WO2013128214A1 - Procédé d'auto-syntonisation de contrôleurs pid et appareil utilisant ledit procédé - Google Patents

Procédé d'auto-syntonisation de contrôleurs pid et appareil utilisant ledit procédé Download PDF

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WO2013128214A1
WO2013128214A1 PCT/GR2012/000010 GR2012000010W WO2013128214A1 WO 2013128214 A1 WO2013128214 A1 WO 2013128214A1 GR 2012000010 W GR2012000010 W GR 2012000010W WO 2013128214 A1 WO2013128214 A1 WO 2013128214A1
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overshoot
controller
tuning
closed loop
parameters
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PCT/GR2012/000010
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WO2013128214A8 (fr
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Nikolaos MARGARIS
Konstantinos Papadopoulos
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Aristole University Of Thessaloniki-Research Committee
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Publication of WO2013128214A1 publication Critical patent/WO2013128214A1/fr
Publication of WO2013128214A8 publication Critical patent/WO2013128214A8/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
    • G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
    • G05B13/024—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a parameter or coefficient is automatically adjusted to optimise the performance

Definitions

  • the invention refers to a method for automatic tuning of various types PID controllers notably for Single Input Single Output closed loop control systems to be applied in any minimum or non minimum phase linear stable SISO process of some form that is met in numerous chemical, mechanical and electrical industrial applications, such as electrical drives.
  • the betragsoptimum design criterion is applied for the design of type-I closed loop control systems, i.e. systems able to track only step reference signals as stated by R.C. Dorf, R.H. Bishop, in "Modern Control Systems” pp. 386-387, Prentice Hall, 2004.
  • the symmetrical optimum design criterion is applied for the control of integrating processes, leading to type-II closed loop control systems, i.e. systems able to track faster than step reference signals such as ramp inputs.
  • a basic feature of the aforementioned design criteria is that both methods try to design a controller such that the final closed loop control system exhibits optimal output disturbance rejection d 0 (s) as set out by Oldenbourg, Sartorius above. This is achieved when the magnitude of the frequency response of the closed loop transfer function is rendered as close as possible to unity in the widest possible frequency range as taught therein.
  • the term optimal is to be understood as the final closed loop (SISO) control system exhibiting optimal rejection of the output disturbance d 0 (s).
  • the design via said betragsoptimum criterion leads always to a closed loop control system that exhibits a step and frequency response with specific shape. Indeed, it was found that despite the type of control applied to the process via the betragsoptimum design criterion, the shape of the step response of the final closed loop control system is preserved.
  • One of the step response features that are being preserved is the overshoot, which remains constant and equal to 4,47%.
  • the property of the shape preservation is also observed in the frequency domain. The transition from I to PID control increases the robustness of the final closed loop control system. The property of shape preservation appears to constitute a much attractive feature that drives effortlessly to the automatic tuning of PID type controllers.
  • controller's design via the betragsoptimum and the symmetrical optimum methods presents two critical drawbacks that lead to suboptimal results in terms of output disturbance rejection.
  • controller parameters zeros of the controller transfer function
  • exact pole-zero cancellation between process's poles and controller's zeros has to be achieved.
  • This assumption results in a suboptimal control law, since it restricts the controller parameters to be tuned only with the dominant time constants of the process.
  • both the betragsoptimum and symmetrical optimum methods determine the optimal values of the PID type controller via compensation between the process's poles and the controller's zeros.
  • exact pole-zero cancellation between the process poles and the controller's zeros has to be achieved so that both design methods are applied.
  • both the betragsoptimum and symmetrical optimum methods make use of the controllers that restrict their parameters to be tuned only with real zeros. This constraint leads to suboptimal results, since for the derivation of the optimal control law, only the dominant time constants of the process are considered.
  • controller parameters are determined analytically as a function of all plant parameters, and not as a function of the plant's dominant time constants. More specifically, for a clear presentation of the invention, some assumptions are made as to the linear time invariant process described by its transfer function.
  • the revised optimal controller parameters actually depend on all process parameters, and not only on the dominant time constants of the process, in contrast with the betragsoptimum design criterion.
  • the revision of the symmetrical optimum method leads to similar results concerning the revision of the betragsoptimum method.
  • the revision of the symmetrical optimum criterion determines the controller parameters as a function of all process parameters, and not as a function of the dominant time constants of the process. For that reason, the application of the revised control law to any given process leads to improved output d 0 (s) disturbance rejection compared to the symmetrical optimum method.
  • the problem is to find automatically the optimal values for parameters so that the final closed loop
  • the loop control system exhibits a determined shape of overshoot, in particular wherein the overshoot of the final closed loop control system remains substantially constant and equal to a predetermined value, in particular 4,47%.
  • the tuning procedure is remarkable in that it is automatic wherein it consists of the following steps including
  • Step 1 determination of the plant's dc gain k p ,
  • Step 2 determination of the time constant T ⁇ x _
  • Step 3 determination of the time constant ⁇
  • Step 4 determination of the time constant Tvx.
  • the integration time constant T h which results via the betragsoptimum method, preserves the shape of the system time responses. This is true in cases of PI and PID control law, and only if exact zero-pole cancellation between the process poles and the controller's zeros occurs. As a result, if the dominant plant time constants are known, the PID type controller parameters can be automatically tuned properly via the integration time constant, so that the overshoot of the step response reaches the limit of 4,47%.
  • said gain k p is determined from the step response of the plant at steady state, in particular wherein an estimation of the sum time constant T ⁇ p of the plant is derived from the step response in some way, more particularly wherein
  • t ss is the settling time of the process, wherein an auxiliary loop is then placed in the closed loop system for tuning said controller C x (s).
  • the operation of the auxiliary loop is the following: a series of small step variations of the reference input with alternating sign are imposed, so that the plant does not diverge far from its operating point, wherein during these variations, the overshoot, undershoot, is measured and is compared with the reference overshoot, respectively undershoot.
  • the controlled process is represented by G(s), which method is remarkable in that the tuning of said controller's parameters C x (s) is based on measuring the output's overshoot, wherein an overshoot reference ovs re / is adjusted at the output of the process with which the actual overshoot of the output is every time compared at every tuning step.
  • the absolute value of the reference overshoot is 0,0447, which method is remarkable in that the error is fed into a PI controller, which tunes the controller C x (s) in succession, so that the overshoot, respectively undershoot, of the closed loop step response converges to said predetermined value.
  • the absolute value of the reference overshoot is 0,0447, which method is remarkable in that the controller C x (s) is given the form where T ⁇ x , T m and T vx are time constants that are determined.
  • both T m & T vx are set 0, wherein a series of step variations is imposed in succession on the reference input and the time constant is tuned, so that the
  • overshoot, resp. undershoot is 4,47 %, for which
  • for determining the time constant is set 0 with the value of given, wherein a series of step variations of the reference input is imposed again in succession, and is tuned, so
  • the parasitic time constant is relatively large, wherein the procedure is
  • step 4 continued by attempting the abovementioned step 4, in particular wherein the parasitic time constant is sufficiently small, wherein PI control is retained.
  • I control is initially applied to the process according to Step 2, and the integration time constant is tuned properly so that the final closed loop control system exhibits overshoot equal to 4,47%.
  • the next step is to implement a mechanism able to estimate the desired overshoot responsible for tuning properly the PI controller parameters, wherein the same mechanism operates in the case of PID control for tuning also its parameters properly, wherein for implementing this specific mechanism an Adaptive-Network-based Fuzzy Inference System designated as ANFIS is used.
  • ANFIS Adaptive-Network-based Fuzzy Inference System
  • said controller has the form of
  • step open loop experiment at the controlled process so that the plant's dc gain and settling time are measured;
  • step 2' tuning of parameter T ⁇ ,
  • step 3' estimation of the desired overshoot reference for tuning the PI controller's parameters
  • step 4' estimation of the desired overshoot reference for tuning the PID controller's parameters, thereby yielding automatically the optimal values for parameters X x , Y x , T ⁇ x , so that the step response of the final closed loop control system exhibits the observed shape.
  • said Step 1 ' consists of an open loop experiment of the process carried out at the controlled process so that the plant's dc gain and steady state time are measured, in particular wherein the plant's dc gain k p (2), and the settling time of the plant's step response t ss are measured, in particular wherein
  • a max-min detector is adjusted at the output of the process that is responsible of detecting the maximum and minimal value of the step response of the closed loop control system during the time of tuning, and an overshoot reference ovs re f is adjusted at the output of the process with which, the actual overshoot of the output is every time compared at every tuning step whereby the tuning of the controller's parameters is based on measuring the output's overshoot.
  • said operation of the auxiliary loop is the following: a series of small step variations of the reference input with alternating sign is imposed, so that the plant does not diverge far from its operating point, wherein during these variations, the overshoot (undershoot) is measured and is compared with the reference overshoot (undershoot).
  • said control law, the absolute value of the reference overshoot varies in the range of values presented, the error is fed into a PI controller, which tunes the controller
  • the overshoot of the final closed loop control system remains constant and equal to said predetermined value, in particular 4,47%, parameter being tuned, yielding that the final closed loop control system exhibits overshoot equal to being said predetermined value.
  • said step 2' consists of tuning of parameter
  • Controller is initialized by setting
  • the process is conceived as a first order one.
  • the tuning of parameter follows the next steps. At every rise-fall of the step reference input during the series of small step variations, the actual overshoot (undershoot) of the closed loop control system is measured by the max-min detector and is compared with the overshoot reference value said predetermined value.
  • the tuning procedure keeps carrying on until an actual overshoot (undershoot) of said predetermined value is observed by the max-min detector. The moment that the max-min detector measures that the actual overshoot is equal to the reference overshoot, the tuning procedure is terminated.
  • said step 3' consists in that for tuning the PI controller's parameters, the desired overshoot reference is estimated which acts as a guide for tuning the C x (s) PI controller's 1 parameters, particularly wherein the estimation of the desired overshoot is carried out by said ANFIS 7 network, wherein the stored parameters of the previous step, enter the ANFIS network 7
  • the tuning of parameter X x is carried out as follows. Again a series of small step variations at the reference input with alternating sign are imposed, so that the plant does not diverge from its operating point. At every rise-fall of the step reference input, the actual overshoot (undershoot) of the closed loop control system is measured by the max-min detector and is compared with the overshoot reference , wherein
  • the tuning procedure is terminated.
  • the shape of the step response of the final closed loop control system is identical to the expected one observed during the design of the closed loop control system after the application of the proportional integral control law to any given process.
  • the known parameters are
  • said step 4' further consists of the estimation of the desired overshoot reference for tuning the PID controller's parameters.
  • optimal automatic tuning of the PI, PID type controller's parameters for SISO closed loop control systems is remarkable by a constancy of the shape of the step response of the closed loop control system despite the type of controller applied to the process.
  • said parameters of the PID type controller are automatically tuned according to a fixed relationship.
  • the fixed relationship yields to a closed loop control system exhibiting optimal disturbance rejection.
  • the reference overshoot is estimated by an adaptive network based fuzzy inference system.
  • a control system for use to automatically tune the PID controller parameters according to the invention, it comprises the structure of the PID type controller which is automatically tuned wherein the structure allows the PID type Controller parameters to be tuned either with real or conjugate complex values, on the one hand, and the reference overshoot responsible for the automatic tuning of the PID type controller parameter, on the other hand.
  • the adaptive network fuzzy inference system for estimating the reference overshoot for tuning the PI controller, resp. the PID controller, and/or the product of the controller zeros for tuning the PID controller.
  • Figure 1 is a block diagram showing a general structure of a closed loop control system.
  • Figure 2 shows the step response of the final closed loop control system after the application of an I, PI, resp. PID control to the process.
  • Figure 3 shows the frequency response of the final closed loop control system with I, PI and PID control.
  • Figure 4 shows the step response and output disturbance rejection of the type-II closed loop control system according to the symmetrical optimum criterion.
  • Figure 5 shows the frequency response of type-II closed loop control system.
  • Figure 6 shows a so-called closed loop system with a two degree of freedom controller.
  • Figure 7 shows the step response and output disturbance rejection for said two degree of freedom controller.
  • Figure 8 shows the closed loop control system during the automatic tuning of the PID type controller according to the invention.
  • Figure 9 shows a typical example of an open loop of the process.
  • Figure 10 shows the block diagram of the control system and tuning loop according to the invention, wherein the overshoot reference is equal to 4,47%.
  • Figure 11 represents a series of small step variations at the reference input with alternating sign being imposed, so that the plant does not diverge far from its operating point.
  • Figure 12 shows the block diagram of the control system and tuning loop, that includes the ANFIS network for estimating the desired reference overshoot, according to the invention.
  • Figures 13 and 14 show the snapshots from the tuning procedure, wherein the transition from I to PK) control leads to a faster closed loop control system, although the shape of the step response is preserved.
  • Figure 1 shows the general structure of the SISO closed loop control system, wherein G(s) is the plant transfer function, C(s) is the controller transfer function, r(s) is the reference signal, d a (s) and dj(s) are the input and disturbance signals respectively and are the noise signals at
  • the invention can be applied in any minimum or non-minimum phase linear stable SISO process of the form
  • a basic feature of the aforementioned betragsoptimum and the symmetrical optimum design criteria is that both methods try to design a controller such that the final closed loop control system exhibits optimal output disturbance rejection d 0 (s). This is achieved when the magnitude of the frequency response of the closed loop transfer function is rendered as close as possible to unity in the widest possible frequency range. In other words, if T(s) stands for the closed loop transfer function, then the magnitude of the frequency response of T(s) has to satisfy condition
  • controller's design via the betragsoptimum and the symmetrical optimum methods presents two critical drawbacks that lead to merely suboptimal results in terms of output disturbance rejection d 0 (s).
  • controller parameters zeros of the controller transfer function
  • exact pole-zero cancellation between process's poles and controller's zeros has to be achieved.
  • This assumption results in a suboptimal control law, since it restricts the controller parameters to be tuned only with the dominant time constants of the process.
  • pole-zero cancellation the attenuation of load disturbances may be poor if the cancelled poles are excited by disturbances and if they are slow compared to the dominant closed- loop poles.
  • FIG.3 shows the frequency response of the final closed loop control system, I PI PID control.
  • the design of PID type controllers via the symmetrical optimum design criterion reveals advantages and disadvantages that are similar with the betragsoptimum method. It is assumed again a SISO linear integrating process of the form
  • T m stands for the integrating time constant of the plant.
  • process eq. (53 ) can be considered of having the form
  • the step response of eq.69 is represented in Fig.4 showing that the control system's output exhibits an undesired overshoot of 43,4%.
  • the frequency response of type-II closed loop control system of eq. 69 represented in Figure justifies the great overshoot in the time domain since in the higher frequency region, an undesired maximum is also observed.
  • the reference signal is filtered by an external controller as shown in Fig.6
  • Fig.7 representing the step response and output disturbance rejection for said two degree of freedom controller.
  • both the betragsoptimum and symmetrical optimum methods determine the optimal values of the PED type controller via compensation between the process's poles and the controller's zeros. In other words, exact pole-zero cancellation between the process pole's and the controller's zeros has to be achieved so that both design methods are applied.
  • the current optimization method is getting improved by revising the drawbacks described above.
  • the current invention firstly introduces the PID controller of the form
  • controller parameters are determined analytically as a function of all plant parameters and not as a function of the plant's dominant time constants.
  • Table 3 shows the range of overshoot of the final closed loop control system after the application of the revised control law to any given process - Type II closed loop control systems.
  • the revision of the symmetrical optimum method leads to similar results presented previously concerning the revision of the betragsoptimum method.
  • the revision of the symmetrical optimum criterion determines the controller parameters as a function of all process parameters and not as a function of the dominant time constants of the process. For that reason, the application of the revised control law to any given process leads to improved output d 0 (s) disturbance rejection compared to the symmetrical optimum method.
  • the property of the shape conservation of the step response of the final closed loop control system still exists after the revision of the symmetrical optimum criterion, Table 3.
  • the integration time constant ⁇ which results via the betragsoptimum method, preserves the shape of the system time responses. This is true in cases of PI and PID control law and only if exact zero-pole cancellation between the process poles and the controller's zeros occurs. As a result, if the dominant plant time constants gets known, the PID type controller parameters can be automatically tuned properly via the integration time constant, so that the overshoot of the step response reaches the limit of 4,47 %.
  • the invention is implemented based on the betragsoptimum method for the implementation of the invention, reference is made to Fig. 8, showing a closed loop control system during the automatic tuning of the PID type controller, where C x (s) (1) stands for the PID type controller, the parameters of which are getting automatically tuned.
  • the closed loop control system exhibits the specific shape observed in terms of overshoot. According to the betragsoptimum design criterion, the overshoot of the final closed loop control system remains constant and equal to 4,47 %.
  • the automatic tuning procedure consists of the following steps.
  • a first step consists of the determination of the gain k p .
  • the gain k p is determined from the step response of the plant at steady state as shown in Fig.9 representing a typical example of an open loop of the process.
  • an estimation of the sum time constant T ⁇ p of the plant can be derived from the step response in various wa s. For example,
  • t ss is the settling time of the process.
  • an auxiliary loop is placed in the closed loop system of Fig. 8, as shown grey shaded in Fig. 10 representing a block diagram of the control system and tuning loop.
  • the purpose of this loop is the tuning of the controller C x (s).
  • the overshoot reference is equal to 4,47%.
  • C x (s) 1 stands for the controller whose parameters are getting automatically tuned.
  • the plant's dc gain is represented by k p 2 whereas the controlled process is represented by G(s) 3.
  • an overshoot reference ovs re / is adjusted at the output of the process with which the actual overshoot of the output is compared every time at every tuning step as shown in Fig. 11.
  • the operation of the auxiliary loop is thus the following: A series of small step variations of the reference input with alternating sign are imposed, so that the plant does not diverge far from its operating point, as represented in Fig. 11. During these variations, the overshoot, resp. undershoot is being measured and is compared with the reference overshoot, resp. undershoot. According to the preceding analysis, the absolute value of the reference overshoot is 0,0447. The error is fed into a PI controller 5, which tunes the controller C x (s) in succession, so that the overshoot, resp. undershoot of the closed loop step response converges to 4,47%.
  • the controller C x (s) is given the form where ⁇ & , T m and T vx are time constants that must be determined.
  • Step 2 then consists of the determination of the time constant T ⁇ x .
  • a series of step variations on the reference input is imposed in succession, and the time constant T ⁇ x is tuned so that the overshoot, resp. undershoot, is 4,47%. As shown above, this occurs when T ⁇ x ⁇ T ⁇ .
  • a further step 3 consists of the determination of the time constant T m .
  • Said step 4 consists of the determination of the time constant Tvx. Given the values of T ⁇ x and Tm, Tvx is tuned, so that the overshoot is again 4,47%, by imposing again a series of step variations on the reference input. As shown above, this occurs when Tvx ⁇ T P 2.
  • the optimal control law set out in Table 2 shows that the preservation of the shape of the final step response in the control loop, in terms of the overshoot, does not remain constant and equal to 4,47% but ranges in the region according to Table 2. For that reason, a mechanism able to estimate the desired overshoot has to be provided for enabling to automatically tune the controller parameters so that the final control loop exhibits a specific shape in terms of the overshoot.
  • the purpose of the invention is to initially apply I control to the process according to Step 2, and tune properly the integration time constant so that the final closed loop control system exhibits overshoot equal to 4,47%. Based on Table 2, the resulting closed loop control system is optimal according to the analysis presented above.
  • the next step is to implement a mechanism able to estimate the desired overshoot responsible for tuning properly the PI controller parameters.
  • the same mechanism has to operate in the case of PID control for tuning also its parameters properly.
  • ANFIS Adaptive-Network-based Fuzzy Inference System
  • the problem is to find automatically the optimal values for parameters so that the final
  • closed loop control system exhibits the specific shape observed in terms of overshoot.
  • the problem is to find automatically the optimal values for parameters so
  • the automatic tuning procedure consists of the following steps :
  • Step 1 consists of the Open loop experiment at the controlled process so that the plant's dc gain and steady state time are measured.
  • Fig. 12 shows a block diagram of the control system and tuning loop.
  • the tuning loop includes the ANFIS network for estimating the desired reference overshoot. Because of the fact that there is sufficiently little information about the process integral control is initially applied so
  • a max-min detector 6 responsible of detecting the maximum and minimal value of the step response of the closed loop control system during the time of tuning is adjusted at the output 8 of the process. Moreover, because of the fact that the tuning of the controller's parameters 1 is based on measuring the output's overshoot 8, an overshoot reference ovs ref is adjusted at the output of the process with which, the actual overshoot of the output will every time be compared at every tuning step shown in Fig. 11.
  • the operation of the auxiliary loop is the following.
  • a series of small step variations of the reference input with alternating sign is imposed, so that the plant does not diverge far from its operating point, as shown in Fig. 11.
  • the overshoot, resp. undershoot is being measured and is compared with the reference overshoot, resp. undershoot.
  • Table 1 the absolute value of the reference overshoot varies in the range of values presented in Table 2.
  • the error is fed into a PI controller 5, which tunes the
  • controller C x (s) 1 in succession, so that the overshoot , resp. undershoot of the closed loop step response converges to The time the controller parameters are considered to
  • parameter T ⁇ x is tuned so that the final closed loop control system exhibits overshoot equal to
  • Step 2 consists of the tuning of parameter Controller 95 is initialized by setting
  • Step 3 consists of the estimation of the desired overshoot reference for tuning the PI controller's parameters.
  • the desired overshoot reference acting as a guide for tuning the C x (s) PI controller's (1) parameters has to be estimated.
  • the estimation of the desired overshoot is carried out by an ANFIS (Adaptive Neurofuzzy Inference System) 7 network.
  • the stored parameters of the previous step enter the
  • the tuning of parameter X x is carried out as follows. Again a series of small step variations at the reference input with alternating sign are imposed, so that the plant does not diverge from its operating point. At every rise-fall of the step reference input, the actual overshoot, resp. undershoot of the closed loop control system is measured by the max-min detector and is compared with the overshoot reference .
  • parameter ⁇ is increased by the PI controller 5, as shown in Fig. 12.
  • the integral gain of the controller is automatically tuned according to eq.(99).
  • the tuning procedure keeps carrying on until an overshoot, resp. undershoot of is observed by the max-min detector. The moment the max-min detector measures that the actual overshoot is equal to the overshoot reference, the tuning procedure is terminated.
  • the shape of the step response of the final closed loop control system is identical to the expected one observed during the design of the closed loop control system after the application of the proportional integral control law to any given process Table 1.
  • the known parameters are
  • Step 4 consists of the estimation of the desired overshoot reference for tuning the PID controller's parameters. Since the optimal overshoot of the final closed loop control system ranges when the PID control law Table 1 is applied to any given process Table 2 (3% - 8,5%), the desired overshoot reference acting as a guide for tuning the PID controller's (I) parameters has to
  • the estimation of the desired overshoot is carried out by an ANFIS (Adaptive Neurofuzzy Inference System) 7 network.
  • ANFIS Adaptive Neurofuzzy Inference System
  • Controller C x (s) eq.93 takes the form
  • Controller C x (s) eq.93 is initialized with
  • X P1 is the value we found at the end of the previous step.
  • X x value is tuned the same way as described in Step 3.
  • Y x parameter is not related with X x through a straightforward expression, as visible in control law Table 1, every time X x is tuned, parameter Y x has to be estimated. This estimation is carried out through the ANFIS network 7. For that reason, if the actual overshoot, resp. undershoot is then parameter X x is decreased by the PI controller 5 and parameter
  • Y x is estimated through the ANFIS network, Fig. 12.
  • Y x we use is made of which act as in input at the ANFIS network.
  • X PI is the value found at
  • parameter Y x is estimated through the ANFIS network, Fig.12.
  • X P1 is the value found at the end of step 3 and X x is the output of the PI controller at every rise-fall of the step reference input.
  • the integral gain of the controller is automatically tuned through eq.(102).
  • the tuning procedure keeps carrying on until an overshoot (undershoot) of is observed by the max-min detector. The moment the max-min detector measures that

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Abstract

La présente invention concerne un procédé fiable et un appareil d'auto-syntonisation optimale pour des contrôleurs de type PID. Le procédé peut être appliqué dans n'importe quel processus linéaire stable à entrée unique/sortie unique. Le procédé fournit automatiquement les paramètres corrects du contrôleur de type PID de sorte que le système de commande en boucle fermée final offre un rejet optimal des perturbations de sortie.
PCT/GR2012/000010 2012-02-28 2012-02-28 Procédé d'auto-syntonisation de contrôleurs pid et appareil utilisant ledit procédé WO2013128214A1 (fr)

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CN104155875A (zh) * 2014-07-18 2014-11-19 武汉滨湖电子有限责任公司 一种主从轴控制方法
CN105955026A (zh) * 2016-05-30 2016-09-21 神华集团有限责任公司 模糊pid控制方法和装置及系统
TWI564683B (zh) * 2015-10-21 2017-01-01 財團法人工業技術研究院 未知pid控制器之參數調諧方法
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