JP5585381B2 - Auto tuning device and auto tuning method - Google Patents

Description

  The present invention relates to an auto-tuning device and an auto-tuning method, and more particularly to an auto-tuning device and method for adjusting control parameters in a cascade control system.

  When disturbances such as fluctuations in manipulated variables are expected in the feedback control system, a cascade control method is known in which a control point is provided in the main control loop by providing a measurement point that can detect the disturbance. (For example, refer to Patent Document 1).

In such cascade control, since two PID controllers are used, two sets of PID parameters need to be adjusted. The two sets of PID constants need to be adjusted manually by the operator while checking the control response or on the slave side. In addition, the PID parameters are determined using the auto-tuning (AT) function mounted on each PID controller on the master side.
One method for auto-tuning control parameters is disclosed in, for example, Patent Documents 2 and 3.

Japanese Utility Model Publication No. 6-2402 JP-A-3-3005 JP 58-68106 A

However, since the master controller in the cascade control is a control system including the control system feedback-controlled by the slave-side PID controller and the master-side control object, even if auto-tuning is executed by the master controller, for example, It has been affected by the output saturation of the slave controller in the slave loop, and it has been difficult to obtain a good PID parameter.
In view of the above points, an object of the present invention is to obtain control parameters of cascade-connected PID controllers by auto-tuning.

First, the concept of processing for obtaining control parameters of the slave PID controller and the master PID controller will be described.
(1) based on the execution command of the auto-tuning, the slave control amount: PV _s or master control amount: having 2 position control unit for two-position control for PV _m.
First, the slave control amount: PV _s is two-position controlled with a preset slave target value, and the slave identification unit calculates the PID parameter of the slave controller from the limit cycle waveform generated by the two-position control. The slave controller often uses not only PID control but also P control. Even if a steady deviation occurs with respect to the slave target value as the P control in the slave loop, the steady deviation of the master control amount, which is the main control amount, can be eliminated if the important master controller has an integral operation. This is because it can be done.

但し、Ｋ_ｓはスレーブ側制御対象の定常ゲイン、Ｔ_ｓは等価時定数、Ｌ_ｓは等価むだ時間である。 (2) Next, the AT management unit changes the target value and again executes the two-position control on the slave side, whereby the slave identification unit (primary transfer function is set to G _s ) in the slave identification unit Identification is performed using a delay + dead time approximation model.

However, K _s is a steady gain of the slave side control target, T _s is an equivalent time constant, and L _s is an equivalent dead time.

で算出できる。 First, the steady gain of the slave side control target: K _s is SV _s1 which is the target value of the two-position control executed in the first AT operation, the duty ratio of ON / OFF is θ _s1 , and the two-position control executed in the second AT operation. When the target value is SV _s2 and the on / off duty ratio is θ _s2 ,

It can be calculated by

(3) Further, the limit gain: K _cs and limit period: T _cs of the slave-side control target are calculated from the limit cycle waveform at AT, and the equivalent time constant: T _s and the dead time equivalent to T _s : L _s are obtained by equation 3 Output to the PID parameter calculator.

(4) The target value for performing the second two-position control is a coefficient k of the limit cycle amplitude from the first SV _s1 value based on the amplitude of the limit cycle waveform obtained by the first two-position control. This can be determined by setting the value twice as the target value for the second time. The coefficient k can be predetermined. For example, when the amplitude of the limit cycle waveform obtained in the first AT is X _s1 , the second target value: SV _s2 is set to SV _s2 = SV _s1 −k × X _s1 or SV _s2 = SV _s1 + k ×. X _s1 may be used.

但し、Ｋ_ｍ：マスタ側制御対象の定常ゲイン
Ｔ_ｍ：等価時定数
Ｌ_ｍ：等価むだ時間
マスタ側制御対象の定常ゲイン：Ｋ_ｍは
Ｋ_ｍ＝（ＳＶ_ｍ１−ＳＶ_ｍ２）／（θ_ｍ１−θ_ｍ２）／Ｋ_ｓ … 式５
となる。但し、ＳＶ_ｍ１、θ_ｍ１は、１回目の２位置制御の目標値とオンオフデューティ比、ＳＶ_ｍ２、θ_ｍ２は、２回目の２位置制御の目標値とオンオフデューティ比であり、Ｋ_ｓは式１より求まるスレーブ側制御対象の定常ゲインである。 (5) When tuning on the slave side is completed, the two-position control unit executes two-position control on a master target value set in advance with respect to the master control amount: PV _m . Two-position control is performed for each of two different target values with respect to the master control amount, and the master identification unit performs master- side control from the limit cycle waveforms of the master control amount: PV _m and slave control amount: PV _s generated thereby. Get the target mathematical model. Master-side control object: If G _m is approximated by the following dead time + first order delay model,

However, _{K m:} constant gain in the master-side control object T _m: equivalent time constant L _m: equivalent dead time master side control object steady gain: _{K m} is _{K m = (SV m1 -SV m2} ) / (θ m1 - θ _m2 ) / K _s Equation 5
It becomes. Where SV _m1 and θ _m1 are the target value and on / off duty ratio of the first two-position control, SV _m2 and θ _m2 are the target value and on / off duty ratio of the second two-position control, and K _s is an equation 1 is a steady gain of the slave side control target obtained from 1.

但し、Ｋ_ｍ：マスタ側制御対象の定常ゲイン（式５から算出）
Ｔ_ｃｍ：リミットサイクル周期
Ｘ_ｓ：スレーブ制御量：ＰＶ_ｓのリミットサイクル波形の振幅
Ｘ_ｍ：マスタ制御量：ＰＶ_ｍのリミットサイクル波形の振幅
φ：スレーブ制御量：ＰＶ_ｓとマスタ制御量：ＰＶ_ｍのリミットサイクル波形の位相差 (6) Further, the master identification unit calculates a limit gain: K _cm and a limit period: T _cm of the master side control target, and obtains an identification result by obtaining an equivalent time constant: T _m and an equivalent dead time: L _m by the following equation. Output to the master PID parameter calculator.

However, K _m : Steady gain of the master side control target (calculated from Equation 5)
T _cm : limit cycle period X _s : slave control amount: amplitude of limit cycle waveform of PV _s X _m : master control amount: amplitude of limit cycle waveform of PV _m φ: slave control amount: PV _s and master control amount: PV Phase difference of limit cycle waveform of _m

但し、ｎはｎ＞０の自然数である。 (7) The master PID parameter calculation unit starts calculating the PID parameter of the master controller when the identification of the master side control target is completed.
First, the slave loop closed-loop transfer function: G _s ′ is calculated (FIG. 6). Slave side control target: G _s is approximated by the first order lag + dead time shown in Equation 2, but in general process control systems, it is often a higher order lag system than pure dead time. The dead time term is approximated by the following equation.

However, n is a natural number of n> 0.

As a result, the slave-side control target: G _s can be expressed by a higher-order system shown in Expression 8, and as a result, the slave-side closed loop transfer function: Gs ′ can be approximated as Expression 9.

(8) By the way, since the master controller is the control object, the transfer function: W shown in Expression 10 in which the slave side closed loop: G _s ′ and the master side control object: G _m are connected, this transfer function: the limit period of W If the limit gain is obtained, the PID parameter of the master controller can be obtained by applying the adjustment rule of Ziegler and Nichols.

このプラント：Ｈに対する周波数特性は、式１２および式１３に示すとおりであるため、制御対象：Ｈの限界ゲインをＫ_ｃとすると式１４が成立することになる。

従って、この方程式を解くことで限界周期：Ｔ_ｃ＝２π／ω_ｃと限界ゲイン：Ｋ_ｃを求めることが可能になる。 (9) Now, consider the plant: H in Formula 11 in which the controlled object expressed by the first order delay + dead time is connected in series.

The plant: Frequency characteristics for H, because is as shown in Formula 12 and Formula 13, can be controlled: when the limit gain of H and K _c Equation 14 will be established.

Therefore, by solving this equation, it is possible to obtain the limit period: T _c = 2π / ω _c and the limit gain: K _c .

As a means for solving the equation 14, first, the limit period: T _c or the limit angular frequency: ω _c is obtained from the phase characteristics using a numerical analysis method such as Newton's method, and then the equation 14 is used using the obtained limit angular frequency. limit from the gain characteristic equation gain: by obtaining the K _c, can be easily calculated even MCU mounted on a small PID controller.
As described above, if the control target of the master controller is expressed in the above-described form of the plant H and the limit gain and the limit period are obtained, the PID parameter of the master controller can be obtained by applying the adjustment rule of Ziegler / Nichols. it can.

のように展開し、分母：

を式７の分母：

で低次の項から除算することでむだ時間分を抽出し、さらに除算の商の１次の項を一次遅れの等価時定数として近似する。 (10) Therefore, the master PID parameter calculation unit converts the slave-side closed loop transfer function represented by the high-order delay system obtained by Equation 9 into a first-order delay + dead time model.
Even if a control system including a dead time is subjected to negative feedback, the response characteristic of the closed loop also includes a dead time.

Expands as the denominator:

Is the denominator of Equation 7:

Then, the dead time is extracted by dividing from the low-order term, and the first-order term of the quotient of the division is approximated as an equivalent time constant of the first-order lag.

  As a result, the control target for the master controller can be expressed in the form of Equation 11, and the limit gain and limit cycle of this control target can be calculated from the relationship of Equation 14, so that the PID parameter of the master controller can be determined.

According to the first solution of the present invention,
An auto-tuning device for performing auto-tuning for adjusting control parameters of the master controller and the slave controller in a cascade control system in which a master controller that performs PID control and at least a slave controller that performs P control are cascade-connected. And
An auto tuning management unit that receives an auto tuning execution command and determines a target value for auto tuning;
And second position control unit for each two-position control the slave control amount and the master control amount with respect to the auto-tuning target value set by the management unit,
From the slave control amount of limit cycle waveform generated by the second position control for the slave side, the slave controller obtains the control parameters of the slave system first order lag + dead time from your amount limit cycle waveform slave-side control object A slave identifying unit that identifies each mathematical model of the slave side control target by obtaining each parameter of the model that is mathematically approximated by the model;
From master control amount of limit cycle waveform generated by the two-position control for the master, the master-side control object to seek parameters of the model equation approximated by first-order lag + dead time model master-side control object mathematical model A master identification unit for identifying
Based on the control parameter of the slave controller obtained by the slave identification unit and the mathematical model of the slave side control object, a slave side closed loop transfer function between the slave side control object and the slave controller is obtained, and obtained by the master identification part. based on the obtained master side control object mathematical model, the product of the slave closed loop transfer function and the master side control object mathematical model as a control target of the master controller, the master control parameter for calculating a control parameter of the master controller There is provided the auto-tuning apparatus including a calculation unit.

According to the second solution of the present invention,
In a cascade control system in which a master controller that performs PID control and at least a slave controller that performs P control are cascade-connected, an auto-tuning method for performing auto-tuning that adjusts control parameters of the master controller and the slave controller,
In response to an auto tuning execution command, the target value for auto tuning is determined,
Each two-position control the slave control amount and the master control amount with respect to the determined target value,
From the slave control amount of limit cycle waveform generated by the two-position control for the slave obtains the control parameters of the slave controller, the slave control amount of the limit one slave-side control object from cycle waveform order lag + dead time model To identify each parameter of the model approximated by the mathematical formula to identify the mathematical model of the slave side control target,
From master control amount of limit cycle waveform generated by the two-position control for the master, the master-side control object to seek parameters of the model equation approximated by first-order lag + dead time model master-side control object mathematical model Identify and
Based on the calculated control parameter of the slave controller and the mathematical model of the slave side control object, a slave side closed loop transfer function between the slave side control object and the slave controller is obtained, and based on the obtained master side control object mathematical model The auto-tuning method is provided for calculating a control parameter of the master controller using a product of the slave-side closed loop transfer function and a mathematical model of the master- side control target as a control target of the master controller.

(11) According to the present invention, it is possible to automatically calculate control parameters for two cascade-connected PID controllers.

The block diagram of the cascade control system of this Embodiment. Cascade auto tuning process flow. The operation explanatory view at the time of cascade auto tuning. Explanatory drawing of the auto-tuning process and operation on the slave side. Explanatory diagram of auto-tuning processing and operation on the master side. Explanatory drawing of a closed loop transfer function.

(12) An embodiment of the present invention will be described below.
FIG. 1 is a block diagram of a cascade control system (cascade control system) showing an embodiment of the present invention.
The cascade control system includes, for example, a control unit 1, an auto tuning processing unit (AT processing unit) 2, a parameter determination unit 3, and control objects 9 and 10. Controlled object, the slave-side control object 9: and _{G s,} the master-side control object 10: are described as _{G m.}

Control unit 1 in FIG. 1, the target value: SV and the master control amount: master PID controller for outputting an operation amount based on a difference between the PV _m 4: and C _m, as a target value the operation amount of the master PID controller 4 A slave PID controller 5: C _s which performs control calculation so as to eliminate the difference between the target value and the slave control amount: PV _s and calculates an operation amount: MV, and a selector switch 6 which switches the operation amount by PID control and auto-tuning Have This change-over switch 6 is operated by an auto-tuning management unit (AT management unit) 7 to be described later. The switch contact is set to the a side (controller side) during normal control, and the contact is set to the b side (when performing auto-tuning). Switch to the AT processing unit side).

(13) Next, the AT processing unit 2 operates based on an AT command from a management device or the like operated by an operator, and an AT management unit 7 that determines a target value for two-position control in auto-tuning, and an AT management unit 7 And a two-position control unit 8 that performs two-position control on the determined target value. The initial value of the target value for the two-position control can be determined in advance, and may be the same as or different from the control target SV.

(14) Further, the parameter determination unit 3 determines and outputs the PID parameter of the slave PID controller 5 from the two-position control result for the slave control amount: PV _{s and} sets the slave-side control target 9 in the first order delay + dead time model. Approximate and identify the slave identification unit 11 for identifying each parameter of the model, and approximate the master-side control target 10 from the two-position control result with respect to the master control amount: PV _m by a first order delay + dead time model. A master identification unit 12 that identifies each parameter, and a master PID parameter calculation unit (master control parameter calculation unit) 13 that inputs the approximate models of the slave side and the master side control target, calculates and outputs the PID parameters of the master PID controller, and Have.

  In the present embodiment, the slave PID controller 5 is not limited to PID control, and may be, for example, a controller that performs at least one of P control, PI control, and PD control and that includes at least P control. The slave PID controller 5 and the master PID controller 4 may be simply referred to as a slave controller or a master controller in the present embodiment. The required PID parameters (control parameters) are, for example, parameters such as proportional gain (P element), integration time (I element), derivative time (D element), etc. When the slave controller performs only P control, for example. , The control parameter of the corresponding P element is obtained.

(15) Processing will be described below according to the flowchart.
FIG. 2 shows the processing flow of cascade auto tuning, and FIG. 3 shows the operation during cascade auto tuning. FIG. 4 shows the operation of auto tuning on the slave side. FIG. 4 is an enlarged view of the left end portion of FIG.

First, the slave side auto-tuning process and operation (FIG. 4) will be described.
When the AT management unit 7 of the AT processing unit 2 receives an auto-tuning execution command, the AT management unit 7 sets the changeover switch 6 to the b side (AT processing unit 2 side), and the 2-position control unit 8 sets in advance. The slave control amount: PV _s is controlled by two positions with respect to the target value: SV _S1 (flow f1). Since the number of on / off switching of the two-position control is set in advance, the first slave-side tuning process is terminated when the set number of on / off switching ends (flow f2). In the example of FIG. 3 and FIG. 4, the number of on / off switching is set to 5 as an example.

When the first slave tuning process is completed, the slave identification unit 11 calculates the PID parameter of the slave controller 5 based on the operation amount: MV and slave control amount: PV _s in the current process and sets the slave controller 5 in the slave controller 5 ( Further, the on / off duty ratio: θ _S1 is calculated and stored until at least the second slave-side tuning process is completed and the calculation of the approximate model of the slave-side control target Gs is completed (flow f4). .

Note that the PID parameter on the slave side can be obtained by applying the adjustment rule of Ziegler / Nichols. The on / off duty ratio can be calculated by using, for example, θ _s1 = tb / (ta + tb) for ta and tb in FIG. The slave side of cascade control is mainly intended to perform dynamic compensation for disturbances, so P control may be used.

(16) Further, the 2-position control unit 8 performs the second slave-side 2-position control based on the slave control amount: PV _s limit cycle waveform amplitude: X _S1 generated by the first 2-position control. : SV _S2 is calculated (flow f5).
In the example of FIG. 3, the control point SV _S2 = SV _S1 −2X _S1 obtained by subtracting a value twice the amplitude of the limit cycle waveform generated by the first slave-side two-position control is set as the second target value. Yes.

(17) when the target value SV _s2 slave second auto-tuning is determined, two-position control unit 8, the first as well as preset by off times again slave control amount with respect to the target value : Two-position control of PV _s is executed (flow f6, flow f7).
When the second slave-side auto-tuning is completed, the slave identification unit 11 determines the limit gain: K _cs and the limit of the slave-side control target calculated from the ON / OFF duty ratio of the two-position control: θ _S2 and the limit cycle waveform in the current process. The mathematical model of the slave side control target is calculated from the period: T _cs (flow f8). More specifically, the slave identification unit 11 calculates the approximate values of the parameters of the steady gain K _s , the equivalent time constant T _s , and the equivalent dead time L _{s in} the first-order lag + dead time model (Equation 2), as in Equations 1 and 3. Respectively, and output to the master PID parameter calculation unit 13.

Since the steady gain: K _s > 0, the limit gain: K _cs > 0, and the limit period: T _cs > 0, the time constant: T _s > 0, and tan ⁻¹ (x) <π / 2. Therefore, the dead time: L _s > 0.
As a method for obtaining a limit gain and a limit period from a limit cycle waveform generated by two-position control, a method using a description function is known. For example, this method can also be used in this embodiment.

Further, Expression 3 pays attention to the condition that the first order delay + dead time model is continuously oscillating, that is, the gain characteristic of the loop transfer function of the slave loop is 0 db and the phase characteristic is delayed by 180 degrees, and the time constant is T _s . The time L _s is obtained.
With the above processing, the two-position control is performed twice on the slave side, whereby the control parameters of the slave controller and the parameters in the approximate expression of the first order delay + dead time model of the slave side control target can be obtained.

(18) When the tuning process on the slave side ends, the AT management unit 7 sets the preset target value: SV _m1 to the two-position control unit 8 in order to perform two-position control on the master control amount: PV _m . Output. As the target value SV _m1 , the same value as the SV _{s1 in} the tuning on the slave side may be used, or a different value may be set in advance.

The two-position control unit 8 performs two-position control on the target value: SV _{m1 so} that the manipulated variable is turned on and off the master control amount: PV _m a specified number of times (flow f9, flow f10).
When the specified number of on / off operations for the master control amount are completed, the master identification unit 12 calculates an on / off duty ratio: θ _m1 in the two-position control based on the operation amount MV and the master control amount PV _m in the current process, Store (flow f12). Further, the 2-position control unit 8 calculates a target value: SV _m2 for performing the second master-side 2-position control from the amplitude: X _m1 of the limit cycle waveform of the master control amount: PV _m (flow f13). In the example of FIG. 3, the second target value: SV _m2 is set to SV _m2 = SV _m1 -2X _m1 .

(19) when the target value of the master-side second time determined, two-position control unit 8, the first as well as the target value: the master control amount to the SV _{m @ 2:} performing predetermined number of times by two position control PV _m ( Flow f14, flow f15).
When the second master auto-tuning is completed, the master identification unit 12 performs the two-position control on / off duty ratio shown in FIG. 5 based on the operation amount MV, the master control amount PV _m, and the slave control amount PV _s in the current process: θ _m2 , limit cycle period: T _cm , master control amount amplitude: X _m , slave control amount amplitude: X _s , phase difference between slave control amount and master control amount: φ measurement results are obtained, and these measurement results Then, the steady-state gain: K _m , time constant: T _m , and dead time: L _m when the master side controlled object 10 is approximated by the first order delay + dead time model (Formula 4) are calculated according to Formula 5 and Formula 6, It outputs to the master PID parameter calculation part 13 (flow f16).

(20) Master PID parameter calculation unit 13, and the parameters of the slave-side control object mathematical model shown in Equation 2 which is output from the slave identification unit 11, the master-side control shown in Equation 4, which is outputted from the master identification unit 12 The PID parameter of the master controller 4 is derived from each parameter of the target mathematical model.

なお、スレーブコントローラがＰ制御ではなくＰＤ制御やＰＩ制御、ＰＩＤ制御の場合も、同様の手続きで処理を行えばよい。 First, using the dead time term is approximated by Equation 7, the transfer function of the slave-side control object 9 which approximates the term dead time order lag system of the transfer function of the slave-side control object 9 represented by the formula 2 The slave side closed loop transfer function shown in Equation 9 is derived.
When the slave controller is set to P control with proportional gain: K _ps , the closed-loop transfer function: G _s ′ expressed by Expression 9 is expressed by Expression 17 (flow f17).

In addition, when the slave controller is not P control but PD control, PI control, or PID control, the same procedure may be used.

なお、スレーブコントローラがＰＤ制御やＰＩ制御、ＰＩＤ制御の場合、Ｐ制御の場合と同様にスレーブ側閉ループ伝達関数Ｇ_ｓ’の分母を式７の分母で除算することで式７のむだ時間相当分の抽出とＧ_ｓ’の分母の低次元化を行えばよい。 (21) Next, the master PID parameter calculation unit 13 divides the denominator of Expression 17 by the denominator of Expression 7 in order to transform the slave-side closed loop transfer function expressed by Expression 17 into a first-order delay + dead time format. Extraction and reduction in dimension corresponding to the dead time in Expression 7 are performed (Expression 18, Expression 19) (Flow f18).

When the slave controller is PD control, PI control, or PID control, the dead time equivalent to Equation 7 is obtained by dividing the denominator of the slave-side closed loop transfer function G _s ′ by the denominator of Equation 7 as in the case of P control. And lowering the denominator of G _s ′.

However, the slave closed loop transfer function G _{s 'if} the molecule is a polynomial of Laplace operator S is the slave closed loop transfer function G _s' is not a first-order lag + dead time format, limit cycle, the limit gain It can be calculated by the Newton method. For example, when the slave controller is PID controlled, the result of extracting the dead time of the slave-side closed loop transfer function G _s ′ and reducing the denominator is shown.

以降、式導出を簡単化するため、Ｐ制御の場合とＰＩＤ制御の場合について説明するがスレーブコントローラがＰＤ制御やＰＩ制御の場合も同様の手続きを行えばよい。 When the slave controller is set to PID control with a proportional gain: K _ps , an integration time: T _is , and a differential time: T _ds , the slave side closed loop transfer function G _s ′ is expressed by Equation 20.

Hereinafter, in order to simplify formula derivation, the case of P control and the case of PID control will be described. However, the same procedure may be performed when the slave controller is PD control or PI control.

となり、上記の式１４の条件より限界周期：Ｔ_ｃ＝２π／ω_ｃと限界ゲイン：Ｋ_ｃを求めることができる。 (22) By the above processing, when the slave controller is in the P control, the control object H to be controlled by the master controller: H is obtained from Equation 19 and Equation 4.

Thus, the limit period: T _c = 2π / ω _c and the limit gain: K _c can be obtained from the condition of the above-described Expression 14.

となり、Ｐ制御の場合と同様に限界周期：Ｔ_ｃと限界ゲイン：Ｋ_ｃを求めることができる。 When the slave controller is in PID control, the control target controlled by the master controller: H is

Next, similarly limits the period in the case of P control: T _c and the limit gain: it is possible to obtain the K _c.

式２３を

とおくと、Ｌ_ｓ＞０、Ｌ_ｍ＞０、Ｆ（ω_ｃ）は微分可能であることから、ニュートン法等を利用することにより限界角周波数：ω_ｃを求めることができる。なお、ニュートン法以外にも適宜の数値計算手法を用いてもよい。なお、式２４を微分すると以下のようになる。

なお、ω_ｃ＝２π／Ｔ_ｃで有るため、限界周期：Ｔ_ｃ＝２π／ω_ｃとなる（フローｆ１９）。 (23) First, when the slave controller is in the P control, since the equation 23 is established from the frequency equation of the control target: H, the limit angular frequency: ω _c is calculated therefrom.

Equation 23

Since L _s > 0, L _m > 0, and F (ω _c ) are differentiable, the limit angular frequency: ω _c can be obtained by using the Newton method or the like. In addition to the Newton method, an appropriate numerical calculation method may be used. In addition, when Expression 24 is differentiated, it is as follows.

Since ω _c = 2π / T _c , the limit cycle is T _c = 2π / ω _c (flow f19).

式２６を

とおくと、Ｌ_ｓ＞０、Ｌ_ｍ＞０、Ｆ（ω_ｃ）は微分可能であることから、Ｐ制御の場合と同様にニュートン法等を利用することにより限界角周波数：ω_ｃを求めることができる。なお、式２７を微分すると以下のようになる。

Further, when the slave controller is under PID control, since the equation 26 is established from the frequency equation of the control target: H, the limit angular frequency: ω _c is calculated from this.

Equation 26

Since L _s > 0, L _m > 0, and F (ω _c ) are differentiable, the critical angular frequency: ω _c is obtained by using the Newton method or the like as in the case of P control. be able to. In addition, when the expression 27 is differentiated, it is as follows.

また、スレーブコントローラがＰＩＤ制御の場合には、制御対象：Ｈのゲイン方程式より式３０が成り立つため、式３０に求まった限界角周波数：ω_ｃを代入し、式１４を用いることで、限界ゲイン：Ｋ_ｃを求めることができる。

(24) Next, when the slave controller is in P control, Equation 29 is established from the gain equation of the control target: H, and therefore, the limit angular frequency ω _c obtained in Equation 29 is substituted and Equation 14 is used. in the limit gain: it can be obtained _{K c} (flow f20).

Further, when the slave controller is under PID control, Expression 30 is established from the gain equation of the control target: H. Therefore, the limit angular frequency: ω _c obtained by Expression 30 is substituted and Expression 14 is used to obtain the limit gain. : it is possible to determine the _{K c.}

(25) the transfer function: it is possible to obtain the PID parameters of the master PID controller by limiting the period _{T c} and the limit gain _{K c} is applicable to for example the adjustment rule Ziegler · Nichols Motomare of H, master PID parameter calculation The unit 13 sets the PID parameter thus obtained in the master PID controller 4 and ends the auto-tuning process (flow f21).

(Configuration example)
In the cascade auto-tuning method of the present embodiment, for example, the system
A master PID controller and a slave PID controller connected in cascade;
Auto-tuning: Upon receipt of an AT execution command, an operation amount selector switch is operated so that an operation amount for the AT is output to the control target, and an AT management unit that determines a target value for executing the AT;
And second position control unit for two-position control the slave control amount and the master control amount to the target value set by the AT management unit,
A slave identification unit that mathematically approximates the PID parameter of the slave PID controller and the slave-side control target by a first order delay + dead time model from a limit cycle waveform generated by two-position control on the slave side;
A master identification unit that mathematically approximates a master side control target with a first order delay + dead time model from a limit cycle waveform generated by two-position control on the master side ;
Comprising a master PID parameter calculation unit for calculating a PID parameter of the master PID controller from the mathematical model and the master side control object mathematical model of the slave-side control object,
The slave side control target is approximated by a first order delay + dead time model.

In addition, for example, the master side control target is approximated by a first order delay + dead time model by the above-described cascaded auto tuning method.
Also, for example, in the above cascaded auto-tuning method, the slave- side control target dead time term is approximated by a high-order delay system to obtain the slave-side closed loop transfer function, and the obtained closed-loop transfer function is approximated by a high-order delay system. It is characterized by extracting the dead time term and approximating the closed-loop transfer function with a first order delay + dead time model.

Further, for example, in the above-described cascade autotuning method, when the master and slave control object is the first-order lag + dead time model, the limit gain and limit cycles using a numerical analysis method according to Newton's method from the frequency characteristics of the controlled object It is characterized in that a calculation PID parameter is calculated.

  The present invention can be used, for example, in a cascade control system in which two controllers are cascade-connected.

1 Control unit 2 Auto tuning processing unit (AT processing unit)
3 Parameter determination unit 4 Master PID controller 5 Slave PID controller 6 Changeover switch 7 Auto tuning management unit (AT management unit)
8 2-position control unit 9 slave-side control target 10 master-side control target 11 slave identification unit 12 master identification unit 13 master PID parameter calculation unit (master control parameter calculation unit)

Claims (5)

An auto-tuning device for performing auto-tuning for adjusting control parameters of the master controller and the slave controller in a cascade control system in which a master controller that performs PID control and at least a slave controller that performs P control are cascade-connected. And
An auto tuning management unit that receives an auto tuning execution command and determines a target value for auto tuning;
And second position control unit for each two-position control the slave control amount and the master control amount with respect to the auto-tuning target value set by the management unit,
From the slave control amount of limit cycle waveform generated by the second position control for the slave side, the slave controller obtains the control parameters of the slave system first order lag + dead time from your amount limit cycle waveform slave-side control object A slave identifying unit that identifies each mathematical model of the slave side control target by obtaining each parameter of the model that is mathematically approximated by the model;
From master control amount of limit cycle waveform generated by the two-position control for the master, the master-side control object to seek parameters of the model equation approximated by first-order lag + dead time model master-side control object mathematical model A master identification unit for identifying
Based on the control parameter of the slave controller obtained by the slave identification unit and the mathematical model of the slave side control object, a slave side closed loop transfer function between the slave side control object and the slave controller is obtained, and obtained by the master identification part. A master control parameter that calculates a control parameter of the master controller based on the master-side control target mathematical model, with the product of the slave-side closed loop transfer function and the master-side control target mathematical model as the control target of the master controller The auto-tuning apparatus comprising a calculation unit. The master control parameter calculation unit
The slave-side controlled loop is approximated by a high-order delay system to obtain a slave-side closed-loop transfer function, and the slave-side closed loop is extracted from the obtained closed-loop transfer function by approximating the dead-time term approximated by a high-order delay system. Further approximate the transfer function with a first order delay + time delay model,
2. The control target of the master controller is represented by a product of the slave side closed loop transfer function approximated by a first order delay + dead time model and a mathematical model of the master side control target. Oh-tuning device. The master control parameter calculation unit
For the control object of the master controller, a limit gain and a limit period are obtained from the frequency characteristics of the control object of the master controller using a Newton method or other numerical analysis method, and a PID parameter that is a control parameter of the master controller is calculated. O-tuning device according to claim 2, characterized in that. It further includes a changeover switch for switching the connection destination for inputting the operation amount to the control target,
The auto tuning management unit
When receiving the auto tuning execution command, the switch is operated so that the operation amount from the two-position control unit for auto tuning is output to the control target,
After auto-tuning, O-tuning device according to any one of claims 1 to 3 operation amount from the slave controller operates the change-over switch so as to be output to the controlled object. In a cascade control system in which a master controller that performs PID control and at least a slave controller that performs P control are cascade-connected, an auto-tuning method for performing auto-tuning that adjusts control parameters of the master controller and the slave controller,
In response to an auto tuning execution command, the target value for auto tuning is determined,
Each two-position control the slave control amount and the master control amount with respect to the determined target value,
From the slave control amount of limit cycle waveform generated by the two-position control for the slave obtains the control parameters of the slave controller, the slave control amount of the limit one slave-side control object from cycle waveform order lag + dead time model To identify each parameter of the model approximated by the mathematical formula to identify the mathematical model of the slave side control target,
From master control amount of limit cycle waveform generated by the two-position control for the master, the master-side control object to seek parameters of the model equation approximated by first-order lag + dead time model master-side control object mathematical model Identify and
Based on the calculated control parameter of the slave controller and the mathematical model of the slave side control object, a slave side closed loop transfer function between the slave side control object and the slave controller is obtained, and based on the obtained master side control object mathematical model The auto-tuning method for calculating a control parameter of the master controller using a product of the slave-side closed loop transfer function and a mathematical model of the master-side control target as a control target of the master controller.

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