JP4955237B2 - Control system and method for time-varying control target with dead time - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To control a target to be controlled of a time-variant system having idle time with good precision. <P>SOLUTION: Set values expressing the idle time of the target 200 to be controlled, time constant, and process gain are previously set. The set value of the process gain has a predetermined time-variant property. Output value y and its first and second order time differential values are used as the state variable x of the target 200 to be controlled. A nonlinear state estimator 206 estimates the value x(t+Ld) of the state variable x at a future time point after the idle time from present time based on the present output value y and the set values of the idle time, the time constant and the process gain. A gain scheduled sliding mode controller 212 performs a gain scheduled sliding mode control operation based on the estimated value of x(t+Ld) of the state variable x at the future time point, the output deviation z(t+Ld) at the future time point, and the set values of the time constant and the process gain at the future time point so as to determine the operation quantity u<SB>T</SB>to the target 200 to be controlled. <P>COPYRIGHT: (C)2007,JPO&amp;INPIT

Description

  The present invention relates to a control system and method for a time-varying control target having a dead time, and for example, a single crystal rod (single crystal) of a specific substance such as a semiconductor material is manufactured by a Czochralski method (pull-up method). It is suitable for controlling the process.

  As a typical example of time-varying system control with dead time, we will take up the process for manufacturing a single crystal rod (single crystal) of a specific substance such as a semiconductor material by the Czochralski method (pull-up method). explain.

  Needless to say, in the production of a single crystal rod by the Czochralski method or other methods, it is very important to reduce crystal defects of the single crystal rod. It is also very important to control the diameter of the straight body of the single crystal rod to a desired value. In order to better satisfy these requirements, for example, the following control method has been proposed.

  Patent Document 1 discloses a method for making the diameter of a straight body portion of a single crystal rod constant in the Czochralski method and suppressing the occurrence of polycrystals. According to this method, while the straight body portion is formed while the single crystal rod is pulled up, the weight of the single crystal rod is measured, and the current outer diameter value of the single crystal rod is calculated from the measured weight. Based on the calculated current outer diameter value and a response function of a preset prediction model (for example, a step response model), an outer diameter prediction value of the single crystal rod after a predetermined time has elapsed is calculated. The calculated outer diameter predicted value is compared with a predetermined outer diameter target value to calculate a deviation between them, and the heater output is controlled according to the deviation.

  Further, for example, Patent Document 2 discloses a control method obtained by improving the control method disclosed in Patent Document 1. According to this method, the time constant or gain in the response function of the prediction model is adjusted so as to monotonously decrease with time.

  Patent Document 3 discloses a method for growing a diameter-enlarged portion (cone portion or shoulder portion) of a single crystal rod so as not to disturb the crystal of the straight body portion of the single crystal rod in the Czochralski method. ing. According to this method, while the cone part (shoulder part) is grown, the change rate of the diameter of the cone part and the temperature of the melt are measured. The measured cone diameter change rate is compared with a preset target value, and the temperature target value is adjusted according to the difference between the two. The adjusted temperature target value and the measured melt temperature are compared, and the power supplied to the heater is PID controlled according to the deviation between the two.

Japanese Patent No. 2813439 JP-A-9-165293 Japanese Patent Publication No. 7-77996

  The control method using the prediction model disclosed in Patent Literatures 1 and 2 is applied to the formation of the straight body portion, and is not applied to the shoulder forming step before that. On the other hand, the method described in Patent Document 3 relating to the shoulder forming step may be applied when pulling up a single crystal rod having a small diameter at a very low speed. However, for example, when manufacturing a large-diameter single crystal rod having a diameter of 200 mm or 300 mm while pulling up at a high speed like pulling up a silicon single crystal, the heater temperature in the formation process of the first half of the straight body portion from the shoulder portion Since the unsteadiness and nonlinearity between the crystal diameters remarkably appear, it is difficult to form a desired shoulder by the method described in Patent Document 3.

  As described above, according to the conventional control method, it is difficult to accurately control a time-varying system control target having a dead time, as represented by a single crystal manufacturing apparatus using the Czochralski method.

  Accordingly, an object of the present invention is to accurately control a time-varying control target having a dead time.

  Another object of the present invention is to improve the controllability of the diameter of both the shoulder portion and the straight body portion of the single crystal rod when applied to a single crystal production apparatus by the Czochralski method, and The purpose is to improve the crystal quality in the body.

  According to one aspect of the present invention, a control system for a time-varying control target having dead time includes a target value for an output value of a control target, and a plurality of system parameters representing the plurality of system parameters of the control target A storage device that stores setting values and all or a part of the plurality of system parameter setting values are set to have a predetermined time-varying characteristic; a system parameter setting value stored in the storage device; and a control target A state predictor for predicting a value of a predetermined state variable including an output value at a future time after a dead time based on an output value at a current time and a past input value; stored in a storage device State variable at the future time based on the target value and system parameter setting value at the future time and the state variable at the future time predicted by the state predictor. It performs sliding mode control operation so as to restrain the coming time sliding mode, and a sliding mode controller for outputting an operation value to be applied to the controlled object.

  According to this control system, a plurality of system parameter setting values respectively representing a plurality of system parameters (for example, dead time, time constant and process gain) possessed by the controlled object are set and stored in advance. All or some of these system parameter set values are set to have predetermined time-varying characteristics reflecting the time-varying characteristics of the controlled object. As a method of setting a certain system parameter setting value so as to have a time-varying characteristic, the system parameter setting value is set, for example, in the form of a predetermined progress variable indicating the progress of control or a function of elapsed time. can do. The stored system parameter setting value, the current output value output from the controlled object, and the input value previously input to the controlled object are input to the state predictor. Based on these input values, the state predictor predicts the value of the state variable to be controlled at a future time after the dead time from the current time. Here, the state variable may include an output value to be controlled and its time differential value. A deviation between the output value at the predicted future time and the target value at the preset future time is obtained. The sliding mode controller uses the system parameter settings at the future time stored in the future based on the deviation at the future time and the state variable at the predicted future time. A sliding mode control operation is performed so as to be constrained to the time sliding mode, and an operation value to be applied to the control target is determined. Such a state prediction operation for predicting the state variable value after the dead time and the time-varying system parameter setting value are performed so as to constrain the predicted state variable value after the dead time to the sliding mode. In combination with the sliding mode control operation, the output value of the time-varying control target having dead time can be accurately controlled to the target value.

  This control system has a simple structure that constrains the predicted state to a future sliding mode against a dead time system having nonlinearity, and requires complex calculation and optimization like nonlinear model predictive control. do not do.

  In a preferred embodiment, in addition to the above configuration, the deviation between the output value at the future time predicted by the state predictor and the target value is obtained, and the deviation is integrated to obtain the deviation integrated value at the future time. A further integrator is provided. The sliding mode controller is configured as a type 1 servo system, and uses an expanded state variable formed by adding a deviation integral value at a future time from the integrator to a state variable at a future time from the state predictor. Then, the sliding mode control operation is performed. Thereby, since the steady deviation is suppressed, the control accuracy is further improved.

  As an example of a time-varying control target having a dead time, a single crystal pulling machine that pulls a single crystal rod of a specific substance by the Czochralski method can be cited. A single crystal manufacturing apparatus according to another aspect of the present invention includes the single crystal pulling machine as a control target and a control system having the above-described configuration for controlling the single crystal pulling machine. In this single crystal manufacturing apparatus, the diameter value of the single crystal rod pulled up by the single crystal puller is adopted as the output value of the single crystal puller. The “diameter value” here may be a literal diameter value or a time differential value of the weight of the single crystal rod being pulled (referred to as “pseudo diameter” in this specification). May be. Moreover, the diameter value of a single crystal rod and the differential value of the 1st floor and the 2nd floor by the time of the diameter value are employable as a state variable. Furthermore, as an operation value applied to the single crystal puller, a numerical value for operating the melt temperature in the crucible or the temperature of the heater for heating the melt can be adopted. Further, the pulling speed of the single crystal rod in the single crystal pulling machine can be controlled according to a pulling speed setting value set in advance as a function of time. In addition, the system parameters of the single crystal puller include dead time, time constant and process gain. Among them, at least the time constant and process gain set values have predetermined time-varying characteristics, for example, It can be set in the form of a function of the length of the single crystal rod pulled up or the elapsed time.

  The pulling speed set value is preferably such that the temperature gradient at the interface between the solid of the single crystal rod and the liquid of the melt in the crucible is maintained at an appropriate value. In addition, the process gain setting value changes according to the length of the single crystal rod in the process of forming the shoulder portion and the straight body portion of the single crystal rod, and particularly in the process of forming the straight body portion, the pulling speed of the single crystal rod is changed. It can be set to change in response to changes. The control system applied to the single crystal pulling machine in this way improves the controllability of the diameter of both the shoulder and the straight body of the single crystal rod, and improves the crystal quality in the straight body. .

  According to another aspect of the present invention, a control system for a time-varying control target having dead time includes a target value for an output value of the control target, a proportional gain setting value, an integral gain setting value, and a differential gain setting. And a storage device in which at least the proportional gain setting value of the control gain setting values is set to have a predetermined time-varying characteristic; and has a predetermined time-varying characteristic in advance. A feedforward compensator for outputting a first operation value set in such a manner; a subtractor for calculating a deviation between a target value stored in a storage device and an output value from a controlled object; and a subtractor A gain scheduled PID controller that performs a PID control operation and outputs a second operation value based on a deviation from the control gain and a control gain setting value stored in a storage device; a first from a feedforward compensator; Operation of A synthesizer that inputs a value and a second operation value from the gain scheduled PID controller and outputs a third operation value to be applied to the controlled object.

  According to this control system, the feedforward compensator outputs a first operation value that is set in advance to have a predetermined time-varying characteristic (for example, in the form of a function of control progress or elapsed time). To do. As the first operation value, an operation value obtained empirically for the purpose of controlling the output value to be controlled to the target value can be employed. In addition to the feedforward compensator, a gain scheduled PID controller that outputs the second operation value is provided. Control gains such as proportional gain, integral gain, and differential gain used in the gain scheduled PID controller are preset and stored. These control gain setting values can be determined based on the system parameters of the controlled object examined in advance, and at least the proportional gain setting value reflects the time-varying characteristics of the controlled system parameters. Are set to have predetermined time-varying characteristics (eg, in the form of a function of control progress or elapsed time). The gain-scheduled PID controller uses a control gain setting value that includes a proportional gain setting value with a predetermined time-varying characteristic for the deviation between the output value to be controlled and the target value. A control operation is performed and a second operation value is output. The third operation value is synthesized from the first operation value and the second operation value, and the third operation value is applied to the control target. Thus, the preset first operation value is corrected by the second operation value obtained by the gain scheduled PID control operation in which the time-varying characteristic of the control target is reflected, and the corrected operation value is obtained. The control target is operated by (third operation value). As a result, the output value of the time-varying control target having dead time can be accurately controlled to the target value.

  The present invention can be applied not only to a single crystal pulling machine based on the Czochralski method but also to a control target of a dead time system having various other nonlinearities.

  According to the present invention, it is possible to accurately control a time-varying control target having a dead time. When applied to a single crystal pulling machine using the Czochralski method, the control system of the present invention improves the controllability of the diameter of both the shoulder and the straight body of the single crystal rod, Crystal quality can be improved.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

  FIG. 1 shows an overall configuration of an embodiment of a single crystal manufacturing apparatus for manufacturing a single crystal rod of a specific substance, for example, silicon by the Czochralski method to which the present invention is applied.

  As shown in FIG. 1, a single crystal manufacturing apparatus 100 controls a furnace body (hereinafter, abbreviated as “CZ machine”) 102 of a single crystal pulling machine by the Czochralski method and the operation of the CZ machine 102. Controller 104. The controller 104 includes a computer (not shown) that performs control calculation described later, and various electric / electronic circuits that are various input / output interfaces between the computer and the CZ machine 102 and an operator.

  The CZ machine 102 has a chamber 106, air inside the chamber 106 is removed by a vacuum pump (not shown), and an inert gas 107 such as argon is supplied into the chamber 106 at a predetermined flow rate. A crucible 108 is installed in the chamber 106, and a heater 110 for heating the crucible 108 is disposed around the crucible 108, and a heat insulating material 111 surrounds them from the outside. To surround them, there is a magnetic field generator 114 outside the chamber 106, which provides a magnetic field in the crucible 108. The crucible 108 contains a raw material such as silicon, which is heated by the heater 110 to become a melt 112. The crucible 108 is rotated horizontally by the crucible rotating / lifting device 113 and raised so as to maintain the liquid level of the melt 112 constant.

  A seed 115 is suspended from the top of the CZ machine 102 by a wire 117. A pulling motor 118 disposed at the top of the CZ machine 102 operates the wire 117 to immerse the seed 115 in the melt 112 in the crucible 108, and then pulls up the seed 115 at a predetermined speed. Further, the rotary motor 120 operates the wire 117 to rotate the seed 115 at a predetermined speed. The controller 104 controls the pulling speed and rotation speed of the seed 115, the temperature of the heater 110 (temperature of the melt 112), the rotation speed of the crucible 108, and the like. Thereby, as the seed 115 is pulled up, the single crystal rod 116 is formed under the seed 115.

  While the weight / position measuring device 119 provided at the top of the CZ machine 102 is being pulled up, the weight of the single crystal rod 116 (from which the diameter of the single crystal rod 116 can be grasped) and the position of the seed (from now on) The crystal weight signal 126 and the seed position signal 128 are supplied to the controller 104. An optical heater temperature detector 132 disposed in a window for observing the heater 110 of the chamber 106 measures the temperature of the heater 110 and provides a heater temperature signal 134 to the controller 104. Further, an optical diameter measuring device 138 disposed in a window for observing the single crystal rod 116 in the chamber 106 measures the diameter of the single crystal rod 116 and outputs a crystal diameter signal 140 to the controller 104. In this embodiment, the diameter of the single crystal rod 116 is basically calculated based on the crystal weight signal 126, but it is difficult to accurately grasp the diameter of the single crystal rod 116 based on the crystal weight signal 126. A small diameter at an early stage of pulling (for example, a diameter of 40 mm or less) can be measured using the diameter measuring device 138 instead. As a modification, the diameter may be measured using the diameter measuring instrument 138 from beginning to end.

  The controller 104 inputs the crystal weight signal 126, the seed position signal 128, the heater temperature signal 134, and the crystal diameter signal 140 described above, and performs control operations described in detail later using the values of these signals. As a result of the control operation, the controller 104 outputs a pulling control signal 124 to the pulling motor driver 122 to control the pulling speed of the single crystal rod 116 by the pulling motor 118. In addition, as a result of the control operation, the controller 104 outputs a heating control signal 136 to the heater power supply circuit 130 to control the power supplied to the heater 110, thereby controlling the temperature of the heater 110. Further, the controller 104 controls the rotation speed of the single crystal rod 116 by the rotation motor 120, the rotation speed and lifting speed of the crucible 108 by the crucible rotation / lifting device 113, and the flow rate of the argon 107. When the CZ machine 102 includes the magnetic field generation device 114 as in the present embodiment, the controller 104 further controls the magnetic field intensity by the magnetic field generation device 114.

  Specific process conditions are preset in the controller 104. The main variables included in the process conditions include the rotational speed and pulling speed of the single crystal rod 116, the rotational speed of the crucible 108, the flow rate of the argon 107, and the strength of the magnetic field. The values of these process condition variables are each as a function (particularly a non-linear function) of the length (or elapsed time from the start of pulling) of the pulled single crystal rod 116 (hence the single crystal rod length or elapsed time). Can be set in the controller 104 (some variables may be set as fixed values). The method of changing the set value of the pulling rate according to the elapsed time or the length of the single crystal rod is determined by the temperature gradient at the interface between the solid of the single crystal rod 116 and the liquid of the melt 112 (temperature gradient in the direction perpendicular to the interface). It is chosen to keep it at a reasonable value. While the single crystal rod 116 is being pulled up, the controller 104 variably controls the above-described process condition variables so as to have respective set values according to the single crystal rod length (or elapsed time).

  In addition to controlling the process conditions as set above, the controller 104 controls the temperature of the heater 110 (and thus the temperature of the melt 112) by a “nonlinear state prediction sliding mode control” method as will be described in detail later. (Hereinafter, “sliding mode control” is abbreviated as “SMC”). The control operation of the heater temperature (melt temperature) is basically performed so that the weight differential value obtained by differentiating the weight of the single crystal rod 116 with time is controlled to a preset target value. Here, the weight differential value is a variable corresponding to the diameter of the single crystal rod 116 when the pulling speed is constant, and this is hereinafter referred to as “pseudo diameter”.

  The operation of controlling the heater temperature (melt temperature) by the nonlinear state prediction SMC method includes an operation called “nonlinear state prediction” and an operation called “gain scheduled SMC”. In the non-linear state prediction operation, the long dead time of the CZ machine 102 to be controlled is taken into consideration, and the state variable vector related to the pseudo diameter (that is, the pseudo diameter itself, the first and second derivative values depending on the time). It is predicted that each of the three state variable sets) will have a value at the future time after the dead time has elapsed from the current time. Then, the gain scheduled SMC operation is executed for the current heater temperature (melt temperature) so that the predicted pseudo diameter at the future time matches the target value of the pseudo diameter at the future time.

  In gain-scheduled SMC operation, the time-varying characteristics of the system parameters (process gain, time constant, dead time) of the CZ machine 102 to be controlled (for example, from the shoulder of the single crystal rod to the front part of the straight body part) In the process of forming, the process gain changes significantly or the time constant changes). That is, the single crystal rod length (or elapsed time) so that all or part of the system parameters (process gain, time constant, dead time) (especially process gain and time constant) each have a predetermined time-varying characteristic. (In this embodiment, as will be described later, only the dead time is set to a constant value (Ld) instead of a time-varying value. However, the dead time may also be set to a time-varying value like the process gain and time constant. Then, the set value at the future time of the time-varying system parameter set in advance is used so as to constrain the state variable vector at the future time predicted by the nonlinear state prediction operation to the sliding mode at the future time. Then, the SMC is calculated, and the current operation value of the heater temperature (melt temperature) is determined.

  Hereinafter, the control of the heater temperature (melt temperature) by the nonlinear state prediction SMC method outlined above will be described in more detail.

  FIG. 2 shows the overall configuration of a control system for controlling the heater temperature (melt temperature) by the nonlinear state prediction SMC method.

In FIG. 2, a block 200 indicates a control target (that is, the CZ machine 102 shown in FIG. 1). Other blocks 202-212 show control operations performed by the controller 104. That is, the controller 104 operates as the pulling speed setting unit 202, the incomplete differentiator 204, the nonlinear state predictor 206, the subtractor 208, the integrator 210, and the gain scheduled SMC unit 212. The controller 104 not only controls the heater temperature (melt temperature) but also controls the various process condition variables as described above. In FIG. Only the function for controlling the pulling speed is shown, and the function for controlling other variables is not shown. The system parameters (process gain k ₀ , time constant T, dead time L) of the control target 200 are preset and stored in the controller 104. In this embodiment, since the CZ machine 102 of FIG. 1 that is the control target happens to have such a transfer characteristic, the process gain k ₀ and the time constant T are set to have predetermined time-varying characteristics, respectively, and on the other hand, The time L is set to a constant value Ld. However, this is merely an example, and all of the process gain k ₀ , time constant T, and dead time L _d can be set to have time-varying characteristics according to the characteristics of the controlled object.

  As shown in FIG. 2, the pulling speed setting unit 202 sets the pulling speed of the single crystal bar 116 according to the set value of the pulling speed set as a nonlinear function of the single crystal bar length (or elapsed time). Change according to length (or elapsed time). As described above, the method of changing the set value of the pulling rate according to the length (or elapsed time) of the single crystal rod is suitable for the temperature gradient at the interface between the solid of the single crystal rod 116 and the liquid of the melt 112. It is chosen to keep the value. In general, the density of crystal defects formed in the pulled single crystal rod 116 is determined by the temperature gradient of the interface and the crystal growth rate. By maintaining the temperature gradient of the interface at an appropriate value while the single crystal rod 116 is being pulled up, it becomes easy to manufacture a high quality single crystal rod 116 while suppressing the generation of crystal defects.

The incomplete differentiator 204 inputs the crystal weight w (crystal weight signal 126 shown in FIG. 1) detected from the control target (CZ machine) 200, and calculates the first-order differential value of the current crystal weight according to the time t. calculate. As described above, the first-order differential value of the weight w by the time t corresponds to the diameter of the single crystal rod 116 when the pulling speed is constant, and is referred to as “pseudo diameter” in this specification. In FIG. 2, it is indicated by the symbol y (t). By the way, when calculating the pseudo-diameter y (t), the incomplete differentiator 204 does not perform full differentiation on the crystal weight w, but uses an incomplete differentiation low-pass filter having a predetermined time constant L _f1. Apply. Thereby, the influence of noise included in the detected crystal weight w (crystal weight signal 126) is removed.

The non-linear state predictor 206 inputs the pseudo diameter y (t) at the current time t and the operation value u _{T of the} heater temperature (melt temperature), and stores system parameters (process gain k ₀ , hour) constant T, by using the dead time set value of L _d), a future time after a predetermined dead time L _d elapses from the current time t (t + L _d) states for the pseudo diameter at the variable vector x (t + L _d) Predictive calculation. Here, the state variable vector x (t + L _d) includes a pseudo diameter y (t + L _d) in the dead time L _d after the future time (t + L _d), the pseudo diameter y (t + L _d) A set of three state variables of the first derivative y ′ (t + L _d ) and the second derivative y ″ (t + L _d ) according to the time (in other words, the future time (t + L _d ) In the crystal weight w (t + L _d ) over time, a set of first-order derivative values, second-order derivative values, and third-order derivative values).

Subtracter 208, a future time predicted by the nonlinear state predictor 206 (t + L _d) pseudo diameter at y (t + L _d), the target value r of the pseudo diameter at future time (t + L _d) ( t + L _d) inputs an, calculates the deviation e (t + L _d) between the target value r (t + L _d) the pseudo diameter y (t + L _d). Here, the target value r (t + L _d ) of the pseudo diameter is preset and stored in the controller 104 as a nonlinear function of the length of the pulled single crystal rod 116 (or the elapsed time after the start of pulling). Yes.

The integrator 210 inputs the deviation e (t + L _d ) from the subtracter 208, integrates this deviation e (t + L _d ) with time, and subtracts from the start of the pulling up to the current time. An integral value z (t + L _d ) of the deviation e (t + L _d ) output from 208 is obtained.

The gain scheduled SMC unit 212 is an integrated value z (t + L _d ) of the state variable vector x (t + L _d ) from the nonlinear state predictor 206 and the deviation e (t + L _d ) from the integrator 210. And the state variable vector as the state variable using the set values at the future time (t + L _d ) of the system parameters (process gain k ₀ , time constant T, dead time L _d ) stored in advance Executes SMC operation of type 1 servo system with deviation integrated value z (t + L _d ) added to x (t + L _d ), thereby determining the operating value u _T of the heater temperature (melt temperature) To do. The actuation value u _T is the heater temperature at the start of pulling, shows the temperature difference to the target value of the heater temperature at the current time. As shown in FIG. 1, a heating control signal 136 corresponding to the operation value u _T is given from the controller 104 to the heater power supply circuit 130, whereby the actual heater temperature (melt temperature) is changed to the operation value u _T. The heater temperature (melt temperature) specified by is controlled to coincide with the target value.

  Next, a specific example of a heater temperature (melt temperature) control system based on the nonlinear state prediction SMC method shown in FIG. 2 will be described in more detail.

1. Modeling of controlled object 200 The mechanism of crystal growth is very complex, and a model cannot be derived from the laws of physics. Therefore, the model of the controlled object 200 can be derived by applying the expanded least square method to the input / output data obtained in the identification experiment.

1.1 Identification Experiments Identification experiments can be performed using an open-loop identification system as shown in Fig. 3 in order to grasp the exact dynamic characteristics during pulling. In the identification system shown in FIG. 3, the feedforward compensation signal is output from the feedforward temperature compensator 220 with the pulling speed and the melt temperature PID control removed, and the identification input signal u _Ti is manually set. is inputted, the operation value u _T next to both signals are added to produce the heater temperature (the melt temperature), the heater temperature (the melt temperature) is operated in accordance with the operation value u _T. Then, the pulling speed according to the pulling speed set value which is a nonlinear function of the single crystal bar length (or elapsed time) provided from the pulling speed setting unit 202 similar to that shown in FIG. 116 is pulled up. Here, the feedforward compensation signal is an operation value of a heater temperature (melt temperature) that is empirically obtained and preset in order to control the diameter of the single crystal rod 116 to a predetermined target value. However, it is difficult to satisfactorily maintain the diameter of the single crystal rod 116 at a predetermined target value only with the feedforward compensation signal. Therefore, in order to adjust the feedforward compensation signal to a more appropriate value, the identification input signal _uTi is given by manual operation about every hour in the entire pulling process. The magnitude of the identification input signal u _Ti is, for example, in the range of −3.0 to +3.0 [° C.]. By the said feed-forward compensation signal and the identification input signal u _Ti, the diameter of the pulled up single crystal ingot 116 is to be satisfactorily maintained to a predetermined target value. By this identification experiment, input / output data in the vicinity of the operating point when the single crystal rod 116 is pulled up at a preset pulling rate (crystal growth rate) is obtained. Here, the input data is the operation value u _T of the heater temperature (melt temperature), and the output data is the pseudo diameter (differential value of the weight w) dw / dt of the pulled single crystal rod 116. Obtained as a function of single crystal rod length (or elapsed time).

The process conditions used in this identification experiment are the same as those used in the control system shown in FIG. 2 designed based on the results of this identification experiment. Specific examples of the process conditions are as follows. The pulling speed varies in the range of 0.8 to 0.4 [mm / min], the single crystal rod rotation speed varies in the range of 6 to 15 [rpm], and the argon supply flow rate is in the range of 20 to 100 [l / min]. The magnetic field strength changes in the range of 0.1 to 0.4 [T] (= 1000 to 4000 [G]), and the crucible rotation speed changes in the range of 0.8 to 3 [rpm]. As already explained, the pulling speed is determined by the length of the single crystal rod pulled up (or the elapsed time) according to a time series of speed setting values set in advance so that the temperature gradient at the solid-liquid interface becomes an appropriate value. Change with time). The numerical values of the above process conditions are only examples, and other numerical values of process conditions can be used. In the following description, one or more types of process conditions adopted are represented by p _i (i = 0, 1 , 2, ...).

1.2 Model structure The model obtained using the above identification method must be a model that takes control system design into consideration. On the other hand, a method for describing a control target having complicated nonlinearity and time-varying characteristics as a set of piecewise linear systems, a just-in-time modeling method, a local modeling method, and the like have been proposed. A CZ device with very complex nonlinearities can also be described as:

ここで、G(s)は制御対象２００の伝達関数である。k₀{・}、 T{・}、 L{・}は、それぞれ制御対象２００のプロセスゲイン、時定数、むだ時間である。Δk₀、 ΔT、 ΔLは、各システムパラメータの不確かさであり、γ_k0、γ_T、γ_Lによって上界値が定義される。l(t)は引き上げられた単結晶棒１１６の長さ、p_i (i=0, 1, 2,・・・)はプロセス条件、tは時間である。引き上げ速度のPID制御を除去した状態では、単結晶棒１１６の長さl(t) は予め時間の関数として与えられる。これより、(1)式は、時変系と考えることができる。

Here, G (s) is a transfer function of the controlled object 200. k ₀ {•}, T {•}, and L {•} are the process gain, time constant, and dead time of the control target 200, respectively. Δk ₀ , ΔT, ΔL are the uncertainties of each system parameter, and the upper bound value is defined by γ _k0 , γ _T , γ _L. l (t) is the length of the pulled single crystal rod 116, p _i (i = 0, 1, 2,...) is the process condition, and t is the time. In a state where the PID control of the pulling rate is removed, the length l (t) of the single crystal rod 116 is given in advance as a function of time. From this, equation (1) can be considered as a time-varying system.

1.3 Application of extended least square method As an identification method of time-varying system parameters in the presence of unknown disturbances, it is possible to use a sequential extended least square method using a forgetting factor. However, the command value u _T of the heater temperature is input (melt temperature), the temperature at which became dislocation in squeezing seeds and equilibrium point (fixed value; shoulder start temperature; initial temperature of the single crystal ingot grown) To do. The upper bounds of the uncertainties defined by γ _k0 , γ _T and γ _L are about 0.25 (25 [%]), respectively.

2. Nonlinear state prediction sliding mode control
In contrast to the large dead time and nonlinearity of CZ machines, the conventional control method based on PID control cannot achieve high diameter control performance only by controlling the heater temperature (melt temperature). In addition, the conventional control method has low robustness and adaptability to the difference in operation technology between different operators, the difference in performance between different CZ machines, and the difference in various process conditions. Therefore, in this embodiment, an SMC having high robustness and adaptability to disturbances and modeling errors is applied, and a nonlinear state that constrains the state after the dead time predicted based on the nonlinear model to the switching hyperplane. Adopt state prediction SMC.

2.1 Description of control target
In order to reduce chattering caused by SMC observation noise, two low-pass filters are added to the above equation (1) from which uncertainty has been removed as shown in the following equation.

ここで、Lf1は、計測された重量を擬似直径に変換する不完全微分のローパスフィルタ（図２に示したブロック２０４)の時定数である。Lf2は、後述の非線形状態予測器の内部に設けられたローパスフィルタの時定数である。

Here, Lf1 is a time constant of an incomplete differential low-pass filter (block 204 shown in FIG. 2) that converts the measured weight into a pseudo diameter. Lf2 is a time constant of a low-pass filter provided in a nonlinear state predictor described later.

The process gain k ₀ {l (t), pi}, the time constant T {l (t), pi} and the dead time L {l (t), pi} obtained from the result of the identification experiment described above are shown in FIG. (Each vertical axis is expressed as a percentage of a predetermined variable range of each numerical value). In FIG. 4, the initial pulling area (hatched area) where the single crystal rod length l (t) is less than 50 mm is in the middle of the calculation of the least square method and is not reliable and exceeds 50 mm. The identification result in the region is reliable. A position indicated by a broken line (for example, l (t) = about 120 mm) is a position where the formation of the straight body portion is started. As can be seen from FIG. 4, the process gain k ₀ {l (t), pi} varies depending on the length of the single crystal rod l (t), and in particular, from the shoulder of the single crystal rod 116 to the front of the straight body portion. It changes remarkably in the interval (for example, l (t) = 0−about 300 mm). In other words, the process gain k ₀ {l (t), pi} decreases to a position just before entering the straight body part in the process of growing the shoulder part, and then rises to increase the front part of the straight body part. After the stage of growth (for example, l (t) = about 300 mm), it can be regarded as a substantially constant value. Here, it is considered that the change in the straight body portion of the process gain k ₀ {l (t), pi} is accompanied by the change in the pulling speed. Further, the time constant T {l (t), pi} rises during the shoulder growing process, and can be regarded as a substantially constant value after entering the straight body part. In addition, the dead time L {l (t), pi} can be regarded as a constant value Ld {pi} that does not depend on the single crystal rod length l (t) throughout. The characteristics of the process gain k ₀ {l (t), pi}, the time constant T {l (t), pi} and the dead time L {l (t), pi} shown in FIG. However, if the control target and process conditions are different, their characteristics will be different. For example, the dead time L {l (t), pi} is not a constant value, but is similar to the process gain k ₀ {l (t), pi} and the time constant T {l (t), pi}. It can have time-varying characteristics. Alternatively, the process gain k ₀ {l (t), pi} or the time constant T {l (t), pi} may be considered constant.

Rewriting equation (2) into a canonical system equation of state gives the following equations (3)-(6). However, since the process condition pi is known, here k ₀ {l (t), pi} ≡k ₀ (t), T {l (t), pi} ≡T (t), Ld {pi} ≡Ld.

2・2 制御系設計
まず、定常偏差を除去するために、(3)式の状態変数x(t)に目標値r(t)と出力y(t)との差の積分値z(t)を付加した拡張状態変数x_s(t)を用いる1型サーボ系(拡大系)を以下のように構成する。

2.2 Control system design A type 1 servo system (enlarged system) using the extended state variable x _s (t) with the added is configured as follows.

つぎに、(7)式を用いて、等価制御系を設計する。むだ時間Ldが存在する場合、等価制御系は、一般に無限個の極をもち、後述するSでそれらすべてを調整することができない。そこで、(7)式の時間を無駄時間Ldだけ進めた次式を用いて等価制御系を設計する。

Next, an equivalent control system is designed using equation (7). When the dead time Ld exists, the equivalent control system generally has an infinite number of poles and cannot adjust all of them with S described later. Therefore, an equivalent control system is designed using the following equation obtained by advancing the time of equation (7) by the dead time Ld.

ここで、時間をLdだけ進めた切換関数σ(t+Ld)は、次式のように定義する。

Here, the switching function σ (t + Ld) in which the time is advanced by Ld is defined as the following equation.

連続時間系のスライディングモードにおいては、

In continuous time sliding mode,

から、等価制御入力ueq(t)は外乱を考慮しないとすれば、

Therefore, if the equivalent control input ueq (t) does not consider disturbance,

となり、等価制御系は次式で表される。

Thus, the equivalent control system is expressed by the following equation.

切換超平面の設計には、等価制御系の入力の数だけ低次元化された3次元システムの極λ1、 λ2、 λ3を希望の特性に指定することができる極配置法を適用する。このとき、閉ループ系の特性方程式は、s³+S3s²+S2s-S1=0となる。ここで注目すべきことは、この特性方程式は時変システムパラメータを含まず、容易に設計可能である。

For the design of the switching hyperplane, a pole placement method is applied in which the poles λ1, λ2, and λ3 of the three-dimensional system reduced in number by the number of inputs of the equivalent control system can be designated as desired characteristics. At this time, the characteristic equation of the closed loop system is s ³ + S3s ² + S2s−S1 = 0. It should be noted that this characteristic equation does not include time-varying system parameters and can be easily designed.

  Finally, design a sliding mode controller. The control input u (t) is assumed to be composed of two independent control inputs, an equivalent control input ueq (t) and a nonlinear control input unl (t) as in the following equation.

SBs(t+Ld)>0のときK>0、SBs(t+Ld)<0のときK<0と選べば、時間をLdだけ進めたスライディングモードが存在する条件

If K> 0 when SBs (t + Ld)> 0, and K <0 when SBs (t + Ld) <0, there is a condition that there is a sliding mode that advances the time by Ld

を満足する。

Satisfied.

2.3 Nonlinear state predictor
The state ahead by the dead time Ld of the nonlinear process expressed by the equation (3) can be derived as follows.

(18)式の両辺を時間t〜t+Ldで積分すると、次式のようになる。

When both sides of equation (18) are integrated at time t to t + Ld, the following equation is obtained.

これより、時間Ldだけ先の状態をxM(t+Ld)とすると、

From this, if the state ahead by time Ld is xM (t + Ld),

となる。ただし、(20)式は、システムパラメータの変化の仕方が予めわかっているという前提のもとで導出された式である。さらに、(20)式に対して、現時刻tでの実測値x(t)と予測値xM(t)との差を用いて、モデル化誤差や外乱等の影響を補正する。これより、10分以上の大きなむだ時間を有する実プロセスにも適用が可能となる。

It becomes. However, Expression (20) is an expression derived on the assumption that the method of changing the system parameters is known in advance. Further, with respect to the equation (20), the influence of modeling error, disturbance, etc. is corrected using the difference between the actual measurement value x (t) and the predicted value xM (t) at the current time t. Thus, it can be applied to an actual process having a large dead time of 10 minutes or more.

ただし、(21)式の実測値x(t)と予測値xM(t)との差に対しては、実プロセスに適用した際の観測ノイズやモデル化誤差に対するロバスト安定性を高めるため、むだ時間Ldよりも十分大きな時定数のローパスフィルタを適用する。

However, the difference between the measured value x (t) and the predicted value xM (t) in Eq. (21) is a waste because it increases robust stability against observation noise and modeling errors when applied to an actual process. A low-pass filter having a time constant sufficiently larger than the time Ld is applied.

The non-linear state prediction SMC control system designed as described above is shown in FIG. In the control system of FIG. 2, the target value r (t + Ld) of the pseudo diameter and the set value u _r of the pulling speed are a nonlinear function of the single crystal rod length l (t) (or the elapsed time t from the start of pulling). Is preset in the controller 104 and stored in the memory 104A in the controller 104. The single crystal rod length l (t) is set in advance in the controller 104 and stored in the memory 104A in the controller 104 as a function of the elapsed time t from the start of pulling. The process gain k ₀ {l (t), pi} and the time constant T {l (t), pi} are also expressed as a nonlinear function of the single crystal rod length l (t) (or elapsed time t from the start of pulling), It is set in advance in the controller 104 and stored in the memory 104A in the controller 104. The dead time L {l (t), pi} can also be a non-linear function of the single crystal rod length l (t) (or the elapsed time t from the start of pulling), but in this embodiment, a constant value Ld {pi} is set in advance in the controller 104 and stored in the memory 104A in the controller 104. The process condition pi is also stored in advance in the controller 104 as a nonlinear function of the single crystal rod length l (t) (or the elapsed time t from the start of pulling) (or some process condition variables may be constant values). It is set and stored in the memory 104 A in the controller 104.

  The control system shown in FIG. 2 does not control the weight w of the single crystal rod 116 but controls the pseudo diameter dw / dt. It is the diameter to be controlled, and such a pseudo-diameter control system is employed in order to increase the stability by advancing the phase lag due to the integral characteristic of the weight by the differential element. When the diameter of the single crystal rod at the initial stage of pulling is small (for example, 40 mm or less), it is difficult to differentiate the weight w and accurately grasp the diameter. Instead, the optical crystal shown in FIG. The diameter can be grasped by the diameter measuring instrument 138. This control system also eliminates feed-forward compensation for melt temperature, which must be determined empirically from PID control of pulling speed and experimental results. If the desired characteristic is designed as a switching hyperplane, the SMC is equivalently constrained and adapted to the desired characteristic. As a result, the desired target value response can be easily obtained with a one-degree-of-freedom control system, and feed-forward compensation of the heater temperature (melt temperature) can be eliminated. System required).

  FIG. 5 shows an example of the control result obtained in the operation test of the control system shown in FIG. 5A and 5B is expressed as a percentage of a predetermined change range of each variable, and the vertical axis in FIG. 5C is shown in comparison with the target diameter D of the straight body portion.

In FIG. 5A, the solid line graph shows a change in pulling speed accompanying the growth of the single crystal bar 116, and the alternate long and short dash line graph shows a change in crucible rotation speed. The pulling speed was constant during the first half of the shoulder growth process, but from a predetermined position slightly before the position where it entered the straight body part in the second half, and thereafter, as the length l of the single crystal rod increased. It was gradually lowered. In addition, the crucible rotation speed was constant in the first half of the shoulder growth process, but gradually increased as the length of the single crystal rod l increased from a predetermined position slightly before the position where the straight body was entered. And when the single crystal rod length l reaches a predetermined value (for example, about 300 mm, which substantially coincides with the position where the process gain k ₀ shown in FIG. 4A is substantially constant). After that, it was kept constant. As described above, the change in the pulling speed is in accordance with a speed setting value set in advance so as to maintain the temperature gradient at the interface between the single crystal rod 116 and the liquid of the melt 112 at an appropriate value. is there. As the single crystal rod 116 becomes longer, the upward heat escape becomes smaller and the temperature gradient becomes smaller. In order to compensate for this, the pulling speed is reduced as shown in the figure.

  As shown in FIG. 5B, the heater temperature (melt temperature) has been lowered from the start of pulling, but is temporarily raised in the latter half of the shoulder formation process, and enters the above-described straight body portion. It reached a maximum at a predetermined position slightly before, and then decreased again. When the length l of the single crystal rod reached the predetermined value (for example, about 300 mm), the heater temperature (melt temperature) was gradually increased. Due to such a change in heater temperature (melt temperature), the single crystal rod diameter is accurately controlled to the target value as shown in FIG. 5C. In particular, in the straight body portion, the target value D in the straight body portion is almost the same. It was controlled almost constant at the same value.

  Further, as can be seen from the above control results, the pulling speed is maintained in the vicinity of a predetermined appropriate value in the entire region of the shoulder portion or the straight body portion, and the temperature gradient at the interface between the solid and the liquid is also substantially appropriate. Maintained. As a result, the crystal quality of the straight body part is also good. That is, generally, when the pulling rate is V and the temperature gradient of the interface is G, for example, in the case of a silicon single crystal rod 116, the density of crystal defects in the single crystal rod 116 is determined by V / G. Are known. According to the above control result, V / G in the straight body portion is not fluctuated greatly and is stably maintained in the vicinity of the appropriate value, so that variation in the density of crystal defects is small and crystal quality is improved.

  FIG. 6 shows a modification of the control system that can be employed in this embodiment instead of the configuration of FIG. In the control system shown in FIG. 6 as well, the process conditions including the above-described pulling speed and other variables are controlled in the same manner as in the control system shown in FIG.

The control system shown in FIG. 6 uses gain scheduled PID control instead of the above-described nonlinear state prediction SMC. That is, in this control system, the single crystal bar weight w detected from the control target (CZ machine) 200 and the single crystal bar weight target value w _ref previously set in the controller 104 and stored in the memory 104A are _reduced to the low pass filter 230. The weight target value after applying is input to the subtractor 232, the weight deviation e is calculated, and the incomplete differentiator 234 is applied to the weight deviation to calculate the pseudo diameter deviation. Then, a gain scheduled PID controller 236 is applied to the pseudo diameter deviation. The proportional gain K _p , integral gain T _I, and differential gain T _p of the gain scheduled PID controller 236 are the single crystal rod length l (t) (or elapsed time) of the controlled object 200 illustrated in FIG. Based on the process gain k ₀ (t), the time constant T (t), and the dead time L (t) (which is considered to be a constant value Ld as described above) It is determined in advance as a function of the single crystal rod length l (t) (or elapsed time), set in the controller 104, and stored in the memory 104 </ b> A in the controller 104. The gain scheduled PID controller 236 performs PID calculation using gains K _p , T _{I and} T _p that change according to the single crystal rod length l (t) (or elapsed time). Among these three control gain, proportional gain K _p only was set as a function of the single crystal ingot length l (t) (or elapsed time), integral and differential gain T _I, the T _p a constant value May be set.

The PID calculation result value output from the gain scheduled PID controller 236 and the temperature compensation value output from the feedforward temperature compensator 220 are added by an adder 238, and the added value is the heater temperature (melt temperature). ) of the controlled object as the operation value u _T (applied to CZ machine) 200. Here, the feedforward temperature compensator 220 is the same as the feedforward temperature compensator 220 used in the identification system shown in FIG. 3, and is a single crystal obtained and set in advance by experience. A temperature compensation value that changes according to the rod length l (t) (or elapsed time) is output. The gain scheduled PID controller 236 compensates for the fact that the single crystal bar weight w cannot be matched with the weight standard value w _ref only by the temperature compensation value output from the feedforward temperature compensator 220, whereby the single crystal The rod weight w is accurately controlled by the weight mark value w _ref .

  FIG. 7 shows an example of the result of the control operation actually performed by the control system shown in FIG. 7A and 7B represents the percentage of each variable with respect to a predetermined change range, and the vertical axis in FIG. 7C represents the comparison with the target diameter D of the straight body portion.

As shown in FIG. 7A, the proportional gain K _p of the gain scheduled PID controller 236 is from the start of pulling until the single crystal rod length l reaches the predetermined value (for example, 300 mm) (that is, in FIG. 4A). (While the indicated process gain k ₀ is fluctuating) is increased and thereafter maintained at a constant value (ie after the process gain k ₀ shown in FIG. 4A has stabilized to a substantially constant value). It was. As shown in FIG. 7B, the heater temperature was lowered from the start of pulling up, but it was temporarily raised in the second half of the shoulder formation process, and at a predetermined position slightly before the position where it enters the straight body section. The maximum value was reached and then decreased again, and after the single crystal rod length l reached the predetermined value, it was gradually increased. The manner of this change was basically the same as the way of changing the heater temperature by the nonlinear state prediction SMC shown in FIG. 5B. As a result, as shown in FIG. 7C, the single crystal rod diameter was well controlled. However, as can be seen from comparison with FIG. 5C, the non-linear state prediction SMC obtained better controllability of the diameter.

  According to this control result, V / G when the pulling speed is V and the temperature gradient of the interface is G is stably maintained in the vicinity of an appropriate value without largely fluctuating in the straight body portion. The crystal quality of is good.

  As mentioned above, although one Embodiment of this invention was described, this is only an illustration and various deformation | transformation can also be applied to this. For example, instead of the method of controlling the heater temperature (melt temperature) by feedback control as in the above-described embodiment, the heater temperature (melt temperature) change pattern illustrated in FIG. 5B or FIG. A control method is adopted in which the temperature is set as a function of the single crystal rod length or elapsed time, and the heater temperature (melt temperature) is changed according to the single crystal rod length or elapsed time according to this temperature set value. You can also.

  In addition, the control target of the control system according to the present invention is not limited to the single crystal pulling apparatus described above, and can be applied to various other control targets having dead time and / or time-varying characteristics. Needless to say. For example, in a system that remotely controls a manipulator of a robot or work machine via a communication network, communication delay of the communication network, response delay of the hydraulic circuit, etc. exist as dead time. The control system of the present invention is also suitable for such a manipulator operating system. Alternatively, in the RCA cleaning system for RCA (Radio Corporation of America) development widely used as a silicon wafer cleaning method in a semiconductor manufacturing process, there is a large dead time and nonlinear time-varying characteristics in temperature control of the cleaning liquid. The control system of the present invention is also suitable for this RCA cleaning system.

  FIG. 8 shows a general-purpose overall configuration of a control system based on the nonlinear state prediction SMC method according to the present invention.

  In FIG. 8, block 300 shows the controlled object (which can be various systems as described above). The control system has blocks 302-308. System parameter setting values each representing system parameters (process gain, time constant, dead time, etc.) of the control target 300 and control target values are stored in advance in this control system. These system parameter set values and control target values are all set as functions of predetermined variables indicating, for example, elapsed time or control progress so as to have predetermined time-varying characteristics corresponding to the controlled object 300, respectively. (Of course, some system parameters may be set to constant values). The non-linear state predictor 302 inputs the output value y (t) and the input value u (t) of the control object 300, and uses a preset value of the system parameter stored in advance, to determine a predetermined value from the current time t. A predetermined state variable vector x {t + L (t)} at a future time {t + L (t)} after the dead time L (t) has elapsed is predicted and calculated. Here, the state variable vector x (t) can include the output value y (t) of the controlled object 300 and the differential values from the first floor to the Nth floor according to the time of the output value y (t).

The subtractor 304 outputs the output value y {t + L (t)} at the future time {t + L (t)} predicted by the nonlinear state predictor 302 and the future time {t + L (t)}). The control target value r {t + L (t)} is input, and a deviation e {t + L (t)} between them is calculated. The integrator 306 inputs the deviation e {t + L (t)} from the subtractor 306, integrates the deviation e (t + L _d ) with time, and starts from the control start to the current time. An integral value z {t + L (t)} of the deviation e {t + L (t)} output from the subtractor 304 is obtained.

The gain scheduled SMC unit 308 includes a state variable vector x {t + L (t)} at a future time {t + L (t)} from the nonlinear state predictor 302 and a deviation e {t + from the integrator 306. Enter the integral value z {t + L (t)} of L (t)} and the deviation integral value at the state variable vector x {t + L (t)} at the future time {t + L (t)} Using the expanded state variable to which z {t + L (t)} is added, the system parameter value stored in advance at the future time {t + L (t)} (process gain setting value k ₀ Execute SMC operation of type 1 servo system using {t + L (t)}, time constant set value T {t + L (t)}, dead time set value L {t + L (t)}) To do. Thereby, the state variable vector x {t + L (t)} at the future time {t + L (t)} is constrained to the sliding mode. By this SMC operation, the current operation value u (t) is determined and applied to the controlled object 300.

  The scope of the present invention is not limited to the embodiment described above. The present invention can be implemented in various other modes without departing from the gist thereof.

The figure which shows the whole structure of the single-crystal manufacturing apparatus with which one Embodiment of this invention was applied. The block diagram which shows the whole structure of the control system for the nonlinear state prediction sliding mode control of the melt temperature performed by the controller 104. FIG. The block diagram which shows the structure of the identification system for modeling of the control object 200. FIG. The figure which shows the specific example of the process gain, time constant, and dead time of the control object 200 obtained from an identification experiment. The figure which shows an example of the control result obtained by the operation test of the control system shown by FIG. The block diagram which shows the modification of a control system. The figure which shows an example of the control result obtained by the operation test of the control system shown in FIG. The block diagram which shows the general purpose whole structure of the control system by the nonlinear state prediction SMC method according to this invention.

Explanation of symbols

100 Single crystal production equipment 102 Czochralski method single crystal pulling machine furnace body (CZ machine)
104 controller 106 chamber 108 crucible 110 heater 112 melt 113 crucible rotating / lifting device 114 magnetic field generator 116 single crystal rod 118 pulling motor 119 weight / position measuring device 130 heater power supply circuit 200 controlled object (CZ machine)
202 Pull-up speed setting device 204 Incomplete differentiator 206 Non-linear state predictor 208 Subtractor 210 Integrator 212 Gain scheduled SMC (sliding mode control) device 220 Feedforward temperature compensator 230 Low-pass filter 232 Subtractor 234 Incomplete differentiator 236 Gain scheduled PID controller 300 Control target 302 Non-linear state predictor 304 Subtractor 306 Integrator 308 Gain scheduled SMC (sliding mode control) unit

Claims (5)

In a control system for a time-varying control target (200) having dead time
A target value (r) for the output value of the control object (200) and a plurality of system parameter setting values representing a plurality of system parameters of the control object (200) are stored, and all or a plurality of the system parameter setting values are stored. A storage device (104A), some of which are set to have predetermined time-varying characteristics;
Based on the system parameter setting value stored in the storage device (104A), the output value at the current time of the control target (200), and the past input value (u _T ), the dead time after the present time. A state predictor (206) for predicting a value of a predetermined state variable (x) including the output value at a future time (t + L) of
The target value (r) and the system parameter set value at the future time (t + L) stored in the storage device (104A), and the future time (t + L) predicted by the state predictor (206) Based on the state variable (x), the sliding mode control operation is performed so as to constrain the state variable (x) at the future time (t + L) to the sliding mode at the future time (t + L), A control system comprising a sliding mode controller (212) for outputting an operation value (u) to be applied to the controlled object (200). The system of claim 1, wherein
By integrating the deviation (e) between the output value predicted by the state predictor (206) at the future time (t + L) and the target value (r), the future time (t + L) An integrator (210) for obtaining a deviation integral value (z) at
The sliding mode controller (212) adds the future time (t + L) from the integrator (210) to the state variable (x) at the future time (t + L) from the state predictor (206). A control system for performing a sliding mode control operation using an expanded state variable (x _s ) formed by adding the deviation integral value (z) in FIG. A single crystal manufacturing apparatus for manufacturing a single crystal rod by the Czochralski method, comprising the control system according to claim 1 and a single crystal pulling machine controlled by the control system.
The output value is a diameter value of a single crystal rod pulled up by the single crystal pulling machine,
The system parameter setting value having the predetermined time-varying characteristic is set to change according to the length or elapsed time of the single crystal rod pulled up by the single crystal pulling machine,
The state variable (x) includes the diameter value and differential values of the first and second floors according to the time of the diameter value,
The operation value (u) is a numerical value for operating the melt temperature of the single crystal production apparatus or the temperature of a heater for heating the melt,
The dead time is a time (L) from when the operation value (u) input from the control system to the single crystal manufacturing apparatus changes until the change of the output value starts,
The single crystal manufacturing apparatus further comprising a pulling speed setting device (202) for controlling the pulling speed of the single crystal rod according to a pulling speed setting value set in advance as a function of time. In the single crystal manufacturing apparatus according to claim 3 ,
One of the system parameter setting values having the predetermined time-varying characteristic is a process gain setting value (k ₀ ), and the process gain setting value (k ₀ ) is a process of forming a shoulder portion and a straight body portion of the single crystal rod The single crystal manufacturing apparatus is set so as to change in accordance with the length of the single crystal rod and to change in accordance with the change in the pulling speed of the single crystal rod in the process of forming the straight body portion. In a control method for a time-varying control target (200) having a dead time,
A target value (r) for the output value of the control object (200) and a plurality of system parameter setting values representing a plurality of system parameters of the control object (200) are stored, and all of the plurality of system parameter setting values are stored. Or a step that is set to have a predetermined time-varying characteristic;
Based on the stored system parameter setting value, the output value at the current time of the control target (200), and the past input value (u _T ), the future time (t + L) after the dead time from the present time ) Predicting a value of a predetermined state variable (x) including the output value;
Based on the target value (r) and the system parameter setting value at the stored future time (t + L), and the state variable (x) at the predicted future time (t + L) A sliding mode control operation is performed so as to constrain the state variable (x) at (t + L) to a sliding mode at a future time (t + L), and an operation value (u) to be applied to the controlled object (200) And a step of outputting the control method.

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