JPH0261041B2 - - Google Patents

Description

[Detailed description of the invention]

[Purpose of the invention] (Field of industrial application) The present invention provides a sample having a function of automatically adjusting the sample value control constant of the sample value PID control calculation unit to an optimum value in accordance with changes in process characteristics while controlling the process in a closed loop. Concerning value PID control device. (Prior Art) 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 the identification of its dynamic properties. 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. (Problem to be Solved by the Invention) This type of control device includes an analog control device that handles analog quantities and a digital control device that controls while sampling data. In reality, there are only analog methods that can determine control constants (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
There is no PID controller that can be identified while controlling the process during closed-loop operation as described above.
You can simply infer the known operating state of the process and manually change the control constants corresponding to changes in the process's output to perform sample value PID control of the process, or if the behavior of the process is unknown. , the output changes of the process were depicted in a characteristic diagram, etc., and the control constants of the control device were determined by knowing the dynamic characteristics of the process by referring to the characteristic diagram. Conventional sampled value PID control devices adjust control constants while observing the response of the process during closed-loop control, so it takes a long adjustment period to adjust the control constants to suit the dynamic characteristics of the process.
The operation was 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, sample value PID control eliminates the need for actual adjustment of the control device, allows the process dynamic characteristics to be identified even during process operation, allows control with optimal control constants, and allows the plant to be operated at high operating rates. The purpose is to provide equipment. [Structure of the Invention] (Means for Solving the Problems) The present invention has a sample value PID control calculation section that controls a process to be controlled using sample values, in which a process controlled by the sample value PID control calculation section is provided. an identification signal generation section that applies an identification signal consisting of a persistent exciting signal into a control loop; an operation signal obtained by adding the output signal of the sampled value PID control calculation section to the applied identification signal; Input the process signals obtained by sampling the process control variables, and calculate the process pulse transfer function using these operation signals and process signals.

A pulse transfer function identification section that identifies [Formula] and a Laplace transform of the response obtained by connecting the step responses of the pulse transfer function of the process obtained by this pulse transfer function identification section with a straight line. A transfer function calculation unit that calculates the transfer function G ^~ _p (s) = 1/h ₀ + h ₁ S + h ₂ S ² + h ₃ S ³ +..., and the sample value PID control calculation from the result calculated by this transfer function calculation unit. This is a sampled value PID control device comprising a sampled value control constant calculation section that calculates a control constant of a sampled value control constant. (Function) A sample value PID that allows the sample value control constant obtained by the sample value control constant calculation unit to be used as the control constant of the sample value PID control calculation unit, and allows the control constant to be quickly and automatically adjusted while controlling the process in a closed loop. It is a control device. 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 belonging to a stationary irregular process such as an M-sequence signal, a random number signal, a white noise signal, etc. For example, I. Gustavsson et al.
-Ldenfiability and Accuracy Aspects-
Defined on page 65 of the magazine Automatica, published in 1977. (Example) An example 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 industry 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.
and the sampled value PID control calculation unit 5 that controls the process 1 based on the sampled deviation signal e ^* (k) output from the sampler 4.
The control device is configured. Here, k is a discrete time, meaning that the actual time t is kτ. Output signal uo ^* (k) of sample value PID control calculation unit 5
is the identification signal v ^* generated by the identification signal generating section 7
(k) and the adder 6, and the added output signal
By inputting u ^* (k) to the sample hold section 2, an operation signal u(t) for operating the process 1 is obtained. Process 1 is controlled by the obtained operation signal u(t). Output signal u ^* (k) of adder 6 and process signal y
Calculate sample value PID control constants Kc (proportional gain), Ti (integral time constant), and Td (differential time constant) using sample process signal y ^* (k) obtained from (t) via sampler 8. . 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 the sample value
Input to PID control calculation section 5. That is, the control constant of this calculation unit 5 is adjusted in accordance with the fluctuation of 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 ^* (k) of the sampler 4 according to the following algorithm using sample value control constants to be described later, and generates the signal uo ^* (k). Output. This algorithm is a well-known speed-type PID algorithm, and if the proportional gain Kc, the integral time constant Ti, the differential time constant is Td, and the sample control period is τ, then the output signal of the sampled value PID control calculation unit 5 is uo ^* (k). is, uo ^* (k)=uo ^* (k-1) + Δuo ^* (k) ...Equation 1 Where, Δuo ^* (k)=Kc{e ^* (k)−(e ^* (k-1)) +τ/Tie ^* (k)+Td/τ(e ^* (k)−2e ^* (k−1)+e ^* (k−2))}...It is expressed by the second equation. This calculation is performed in the order of the flowchart shown in Figure 2, by first executing Δuo ^* (k) in step (12),
Next, execute uo ^* (k) in step (13). The adder 6 adds the output signal uo ^* (k) of the sample value control calculation unit 5 and the identification signal v * (k), and the added signal ^{u * (} k) is sampled and held in the sample hold unit 2. This becomes the operation signal u(t) to process 1. That is, it is expressed by the following equation. u ^* (k) = uo ^* (k) + v ^* (k) ... 3rd formula The identification signal generator 7 adds the identification signal 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 signal period is 127 and the amplitude is Am, the M-sequence signal should be set to an appropriate initial state C(k-i) = 0 or 1 (however, i = 0, 1,...7). This can occur due to In this case, the identification signal v ^* (k) can be obtained by executing the following equations 4 and 5. C(k)=MOD(C(k-1)+(k-7), 2)
...4th equation v ^* (k) = Am (2C(k)-1) ...5th equation Sampler 8 operates in synchronization with sampler 4,
Sample the process signal y(t). This sampled signal was designated as a process signal with the symbol y ^* (k). The pulse transfer function identification unit 9 that identifies the ARMA model uses the output signal u ^* (k) and the process signal y ^* (k) to
The pulse transfer function representing the dynamic characteristics of process 1 is identified by time series processing. The pulse transfer function identification section in this embodiment is composed of a successive approximation maximum likelihood type filter. The identification signal is
Since the M-sequence signal is used as the persistently exciting signal, lEEE Transaciton on Automatic Control,
December 1976, ldentifiability condition for
Linear Multivariable System Operating
Under Feedback, (pp ^{. 837-840} ) T. Soderatrom
According to the theorem described by others, the pulse transmission relationship of process 1 can be identified from the operation signal u ^* (k) to process 1 and the process signal y ^* (k) during closed-loop control. 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, if we focus on the operation signal u ^* (k) and the process signal y ^* (k) and show the equivalent model (ARMA model) of process 1 and observation noise ξ(k), as shown in Figure 3, the process The equivalent parameters of the observation noise are as shown in block 14, and the equivalent parameters of the observation noise are as shown in block 15. Also, the unknown parameters to be identified are ai^, bi^, ci^ (where i=1, 2,...,
m, j = 1, 2,..., n) is expressed as a vector θ^, then θ^ ^T = [a^ ₁ a^ ₂ ,,...a^m, b^ ₁ , b^ ₂ ,..., b^ n, c^ ₁ , c
^ ₂ ,...,c^m〕...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 17. can be shown. θ^(k)=θ^(K-1)+p(k-1)・ψ(k)/λ(k)
+ψ ^T (k)・p(k−1)ψ(k)・ε(K)……Equation 7 Here, p(k) is expressed by the following equation (n+2m)×
It is a (n+2m) matrix. p(k)=[p(k-1)-p(k-1)ψ(k)ψ ^T (k)p(
k
-1) λ(k)+ψ ^T (k)・p(k-1)ψ(k)]/λ(k)...Equation 8 Also, ε(k) is the identification error shown by the following equation. be. ε(k)=y ^* (k)−[−y ^* (k−1), −y ^* (k−2),…
, −y ^* (k-m), u ^* (k-1), u ^* (k-2) ..., u ^* (k-n), ε (k-1), ε (k-2), ...
, ε(k-m)]×θ^(k-1)...Equation 9 Furthermore, ψ(k) is an (n+2m) vector given by the following equation. ψ ^T (k)=[−y〓(k−1), −y〓(k−2), …, −
y〓(k-m), u〓(k-1), ..., u〓(k-n), ε〓(k-1), ..., ε〓(k-
m)]...Equation 10 Here, the elements of the ψ(k) vector are approximated as follows using the approximate maximum likelihood method. Also, λ(k) is a forgetting factor, which is selected as follows. When the process dynamic characteristics do not change, λ(k)=1.0...Equation 14 or λ(k)=α・λ(k-1)+(1-α)...Equation 15 (0.95λ(a) 1 0.95α1) When the process dynamic characteristics change λ(k)=α(0.95α1) ...The initial value of Equation 16 is selected as follows. (θ^(o)=O P(o)=β・I} ...Equation 17 However, β is a real number of about 10 ³ to 10 ⁵ and is a unit matrix. u ^* (k)}, {y ^*
(k)} data is input every sample control period,
For each input, model parameters of process and observation noise are sequentially identified using the approximate maximum likelihood identification algorithm described above. Therefore, among the identification parameters, a^i (i = 1, ..., m), b^j (j = 1,
..., n), the pulse transfer function of the process is
It is shown by the following formula. A series of these algorithms of the pulse transfer function identifying section 9 is shown in FIG. Step (16)
are the calculation blocks of the 11th to 13th equations, step (17) is the calculation block that sets up the ψ ^T (k) vector and the φ ^T (k) vector, and step (18) is the calculation block of the 9th equation Calculate. 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 G^p(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. Here, the algorithm focuses on the fact that the step response of the pulse transfer function of the identified process matches the step response of the actual process. First, by dividing the numerator by the denominator, Equation 18 is expressed as the following equation. G^p (z) = _∞ 〓 ⁱ⁼¹ g^i z ...Equation 19 Therefore, if the step response of the pulse transfer function of the identified process is x(k), then x(k) is expressed as manifest. x(k)= _k 〓 ⁱ⁼¹ g^i ...Equation 20 The response x〓(t) when x(k) is connected by a straight line is calculated using the following equation. x〓(t)= _o-1 〓 ⁱ⁼⁰ g^i+gn/τ・t (n-1)τ≦t<nτ ...The Laplace transform of Equation 12 x〓(t) is x〓(s ), then X〓(s) becomes X〓(s)=e〓 ^s −1/τs ²・_∞ 〓 ⁱ⁼¹ g^i・e ⁻ⁱ 〓 ^s ...the 22nd equation. X〓(s) is the process transfer function G〓p(s)
When considered as a step response, G〓p(s) is expressed by the following equation. G〓(s)=e〓 ^s −1/τs・_∞ 〓 ⁱ⁼¹ g^i・e ^-i 〓 ^s ...Equation 23 The second term on the right side of Equation 23 includes an infinite series, Not realistic. Equation 19 is equivalent to Equation 18, so using this, Equation 23 becomes becomes. Expanding the exponential part and expressing G〓(s) as a denominator transfer function, the coefficients of s up to the third-order terms can be found as follows. G〓p(s)=1/h ₀ +h ₁ s+h ₂ s ² +h ₃ s ³ +… 25th formula h〓 ₀ =D ₀ h〓 ₁ =D ₁ −τ/2h〓 ₀ h〓 ₂ = D ² −τ／2h〓 ₁ −τ ² /6h〓 ₀ h〓 ₃ =D ₃ −τ／2h〓 ₂ −τ ² /6h〓 ₁ −τ ³ /24h ₀ ……2
Equation 6 Here, D ₀ = A ₀ / B ₀ D ₁ = (A ₁ − D ₀ B ₁ ) / B ₀ D ₂ = (A ₂ − D ₀ B ₂ D ₁ B ₁ ) / B ₀ D ₃ = (A ₃ −D ₀ B ₃ −D ₁ B ₂ −D ₂ B ₁ )/B ₀ ...Equation 27 From the above, the transfer function G〓p in the S region of the process
An algorithm for calculating (s) was found. A specific algorithm based on this is shown in a flowchart in FIG. Step 21 in Figure 5 is the 27th step.
In the part that calculates the formula and the 28th formula, step 22
is the part that calculates the 27th equation, and step 23 is the part that calculates the 27th equation.
This is the part that calculates 26 formulas. In this embodiment, the sample value control constant calculation unit 11 calculates the process transfer function G〓p(s) obtained by the transfer function calculation unit 10, as described in Kitamori's Transactions of the Society of Instrument and Control Engineers, Vol. 15, No. 5, 1979. The sampled value control constants are calculated using the method described in No. ^113-136 , Method of designing a sampled value control system based on partial knowledge of the controlled object. After G〓p(s) is set, the sample value PID control parameters (Kc: proportional gain,
The algorithm for deriving Ti: integral time constant, Td: differential time constant is shown in Figure 6. 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 (4) is a part for determining the operation mode of the sample value controller. Step (25) is a block diagram for finding the root of a quadratic equation regarding σ in the case of PI operation, and step (26) is a block diagram for finding a three-dimensional root regarding σ in the case of PI operation. Among the roots found, the minimum positive root σ ^* is found in step (27).
Using this σ ^* , the sample value PID parameter is calculated in steps (28) and (29). Using the new sample value control constant calculated by the sample value control constant calculation unit 11, the sample value control constant calculation unit 5 will perform sample value control calculation, and the automatic adjustment function of the control constant will be executed. It turns out. Next, FIG. 7 shows the results of applying the apparatus of the present invention to a secondary delay process. Section A is
This is an interval in which the M-sequence signal is injected during closed-loop control to identify the process and adjust the sample value control constant. On the other hand, section B shows the response when the injection of the M-sequence signal is stopped and a target value change of 0.2 is applied using the adjusted control constant in order to show the effect of adjusting the control constant. be. A step response with good damping was obtained. As shown above, regardless of the sampling period, the pulse transfer function is identified and then converted to the S-domain transfer function, and the sample value control constant is determined by this S-domain transfer function. 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. [Effects of the Invention] As detailed above, according to the present invention, a small identification signal of several percent 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 pulse transfer function of the process is identified from the operation signal and process signal for each sample control period, and the S area is calculated from the result of Laplace transform of the response that connects the step response of the process transfer function obtained by identifying the pulse transfer function. A stable control constant is determined regardless of the sample period by calculating the transfer function of For example, you can simply lengthen the cycle and slowly calculate the control constants 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. The device according to the present invention uses a minute identification signal during closed-loop control to know the dynamic characteristics of the process, so it is practical because it does not cause large fluctuations in the process compared to the limit sensitivity method, limit cycle method, etc. of conventional devices. It is. Furthermore, since process dynamic characteristics can be identified and control constants can be automatically adjusted while performing closed-loop control, there is almost no need for adjustment of the actual controller. Furthermore, since automatic adjustments can be made even during process operation, the plant can be operated at a high operating rate, which is extremely beneficial. Furthermore, when the proportional gain of the controller is fixed to zero, it becomes an open loop state, but since the identification signal is applied at the output point 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 sequential approximate maximum likelihood filter similar to the Kalman filter is used, and statistical processing is performed automatically, so there is a filter effect, and the observation Stable identification and automatic adjustment of control constants can be performed without being affected by noise. Furthermore, the operation signal for inputting the persistent excite signal to the pulse transfer function identification section is not limited to the output of the adder 6, but may also be a signal obtained from the output of the sampling and holding section via the A/D conversion section. good. 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. In addition, although an M-sequence signal was used as an identification signal, if the signal belongs to a stationary irregular process, a pseudo-random signal other than the M-sequence
BinarySignal), 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 identification process can be made easier because the M-sequence signal takes binary (+1,,-1) or ternary (+1, 0, -1) values. It can be operated without
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 and 3 to 6 are flowcharts explaining the contents of each block in FIG. FIG. 3 is a diagram illustrating a part of the block diagram of the present invention, and FIG. 7 is a curve diagram showing the response as a result of applying the embodiment of the present invention to a quadratic delay process. 1...Process, 2...Sample hold, 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)

[Scope of Claims] 1. In a device having a sample value PID control calculation unit that controls a process to be controlled using sample values, a persistent exciting signal is provided in a control loop controlled by the sample value PID control calculation unit. an identification signal generator that applies an identification signal consisting of a sample value to the applied identification signal;
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 are input, and these operation signals and process signals are used to calculate the pulse transfer function of the process [formula ] A pulse transfer function identification section that identifies the pulse transfer function, and a transfer function in the S (Laplace operator) domain from the result of Laplace transform of the response obtained by connecting the step responses of the pulse transfer function of the process obtained by this pulse transfer function identification section with a straight line.
G〓 _p (s) = 1/h ₀ + h ₁ S + h ₂ S ² + h ₃ S ³ +..., and a transfer function calculation section that calculates 1. A sampled value PID control device, comprising: a sampled value control constant calculating section that calculates a control constant.