JPS6318202B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention provides a sample value PID control device which has a function of automatically adjusting a sample value control constant of a sample value PID control calculation unit to an optimum value in accordance with process operation fluctuations while controlling a process in a closed loop. Regarding.

In order to control a process to be controlled under optimal conditions, a procedure is required to know the dynamic characteristics of the process. This procedure is called identification of its dynamic characteristics. There are two ways to perform this identification: one is to disconnect the control device that controls the process and use open-loop operation, and the other is to connect the control device to the process and perform identification while controlling the process. From the viewpoint of economy, quality control, or safety, it is desirable to perform this identification quickly during closed-loop operation so as to be able to respond to changes in the dynamic characteristics of the process during operation.

Conventional sample value PID controllers do not have the ability to identify while controlling the process during closed-loop operation as described above, but simply estimate the known operating state of the process and manually set control constants that correspond to changes in the process output. If the process is to be controlled by sample value PID while making changes using The control constants of the controller were determined by knowing the dynamic characteristics of the controller.

This type of control device includes an analog type control device that handles analog quantities, and a digital type control device that controls while sampling data. In reality, there are only methods using this method (for example, "Introduction to Optimal Control" by Masubuchi, published by Ohmsha)
(e.g., the adaptive control method described on page 284), and in order to calculate the control constants, a large computer had to be installed, which was extremely uneconomical. In addition, in digital control devices, especially sample values
In the case of a PID control device, since the control constants are adjusted while observing the response of the closed-loop control, it takes a long time to adjust the control constants to match the dynamic characteristics of the process, and the operation is also troublesome.

This invention was made to solve the above-mentioned drawbacks of the conventional device, and is not limited to the sampling period; for example, by increasing the period and making it possible to calculate the control constants even with a simple computer. , the purpose is to configure a sample value PID control device that does not reduce its control performance,
In addition, the sample value PID control system eliminates the need for actual adjustment of the control system, allows identification of the process dynamic characteristics even during process operation, enables control with optimal control constants, and allows the plant to be operated at high operating rates. The purpose is to provide.

The present invention includes a sample value PID control calculation section that performs sample value PID control using sample value control constants, an identification signal generation section that generates an identification signal consisting of a persistent exciting signal, and an identification signal generation section that performs sample value PID control using sample value control constants. A sample and hold section samples and holds an operation signal obtained by adding the generated identification signal, and the output signal of this sample and hold section is used to set the process signal obtained from the operated process and the value to be controlled for the process. A circuit that calculates the deviation from the target value signal and inputs the deviation signal obtained by this calculation to the sample value PID control calculation section at regular intervals, and inputs the operation signal and the process signal. a pulse transfer function identification unit that identifies a pulse transfer function; a transfer function calculation unit that calculates an S-region transfer function from the pulse transfer function identified by the pulse transfer function identification unit; and a transfer function calculated by the transfer function calculation unit. and a sample value control constant calculation unit that calculates a sample value control constant using the sample control period, and the sample value control constant obtained by the sample value control constant calculation unit is controlled by the sample value PID control calculation unit. This is a sample value PID control device that can quickly and automatically adjust the control constant while controlling the process in a closed loop.

This invention particularly uses persistently exciting signals as identification signals.
This is a sample value PID control device using signals. This persistently exciting signal is a signal that belongs to a stationary irregular process, such as an M-sequence signal, a random number signal, or a white noise signal.
Identification of processes in closed loop−
Identification and Accuracy
A magazine published in 1977 as Aspects
Defined on page 65 of Automatica.

An embodiment of the present invention will be described in detail below with reference to the drawings. FIG. 1 is a block diagram showing the circuit configuration of a sample value PID control device according to the present invention.

The controlled object is, for example, a process 1 configured to automatically control the temperature, pressure, etc. in a steel or chemical industrial plant. The control deviation e(t) with the process signal y(t) (e(t)
=r(t)-y(t)), and a sampler 4 that operates at a predetermined sampling control period τ.
A basic sampled value PID control device is constituted by a sampled value PID control calculation section 5 that controls the process 1 based on the sampled deviation signal e*(t) outputted from the sampler 4.

Output signal u′ of sampled value PID control calculation unit 5 ^*
(t) is an identification signal generated by the identification signal generating section 7.
v ^* (t) and is added in an adder 6, and the added output signal u ^* (t) is input to the sample hold unit 2 to obtain an operation signal u(t) for operating the process 1. Process 1 is controlled by the obtained operation signal u(t).

Output signal u ^* (t) of adder 6 and process signal y
(t) by the sample process signal y ^* (t) obtained through the sampler 8.
PID control constants Kc (proportional gain), Ti (integral time constant),
Calculate Td (differential time constant). This calculation is performed by a pulse transfer function identification section 9, a transfer function calculation section 10, and a sample value control constant calculation section 11. The sample value PID control constant calculated here is input to the sample value PID control calculation section 5. That is, the control constant of this calculation section 5 is adjusted in accordance with the fluctuations in the process 1.

Next, each component of the apparatus of the present invention will be explained in more detail.

The sample value control calculation unit 5, which is the controller of the process 1, processes the output signal e ^* (t) of the sampler 4 using the following algorithm using sample value control constants to be described later, and generates the signal u' ^* (t). Output.
This algorithm is a well-known speed-type PID algorithm, where the proportional gain Kc, the integral time constant Ti, the differential time constant Td, and the sample control period τ.
The output signal u' ^* t of the sample value PID control calculation unit 5 is expressed as u' ^* (t) = u' ^* (t - τ) + Δu' ^* (t)...
Formula However, Δu′ ^* (t)=Kc {(e(t)−e(t−τ))+τ
/Tie (t) +Td/τ(e(t)−2e(t−τ)+e(t−2τ)
)} ... is shown by the second formula. This operation is performed in the order of the flowchart shown in FIG. 2: first, u' ^* (t) is executed in step 12, and then u' ^* (t) is executed in step 13.

The adder 6 adds the output signal u′ ^* (t) of the sample value control calculation unit 5 and the identification signal v * (t), and the added signal ^{u * (} t) is sampled and held in the sample hold unit 2. operation signal u to process 1
(t). That is, it is expressed by the following equation.

u(t)=u' ^* (t)+v ^* (t)...3rd formula The identification signal generator 7 generates an identification signal to be added to the operation signal.
Generate v ^* (t). This identification signal v ^* (t) is a signal containing multi-frequency components, and in this embodiment, an M-sequence signal that can be generated by a simple algorithm is used as the identification signal. Since the specific configuration for generating this M-sequence signal is generally well known, detailed explanation will be omitted here. For example, when the period of the signal is 127 and the amplitude is Am, the M-sequence signal is set to an appropriate initial state C(t-1τ) = 0 or 1 (however, i = 0, 1, ... 7). This can occur due to in this case,
The identification signal v ^* (t) can be obtained by executing the following equations 4 and 5.

C(t)=MOD(C(t-τ)+C(t-7τ), 2)
...Fourth equation v ^* (t)=Am(2C(t)-1)...The fifth equation measurement sampler 8 operates in synchronization with the sampler 4,
Sample the process signal y(t). This sampled signal was designated as a process signal with the symbol y ^* (t).

The pulse transfer function identification unit 9 identifies a pulse transfer function representing the dynamic characteristics of the process 1 from the output signal u ^* (t) and the process signal y ^* (t) by time-series processing. The pulse transfer function identification section in this embodiment is composed of a successive approximation maximum likelihood type filter.

Note that the identification signal uses an M-sequence signal as a persistently exciting signal, so the IEEE
Transaction on Automatic Control, 1976 12
Moon, Identifiability Condition for Linear
Multivariable System Operating Under
Feedback, (pp. 837-840) From the theorem described in T. Soderstrom et al., from the operation signal u ^* (t) to process 1 and the process signal y ^* (t) during closed-loop control,
The pulse transfer function of process 1 can now be identified.

Identification methods include the least squares method, the maximum likelihood method, the auxiliary variable method, and the extended least squares method, but in this example, the maximum likelihood method, which is resistant to observation noise and has high identification accuracy, was used. Identification using the maximum likelihood method can be performed using a successive approximation maximum likelihood identification filter algorithm. Now, focusing on the operation signal u ^* (t) and showing the equivalent model of process 1 and observation noise ξ(t), the third
As shown in the figure, the equivalent parameters of the process are as shown in block 14, and the equivalent parameters of the observation noise are as shown in block 15. Also, unknown parameters to be identified ai, bj + ci (where i = 1,
2, ..., m, j = 1, 2, ..., n) is expressed as a spectrum θ^, then θ^ ^T = [a^ ₁ , a^ ₂ , ..., a^m, ・b^ ₁ , b^ ₂ , ..., b^n
,・
c^ ₁ , c^ ₂ , ..., cm] ...Equation 6 (where T represents transposition), and the algorithm of the approximate maximum likelihood identification filter is similar to the Kalman filter using the following Equations 7 to 6.
It can be shown by equation 17.

θ^(t)=θ^(t-τ)+p(t-τ)・(t)/λ(t)+ ^T (t)・p
(t-τ)(t)・ε (t)...Equation 7 Here, p(t) is expressed by the following equation (n+2m)×
It is a (n+2m) matrix.

p(t)=[p(t-τ)-p(t-τ)(t) ^T (t)p(t-τ)/λ(
t)+(t)・p(t-τ)(t)]/λ(t)...8th equation Further, ε(t) is an identification error expressed by the following equation.

ε(t)=y ^* (t)−[−y ^* (t−τ),−y ^* (t−
2τ), ...y ^* (t-mτ); u ^* (t-τ), u ^* (t-
2τ), ..., (u ^* (t-nτ); ε(t-τ), ε(t
−
2τ),...;ε(t-mτ)]×θ^(t-τ)
... Equation 9 Furthermore, (t) is given by the following equation (n+2m)
It is a vector.

^T (t) = [−y〓(t−τ), −y〓(t−2τ),
……−y〓
(t-mτ); u〓(t-τ), ..., u〓(t-nτ);
ε〓(t
-τ), .

Further, λ(t) is a forgetting factor, which is selected as follows.

When the process dynamic characteristics do not change λ(t) = 1.0 ...Equation 14 Or, λ(t) = α・λ(t-τ)+(1-α)
...Equation 15 (0.95λ(o)1 0.95α1) When the process dynamic characteristics change, λ(t)=α(0.95α<1) ...The initial value of Equation 16 is selected as follows.

θ(o)=0 p(o)=β·I} ...Formula 17 Where, β is a real number of about 10 ³ to 10 ⁵ and I is a unit matrix.

By setting like this, {u ^* (t)},
The data of {y ^* (t)} is inputted every sample control period, and model parameters of process and observation noise are sequentially identified for each input using the approximate maximum likelihood type identification algorithm described above. Therefore, among the identification parameters, ai (i=1, ..., m), bj
The pulse transfer function of the process using (j=1, . . . , n) is expressed by the following equation.

A series of these algorithms of the pulse transfer function identifying section 9 is shown in FIG. Step (16)
is the calculation block of the 11th to 13th equations, and step 17 calculates ^{the T} (t) vector and φ ^T (t)
This is a calculation block for setting up a spectrum, and in step (18), the ninth equation is calculated. In step (19), the seventh and eighth equations are calculated. Step (20) is a calculation block that uses the identification result θ(t) to set the pulse transfer function Gp(z) of the process.

The transfer function calculation unit 10 calculates the transfer function of the process in the S domain from the pulse transfer function identified by the pulse transfer function identification unit 9. The calculation method is
A quadratic delay process G〓p including dead time with a step response of the identified pulse transfer function G^p(z)
By determining (s), the transfer function of the process is calculated.

G〓p(s)=Ke ^-Ls /(T ₁ S+1) (T ₂ S+1)...1st
Equation 9 The step response of this process G〓p(s) is shown in FIG. Time at which maximum slope occurs in step response
tmax and T _A and T _B shown in Figure 5 are L ₁ , T ₁ ,
There is a relationship between T ₂ and equations 20 to 22.

tmax=L+T ₁ T ₂ /T ₁ -T ₂ ln ( ^T1 _T2 )... 20th equation T _A = T ₁ (T ₂ / T ₁ ) T ₂ / T ₂ - _{T 1} ... 21st equation T _B = T ₁ + T ₂ ...22nd formula Also, if α=T _B / _TA and β=T ₂ /T ₁ , then L,
T ₁ and T ₂ can be determined as follows.

α=(1+β)・β/β ₁ −p ...23rd formula T ₁ =T _A α/(1+β) ...24th formula T ₂ =T _Aa β/(1+β) ...25th formula L=tmax −T _A αβ・ln(1/β)/(1−β ² ) ...Equation 26Here, once α is determined, β can be calculated backwards by creating a numerical table in advance from the relationship in Equation 23. be able to. Also, when T _A and tmax are found, T ₁ ,
T ₂ and L can be found.

Next, from the identified pulse transfer function e^p(z),
Find tmax, α, and T _A. By dividing the numerator of Equation 18 by the denominator, it can be expressed as Equation 27.

G^p (z) = _∞ 〓 ⁱ⁼¹ g^iz ^-i ...Formula 27 In this case, the impulse g^i (i = 1, 2, ...) is
It can be determined using the following algorithm.

g ₁ =b ₁ g^ ₂ =b^ ₂ −a^ ₁ g^ ₁ g^ ₃ =b^ ₃ −a^ ₁ g^ ₂ −a^ ₂ g^ ₁ ……………………… g ^n＝b^ _o −a^ ₁ g^ _o-1 −a^ _2o-2 …a^ _n g^ _on ……………………………………………Equation 28 This impulse Since the largest one in the series gives the largest slope in the step response, if the largest impulse is g^mx, we get:

g^mx = MAX [g^ ₁ , g^ ₂ , g^ ₃ , ...] ...Formula 29 Assuming that the maximum impulse is the MXth one, the time tmax at which the maximum slope occurs is as follows: .

tmax=(MX-1)・τ...Formula 30 From the tangent that gives the maximum slope, T _A can be obtained as follows.

T _A = τ/gmx·K ...Equation 31 α can be obtained from the following equation from the proportional relationship between T _A , T _B , and K.

α=1−( _nx-1 〓 ⁱ⁼¹ g^i)/K ...Equation 32 Here, the process gain K can be calculated as follows by setting z=i in Equation 18. .

K=( _o 〓 ⁱ⁼¹ b^i)/(1+ _n 〓 ^j=1 a^j) ...Formula 33 As above, tmax, T _A and α could be found from the impulse response. Therefore, using Equations 23 to 26 and Equation 33, T ₁ , T ₂ , L, and K can be obtained, and the process transfer function G〓p(s) can be obtained. For the next step, the 19th
When the exp part of the formula is expanded by Taylor and summarized in the denominator form, the 34th formula is obtained.

G(s)=1/(h〓 ₀ +h〓 ₁ S＋h〓 ₂ S ² +h〓 ₃ S ³ +……
)
...Equation 34 Here, h〓 ₀ = 1/K h〓 ₁ = (T ₁ +T ₂ +L) /K h〓 ₂ = (T ₁ T ₂ + (T ₁ +T ₂ )L + 1/2L ² /K ...Equation 35 h〓 ₃ = (T ₁ T ₂ L + (T ₁ + T ₂ ) L ² /2 + L ³ /6) / K From the above, the transfer function G〓p of the S region of the process
An algorithm for calculating (s) was found and is shown in the flowchart of FIG. In Figure 6, step (21) uses equation 28, step (2) uses equation 29, step (23) uses equations 30 to 33, and step (24) uses equation 23 in advance. The obtained inverse function β=f(α) is expressed as step Equation (25) in the 24th
Step (26) is a block that calculates equations 34 to 35, respectively. Figure 7 shows β=f
This is a diagram illustrating the inverse function (α).

In this embodiment, the sample value control constant unit 11 is calculated from the transfer function G〓p(s) of the process obtained by the transfer function calculation unit 10. The sample value control constant is calculated by the method described in pages 113 to 136, a method for designing a sample value control system based on partial knowledge of the controlled object. After G〓p(s) is set, the sample value PID control parameter (Kc; proportional gain,
The part for deriving Ti: integral time constant (Td: differential time constant) is made into an algorithm and shown in FIG. Note that the sample control period is set to Δt in consideration of the case where it is different from the time of identification. Step (27) is the part that determines the operating mode of the sample value controller. Step (28) is σ in case of PI operation.
This is a block for finding the root of a quadratic equation with respect to σ, and step (29) is for PID operation.
This is a block that finds the roots of the following equation. Among the roots found, the minimum positive root σ ^* is found in step (30).
Using this σ ^* , sample value PID parameters are calculated in steps (31) and (32). Using the new sample value control constant calculated by the sample value control constant calculation unit 11, the sample value control calculation unit 5 will perform sample value control calculation, and the automatic adjustment function of the control constant will be executed. That will happen.

Next, an example will be shown in which the apparatus of the present invention is applied to a secondary delay process. As a result of strict identification, it was found that the transfer function Gp(s) of this second-order lag process is as shown in Equation 36.

Gp (s) = 1/1.387 + 21.628S + 46.377S ² ... Equation 36 For this quadratic delay process, the conventional sample value PI controller (7, 9, 10,
Operation signal u(t) when making a step response (target value change 0.2) using
FIG. 9 shows the state of the process signal y(t).
In addition, sampling period T = 0.2 seconds, proportional gain Kc =
4.11, the integral time constant Ti = 5.0 seconds. An overshoot of 50% was observed, and it took over 60 seconds to settle, which is not a very appropriate response.

Figure 10 shows the case in which process dynamic characteristics are identified during closed-loop control using the device of the present invention, an optimal sample value PI constant is derived from the identification results, and a step response is generated using the derived results. This is the state of the operation signal u(t) and the process signal y(t). Section A is a period in which the control constants Kc = 1.0 and Ti = 15.6 are fixed, and identification is performed in a closed loop while injecting an M-sequence signal with an amplitude of 0.1. Section B
are the pulse transfer function identification section 9 and the transfer function calculation section 10
This is a period in which all sample value control constant calculation units 11 are operated and controlled. Section C uses converged control constants (Ki = 4.063, Ti = 15.605),
This is a step response waveform when the target value is changed.
With 10% overshoot, settling time is 18 seconds.
It can be seen that a well-damped step response was obtained, and that the control constant was tuned to an appropriate value. For reference, the step response (plot) of the pulse transfer function obtained by the pulse transfer function identification section is shown in FIG. The solid line is the step response of the actual process, and it can be seen that it is well identified.

As shown above, even if the sampling period changes, the pulse transfer function is converted into a pulse transfer function, and then converted into an S-domain transfer function of a second-order lag system that has a lot of dead time in the process. Since the sample value control constant is determined by , it can be seen that the control is stable. Furthermore, the dynamic characteristics of the process could be identified online in a very short time using a small identification signal, and the sample value control constants could also be adjusted online based on the results.

As described in detail above, according to the present invention, a small identification signal is added to the output signal of the sample value controller and injected into the process as an operation signal, and while performing closed loop control, the operation signal for each sample control period is From the process signal, identify the pulse transfer function of the process, and from the pulse transfer function S
By calculating the transfer function of the area, calculating the sample value control constant from the transfer function, and performing closed-loop control using the control constant of the calculation result, stable control constants can be obtained regardless of the sample period. For example, it is sufficient to lengthen the cycle and slowly calculate the control constant using a simple calculation method during sampling (there is no need to use a large computer that can perform extremely high-speed calculations).
Moreover, the sample value control constant can be adjusted automatically and appropriately and stably.

Since the device according to the present invention uses a minute identification signal during closed-loop control to determine the dynamic characteristics of the process, it does not cause large fluctuations in the process compared to the limit sensitivity method, limit cycle method, etc. of conventional devices, making it more practical. It is. Furthermore, since process dynamic characteristics can be identified and control constants can be automatically adjusted while executing closed-loop control, there is almost no need for adjustment of the actual controller. Moreover, since automatic adjustment can be performed even during process operation, the plant can be operated at a high operating rate, which is very beneficial.

Furthermore, when the proportional gain of the controller is fixed to zero, a closed loop state occurs, but since the identification signal is added at the output of the controller, the dynamic characteristics of the process can be identified not only in the closed loop but also in the open loop.

In addition, to identify the pulse transfer function of the process, a successive approximate maximum likelihood filter similar to a Kalman filter is used, and statistical processing is performed automatically, so there is no filter effect. , stable identification and automatic adjustment of control constants can be performed without being affected by observation noise.

Further, the operation signal for inputting the persistent excite signal to the pulse transfer function identification section is not limited to the output of the adding section 6, but may also be a signal obtained from the output of the sampling and holding section via an A/D converter. good.

Further, it goes without saying that in the apparatus of the present invention, each calculation block can be realized by software of a digital system using a microcomputer.

In the embodiment of the present invention described above, the approximate maximum likelihood method was used to identify the pulse transfer function of the process, but any identification method that can obtain unbiased matching estimates may be the extended least squares method or the auxiliary variable method. , model reference form parameter identification method, etc. can be used.

Furthermore, although an M-sequence signal was used as the identification signal, if the signal belongs to a stationary irregular process, a pseudo-random signal other than the M-sequence (Pseudo-Random signal) is used.
Binary Signal), normal random number signal, or anything is fine. Furthermore, instead of directly using the M-sequence signal, an output signal obtained by passing the generated M-sequence signal through a digital filter may be used.

In particular, by using the M-sequence signal as the identification signal, the M-sequence signal takes binary (+1, -1) or ternary (+1, 0, -1) values, so the identification process can be made easier. can be made to work,
Can be safely identified. Furthermore, since the M-sequence signal includes many frequency components, the time required for identification can be shortened. Furthermore, since the M-sequence signal is relatively easy to generate and can be obtained with a simple logic configuration, the device can be miniaturized.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing one embodiment of the present invention, and FIGS. 2 to 8 excluding FIGS.
The figures up to this figure are flowcharts explaining the contents of each block in Fig. 1, and Fig. 5 is a waveform diagram showing a step response waveform of a quadratic delay system including dead time.
Figure 7 shows the inverse function f(α) when deriving β from α.
9 is a curve diagram showing the step response of the quadratic delay process. FIG. 10 is a curve diagram showing the step response using the response during automatic adjustment and the control constant after automatic adjustment. FIG. 11 is a curve diagram comparing the step response of the pulse transfer function identified as a second-order delay process. 1...process, 2...sample hold section,
4... Sampler, 5... Sample value control calculation section,
7... Identification signal generation section, 9... Pulse transfer function identification section, 10... Transfer function calculation section, 11... Sample value control constant calculation section.

Claims (1)

[Claims] 1. In a device having a sample value PID control calculation unit that controls a process to be controlled using sample values, an identification signal consisting of a persistent exciting signal is applied to a control loop controlled by the sample value PID control calculation unit. and an identification signal generator that applies the sample value to the applied identification signal.
Input the operation signal obtained by adding the output signals of the PID control calculation unit and the process signal obtained by sampling the control amount of the process, and identify the pulse transfer function of the process using these operation signals and the process signal. a pulse transfer function identification section that calculates a transfer function in the S (Laplace operator) domain of a second-order lag system including dead time from the step response of the pulse transfer function identified by the pulse transfer function identification section; and a sampled value control constant calculation section that calculates a control constant of the sampled value PID control calculation section from the result of calculation by the transfer function calculation section.