WO1998026335A1 - Procede de reglage automatique d'un regulateur proportionnel-integral-differentiel (pid) qui regit un systeme asservi lineaire - Google Patents

Procede de reglage automatique d'un regulateur proportionnel-integral-differentiel (pid) qui regit un systeme asservi lineaire Download PDF

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Publication number
WO1998026335A1
WO1998026335A1 PCT/DE1997/002892 DE9702892W WO9826335A1 WO 1998026335 A1 WO1998026335 A1 WO 1998026335A1 DE 9702892 W DE9702892 W DE 9702892W WO 9826335 A1 WO9826335 A1 WO 9826335A1
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WIPO (PCT)
Prior art keywords
controller
control loop
functional
characteristic
zero crossing
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Application number
PCT/DE1997/002892
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German (de)
English (en)
Inventor
Klaus Weinzierl
Original Assignee
Siemens Aktiengesellschaft
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
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Publication date
Application filed by Siemens Aktiengesellschaft filed Critical Siemens Aktiengesellschaft
Priority to EP97952716A priority Critical patent/EP0944865A1/fr
Publication of WO1998026335A1 publication Critical patent/WO1998026335A1/fr

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Classifications

    • 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
    • G05B13/042—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 in which a parameter or coefficient is automatically adjusted to optimise the performance
    • 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
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.

Definitions

  • a model of the controlled system can be used to construct the frequency characteristics of the Bode diagram.
  • An experienced control engineer can determine suitable controller parameters from this.
  • root locus curves can also be constructed and a simulation of the closed control loop can be carried out.
  • simplifications are often carried out on the route model, e.g. B. performed an approximation of an inert system by a simpler low-order model.
  • suitable controller parameters can already be determined using analytical formulas, e.g. B. after the optimum amount. Simple formulas are often sufficient, e.g. B. according to Ziegler and Nichols, for controller setting.
  • the problem on which the invention is based is to specify a method which is based on the minimization of a
  • an algorithm is developed which can be used for controller calculation for general linear controlled systems.
  • a controller set in this way fulfills the requirements better than a controller which has been calculated using the known method on the basis of a function in the time domain.
  • the controller parameters can be determined, with which it is achieved that the control loop has only a slight overshoot, has great stability and settles quickly.
  • Both functionals evaluate the frequency response of the Bode diagram in the vicinity of the zero crossing and contain the zero crossing itself. By minimizing one of these functions with regard to the controller parameters, the controller can be optimally adjusted.
  • 1 is a block diagram of a control loop
  • FIG. 2 is an illustration of the Bode diagram, the route jump response and the leadership jump response; Fig. 3 of Fig. 2 corresponding diagrams that serve to explain the functional.
  • FIG. 1 shows a basic circuit diagram of a control circuit which is generally known. It shows a controlled system RS that is to be controlled with the aid of a controller RG.
  • the controller RG generates a manipulated variable Y, which is fed to the controlled system RS together with disturbance variables Z.
  • the controlled system RS emits the controlled variable X, which is fed to the controller with a reference variable W.
  • the manipulated variable Y is generated from the difference between the controlled variable X and the reference variable W.
  • the controller RG is set according to the properties of the controlled system RS with controller parameters RP. These controller parameters RP are with
  • the Bode diagram of the controlled system RS is used to design the controller using the frequency characteristic curve method. It is assumed that the controlled system RS is linear, time-invariant and stable.
  • the transfer behavior of the controlled system RS can be described by a transfer function H s (s), which represents a complex-valued function of the complex variables s.
  • log is the tens logarithm and arg is the angle of a complex number in degrees.
  • the function b s (x) thus characterizes the absolute frequency response (absolute characteristic) RS__B (Fig.2a) of the controlled system RS in the Bode diagram, the function p s (x) the associated phase response (phase characteristic) RS_P, Fig.2b.
  • the PID controller can also be shown in the bottom diagram.
  • the transfer function of the PID controller is due to the relationship
  • controller parameters Kp, T v and T n occur in equation (4), where Kp means the proportional gain, T n the reset time and T v the derivative action time.
  • Controller parameters are usually positive constants.
  • the associated functions of the Bode diagram for the PID controller are b r (x) and p r (x) and correspond analogously to the functions of the controlled system, which are given in equation (2) and equation (3).
  • equations (2) and (3) only the index s has to be replaced by the index r.
  • the corresponding magnitude characteristic RG_B and phase characteristic RG_P are also shown in FIGS. 2a, b.
  • H 0 (j ⁇ ): H r (j ⁇ ) H s (j ⁇ ) (5) receives. If the functions b 0 (x) and p 0 (x) are introduced in the same way as the functions b r (x) and p r (x) as well as b s (x) and p s (x), we can one determines the two functions b 0 (x) and p 0 (x) based on equation (5) and logarithmization by a simple summation, ie
  • FIG. 2 shows the magnitude characteristics of the Bode diagram as FIG. 2a, FIG. 2b the phase characteristics, FIG. 2c the step response of the controlled system and FIG. 2d the lead step response.
  • FIG. 2a shows the magnitude characteristics of the Bode diagram as FIG. 2a, FIG. 2b the phase characteristics, FIG. 2c the step response of the controlled system and FIG. 2d the lead step response.
  • H (j ⁇ ) H ° (j , (8) l + H 0 ( D ⁇ )
  • RK_P, RK_B of the open control loop RK in the amount of FIG. 2a or phase FIG. 2b each form the sum of the characteristic curves RG_B or RG_P of the controller and RS_B or RS_P of the controlled system.
  • the distance of the curve RK_P from the -180 ° mark referred to below as the phase reserve PRE, is significant. If this is sufficiently large, a well damped settling behavior of the closed circuit can be expected.
  • the phase reserve PRE the distance of the curve RK_P from the -180 ° mark
  • the example shows how the controller setting works in principle with the help of the Bode diagram. It is noteworthy that the rules of thumb mentioned on the course of the frequency characteristics only in an environment of the
  • Point x 0 based. This is a known fact when designing a controller using the frequency characteristic method and simplifies the design considerably.
  • the following goals are now pursued: by adding a suitable magnitude characteristic RG_B of the controller to the magnitude characteristic RS_B of the route, the point x 0 is tried so far to shift to the right as possible. Variations are available for this by selecting the parameters of the PID controller. It is required as a secondary condition that this sum amount characteristic RK_B falls sufficiently steep in an environment of the point x 0 and the
  • Summer phase characteristic RK_P has a value> -110 ° in an environment of point x 0 .
  • the invention now consists in formulating these known facts in the sense of an optimization task and performing the numerical optimization fully automatically on a digital computer. For this purpose, a corresponding functional is introduced with which the value x 0 and the course of the frequency response in its environment are evaluated.
  • FIG. 3 The effect of the function is illustrated in FIG. 3. There are also the magnitude characteristics Fig. 3a, the phase characteristics Fig. 3b, the
  • the functional is formulated in such a way that any course of the magnitude curve b 0 (x) which lies within the hatched area STRAF in FIG. 3a is punished.
  • the same also applies to the phase characteristic curve Fig. 3b.
  • a high value of x 0 ie a high crossover frequency ⁇ 0, is rewarded in the Bode diagram.
  • the ramp function is used for the formal description of the function
  • the ramp function r explicitly suppresses a reward or punishment if the amplitude specification is exceeded.
  • the function g ⁇ _ ( ⁇ x) the mentioned penalty contribution depends on the distance
  • the properties of the optimal controller setting with regard to the function can still be influenced by varying the penalty areas. For example, if you allow a smaller phase reserve, i.e. H. If you move the penalty area for the phase curve down a bit, you will generally get a faster controller setting with greater overshoot.
  • the result can also be influenced by selecting other weight functions g ⁇ _ and g2.
  • Equation 12 Another function results from equation 12, which can be used to determine the controller parameters.
  • the optimization properties for critical controlled systems are improved by introducing a separate weighting of the controller parameters by means of a function. The functional used is therefore
  • G: (r (b ⁇ (x) + ⁇ )) gi ( ⁇ x) + (r (-90ß ⁇ ° - Po (x))) g 2 ( ⁇ x) fixed
  • ⁇ and ß denote real numbers that should be selected between 1 and 1.2 for low overshoot.
  • ß ⁇ the control speed increases, but so does the tendency to oscillate in the closed circuit.
  • Values with ß ⁇ > 2 generally lead to an unstable control loop.
  • the correction function f (Kp, T n , T v ) includes a small reward for larger values of Kp, 1 / T n and T v and the quotient T n / T v .
  • the functional is again minimized in a known manner with regard to the control parameters Kp, T n and T v . This results in the controller parameters, which are used as optimal setting values for the PID controller.

Abstract

Les paramètres de commande d'un régulateur PID régissant un système asservi linéaire sont déterminés sur la base de la réponse en fréquence logarithmique. Pour ce faire, on prend une fonctionnelle qui comprend un terme représentant la pente de la courbe caractéristique de module pour la boucle ouverte d'asservissement dans le voisinage du passage par zéro, un terme représentant la valeur de la courbe caractéristique de la phase dans le voisinage du passage par zéro et un terme représentant la grandeur du passage par zéro. La fonctionnelle est optimisée sur le plan des paramètres de commande, et le régulateur est réglé en fonction des paramètres obtenus.
PCT/DE1997/002892 1996-12-11 1997-12-11 Procede de reglage automatique d'un regulateur proportionnel-integral-differentiel (pid) qui regit un systeme asservi lineaire WO1998026335A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
EP97952716A EP0944865A1 (fr) 1996-12-11 1997-12-11 Procede de reglage automatique d'un regulateur proportionnel-integral-differentiel (pid) qui regit un systeme asservi lineaire

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE19651526 1996-12-11
DE19651526.2 1996-12-11

Publications (1)

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WO1998026335A1 true WO1998026335A1 (fr) 1998-06-18

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2003052529A1 (fr) * 2001-12-18 2003-06-26 Mts Systems Corporation Procede de determination de parametres de commande pour un systeme de commande
DE102010042625A1 (de) 2010-10-19 2012-04-19 Dr. Johannes Heidenhain Gmbh Verfahren zum Bestimmen eines Bode-Diagramms
EP2246760A3 (fr) * 2009-04-30 2013-05-01 Robert Bosch GmbH Procédé de détermination d'au moins un paramètre de réglage d'une articulation de réglage dans un circuit de réglage de tension de bande pour une machine de traitement
AT519771A1 (de) * 2017-03-20 2018-10-15 B & R Ind Automation Gmbh Verfahren zur Bestimmung von Regelungsparametern für ein Hydrauliksystem

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
BRANDIN B A ET AL: "A METHOD FOR THE IDENTIFICATION OF SYSTEM MODES. GIVEN THE SYSTEM TRANSFER FUNCTION OR BODE DIAGRAM)", TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, vol. 8, no. 5, October 1986 (1986-10-01), pages 250 - 255, XP000674044 *
CHINTAE C ET AL: "Robust control of positioning systems with a multi-step bang-bang actuator", MECHATRONICS, vol. 8, no. 6, December 1996 (1996-12-01), pages 867-880, XP004062836 *
HIGGINSON A M ET AL: "The modelling and automatic commissioning of a high precision co -ordinate measuring machine", MECHATRONICS, vol. 3, no. 6, April 1996 (1996-04-01), pages 261-281, XP004047534 *
MEABURN A ET AL: "A simple predictive controller for use on large scale arrays of parabolic trough collectors", SOLAR ENERGY, vol. 6, no. 56, June 1996 (1996-06-01), pages 583-595, XP004011967 *

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2003052529A1 (fr) * 2001-12-18 2003-06-26 Mts Systems Corporation Procede de determination de parametres de commande pour un systeme de commande
US6917840B2 (en) 2001-12-18 2005-07-12 Mts Systems Corporation Method of ascertaining control parameters for a control system
CN100380254C (zh) * 2001-12-18 2008-04-09 Mts系统公司 确定控制系统控制参数的方法
KR100989395B1 (ko) * 2001-12-18 2010-10-25 엠티에스 시스템즈 코포레이숀 제어 시스템의 제어 파라미터를 확인하는 방법
EP2246760A3 (fr) * 2009-04-30 2013-05-01 Robert Bosch GmbH Procédé de détermination d'au moins un paramètre de réglage d'une articulation de réglage dans un circuit de réglage de tension de bande pour une machine de traitement
DE102010042625A1 (de) 2010-10-19 2012-04-19 Dr. Johannes Heidenhain Gmbh Verfahren zum Bestimmen eines Bode-Diagramms
DE102010042625B4 (de) 2010-10-19 2023-09-28 Dr. Johannes Heidenhain Gmbh Verfahren zum Bestimmen eines Bode-Diagramms
AT519771A1 (de) * 2017-03-20 2018-10-15 B & R Ind Automation Gmbh Verfahren zur Bestimmung von Regelungsparametern für ein Hydrauliksystem
US11149756B2 (en) 2017-03-20 2021-10-19 B&R Industrial Automation GmbH Method for determining closed-control parameters for a hydraulic system

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