JP2010066852A - Method of tuning control parameter - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform tuning in consideration of interference in a multi-variable control system, and to shorten tuning time. <P>SOLUTION: A tuning signal as a pulse operation signal is applied to a controlled target for each channel in order to measure its response, and a PID control parameter of a controller is calculated on the basis of the tuning signal and the response so that the response may be close to a response of a reference model. Input/output data are used to determine a control parameter of the controller so that a response of a closed loop may be close to the response of the reference model. VRFT (Virtual Reference Feedback Tuning) is used to calculate the control parameter. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a tuning method for adjusting a control parameter of a controller that controls a physical state such as temperature and pressure of a controlled object.

  Conventionally, for example, in temperature control in which an object to be heated is placed on a hot plate and subjected to heat treatment, the temperature regulator is heated based on a temperature detected from a temperature sensor disposed on the hot plate. This is performed by controlling energization of a heater disposed on the hot plate so that the temperature of the plate becomes a set temperature (see, for example, Patent Document 1).

When a plurality of heaters and a plurality of temperature sensors are arranged on the hot plate to control a plurality of control points, that is, a plurality of channels, the control points of the hot plate are thermally continuous. In addition, thermal interference between the channels occurs.
Japanese Patent Laid-Open No. 2001-274069

  For example, in a temperature controller that performs PID control, tuning of each channel is performed in order to determine a PID control parameter for each channel. However, it is difficult to perform tuning correctly, and it is necessary to rely on tuning based on the know-how of an expert, and there is a problem that it takes time for tuning.

  The present invention has been made in view of the above points, and in a tuning method for adjusting control parameters of a controller of a multivariable control system, enables tuning in consideration of interference and requires tuning. The purpose is to shorten the time.

 (1) A control parameter tuning method according to the present invention is a tuning method of a control parameter of a controller of a multivariable control system having a plurality of inputs and outputs, and a tuning signal is applied to a control target, and the tuning signal is applied to the tuning signal. The control target response is measured, and the control parameter of the controller is calculated based on the tuning signal and the response so that the response is close to the response of the reference model.

  The multivariable control system refers to a control system in which an operation amount of a certain channel affects the control amount of another channel, that is, a control system in which a large number of operation amounts affect each other.

  The controller is preferably a controller that performs PID control.

  In the control parameter tuning method of the present invention, based on the tuning signal and the response, the control parameter of the controller is calculated so that the response is close to the response of the reference model. The control parameters are calculated by using VRFT (Virtual Reference Feedback Tuning), in which the control parameters of the controller are obtained so that the response of the closed loop is close to the response of the reference model.

  By using a non-interacting model as a reference model, it is possible to calculate a control parameter considering interference.

  Since control parameters can be calculated in consideration of interference in this way, it is possible to perform tuning efficiently without relying on tuning based on expert know-how as in the past, which can shorten tuning time. it can.

  (2) In one embodiment of the control parameter tuning method of the present invention, the tuning signal is applied to the control target in order for each channel, and the response is measured.

  Conventionally, when tuning is performed in order for each channel, it has been necessary to set a sufficient time interval to shift to the tuning of the next channel in order to reduce the influence of other channels. Then, since the control parameter can be calculated in consideration of interference as described above, it is not necessary to take a sufficient time interval as in the prior art, and the time required for tuning can be further shortened.

  (3) In another embodiment of the control parameter tuning method of the present invention, the tuning signal is a pulsed operation signal.

  The application time of the pulsed operation signal is preferably set to be a constant multiple of the measured dead time. For example, this constant is preferably a constant of 2 or more and 5 or less.

  When a pulsed operation signal is applied in order for each channel, the timing of application of the operation signal of the next channel is the time when the control amount of the next channel generated by application of the operation amount of the previous channel decreases. It is preferable to set the slope at the time when the slope becomes the slope constant times when rising, and this constant is preferably, for example, a constant of 1/10 or more and 1/2 or less.

  According to this embodiment, a control parameter can be calculated by applying a pulsed operation signal as a tuning signal.

  (4) In still another embodiment of the control parameter tuning method of the present invention, the tuning signal is an operation signal that accompanies a start of operation of the controller or a change of a target value for the controller.

  According to this embodiment, the control parameter can be calculated using the operation signal corresponding to the start of operation of the controller or the change of the target value as a tuning signal.

  As another embodiment of the present invention, the limit cycle on / off operation amount may be used as a tuning signal.

 (5) In another embodiment of the control parameter tuning method of the present invention, the reference model may include a model that feeds back a control amount difference to an operation amount side through an interference term.

  The model that feeds back the control amount difference to the manipulated variable side via the interference term is a model that feeds back the difference between the two control amounts via the interference term with the corresponding two manipulated variables being different in sign. Is preferred.

  According to this embodiment, a control parameter can be calculated using a reference model including a model that feeds back a control amount difference to an operation amount side via an interference term.

According to the present invention, the control parameter is calculated based on the tuning signal and its response so that the response is close to the response of the reference model, that is, the input and output data is used to determine whether the closed-loop response is the reference model. The control parameter is calculated by using VRFT (Virtual Reference Feedback Tuning), which obtains the control parameter of the controller so as to be close to the response, and interference is taken into consideration by using a non-interfering model as a reference model. The control parameter thus calculated can be calculated.
As a result, it is not necessary to adjust the control parameters by trial and error as in the prior art, and it becomes possible to shorten the application time interval when applying the tuning signal to the control target in order for each channel. The time required for tuning can be shortened.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
FIG. 1 is a schematic configuration diagram of a temperature control system including a temperature controller according to one embodiment of the present invention.

The temperature controller 1 of this embodiment performs two-channel temperature control using two detected temperatures θ ₁ and θ ₂ corresponding to two control points of the controlled object 2 as control amounts.

The temperature controller 1 calculates first and second operation amounts based on deviations between detected temperatures θ ₁ and θ ₂ from two temperature sensors (not shown) and target temperatures SP ₁ and SP ₂ , respectively. PID control units 3 and 4 and tuning means 5 for calculating and setting PID control parameters for the respective PID control units 3 and 4, respectively. 1 and given to the control object 2 via the second change-over switches 8 and 9 to control energization of two heaters (not shown).

The tuning means 5 generates a tuning signal to be described later at the time of tuning and applies it to the controlled object 2 via the first and second change-over switches 8 and 9, and the tuning signal and control. detection temperature theta ₁ from the subject _2, based on the theta _2, and a parameter calculation section 7 which calculates the PID control parameters carries out an operation as described below.

  The PID control units 3 and 4, the tuning means 5, the changeover switches 8 and 9 and the like are configured by, for example, a microcomputer.

  In this embodiment, in a multivariable control system, which is a control system for a plurality of channels with interference, tuning is performed in consideration of interference, and the time required for tuning is shortened as follows.

  That is, in this embodiment, the PID of each PID control unit 3 and 4 using VRFT (Virtual Reference Feedback Tuning), which is a method of adjusting the controller to a desired input / output characteristic using only the input / output data to be controlled. The control parameter is calculated.

  Moreover, as the control object 2, the present applicant uses, for example, a feedback type model structure (hereinafter also referred to as “temperature difference model”) proposed in Japanese Patent Application Laid-Open No. 2004-94939.

  Here, a theoretical explanation of the temperature difference model, which is a model to be controlled, will be given.

  First, in order to simplify the discussion, a hot plate composed of two small homogeneous cells 10-1 and 10-2 shown in FIG. 2 is considered, and heaters 11-1 and 11-2 are connected to the hot plates, respectively. Suppose that

  In this case, it is assumed that the temperature distribution can be regarded as uniform in each of the cells 10-1 and 10-2, and the heat plate can be handled as two concentrated heat capacity models.

  Assuming that each of the cells 10-1 and 10-2 is a homogeneous object having a volume Vi, the change in the internal energy of the cell is described by the following equation from the law of energy conservation.

cρVi (dθi / dt) = − Qi _∞− Qij + Hiui (1)
Where Qi _∞ is the heat flow due to heat transfer from the surface of cell i to the air, Qij is the heat flow from cell i to cell j, θi is the temperature [K] of cell i, and c and ρ are the specific heat of the cell, respectively. [J / (Kg · K)] and density [Kg / m ³ ], ui is an input [%] to the heater, and Hi [W /%] is a conversion coefficient from ui to the heating value of the heater.

Next, the heat flow Qij from the cell j to the cell i is based on Fourier law:
Qij = −Asλ {(θj−θi) / d} (2)
It becomes. Here, λ [W / (m · K)] is the thermal conductivity, As [m ² ] is the cross-sectional area, and d [m] is the distance between the heaters.

Also, Qi∞ is the heat flow due to heat transfer from the surface of cell i to the air, according to Newton's cooling law,
Qi∞ = −Aihi (θi−θ∞) (3)
It becomes. Here, Ai and hi [W / (m ² · K)] are the surface area and the heat transfer coefficient of the cell i, respectively. Further, θ∞ is the ambient temperature of the cell, and generality is not lost even at 0 ° C.
From the above (1) to (3), the block diagram to be controlled is represented in FIG.

In the figure, the transfer function of each block is expressed by the following equation.
Hsi = Ki / (1 + sTi) (4)
Ki = 1 / αi = 1 / hiAi (5)
Ti = Ei / αi = cρVi / hiAi (6)
β = λAs / d (7)
Ei = cρVi, β = λAs / d, αi = hiAi (8)
Here, E represents the heat capacity, β represents the reciprocal of the thermal resistance between the cells, and αi represents the reciprocal of the thermal resistance from the cell to the ambient temperature.

  The model to be controlled shown in FIG. 3 has a structure that feeds back an output temperature difference (temperature difference) via an interference term β, and is a model that explicitly represents thermal interference in the thermal system.

In this embodiment, this temperature difference model is used as the model of the control object 2 as shown in FIG. In the embodiment of FIG. 1, a dead time element e- ^Lis is included in the control target.

  In this embodiment, the above-described VRFT is applied to a temperature difference model, and application of VRFT will be described below.

  In the temperature difference model, as shown in FIG. 3, since the mutual interference is explicitly expressed by the interference term β, if feedback is applied as shown in FIG. The characteristic is made non-interfering as shown in the following equation (9).

If non-interference in the form such as (9), the theta ₁ by u _1, can be controlled independently of theta ₂ by u _2.

  VRFT is applied to the non-interacting system shown in FIG. Let M be the input / output characteristic transfer function (reference model) of the desired control system. At this time, since non-interference is intended, the reference model M is a diagonal matrix as follows.

  By using the non-interfering reference model in this way, it becomes a diagonal matrix and the arithmetic processing becomes easy.

Assume that the input / output data of the control target (plant) is u = [u ₁ , u ₂ ] ^T , θ = [θ ₁ , θ ₂ ] ^T, and θ is regarded as the output of the reference model. A virtual reference r tilde for M to output θ is determined as follows.

  Next, assuming that this signal r tilde is the reference input of the feedback system in FIG. 4 and θ is the output at that time, the virtual manipulated variable u tilde is

It becomes. From equation (11)

It becomes. However, Β = [β ₁ , −β ₂ ] ^T. If the virtual operation amount u tilde is close to the actual operation amount u, the feedback system shown in FIG. That is, if the control parameter B is selected so that u tilde and u are close to each other, the feedback system is considered to be close to the reference model. This is the basic concept of VRFT.

  From this, the problem of obtaining the control parameter B can be obtained by minimizing the following evaluation formula J.

  Further, the zeroing condition of this evaluation formula is as follows.

It can be seen that M _ii given as a reference model is a plant transfer function. However, since it is difficult to give such a transfer function, M _ii is composed of unknown parameters K and T as shown in the following equation.

  Using this, Ki, Ti, and βi that minimize the evaluation formula are obtained by the Gauss-Newton method. However, Hsi is assumed to be a minimum phase system.

In this embodiment, the higher order of equation (16) is omitted,
M _ii = K ₀ / (T ₁ s + T ₀ )
It is said.

As described above, based on the input and output data of the control object _{u = [u 1, u 2} ] T, θ = [θ 1, θ 2] in _^T, can be calculated _{M ii,} therefore, the above-mentioned (4) The steady-state gain Ki and the time constant Ti of the equation can be obtained, and thereby, using the Ziegler-Nichols method, the proportional gain Kp, the integration time T _I , the differentiation time, which are the PID control parameters of the PID control units 3 and 4 the T _D can be calculated by the following equation.

Kp = 1.2 / RL
T _I = 2.0L
T _D = 0.5L
Here, R is the maximum inclination, and is calculated as R = Ki / Ti from the steady gain Ki and the time constant Ti. L is a dead time, and can be obtained by measuring input / output data during tuning.

In this embodiment, the pulsed manipulated variable MV shown in FIG. 5A is applied in turn for each channel as a tuning signal by the tuning means 5 in FIG. 1, and the response PV of the control target 2 at that time is obtained. Based on the input / output data at the time of tuning, the steady gain Ki and the time constant Ti of each channel are calculated according to the VRFT procedure described above, and the time delay L measured from the response waveform is used to calculate the Ziegler using -Nichols method, in which the proportional gain Kp is a control parameter of each PID controller 3,4, integration time _{T I,} and calculates the derivative time _{T D,} it sets the respective PID controller 3,4 . In FIG. 5, the first channel ch1 is indicated by a solid line, and the second channel ch2 is indicated by a one-dot chain line.

  In this embodiment, the application time of the pulsed manipulated variable MV of each channel is a constant multiple of the dead time of each channel to be measured, as shown in FIG. The constant multiple is preferably 2 times or more and 5 times or less, for example.

In this embodiment, as shown in the first channel ch1 of Figure 6, the time for applying a pulsed operation amount is set to 2 times the time L ₁₁ until the 1 ℃ increased after operation amount applied.

  As a result, data including the slope of the response waveform that is the characteristic of the control target can be obtained.

The application timing of the pulsed manipulated variable of the second channel ch2 is such that the slope R ₂₂ when the PV of the second channel ch2 descends due to the application of the pulsed manipulated variable of the first channel ch1 is: is a name was time constant multiple of the slope R ₂₁ at the time of rising. This constant multiple is preferably 1/10 or more and 1/2 or less. In FIG. 6, it is set to 1/3.

  As a result, it is possible to reduce the influence of tuning of the first channel ch1 and obtain data including a slope that is a characteristic of the control target with respect to a response when a pulsed manipulated variable is applied to the second channel ch2. In addition, the time required for tuning can be reduced.

  FIG. 7 is a flowchart for explaining the operation of this embodiment.

  Tuning is started, and a pulsed manipulated variable MV, which is a tuning signal for each channel, is sequentially applied to the controlled object 2 to acquire input / output data up to the final channel (steps n1 and n2). Based on the output data, a PID control parameter is calculated according to the VRFT procedure described above (step n3), and the calculated PID control parameter is set in each of the PID control units 3 and 4, and the process ends.

  Here, the confirmation result of the effectiveness of VRFT used in this embodiment will be described.

A control system shown in FIG. 3 was configured assuming a two-channel aluminum hot plate shown in FIG. 8 as a control target. On the other hand, VRFT was applied to obtain M _ii and decoupling parameter βi. Table 1 shows the plant parameters used in the simulation. However, Hi = 1.

Also, assuming that the structure is known, M _ii is given by the following equation, and parameter learning is performed by the Gauss-Newton method.

  The input / output data used is shown in FIG. Table 2 shows the parameters obtained by VRFT using this input / output data.

  It can be seen that the model to be controlled is correctly learned with an accuracy within an error of 0.1%.

  In the above-described embodiment, the dead time L is measured at the time of tuning. However, if the dead time L cannot be measured, it may be calculated as follows.

When the evaluation function J given by the above equation (14) becomes zero, M _ii and βi are given by the equation (15). That is, if there is a dead time in Hsi, the parameter by adding a dead time e ^-Lis to M _ii by the following equation is correctly learned.

  Therefore, the evaluation formula is as follows.

  However, E is given by the following equation.

  Thereby, the dead time L can be calculated.

In the above-described embodiment, the application timing of the pulsed manipulated variable of the second channel ch2 is the slope of the PV drop of the second channel ch2 caused by the application of the pulsed manipulated variable of the first channel ch1. Although it is assumed that R ₂₂ has reached a constant multiple of the rising slope R ₂₁ , as another embodiment of the present invention, as shown in FIG. When the heater capacity of the channel and the distance from the heater of each channel to the temperature sensor are substantially equal, the application timing of the pulsed manipulated variable of the second channel ch2 is set to the pulsed form of the first channel ch1. It may be a point in time when the PV of the second channel ch2 generated by the application of the operation amount reaches a peak.

  As a result, the time required for tuning can be further reduced.

  In the above-described embodiment, pulsed manipulated variables are sequentially applied as tuning signals. However, as another embodiment of the present invention, when the target value SP is changed sequentially for each channel as shown in FIG. Tuning may be performed using the operation signal as a tuning signal, or tuning may be performed using the operation signal when the operation is started in turn for each channel.

  In this case, the time interval from the change of the target value of the first channel ch1 to the change of the target value of the second channel ch2 may be a constant multiple of the dead time as in FIG.

  Further, as another embodiment of the present invention, as shown in FIG. 12, an on / off limit cycle may be executed channel by channel at intervals.

  Although the above embodiment has been described by applying to two channels, it can be similarly applied to three or more channels.

  The present invention is not limited to temperature control, and can also be applied to adjustment of control parameters of a controller used for controlling other physical states such as pressure, flow rate, speed, or liquid level.

  The present invention is useful for temperature control of a plurality of channels.

It is a block diagram of a temperature control system provided with the temperature regulator which concerns on one embodiment of this invention. It is a figure with which it uses for the theoretical description of a temperature difference model. It is a figure which shows a temperature difference model. It is a figure which shows the decoupling system using a temperature difference model. It is a figure which shows the signal for tuning and its response waveform. It is a figure which shows the timing of application of the signal for tuning. It is a flowchart with which operation | movement description is provided. It is a figure which shows the structure of an apparatus used for a confirmation test. It is a figure which shows the input-output data used for the confirmation test. It is a figure which shows the timing of application of the signal for tuning. It is a figure which shows the signal for tuning corresponding to target value change, and its response waveform. It is a figure which shows the signal for tuning corresponding to a limit cycle, and its response waveform.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Temperature controller 2 Control object 3, 4 1st, 2nd PID control part 5 Tuning means 6 Tuning signal generation part 7 Parameter calculation part

Claims (5)

A method for tuning a control parameter of a controller of a multivariable control system having a plurality of inputs and outputs,
A tuning signal is applied to the control target, a response of the control target corresponding to the tuning signal is measured, and the response is close to a reference model response based on the tuning signal and the response. A control parameter tuning method comprising calculating a control parameter of the controller.   The control parameter tuning method according to claim 1, wherein the tuning signal is applied to the control target in order for each channel to measure the response.   The control parameter tuning method according to claim 1, wherein the tuning signal is a pulsed operation signal.   The method for tuning a control parameter according to claim 1, wherein the tuning signal is an operation signal that accompanies a start of operation of the controller or a change of a target value for the controller.   The control parameter tuning method according to any one of claims 1 to 4, wherein the reference model includes a model that feeds back a control amount difference to an operation amount side through an interference term.

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