WO2008018496A1 - Procédé de commande et dispositif de commande - Google Patents

Procédé de commande et dispositif de commande Download PDF

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Publication number
WO2008018496A1
WO2008018496A1 PCT/JP2007/065510 JP2007065510W WO2008018496A1 WO 2008018496 A1 WO2008018496 A1 WO 2008018496A1 JP 2007065510 W JP2007065510 W JP 2007065510W WO 2008018496 A1 WO2008018496 A1 WO 2008018496A1
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WO
WIPO (PCT)
Prior art keywords
control
transfer function
output
value
deviation
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PCT/JP2007/065510
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English (en)
Japanese (ja)
Inventor
Zenta Iwai
Ikuro Mizumoto
Sirish L. Shah
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National University Corporation Kumamoto University
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Publication date
Application filed by National University Corporation Kumamoto University filed Critical National University Corporation Kumamoto University
Priority to JP2008528852A priority Critical patent/JP4982905B2/ja
Publication of WO2008018496A1 publication Critical patent/WO2008018496A1/fr

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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators

Definitions

  • the present invention relates to a control method and a control apparatus that feed back an output of a control target.
  • a PID control method is widely known as a control method for controlling an output of a controlled object to follow a target value when the output of the control object changes with time!
  • This PID control is equipped with proportional control, integral control, and derivative control. By adjusting these three parameters, better control results are intuitive. It is an extremely field-oriented control method. Therefore, 85-90% of the existing control devices use the lever PID control method! /, And!
  • proportional control is to control the input value as a linear function of the deviation between the output value and the target value, and when the value of the coefficient (proportional gain Kp) of the linear function is constant.
  • the input value is uniquely determined for the output value.
  • integral control when there is a deviation (residual deviation) between the output value and the target value, the input value is changed in proportion to the duration of the deviation.
  • the coefficient (integral gain Ki) that multiplies the integral value of the deviation increases the contribution of the integral control in PI control that combines proportional control and integral control, and the residual deviation is corrected. Can be done quickly.
  • differential control is to change the input value in proportion to the derivative of the deviation when there is a deviation (residual deviation) between the output value and the target value.
  • the coefficient that multiplies the derivative of the deviation (differential gain Kd) in PID control the greater the value, the greater the contribution of the differential control, and it is possible to quickly cope with fluctuations in the residual deviation.
  • the differential gain is too large, this time, it will fluctuate in the opposite direction and the control may become unstable.
  • Gp (s) is a transfer function to be controlled (variable s is a complex number ⁇ + j ⁇ ).
  • Process gain ⁇ is the ratio of the change in input value to the change in output value
  • time constant ⁇ is the rate of change after the response starts.
  • Dead time L is the time required for the output value to start responding when the input value is changed stepwise.
  • a PID controller is provided with a model to be controlled (internal model), and the PID parameter is adjusted so that the output value matches the input value.
  • IMC internal model control
  • a model that is modeled by the first-order lag element and the dead time L is used as the model to be controlled.
  • Non-Patent Document 1 G.J.Silva, A.Dattaand S.P. Bhattacharyya: PID Controllers for Time-Delay Systems, BirkhauserBoston, 2005.
  • Non-Patent Document 2 Astrom and Hagglund: PID Controllers; Theory, Design, and Tuning (2nd Ed.), Instrument Society of America, 1995.
  • Non-Patent Document 3 M. Morari and E. Zafiriou, Robust Process Control, Prentic-Hall, 1998
  • Non-Patent Document 4 F.G.Shinskey, Process Control Systems, MacGraw-Hill, 1996.
  • Non-Patent Document 5 Yasushi Baba, Takashi Shigemasa, Fumio Kojima: Model Driven PID Control, Toshiba Review, Vol.
  • Non-Patent Document 6 Takashi Shigemasa and others 3: Model-driven PID control and its tuning method, Proceedings of the 46th Automatic Control Union Conference, 549-552, 2003.
  • Non-Patent Document 7 Nobuhide Suda (Author): PID Control, System Control Information Society, Asakura Shoten, 1992
  • Patent Document 1 Japanese Patent Laid-Open No. 06-149308
  • Patent Document 2 Japanese Patent Laid-Open No. 2002-532164
  • Patent Document 3 Japanese Patent Laid-Open No. 2002-149204
  • Patent Document 4 Japanese Patent Laid-Open No. 2003-58213
  • Non-Patent Documents 1 to 6 are applicable only to control symmetry that can be modeled by the first-order lag element and the dead time L.
  • control targets that are difficult to model due to dead time L, or for control targets that have a large error from the actual target system even if modeling is based on first-order lag elements and dead time L control Control performance such as system stability, robustness to disturbances, and optimal response cannot be maintained.
  • the PID parameter is indirectly adjusted using the estimated system parameter, so that the control system may become unstable depending on the system parameter fluctuation situation. May be.
  • the control system may become unstable depending on the situation of fluctuations in system parameters.
  • the present invention has been made in view of power and problems, and the purpose of the present invention is to maintain the stability of the control system without obtaining a model to be controlled accurately, and at the same time against disturbances and the like. It is an object of the present invention to provide a control method and a control device capable of maintaining control performance such as robustness and optimal response.
  • the control method of the present invention is a method for controlling a controlled object by a control device including a parallel IJ feedforward compensation unit, and includes the following steps (A) and (B).
  • Deviation (e (t)) between the target value r (t) and the output y (t) of the control target is also the set value (one ya (t)) obtained by subtracting the compensation value yf (t) , Control deviation V (t) using proportional gain kp (t), integral gain ki (t) and differential gain kd (t) adaptively determined using set value (one ya (t))
  • the control apparatus of the present invention includes an adaptive PID parameter adjustment unit and a parallel feedforward compensation unit.
  • the adaptive PID parameter adjustment unit subtracts the compensation value yf (t) output from the feedforward compensation unit from the deviation (one e (t)) between the target value r (t) and the output y (t) to be controlled.
  • the proportional gain kp (t), integral gain ki (t) and differential gain kd determined adaptively using the set value (one ya (t)) and the set value (one ya (t))
  • the control deviation v (t) calculated using (t) is output.
  • the parallel IJ feedforward compensation unit controls the transfer function Gpfc (s) obtained by subtracting the transfer function Gaspr (s) of the almost strong model from the approximate transfer function Gp * (s) to be controlled.
  • the compensation value yf (t) obtained by inputting the deviation v (t) is output! /.
  • the transfer function Gpfc (s) of the parallel I] feedforward compensation unit is obtained from the approximate transfer function Gp * (s) of the control target. It is composed of functions obtained by subtracting Gaspr (s). This gives an approximate transfer function G As long as p * (s) can be obtained, the characteristics of the extended system that combines the controlled object and the parallel feedforward compensator can be realized.
  • Gaspr (s) is almost positive and positive
  • the real part of l / (l + kGas pr (s)) is positive in all s where the real part is positive. This indicates that there is a feedback gain k.
  • the closed-loop frequency response of the expansion system always appears on the right half of the complex plane due to feedback of a certain magnitude or greater. Even if you give feedback, it will not become unstable.
  • the deviation (one e (t)) between the target value r (t) and the output y (t) to be controlled is reduced by the force compensation value yf (t). calculated using the proportional gain kp (t), integral gain ki (t), differential gain kd (t), and the set value (-ya (t)), which are adaptively determined using ya (t))
  • the control deviation v (t) force calculated is input to the transfer function Gpfc (s) of the IJ feedforward compensator.
  • the expansion system having almost positive realness is proportional to the proportional gain kp (t), the integral gain ki (t), and the differential gain that are adaptively determined according to the output deviation ya (t) of the expansion system. Controlled using kd (t).
  • an extended system having a strong positive realness which is a combination of the controlled object and the parallel feed-forward compensation unit, is obtained according to the output deviation ya (t) of the expanded system. Since the control is performed using the adaptively determined proportional gain kp (t), integral gain ki (t), and differential gain kd (t), the output of the controlled object can be stabilized. In addition, even if there is an error between the approximate transfer function Gp * (s) of the controlled object and the model (transfer function Gp (s)) of the actual controlled object, such error is adaptively applied. The model of the actual control object (transfer function Gp (s)) Even if it is not calculated accurately, it is possible to maintain control performance such as robustness to disturbances and optimal response.
  • control method and control apparatus of the present invention can maintain the stability of the control system without accurately obtaining the model to be controlled, and at the same time, robustness to disturbances and the optimality of response. Control performance such as can be maintained.
  • FIG. 1 is a functional block diagram of a control device according to an embodiment of the present invention.
  • Fig. 2 is a relational diagram showing temporal changes in the output of the controlled object in the control device according to the embodiment.
  • FIG. 3 is a relational diagram showing temporal changes of three PID parameters in the control device according to the embodiment.
  • FIG. 4 is a relational diagram showing the time change of the output of the controlled object in the control device according to the example and the comparative example.
  • FIG. 5 is a relationship diagram showing control performance deterioration in the control devices according to the example and the comparative example.
  • FIG. 1 shows the configuration of a control device 1 according to an embodiment of the present invention for each functional block.
  • This control device 1 controls the output y (t) of the controlled object 2 to follow the target value r (t) by PID control, which is a kind of feedback control. 11, an adder 12, a PID controller 13, and a parallel feedforward compensator 14.
  • the PID controller 13 includes an adaptive PID parameter adjustment unit 15 and an internal model 16.
  • the block diagram is configured so that the characteristic of the controlled object 2 is changed by adding the disturbance d (t) to the operation output u (t) of the control device 1. ing.
  • the target value input unit 10 is configured by, for example, a keyboard and a mouse. This target value input unit 10 is connected to the input terminal of the subtraction unit 11 and is connected to the output y (t) of the control target 2. In response to the input of the target value r (t), the input target value r (t) is output to the subtractor 11.
  • the subtraction unit 11, the addition unit 12, the PID controller 13, and the parallel feedforward compensation unit 14 are configured by, for example, a program describing these various functions, and the program is processed by a CPU of a computer or the like. As a result, these various functions are developed.
  • the input end is connected to the output end of the target value input unit 10 and the output end of the control target 2, and the output end is connected to the input end of the addition unit 12.
  • the input end is connected to the output end of subtraction unit 11 and the output end of parallel feedforward compensation unit 14, and the output end is connected to the input end of adaptive PID parameter adjustment unit 15. Yes.
  • the input end is connected to the output end of the addition unit 12, and the output end is connected in parallel.
  • the feedforward compensation unit 14 and the internal model 16 are connected to the input ends, respectively.
  • This adaptive PID parameter adjustment unit 15 integrates proportional control (P control) that controls the control deviation v (t) as a linear function of the set value (-ya (t)) and the set value (-ya (t)). Integral control (I control) that changes the control deviation V (t) in proportion to, and differential control (D) that changes the control deviation v (t) in proportion to the set value (-ya (t)) Control) and PID control.
  • P control proportional control
  • I control Integral control
  • D differential control
  • control deviation v (t) calculated using the set value (one ya (t)), proportional gain kp (t), integral gain ki (t), and differential gain kd (t) (below are output to the parallel feedforward compensator 14 and the internal model 16, respectively.
  • v (t) -k p (t) y a (t) -k d (t) ⁇ - ⁇ — k ⁇ t)! y a (t) dt... Equation (1)
  • the proportional gain kp (t) is a variable parameter in proportional control (P control)
  • the integral gain ki (t) is a variable parameter in integral control (I control)
  • the differential gain kd (t) Is a variable parameter in differential control (D control).
  • this adaptive PID parameter adjustment unit 15 has an unknown part in the model of control target 2 (identification of control object 2 structure and parameters ⁇ t), and therefore determines the above three PID parameters. If it is not possible! /, The three PID parameters are determined adaptively using the set value (one ya (t)). That is, it is determined using the general formulas (2) to (4) shown below.
  • ⁇ is a positive definite symmetric matrix called the adjustment law gain matrix.
  • a positive definite symmetric matrix is one in which the transposed matrix ⁇ ⁇ of the square matrix A of the square matrix A matches the square matrix A itself, and the square matrix A is an arbitrary vector x (x ⁇ 0) On the other hand, it satisfies x T Ax> 0.
  • parallel feedforward compensation unit 14 the input end is connected to the output end of adaptive PID parameter adjustment unit 15, and the output end is connected to the input end of addition unit 12.
  • sup ⁇ in equation (10) means the maximum singular value in the entire frequency range.
  • the input end is connected to the output end of the adaptive PID parameter adjustment unit 15, and the output end is connected to the input end of the controlled object 2 via the addition unit 3.
  • This internal model 16 has a transfer function that ensures that tracking of the output of the expansion system to the target value r (t) guarantees tracking of the actual output y (t) of the controlled object 2 to the target value r (t). 1 / D (s)).
  • the operation output u (t) calculated by inputting the control deviation v (t) to the transfer function (1 / D (s)) is output to the controlled object 2 via the adder 3. Become! / If u (t) is expressed using v (t), the following equations (11) to (; 12) are obtained. Note that d / dt in equation (12) is a fractional operator.
  • the actual output y (t) of the controlled object 2 is a disturbance satisfying the above equation (14). Even if exists, the target value r (t) that satisfies Equation (13) can be followed. In other words, when the disturbance d (t) passes through the internal model 16, the disturbance d (t) disappears. In addition, if the target value r (t) passes through the internal model 16, the target value r (t) can be apparently erased, and as a result, the influence from the parallel IJ feedforward compensation unit 14 can be removed. it can.
  • D (s) is set to 1, as described above, the force S to cause the actual output y (t) of the controlled object 2 to follow the target straight r (t) that changes in a stepwise manner.
  • a deviation (one e (t)) is calculated by subtracting the output y (t) of the control target 2 from the input target value r (t).
  • a set value (one ya (t)) is calculated by subtracting the compensation value yf (t) from the deviation (one e (t)).
  • the set value (one ya (t)) is used to adaptively determine the proportional gain kp (t), integral gain ki (t), and differential gain kd (t). 1 ya (t)), proportional gain kp (t), integral gain (t), and differential gain kd (t) are used to calculate control deviation v (t).
  • the transfer function Gpfc of the parallel IJ feedforward compensator 14 obtained by subtracting the transfer function Gas pr (s) of the roughly strong positive model from the approximate transfer function Gp * (s) of the controlled object 2
  • the compensation value yf (t) is calculated by inputting the control deviation v (t) in (s).
  • the output y (t) of the controlled object 2 is converted into the disturbance d (t ) Will change according to the value added.
  • the output y (t) of the controlled object 2 is immediately fed back to the adaptive PID parameter adjusting unit 15, and the operation output u that acts to mitigate the influence of the disturbance d (t). (t) is output from the PID controller 13.
  • the compensation value yf (t) is calculated by subtracting the compensation value yf (t) from the deviation (one e (t)) between the target value r (t) and the output y (t) to be controlled.
  • the proportional gain kp (t), integral gain ki (t), and differential gain kd (t) that are adaptively determined using the set value (one ya (t)) and the set value (one ya (t) )
  • the control deviation v (t) force calculated using the IJ feedforward compensation unit 14 transfer function Gpfc (s).
  • the expansion system having almost positive realness is proportional to the proportional gain kp (t) and the integral gain ki (t) that are adaptively determined according to the output deviation ya (t) of the expansion system. And the differential gain kd (t).
  • the controlled object Even if there is an error between the approximate transfer function Gp * (s) of the model and the actual control target model (transfer function Gp (s)), such errors must be absorbed adaptively. Therefore, it is possible to control the robustness against disturbances and the optimality of response without accurately obtaining the actual control target 2 model (transfer function Gp (s)) for all control targets. Performance can be maintained.
  • the stability of the control system can be maintained without accurately obtaining the model of the control target 2, and at the same time, control performance such as robustness to disturbances and optimal response Can keep.
  • Fig. 2 represents a time change of the output y (t) of the control target 2 in the present embodiment.
  • FIG. 3 (A) to (C) show the time changes of the three PID parameters in this example.
  • Figure 2 shows that the output y (t) was able to accurately follow the set value (one ya (t)).
  • Figure 3 also shows that the influence of the disturbance d (t) was able to be accurately canceled because the fluctuations of the three PID parameters were small.
  • Fig. 4 shows the output y (( The time change when t) is made to follow the set value (one ya (t)) is shown in comparison with the result of this example.
  • the values of the three PID parameters in each control method are shown in Table 1. From Fig. 4, it can be seen that this example is superior to other control methods.
  • Fig. 5 shows poor control performance when 50% fluctuation occurs in the parameter of control target 2. This embodiment is shown in comparison with the above control methods. From Fig. 5, it is clear that this example has less control performance degradation than other control methods.

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  • Engineering & Computer Science (AREA)
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Abstract

Un moyen (15) de réglage adaptatif de paramètre PID génère une différence de commande v(t) à partir d'une valeur de consigne -ya (t) représentant la somme d'une valeur compensée yf(t) et d'une différence -e(t) représentant le reste de la soustraction de la sortie y(t) d'un objet commandé (2) d'une valeur cible r(t), et d'un paramètre PID déterminé de façon adaptative à partir de la valeur de consigne. Un moyen de compensation par anticipation parallèle (14) injecte la différence de commande v(t) dans une fonction de transfert représentant le reste de la soustraction de la fonction de transfert d'un modèle réel sensiblement strictement positif d'une fonction de transfert approximative de l'objet commandé (2) et produit la valeur compensée yf(t).
PCT/JP2007/065510 2006-08-11 2007-08-08 Procédé de commande et dispositif de commande WO2008018496A1 (fr)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2013031082A1 (fr) 2011-08-30 2013-03-07 川崎重工業株式会社 Dispositif et procédé de commande adaptative, ainsi que dispositif et procédé de commande pour une machine de moulage par injection
WO2013187414A1 (fr) * 2012-06-12 2013-12-19 国立大学法人熊本大学 Système de régulation, méthode de conception et compensateur parallèle prédictif
CN110210076A (zh) * 2019-05-14 2019-09-06 深圳臻宇新能源动力科技有限公司 控制车辆爬行工况的方法和装置
CN114353044A (zh) * 2022-01-10 2022-04-15 润电能源科学技术有限公司 锅炉汽包水位的闭环辨识方法及相关设备

Citations (3)

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Publication number Priority date Publication date Assignee Title
JPH06138905A (ja) * 1992-10-30 1994-05-20 Nissan Motor Co Ltd フィードバック補償器
JPH09174215A (ja) * 1995-12-22 1997-07-08 Nippon Steel Corp 連続鋳造の鋳型内湯面レベル制御方法
JPH10143205A (ja) * 1996-11-12 1998-05-29 Yamatake Honeywell Co Ltd Ｓａｃコントローラ

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH06138905A (ja) * 1992-10-30 1994-05-20 Nissan Motor Co Ltd フィードバック補償器
JPH09174215A (ja) * 1995-12-22 1997-07-08 Nippon Steel Corp 連続鋳造の鋳型内湯面レベル制御方法
JPH10143205A (ja) * 1996-11-12 1998-05-29 Yamatake Honeywell Co Ltd Ｓａｃコントローラ

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2013031082A1 (fr) 2011-08-30 2013-03-07 川崎重工業株式会社 Dispositif et procédé de commande adaptative, ainsi que dispositif et procédé de commande pour une machine de moulage par injection
KR101516924B1 (ko) 2011-08-30 2015-05-04 카와사키 주코교 카부시키 카이샤 적응 제어 장치 및 적응 제어 방법 및 사출 성형기의 제어 장치 및 제어 방법
WO2013187414A1 (fr) * 2012-06-12 2013-12-19 国立大学法人熊本大学 Système de régulation, méthode de conception et compensateur parallèle prédictif
CN110210076A (zh) * 2019-05-14 2019-09-06 深圳臻宇新能源动力科技有限公司 控制车辆爬行工况的方法和装置
CN114353044A (zh) * 2022-01-10 2022-04-15 润电能源科学技术有限公司 锅炉汽包水位的闭环辨识方法及相关设备

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