JPS6394304A - Discrete time controller - Google Patents

Abstract

PURPOSE:To improve a responsiveness at the time of a rise and to execute a stable control at the time of a steady state by using an adaptive on and off control function in a transient state and executing a minimum discrete control in the steady state. CONSTITUTION:In the transient state, the controlled variable is detected for a prescribed sampling time, an operation by a binary switching is carried out to a controlled system for every sampling interval, the parameter of the model of the controlled system is estimated based on the controlled variable and the manipulated variable by using the discrete time type adaptive on and off control means 5 and the controlled variable sequence predicted as a response when the manipulated variable throughout several steps in future is applied to the model is estimated. In the steady state, the minimum discrete control 32 is carried out from the parameter of the model of the controlled system obtained at the time of controlling the transient state is executed and the controlled system is controlled by the successive control for the controlled variable according to a self-tuning.

Description

[Detailed description of the invention] The present invention will be explained in the following order.

field of invention Summary of the invention Background of the invention technical challenges Structure and effects of the invention Description of examples Overall configuration of the example (Fig. 1) ASC functional block (Fig. 1, Fig. 2).

(Fig. 3) Steady-state control function block Control function switching mechanism (Fig. 4) [Field of the Invention] The present invention relates to a discrete-time control device for a continuous-time controlled object, and particularly relates to a discrete-time on-off adaptive control function and a continuous operation amount agent. ? This invention relates to a discrete time control device having II functions.

[Summary of the invention]

The present invention is a control device that controls a continuous-time controlled object, and in a transient state, the control amount is detected at every predetermined sampling time, and the controlled object is operated by binary switching at every sampling interval. , the parameters of the model to be controlled are estimated based on past controlled and manipulated variables, and when the manipulated variables over several future steps are given to the model, what is the predicted response? [Ut
Using a discrete-time on-off adaptive control function that estimates the control amount and controls the continuous-time controlled object so as to obtain the optimal control amount, in the steady state, the Distributed control is performed, and the controlled object is controlled by continuous operation amount control using self-tuning.

(Background of the Invention) PID control devices are widely used for process control of plastic processing, industrial furnaces, chemical plants, etc. In order to correctly control the controlled object using such a control device, it is necessary to set the PID parameters correctly.
Tuning of the D parameter largely depends on the experience of the on-site operator, and it has been difficult to appropriately set this parameter when the characteristics of the controlled object change significantly. Therefore, auto-tuning PID control devices that use the step response method or the limit sensitivity method have been proposed in the past, but it is necessary to start up and operate the controlled object in advance for tuning, and it is necessary to start up and operate the controlled object. It has been difficult to achieve both stability and steady-state stability.

On the other hand, in response to the need to use an inexpensive and robust binary switching actuator for continuous control objects, a discrete-time on-off switching adaptive control device (hereinafter referred to as ASC) has been proposed ( JP-A-60-41101). This AS
It is known that C is extremely superior to conventional PID controllers in terms of rise characteristics and stabilization against disturbances for objects to be controlled with relatively large time constants, such as temperature control.

However, in this adaptive control device, the operation amount is always binary (on and off), and a large amount of calculation is required, so the sampling period cannot be made very short. Therefore, in a steady state, there is a problem in that the fluctuation of the controlled variable may be larger than that in a general sampling control device using a continuous manipulated variable.

[Technical issues]

The present invention is a control device for a continuous time controlled object, comprising:
The technical challenge is to use the ASC control function to improve responsiveness at startup and when changing set values, and also to improve stability in a steady state, and to be able to automatically determine the control parameters through auto-tuning. do.

[Structure and effects of the invention]

(Means for Solving the Problems) The present invention is a discrete-time control device that controls a continuous-time controlled object, and as shown in FIG. A sampling detection means for detecting, and an operation means for selectively switching between operation by value switching and continuous operation by external input to operate the continuous-time controlled object at each sampling interval, and a discrete-time controlling object for the continuous-time controlled object. Using the type model,
In order to adapt the model to the controlled object, the parameters of the model are estimated and updated at each sampling interval based on the amount of operation to the binary switching actuator and the amount of control detected by the sampling detection means. Operation of a binary switching actuator by selecting a plurality of predicted control variable sequences over a plurality of sampling intervals that are predicted as a response when a possible control variable sequence is given to a discrete-time model. Continuous operation control is performed on a continuous-time controlled object by minimum variance control based on a discrete-time adaptive on-off control means that determines the amount, and parameters obtained by a discrete-time model estimated by the discrete-time adaptive on-off control means. It is characterized by comprising continuous operation amount control means and switching means for selectively switching between the discrete time adaptive on/off control means and the continuous operation amount control means according to the target setting value and the current control amount. .

(Function) According to the present invention having the above-mentioned characteristics, the adaptive on/off control function is used during system start-up or in transient states such as setting value changes to achieve control characteristics with quick response and little overshoot. There is.

In the steady state, minimum variance control is performed using the parameters of the discrete time model estimated by the discrete time adaptive on/off control means in the transient state, and the parameters are determined by the discrete time model and autotuning is performed. , and automatically switches between a steady state and a transient state.

(Effects of the Invention) Therefore, according to the present invention, when changes are made during startup or settings, responsiveness is improved and excellent characteristics are exhibited with less overshoot, and even in a steady state there is less fluctuation. The controlled object can be controlled stably. In addition, since parameters for steady-state control with continuous manipulated variables can be obtained using the discrete time type model, there is no need to tune the parameters, and the burden of calculation time is relatively low. can be controlled by continuous operation amount.

[Explanation of Examples]

(Overall Configuration of Embodiment) FIG. 1 is a block diagram showing the conceptual structure of a discrete time control device according to the present invention. As shown in the figure, this discrete time control device has an ASC control function and a steady state control function. That is, the controlled object 1 is provided with an operating section 2 having a function of holding input signals. If the controlled object 1 is, for example, a plastic processing object, the operating section 2 is, for example, a heating means. Controlled object 1 system? The amount of Il, for example, the temperature, is detected by the measurement unit 4 with disturbance added from the addition point 3, sampled at a predetermined period, and sent to the ASC function block 5. It is provided to the steady state control function block 6 and the control function switching mechanism 7. Further, a set value for the controlled object 1 is given to the terminal 8, and the set value is given to the control function switching mechanism 7 and the switch 9. ASC function block 5
is a control II mechanism block to which a sampled measured value of the control amount is given from the measuring section 4 and a set value is given from the switch 9, and which performs a binary switching operation on the control object 1 at predetermined sampling intervals. The ASC function block 5 is used for control in a transient state, and a sequence of optimal manipulated variables is output to the switch 10. Further, the steady-state control function block 6 is supplied with set values and sampling measurement values of the controlled object 1 via a switch 9, and is further supplied with parameters of the discrete-time model estimated by the ASC function block 5, as will be described later. . The steady-state control function block 6 continuously controls the amount of operation of the controlled object 1, and calculates the amount of control under minimum variance control based on the parameters of the discrete-time model of the ASC function block 5, as described later. Minimum variance control is performed. The output of steady state control function block 6 is provided to switch 10.

The control function switching mechanism 7 selectively provides these outputs to the operating section 2 by simultaneously switching the switch 9 and the switch 10. Further, the operation amount sequence held in the operation section 2 is given to the ASC function block 5. The control function switching mechanism 7 discriminates between a transient state and a steady state based on the set value and the control amount obtained from the measuring section 4, and selectively operates the ASC function block 5 and the steady control function block 6.

(ASC Functional Block) Next, the ASC functional block 5 will be explained in more detail. Controlling the temperature, etc. of controlled object 1? The amount of il is taken out from the measurement unit 4 at fixed sampling intervals T.

Here, in order to estimate the parameters of the controlled object 1, the controlled variable Y(1) measured at equal time intervals T and the manipulated variable U(11) actually applied to the controlled object 1 are used.

Then, from these values Y(1) and U(1), the DC components of the equilibrium values Uo and Yo of the manipulated variable and controlled variable at the time of starting the operation are subtracted, and the controlled variable and manipulated variable are expressed by the following equation.

y(ll=Y(t)-Y.

u (1) = U (11-U o
--------(1) Here, i is a parameter for discretely representing time, and time is the sampling interval T
It is expressed as i·T (i=o, 1.2−・−・−) using . These manipulated variables u (1) and controlled variables) + +11
is used in the parameter estimation block 21, and a discrete-time model 22 of the controlled object 1 is determined. This discrete time model 22 is given by the following equation.

and B(z-') are respectively given by the following equations. Here, "" indicates an estimated value.

A(z-') = 1 +a, -z-'+ ---+
a, -1-+1air ""-""+ an, b
a+'------'+bn is the parameter to be estimated by the parameter estimation block 21.

The dimension n of the discrete-time model is appropriately selected depending on the object to be controlled.

Using this transfer function, the control 13 y(11) and the manipulated variable u (1) at the i-th sampling time are expressed by the following equation.

y (1) = G fZ) -u (11・----
(41 The control amount yi is described in the form of a vector as follows. The symbol - represents a vector.

Parameter vector = ('a+・----a n l b hee----
b J ” −・−(5) Signal vector ball (ll=()′ (i−1) −−−−−1・−y(
i-n) l u (i -1) -----u (i -
n))' --------(6) Next, this parameter estimation method will be explained.

Parameter estimation is performed, for example, by the iterative least squares estimation method, and is realized by minimizing the so-called equation residual e(1) of the loss function.

e (i)= y (1) −x” (1) ・a (
i-1) ------17) The successive estimation of the parameter vector L is performed by multiplying the correction term, that is, the equation residual e (1) by the correction vector 1).That is, the sequential estimation equation is given by the following equation.

Correction vector 1 (11 is Sukasi (Equation (lO)) and the normalized covariance matrix of parameter residuals (Equation (11))
including.

z(ll=□・ヱ(i-1)・x (1) --
−1～(9)α2(1) α2(1)−5” (1)・ヱ(i−1)・x (1)
+ρ;0kuρ≦1 −・−・・(10) Upper(11= (±−1(11・dama” +11)・dan(i
1)/ρ−...(11) (±=identity matrix) The adaptation coefficient ρ in equations (10) and (11) represents the weight of data, and this ρ allows The current data is also highly evaluated. Choosing ρ such that ρ<1 changes the parameters more significantly.

In this way, there is greater margin for changing parameters, and it becomes easier to follow a control target that changes over time.

A general description of this parameter estimation is given in the following document (11).

Astrom/Eykhoffr System Identification Method” - Actual System Identification
-A 5urvey) JAutomatica
, Vol., 7. I) L 123-162+ Pe
rgamonPress, 1971 and V,
5trejc r least squares parameter estimation method (Lea
st 5quares ParameterEst
imation) J Automatica,
Vol, 16 + pp.

535-550. Pergamon P res
s, 1980° The discrete time model 22 thus obtained is used in the next predictive on/off switching control to determine the amount of on/off operation to be applied to the controlled object 1 at the next sampling interval. In the transient state control, the discrete time model 22 calculates the switching point of the binary manipulated variable level that provides the optimum transient characteristics over a plurality of future sampling steps.

FIG. 2(a) is a graph showing changes in the control amount in a transient state in continuous time control, and FIG. 2(b) is a graph showing control in a transient state in discrete time control.

Assuming that the target value is changed from 1 to odor at time t0 in FIG. 2(a), the control amount y(t) approaches the new target value -2 as time passes. and time L0
At a later point in time t2, the control amount y2 is expressed by the following formula % formula % (1
2) There exists an optimal switching point t1 of the manipulated variable level such that: And time 1. By switching the manipulated variable to the new target value -2, it is possible to quickly change the target value to the new target value -2 without overshooting and with optimal transient characteristics.

Even in discrete time control, if the sampling time T is sufficiently small, the time tt-to can be approximated by the time (t+1o)T, so this characteristic can be realized.

In Fig. 2, the dash-dotted line indicates the operation N u (1) and the corresponding control 11ty (t>) which are switched to the opposite level after the next sampling interval within the prediction time starting from time (il-2). .Also, the solid line is the time (
The predicted values of the manipulated variables and controlled variables within the predicted time starting from i+1) are shown. Transient state control is control until the predicted future control amount y(k) reaches the new target value -2, so for prediction, the extreme value point y of the control amount,
It is sufficient to determine the position of X. At a sampling point i in a transient state, the manipulated variable sequence generator 2
If the target value change (wz w+) is positive, then U (t +
1) = (u msx, u mtn, −'-”'
u *t+t) ” '−−−−−−−' (14) When the target value change (wz w+) is negative" and (1"1) =
(u earn, un□, ・--1~・-u,
, , ) Ding - - - (15) Assuming that the sequence of manipulated variables is generated, the predicted controlled quantity sequence by the prediction mechanism block 24 is predicted as shown in the following equation.

)'(i+1)=(y(i+2), −−−−−・−
y (i+ r +1)) ・−・−(16) The evaluation mechanism 25 determines whether to switch the manipulated variable <i+1) at the next sampling point based on the position of the extreme point of the predicted controlled variable sequence obtained in this way. do. For example, as shown in Figure 3, when the target value change is positive, the chain line indicates the control amount sequence predicted at the previous sampling interval, and the solid line indicates the two types of control predicted this time based on equation (14). Quantities 1 and 2 are shown respectively. When the target value deviation '/a(=Wt)' @X) at the extreme point y1111 has a positive value smaller than the target value deviation y4° predicted at the previous sampling interval, as in the predicted control amount sequence a. For (ya >3'a., ya > 01, the manipulated variable sequence of equation (14) is considered to be optimal, and the manipulated variable y(i+1) is held at u,,X. Also, the predicted controlled variable sequence b If the sign of the target value deviation yd changes at the extreme point as shown in FIG. If it does not exist, the same process is performed by treating the final value of the prediction step as the extreme value.In this way, when the deviation force <,, < w, at the extreme value point of the predicted control amount sequence, the minimum positive When the number w, >w, the control variable sequence is considered to be optimal when it takes the largest negative value, and discrete-time control in the transient state is performed.Next, the optimal manipulated variable sequence selection block 26 evaluates such an evaluation mechanism. The operation amount generated by the operation amount sequence generator 23 is selected in accordance with the operation amount sequence generator 23, and is applied to the changeover switch 10.

(Steady State Control Function) Now, in the steady state control function block 6, the parameters of the minimum variance control are estimated by the discrete time model 22 used in the ASC function pronk 5 described above. Minimum variance control is described in Reference 1 (Theory and Applica
tions of Self-Tuning Regu
lators K, J.

ASTROM, others atomatica, Vo1.1
3+ pp, 457-476° Pergamon Pr
ess+ (1977), this is a control method that minimizes the variance of the difference between the control amount obtained from the controlled object 1 and a preset setting value, and the input/output obtained at time t. This is a method in which a predicted value of the output for a predetermined period of time is calculated from information, and the control input is determined so that the difference between this and a set value becomes 0. Here, it is assumed that the input/output characteristics of the controlled object 1 are expressed by the following 2.

A(z-') y(1)=z-'B(z-') u(
1) + C (Z-ri ξ(1)...-(17) where ξ11) is white noise with zero mean, and d is dead time.

z −1 is a time delay work element, A (z−′),
B(z-') and C(z-') are coefficient polynomials given by the following equations, respectively.

A (z-') = 1 + a+2-' + a
zZ-" +～--・-+ B, 1z-11B (z-
') =b+ +b2z-'+b,z-"10'-
"""+bl@Z-(+*-1)C(2-') = 1
+C+2-'+Cz2-"+'-'-""'+C
tZ-'...-(18) And the controlled object is dead time d≧1, and the coefficient polynomial A
The degrees n, m, and L of (z-'), B(z-'), and C(z-') are known, and the coefficient polynomials are irreducible to each other and are all asymptotically stable.

Now, as an evaluation standard, the output V that minimizes the following formula
It is necessary to determine the control force u (1) that minimizes the difference between (1) and the reference value w (t).

J Gourd E [((yfl) −w(1)) ”]
・・・・・・−・−(19) The input/output information obtained at time t is y(11°)′(j−1)+′−”′−+
There are u(11, u(i-1), . )u(1)+
C(z-')ξ(i+d)・-1111・(20) Here, the control human power u (1) is the output y (i+d
), but has no effect on previous outputs. Also, the second term on the right side of equation (20) is ξ(i+d)
, ξ(i+d-1) +-・-・ξ(i-1) ,
It is a linear function of ξ(11. Here, ξ(1), ξ(i−
1) ... can be calculated backwards from the information obtained at time i. Therefore, the following identity is used.

C (z-') = A (z-') F (z-')
+ z −'G (z-')−・−・−・(21) However, F(z−1)=1+flz−′+−・・−+f4−1z
−”−breath)G (Z−') =go”g+Z−' 10−
−=+g, −, z −”−”・・・・・・−(22) Here, the orders of F (z−′) and G (Z−′) are determined in the − meaning in equation (21), so Respectively (
d-1) order, (n-1) order. Now, by multiplying both sides of equation (20) by F(z-') and substituting equation (21), the following equation is obtained.

(C(z-')-z-'G(z-')) y (i+d
)=B(z-')F(z-')u(1)+C(z-')
F (z-')
+d) = [G (one z)F (11+ B (
z-')F (Z-')u (1)ko /C(z-')
+ F (z-')ξ(i+d) -
1--(24) Further, by subtracting the set value w (1) from both sides, the following 2 is obtained.

y (i+d) −w (1) = [F(z-')y(ll+B(z-')F(z-'
) u(11-C(z-') w(1)] / C(z-
') + F (z-')ξ(i+d) where H(Z-
') = B (z-') F (z-') and taking the variance of each side, E [(y(i+d)-w(11) ''1=E [(G
(z-')y(1)+H(z-')u(1)-C(z-
riw (1)) ”/C(z-ri]+E [(F(Z
−')ξ(i+d)) 2] −−−−−(26
) and y(1), )F (i-1) --, u(
1), u(i-1) ---.

w tl), w (i-1) -- and ξ(i+d)
−−−−1ξ(i+d−1) ・−・・・ξ(i+1
), the expected value term of the mixed product is zero. Therefore, the predicted value y''(t+a l t
) is determined by the following formula.

y”(i+d l i)=[G(z-') y(1)
+ H(z-') ufl)-C(z-') w(t)
] / C(z-') -・------(27)
In minimum variance control, this equation (27) is controlled to be zero. That is, the control input at that time is given by the following equation.

u(1)=-[G(z-')y(1)-C(z-') w(it]/H(z-')
----(28) In this case, equation (26) is transformed as follows.

E [(y (i+d) −w(i)) “ko”E C
(F(z-')ξ(i+d)) ”] −・・−
(29), and the control unit receives only uncontrollable noise.

Here d=1. When L=Q and m=n, the following equation holds true.

C(z-')=1. F(z-')=1゜G(z-
') = -(at +a, z-' + -...
-anz-(-”)-...-(30) Therefore, the operation tQ (i) is given by the following equation.

bl + bzz-' +-・-b, lz-+11-1
>・−・−(31) u (1)−1/b+ (at y (1) +fi
, y (i-1) + -------aay(i-
n+1) +w(1)-btu(i-1)-b3u(
i-2)---b a u (i-n+1) 'i
-・---(32) Thus ASC
Discrete-time type of control function block 5 ^ ^ ^ Parameters a, ~an+ l) estimated by model 22
Using l to b1 as they are as a1 to an and bl to b7, the design calculation mechanism of block 31 calculates the manipulated variables for minimum variance control. Block 32 holds this control amount for a predetermined sampling period and outputs it to switch 10. The operation amount under the minimum variance control thus obtained is applied to the operation section 2 via the switch 10.

(Operation of control function switching mechanism) Now, transient state control using the ASC function block 5 and steady state control using the steady state control function block 6 are switched by the control function switching mechanism 7. A signal given to is selected as an input/output of one of the blocks. The control function switching mechanism 7 is given a set value w (1) and a control amount (a) (11), and one of them is selected by comparing the deviation yd (1) with the full control range. Deviation y4 (i) is expressed by the following formula.

ya (1)=l)'(1) w(1)l
-...- (33) Fig. 4 is a graph showing temporal changes in the control amount when changing the set value. In the figure, when the operation starts at time t3, the deviation y4 is sufficiently larger than the full range of control, so first, the changeover switch 9.10 is operated until time t4 to switch the input/output to the ASC function block 5. Then, as shown in Figure 4, the AS
Transient state control is performed by C. And the control amount y+
increases and the deviation yd mentioned above becomes 0.5 of the full range of control.
%, the control function switching mechanism 7 operates the changeover switches 9 and 10 to switch the input/output to the ASC function block 5 to the input/output to the steady state control function block 6. At this time, the minimum variance control design calculation mechanism 31 calculates the parameters as described above based on the discrete time model 22 of the ASC control function block, and the minimum variance control block 32 performs minimum variance control after time t4. Execute. Then, when the set value is switched at time t5, ASC control is similarly executed in a transient state,
Time 1. Thereafter, minimum variance control is executed again.

[Brief explanation of the drawing]

FIG. 1 is a schematic block diagram showing the overall configuration of a discrete time control device according to the present invention, and FIG. 2 is a diagram showing how the controlled variable approaches a new target value when the manipulated variable is switched once in a transient state. , Fig. 2(a) shows the second
Figure (bl is a diagram for the case of discrete time using the ASC control function block 7. Figure 3 is a diagram showing the predicted control amount sequence and its evaluation, and Figure 4 is a diagram showing the temporal change of the set value and the control amount. It is a graph showing an example of a control state. 1. --- Controlled object 2 --- Operation section (operation means) 4 --- Measurement section (sampling detection means) 5 --A SC function block (discrete time type adaptive on/off control means) 6... Steady state control function block (continuous operation amount control means)
7-- Control function switching mechanism (switching means) 9.
10-...-Switch switch 21--Parameter estimation mechanism 22--Discrete time model 23-- Manipulated amount sequence generator 24-
...-Prediction mechanism 25---Evaluation mechanism 26
・−・・Optimum manipulated variable sequence selection block 3
1.--Design calculation mechanism 32.--Minimum dispersion control block Patent applicant Tateishi Electric Co., Ltd. Agent Patent attorney Yoshiki Okamoto (and 1 other person) Figure 2 (a) Figure 2 (b) Figure 3 Figure io i・T iT+Tp Figure 4 Procedures Amendment (Spontaneous) November 1986
January 28th 1, Incident indication 1986 Patent Application No. 240748 2 Name of invention Discrete time control device 3 Name of person making amendment Name (294) Representative of Tateishi Electric Co., Ltd.
Takao Tateishi 4, Agent address 5, 3rd floor, Shinkosan Building, 1-13-38 Nishihonmachi, Nishi-ku, Osaka-shi, Osaka 8550, Column 6 for detailed description of the invention in the specification subject to the amendment, Contents of the amendment ( 1) ry (i
+d) -W (11...-(25) Correct the description of J as follows. r V (i+d) -w (11 = [G(z-')y(ll+B(z- ')F(z-'
)ufll-C(z-')wll)] /C(z-')
+F(z-riξ(i+d)----1...(25)J or more

Claims (1)

[Claims] (1) A discrete-time control device for controlling a continuous-time controlled object, comprising: a sampling detection means for detecting a control amount of the continuous-time controlled object at every predetermined sampling interval; an operating means for selectively switching the operation between a binary switching operation and a continuous operation based on an external input; The parameters of the model are estimated and updated at each sampling interval based on the operation amount to the binary switching actuator and the control amount detected by the sampling detection means, and the model parameters are estimated and updated at each sampling interval. determining a manipulated variable for the binary switching actuator by selecting a plurality of predicted control variable sequences over a plurality of sampling intervals that are predicted as a response when the manipulated variable sequence is given to the discrete-time model; discrete-time adaptive on-off control means; and continuous operation for performing continuous operation control on the continuous-time controlled object by minimum variance control based on parameters obtained by the discrete-time model estimated by the discrete-time adaptive on-off control means. Discrete time control characterized by comprising: a quantity control means; and a switching means for selectively switching the discrete time type adaptive on/off control means and the continuous operation quantity control means according to a target set value and a current control quantity. Device.