PI (s). identifying the frequency characteristic, the adaptive gain used when obtaining the amplitude of the frequency characteristic of the specific sensitivity function _{S SAC (s) ((41} ) adaptive gain given to K _emax _ _temp of formula), adaptive gain The upper limit value K _emax of K _e (t) is set.

Here, the amplitude of the sensitivity function S _PI (s) when the PI controller is used is 0 so that the predetermined frequency range includes at least part of the frequency assumed as the fluctuation level of the molten metal surface level. [DB] It is set from the frequency range which becomes below. As such a frequency range, a constraint that the slope in the Bode diagram (frequency characteristic of amplitude) is within a predetermined range can be added. In the present embodiment, 0.001 [Hz] to 0.04 [Hz] is employed as the predetermined frequency range. As the predetermined frequency range, the same frequency range as that used when the second PFC parameter determining unit 405 derived the PFC poles α ₁ and α ₂ (0.005 [Hz] in the above example) 0.04 [Hz]) may be adopted.
By doing so, it is possible to prevent the adaptive gain K _e (t) from being raised excessively more than necessary when the SAC controller exceeds the performance of the PI controller.

FIG. 13 is a diagram conceptually illustrating an example of processing for deriving the upper limit value K _emax of the adaptive gain K _e (t).
In FIG. 13, the amplitude is the amplitude of the sensitivity function. A graph 1301 shows the frequency characteristic of the amplitude | S _PI (s) | of the sensitivity function S _PI (s), and a graph 1302 shows the frequency of the amplitude | S _SAC (s) | of the sensitivity function S _SAC (s). Show properties.
In the present embodiment, the adaptive gain upper limit determination unit 406 determines the sensitivity function S _PI (s) at each of the lower limit (= 0.001 [Hz]) and the upper limit (= 0.04 [Hz]) of the predetermined frequency range. the give (and as match ((41 s) | and sensitivity function S amplitude of _{SAC (s) | | S SAC} (s)) equation K _emax _ _temp) adaptive gain, | amplitude) S _PI The search is performed as the upper limit value K _emax of the adaptive gain K _e (t).

FIG. 14 shows a first example of a Bode diagram (frequency response diagram) of a plurality of sensitivity functions S _SAC (s) with different adaptive gains (given to K _{emax — temp} in equation (41)). It is a figure shown with an example of the Bode diagram (frequency response diagram) of _PI (s).
In FIG. 14, a graph 1401 shows the frequency characteristic of the amplitude | S _PI (s) | of the sensitivity function S _PI (s), and is the same as the graph 1101 shown in FIG. 11 and the graph 1201 shown in FIG.
Graphs 1402 and 1403 show frequency characteristics of the amplitude | S _SAC (s) | of the sensitivity function S _SAC (s).

The upper limit value K _emax of the adaptive gain K _e (t) used when the graph 1402 is obtained is larger than the upper limit value K _{emax of} the adaptive gain K _e (t) used when the graph 1403 is obtained. Other conditions when the graphs 1402 and 1403 are obtained are the same.

In the frequency range of about 0.001 [Hz] to 0.04 [Hz], the value of the graph 1403 is not less than the value of the graph 1401. Therefore, the applied gain (adaptive gain given to K _{emax — temp} in the equation (41)) used when obtaining the graph 1403 is not adopted as the upper limit value K _emax of the applied gain K _e (t). On the other hand, in the frequency range of 0.005 [Hz] to 0.04 [Hz], the value of the graph 1402 is equal to or less than the value of the graph 1401, and 0.005 [Hz] and 0.04 [Hz]. In both cases, the value of the graph 1401 and the value of the graph 1402 match. Therefore, the adaptive gain (the adaptive gain given to K _{emax — temp} in the equation (41)) used when obtaining the graph 1401 is adopted as the upper limit value K _emax of the applied gain K _e (t).

FIG. 15 shows a second example of a Bode diagram (frequency response diagram) of a plurality of sensitivity functions S _SAC (s) having different adaptive gains (given to K _{emax — temp} in equation (41)). It is a figure shown with an example of the Bode diagram (frequency response diagram) of _PI (s).
In FIG. 15, a graph 1501 shows the frequency characteristic of the amplitude | S _PI (s) | of the sensitivity function S _PI (s), and is the same as the graph 1401 shown in FIG.
Graphs 1502 and 1503 show frequency characteristics of the amplitude | S _SAC (s) | of the sensitivity function S _SAC (s). The graph 1502 is the same as the graph 1402 shown in FIG. Graph 1503 includes a case to obtain a graph 1502, which was obtained by varying only the value of the upper limit value K _emax of ((41) gives the equation of K _emax _ _temp) adaptive gain K _e (t) is there. Specifically, the adaptive gain used when obtaining the graph 1503 is larger than the adaptive gain used when obtaining the graph 1502.

FIG. 16 is a diagram illustrating an example of a Bode diagram (frequency response diagram) of transfer functions T _SAC (s) and T _PI (s) from the disturbance d to the opening degree commands u ₀ and u ₀ ′. From disturbance d opening command u _0, u ₀ 'transfer function T _SAC to _{(s), T PI (s} ) , the disturbance d is opening command u _0, u _0' whether appear is amplified how to Means.
The transfer functions T _SAC (s) and T _PI (s) are expressed by the following equations (45) and (46), respectively.

In FIG. 16, a graph 1601 shows the frequency characteristic of the amplitude of the transfer function T _PI (s) in the block diagram shown in FIG.
Graphs 1602 and 1603 show frequency characteristics of the amplitude of the transfer function T _SAC (s) in the block diagram shown in FIG. The graph 1602 differs from the graph 1503 when only the adaptive gain value (given to K _{emax — temp} in the equation (41)) is _obtained . Specifically, the adaptive gain used when obtaining the graph 1602 is smaller than the adaptive gain used when obtaining the graph 1603.

Comparing the graphs 1502 and 1503 shown in FIG. 15, it appears that as the upper limit value K _emax of the adaptive gain K _e (t) is increased, the fluctuation of the melt level in the low frequency region is improved. However, as shown in the graphs 1602 and 1603 shown in FIG. 16, if the upper limit value K _emax of the adaptive gain K _e (t) is excessively increased, the variation in the opening degree of the stopper 13 increases in the high frequency range, There is a possibility that the stopper 13 reacts excessively with the swell. For example, when saturation of the open / close pulse signal (a pulse signal indicating a change in the opening degree of the stopper 13) occurs, the control cannot be stabilized and a divergent behavior is expected.

From the above, it is not preferable that the upper limit value K _emax of the adaptive gain K _e (t) is too large or too small. By appropriately setting the upper limit value K _emax of the adaptive gain K _e (t), the low value can be reduced. It is possible to suppress both the fluctuation of the molten metal surface level in the frequency region and the appearance of the disturbance in the opening degree command of the stopper 13 by amplifying the disturbance.

FIG. 17 is a diagram showing an example of the relationship between the hot water level and time. FIG. 17A shows the result of simulating the control of the _{molten metal} surface level according to the block diagram shown in FIG. 3 without setting the upper limit value K _emax of the adaptive gain K _e (t). FIG. 17B shows the result of simulating the control of the _{molten metal} surface level according to the block diagram shown in FIG. 3 by setting the upper limit value K _emax of the adaptive gain K _e (t) as described above. The difference between the condition for obtaining the result shown in FIG. 17A and the condition for obtaining the result shown in FIG. 17B is only whether or not the upper limit value K _emax of the adaptive gain K _e (t) is set. is there.

In FIG. 17 (a) and FIG. 17 (b), the level target value indicates the target value of the molten metal surface level, and the level actual value indicates the result of simulation.
In the example shown in FIG. 17A, since the upper limit value K _emax of the adaptive gain K _e (t) is not set, the molten metal surface level is greatly hunted and the casting cannot be continued. For example, when the movement speed of the stopper 13 is limited, the high control capability of simple adaptive control (SAC) may not be exhibited.
On the other hand, in the example shown in FIG. 17 (b), sets the upper limit value K _emax adaptive gain K _e (t), since the adaptive gain K _e (t) is prevented from becoming excessive, the hunting of the molten metal surface level Is suppressed, and simple adaptive control (SAC) can be stably executed.

The adaptive gain upper limit determination unit 406 obtains the upper limit value K _{emax of} the adaptive gain K _e (t) obtained as described above, the PFC gain β derived by the first PFC parameter determination unit 403, and the second The PFC poles α ₁ and α ₂ derived by the PFC parameter determination unit 405 are output. Examples of the output form include at least one of transmission to the hot water level control device 100, storage in a portable storage medium, and display on a computer display. That is, the adaptive gain upper limit determining unit 406 directly sets the parameters (α ₁ , α ₂ , β, K _emax ) of the molten metal level control device 100 operating as a SAC controller in the molten metal level control device 100. Alternatively, it may be set indirectly (for example, through an operation by an operator).

(Summary)
As described above, in the present embodiment, the PFC gain β is derived so as to satisfy the constraint requirement indicating that the ASPR condition is theoretically satisfied. Further, a proportional gain that becomes an oscillation limit (gain margin = 0, phase margin = 0) with respect to the transfer function P (s) of the process model 207 is set as a temporary upper limit value K _{emax — temp} of the adaptive gain K _e (t). Derived as Then, the temporary upper limit value K _{emax — temp of} the adaptive gain K _e (t) and the PFC gain β are fixed with the derived values, the PFC poles α ₁ and α ₂ are changed, and the sensitivity function S _PI is changed. The amplitudes of the sensitivity functions S _PI (s) and S _SAC (s) | S _{PI in} a predetermined frequency range lower than the region where the amplitude | S _PI (s) | exceeds 0 [dB]. PFC poles α ₁ and α ₂ when the difference between (s) | and | S _SAC (s) | is minimized are derived. Next, the adaptive gain is changed after fixing the PFC poles α ₁ and α ₂ and the PFC gain β with the derived values, and the amplitude | S _PI (s) | of the sensitivity function S _PI (s) is 0 [dB. ], The amplitudes of the sensitivity functions S _PI (s), S _SAC (s) | S _PI (s) |, | S _SAC (s) | Is derived as the upper limit value K _emax of the adaptive gain K _e (t).

Therefore, it becomes possible to systematically design the SAC controller that was mostly designed by trial and error. As a result, the PFC poles α ₁ and α ₂ , the PFC gain β, and the upper limit value K _emax of the adaptive gain K _e (t), which are necessary for realizing control performance that exceeds the PI controller, are used without trial and error. Can be sought. In this way, it is possible to systematically design a SAC controller for realizing high-precision control of the molten metal surface level in a continuous casting machine using the stopper 13 by simple adaptive control (SAC).

(Modification)
<Modification 1>
In the present embodiment, the case where the transfer function PFC (s) of the parallel forward compensator 205 is expressed by Expression (21) has been described as an example. However, the transfer function PFC (s) of the parallel forward compensator 205 is not limited to the equation (21). The transfer function PFC (s) of the parallel forward compensator 205 can be, for example, a transfer function in which the denominator order is one greater than the numerator order and the numerator order is greater than or equal to the first order. Furthermore, the transfer function PFC (s) of the parallel forward compensator 205 can also be expressed without a direct term.

<Modification 2>
In the present embodiment, the case where the transfer function P (s) of the process model 207 is expressed by Expression (22) has been described as an example. However, the transfer function P (s) of the process model 207 is not limited to the expression (22). For example, the transfer function P (s) of the process model 207 may be expressed by the following equation (47) or (48).

<Modification 3>
In the present embodiment, the case of obtaining the PFC pole α ₁ that minimizes the evaluation function J shown in the equation (42) has been described as an example. However, this is not always necessary. For example, all parameters of the SAC controller may be derived so that the evaluation function J shown in the equation (42) is minimized. A specific example in this case will be described. A constraint condition indicating that the ASPR condition is satisfied (for example, a constraint condition that all of N _{0 to} N ₅ shown in the proviso of equation (29) exceed 0 (zero)). The PFC poles α ₁ and α ₂ and the PFC gain β that minimize the evaluation function J shown in the equation (42) may be derived within a range that satisfies the above. Such derivation can be realized, for example, by using an optimization calculation method in a known mathematical programming method. Further, in this case, the controller parameter deriving device 400 may not have the function of the first PFC parameter determining unit 403. Even when the transfer function PFC (s) of the parallel forward compensator 205 is not expressed by the equation (21), all parameters of the SAC controller can be derived in this way. Further, as described in the present embodiment, the time constants T _CYL and T _S of the equipment (hydraulic cylinder 300, level meter 19) for controlling the hot water level are set to 0 (zero) to define the constraint conditions. be able to.

<Other variations>
The embodiment of the present invention described above can be realized by a computer executing a program. Further, a computer-readable recording medium in which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

  11: Tundish, 12: Immersion nozzle, 13: Stopper, 14: Mold, 15: Pinch roll, 16: Cooling spray, 17: Molten metal, 18: Solidified shell, 19: Level meter, 100: Level controller, 200 : ST controller, 300: hydraulic cylinder, 400: controller parameter derivation device, 401: process model acquisition unit, 402: PI controller design unit, 403: first PFC parameter determination unit, 404: adaptive gain upper limit provisional determination 405: second PFC parameter determination unit 406: adaptive gain upper limit determination unit

Claims (8)

A reference model for outputting a target level value of a molten metal level in a mold in a continuous casting machine and outputting a molten metal level level that the detected value of the molten metal level should follow,
A variable adaptive gain for the deviation between the output of the reference model and the detected value of the molten metal level;
Compensates for the output of the process model that outputs the detected value of the molten metal level with the command about the opening of the stopper that adjusts the flow rate of the molten metal stored in the tundish of the continuous casting machine into the mold. A parallel forward compensator (PFC),
A controller parameter derivation method for deriving a parameter of a controller that controls the molten metal level by simple adaptive control,
A PI controller design step of deriving the frequency characteristic of the amplitude of the first sensitivity function, which is a sensitivity function when the molten metal surface level control is performed by PI control, by the PI controller design means;
An adaptive gain upper limit tentative determination step of determining a temporary upper limit value of the adaptive gain by an adaptive gain upper limit temporary determination means;
The frequency characteristic of the amplitude of the first sensitivity function derived by the PI controller design process and the frequency of the amplitude of the second sensitivity function, which is a sensitivity function when the level control is performed by simple adaptive control. A PFC parameter determining step of determining a parameter of a transfer function of the parallel forward compensator by a PFC parameter determining means using the characteristics and the temporary upper limit value of the adaptive gain determined in the adaptive gain upper limit temporary determining step; ,
The frequency characteristic of the amplitude of the first sensitivity function derived by the PI controller design step, the frequency characteristic of the amplitude of the second sensitivity function, and the parallel forward compensation determined by the PFC parameter determination step An adaptive gain upper limit determining step for determining an upper limit value of the adaptive gain by an adaptive gain upper limit determining means using a parameter of a transfer function of the device,
In the PFC parameter determination step, the adaptive gain is assumed to be a temporary upper limit value of the adaptive gain determined in the adaptive gain upper limit temporary determination step, and at least one transfer function of the parallel forward compensator is determined. Based on the result of comparing a plurality of frequency characteristics of the amplitude of the second sensitivity function derived by different parameters and the frequency characteristics of the amplitude of the first sensitivity function, the first sensitivity function The amplitude of the second sensitivity function is such that the difference between the amplitude of the first sensitivity function and the amplitude of the first sensitivity function is minimum under a predetermined condition in a predetermined frequency range lower than the frequency where the amplitude of the first sensitivity function exceeds 0 [dB]. Search the frequency characteristics, specify the parameters of the transfer function of the parallel forward compensator used to derive the frequency characteristics of the amplitude of the searched second sensitivity function,
The adaptive gain upper limit determining step is derived by making the parameter of the transfer function of the parallel forward compensator the parameter derived in the PFC parameter determining step and varying the value of the adaptive gain. Based on the result of comparing the plurality of frequency characteristics of the amplitude of the second sensitivity function with the frequency characteristics of the amplitude of the first sensitivity function, the amplitude of the first sensitivity function is 0 [dB]. Search for the frequency characteristic of the amplitude of the second sensitivity function in which the values at the upper and lower limits of the predetermined frequency range on the lower frequency side than the higher frequency match the frequency characteristic of the amplitude of the first sensitivity function. And the adaptive gain used to derive the frequency characteristic of the amplitude of the searched second sensitivity function is specified as an upper limit value of the adaptive gain. Meter derivation method. The PFC parameter determination step includes:
A constraint condition indicating that a sum of the transfer function of the process model and the transfer function of the parallel forward compensator satisfies an ASPR (Almost Strictly Positive Real) condition, and the time constant of the facility in the transfer function of the process model The coefficient multiplied by the Laplace operator of the highest order numerator of the transfer function of the parallel forward compensator is set to a parameter of the transfer function of the parallel forward compensator so as to satisfy the constraint when 0 is set to 0 (zero) A first PFC parameter determination step identified as
The adaptive gain is the temporary upper limit value of the adaptive gain determined in the adaptive gain upper limit temporary determination step, and the coefficient is the coefficient determined in the first PFC parameter determination step. And comparing the plurality of frequency characteristics of the amplitude of the second sensitivity function derived by making the transfer function poles of the parallel forward compensator different from the frequency characteristics of the amplitude of the first sensitivity function. Based on the result, the difference between the amplitude of the first sensitivity function and the amplitude of the first sensitivity function is minimum under a predetermined condition in a predetermined frequency range lower than the frequency where the amplitude of the first sensitivity function exceeds 0 [dB]. The frequency characteristic of the amplitude of the second sensitivity function is searched, and the pole of the transfer function of the parallel forward compensator used for deriving the frequency characteristic of the amplitude of the searched second sensitivity function is Forward compensator Controller parameter derivation method according to claim 1, the second PFC parameter determining step of identifying as a parameter of the transfer function, characterized in that it further comprises a. The transfer function of the parallel forward compensator is the following equation (A):
The second PFC parameter determination step derives the poles α ₁ and α ₂ in the equation (A),
3. The controller parameter derivation according to claim 1, wherein the first PFC parameter determination step derives a coefficient β in the equation (A) so as to satisfy the following equation (B): 4. Method.
In the formula (A), s is a Laplace operator, in the formula (B), KK is a flow coefficient [m ² / sec] of the stopper, and A is a horizontal direction of the cavity portion of the mold. Is the cross-sectional area [m ² ].

4. The controller parameter deriving method according to claim 3, wherein the first PFC parameter determining step derives a coefficient β by the following equation (C).

  The adaptive gain upper limit tentative determination step is a proportional gain when the molten metal surface level control is performed by P control, and a proportional gain that becomes an oscillation limit with respect to the transfer function of the process model is determined as a temporary gain of the adaptive gain. The controller parameter derivation method according to claim 1, wherein the controller parameter derivation method is derived as an upper limit value of the controller parameter.   In the adaptive gain upper limit determining step, the adaptive gain upper limit value derived from the adaptive gain upper limit temporary determining step is used as an initial value, and the value of the adaptive gain is varied to change the second sensitivity function. 6. The controller parameter derivation method according to claim 1, wherein a plurality of frequency characteristics of amplitude are derived. A reference model for outputting a target level value of a molten metal level in a mold in a continuous casting machine and outputting a molten metal level level that the detected value of the molten metal level should follow,
A variable adaptive gain for the deviation between the output of the reference model and the detected value of the molten metal level;
Compensates for the output of the process model that outputs the detected value of the molten metal level with the command about the opening of the stopper that adjusts the flow rate of the molten metal stored in the tundish of the continuous casting machine into the mold. A parallel forward compensator (PFC),
A controller parameter deriving device for deriving a parameter of a controller for controlling the molten metal surface level by simple adaptive control,
PI controller design means for deriving the frequency characteristic of the amplitude of the first sensitivity function, which is a sensitivity function when the molten metal surface level is controlled by PI control;
Adaptive gain upper limit temporary determination means for determining a temporary upper limit value of the adaptive gain;
The frequency characteristic of the amplitude of the first sensitivity function derived by the PI controller design means and the frequency of the amplitude of the second sensitivity function, which is a sensitivity function when performing control of the molten metal surface level by simple adaptive control PFC parameter determining means for determining a parameter of a transfer function of the parallel forward compensator using characteristics and a temporary upper limit value of the adaptive gain determined by the adaptive gain upper limit temporary determining means;
The frequency characteristic of the amplitude of the first sensitivity function derived by the PI controller design means, the frequency characteristic of the amplitude of the second sensitivity function, and the parallel forward compensation determined by the PFC parameter determination means Adaptive gain upper limit determining means for determining an upper limit value of the adaptive gain using a parameter of a transfer function of the device,
The PFC parameter determining means assumes that the adaptive gain is a temporary upper limit value of the adaptive gain determined by the adaptive gain upper limit temporary determining means, and at least one of the transfer functions of the parallel forward compensator Based on the result of comparing a plurality of frequency characteristics of the amplitude of the second sensitivity function derived by different parameters and the frequency characteristics of the amplitude of the first sensitivity function, the first sensitivity function The amplitude of the second sensitivity function is such that the difference between the amplitude of the first sensitivity function and the amplitude of the first sensitivity function is minimum under a predetermined condition in a predetermined frequency range lower than the frequency where the amplitude of the first sensitivity function exceeds 0 [dB]. Search the frequency characteristics, specify the parameters of the transfer function of the parallel forward compensator used to derive the frequency characteristics of the amplitude of the searched second sensitivity function,
The adaptive gain upper limit determining means is derived by assuming that the parameter of the transfer function of the parallel forward compensator is the parameter derived by the PFC parameter determining means, and varying the value of the adaptive gain. Based on the result of comparing the plurality of frequency characteristics of the amplitude of the second sensitivity function with the frequency characteristics of the amplitude of the first sensitivity function, the amplitude of the first sensitivity function is 0 [dB]. Search for the frequency characteristic of the amplitude of the second sensitivity function in which the values at the upper and lower limits of the predetermined frequency range on the lower frequency side than the higher frequency match the frequency characteristic of the amplitude of the first sensitivity function. And the adaptive gain used to derive the frequency characteristic of the amplitude of the searched second sensitivity function is specified as an upper limit value of the adaptive gain. Meter derivation device.   A program for causing a computer to execute each step of the controller parameter derivation method according to any one of claims 1 to 6.

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