CS213872B1 - Regulator with exponential predictor of the first degree - Google Patents

Description

BACKGROUND OF THE INVENTION The present invention relates to a first-stage exponential precluder regulator which extrapolates an input function by a balancing method with scales forming an exponential sequence.

Previously known predictors, used in the regulation of interval energy consumption, e.g., quarter-hour electricity consumption, hourly consumption, extrapolate Taylor's input function by first order development. The relatively small random change of the input function affects its first derivative in particular, which makes the extrapolation scatter large and the prediction inaccurate. Moreover, extrapolation depends only on the last value of the input function and its derivative and neglects all previous values of the input function, which is contrary to the general theory of prediction. Even the least-squares extrapolating predictor does not eliminate sufficiently stated errors. Moreover, its memory requirements are increasing and the number of input sequence values on the basis of which the predictor extrapolates. Moreover, the weights of all processed information are the same regardless of their age, which again disagrees with the theory of prediction.

The above-mentioned drawbacks are eliminated by the controller according to the invention, which is based on the fact that the first sampling member is connected to the controller input, the output of which is connected both the first input of the first summation member and the second input of the second summation member. sum member. The second input of the second summation member is connected to the second input of the first summation member via the first delay member and the second input of the fourth summation member is connected to the third input of the first summation member and one

213 872:

nak through the second delay member, the exit of the fourth sum member, connected simultaneously with the second entry of the fifth member. Output of the first summation element It is connected both through the second amplifier and the first input of the fourth summation member and through the first amplifier to the third input of the second summation member whose output is connected to the first input of the third summation member connected by its second input through the second sampling member to the control input. regulator. The output of the third summation element is connected via a time-amplified amplifier to the first input of the fifth summation element whose output is connected via the third amplifier to the controller output.

Let be T sampling period and n-1 'n-2 ¹ nk / a / pulse sequence at discrete times nT _# , / nl / T®, / n-2 / E ₀ , ..., / nk / Í ₀ , where nak are integers. The sequence Za / is approximated by a polynomial of the first degree with parameters β _β ab _Q. If we predict, ie extrapolate the sequence / a / at time nt _Q to time T, the prediction y "= a + b" / T-nI / * n π no

Zb /

Parameters a _n and _{n n} can be found from the condition of minimizing the sum of weighted squares of deviations Cxc ⁱⁿ ΣΖ / ^{3 k} ' ^{/ x} bk ^and n ^{+ kT} o ^b n ^{/ 2 / c /} k * o where weight constant ^ Is 0 </ 3θ · by derivatives by a _n and b _n and by adjustments we obtain the equations / a-1 ♦ I b „

Vo'Vn-1 Wl-V ^{/ e /}

· Let T be the time interval width, B the number of sampling periods Τθ in the interval T * NT ₀ / N Is the natural number (aw) and the required (control) value of energy consumption over time T. Prediction at time n £ T, no '

0, 1, 2, ..., N-1 of the value of the sequence (a) expected at the end of the interval T is given by (b). In order to reach the set point * at the end of the interval T, the power input of the controlled system must be changed by the value T-nI ₀

- w p »-

^and n ' ^w / f /

Která · which ae calls the reduction power · The input sequence (a) monotonically increases within the interval and reaches the value Xjj at the end of the interval. In the following interval T the sequence increases again from zero, which is actually a superposition of continuation of the original sequence / a / and the value -x ^ · Ba thus the subtraction Xjj and the new one from β &, given by / d / save the value. The parameter a _R for n 1, 2, ..., N-1 is then calculated according to the / d / algorithm. The b _R parameter is always calculated according to the Ze / algorithm, ie i for n »0 resp. dfN. The advantage of the controller (predictor) according to the invention lies in the fact that when calculating the prediction it takes into account all known values of the input sequence (a) according to (c), while

The 213 872 prediction algorithm / & /, / and / is simple. Only two values are stored. Furthermore, the weights of the deviation squares decrease exponentially with the age of the / and / sequence values. By choosing the weighting constant / 3, the rate of descent of the weights can be changed: the smaller the / 3, the less the influence of the older values of / a / on the prediction of / d /, / eZ and vice versa. The decreasing influence of sequence values with their age is consistent with the theory of prediction and logic.

The attached drawing shows a block diagram of a controller according to the invention in analogue form. Connected to the controller input is a first sampling member 12, the output of which is connected to the first input of the first summation member 1, the second, the input of the second summation member 8, and the third input member 14 to the second input of the first summation member. the second input member 8 is connected via the first delay member 33 ' The output of the first summation element JZ is connected both through the second amplifier 2 and the first input of the fourth summation element 10 and through the first amplifier 1 to the third input of the second summation element 8 whose output is connected to the first input of the third summation element% sp wired by its second input through the second sampling member 13 with the control input of the controller. Třetíhs output of adder 9 is connected through an amplifier with time-varying gain to an input of the fifth adder 11 whose output is connected via a third amplifier and the output of the controller, amplifying the first, second and third amplifiers _1 and 6. £ / 9 ² / 1 - a T _e ^_1 . 5 is a time-amplification amplifier / Nn / ^-1 , n 0 0, 1, 2, ..., N1 and with a period N. The output values of the first and second delay members 3 and 4 are delayed by time T * relative to the input. The first and second sampling members 12 and 13 are T _# ; the period of the sampling member 14 is T.

Suppose that at time ni = 0 © ⁼ Ve the initial conditions of the controller are zero. Then and reduced power

At time T _Q , the pulses χ _{Σ a are} added in the second summation element .8 so that ^a l ^s * 1 ~ ^2χ 1 *

From this value, the setpoint w is subtracted in the third summation element 9, and this difference is multiplied in amplifier J1 and by variable crosslinking by the value / ΪΜ / ¹¹ , so that at its output the quantity a ^ - «

ΤΤΓ ·

At the same time, it extends from the fourth adder 10 signal Ι _Λ - Λ * - / ^3/4 x.

the fifth summation member 11 generates a quantity

213 872 so the reduction power at the output of the third amplifier · 6_bude 1 * 1 ~ * ^P 1 'V “ ^Z * Vi' ·

At time 2T _{q a} quantity is output from the first summation member J7

-¾ * ^a l * ^T o ^b lThe output of the second summation element 8 will be, 2 ^and 2 ^ex 2 * / ³ and the first input of the fifth summation element 11 will be & 2 “* ~ N-2 °

The output of the fourth adder 10 ^{b will} be about 2 "®o ^b l '' / ^3/2 / - Xg ⁺ ®1 ^{+ T} e l ^b · ^Z

The reduction power at the output of the third amplifier 6 will be 1 Bg-w

P --- / ------- + 1b, /.

of τ - 2 ⁰²

O

This procedure is repeated analogously until (K-1A). At the time T »HT _tf , the third sampling member 14 also closes. In the second summation member 8, the quantities" Ν "/ 3 ^{2 /} ~ * N ⁺ * n are added - χ * ^T o ^b Nl ^{/ 8} " ^x n * so its output will be β - x „♦ ajj ^ ♦

The fifth adder enter quantities ^and »- ^'T o ^b H ·

The reduction power at the output of the third amplifier 6 will be

Bm “w *» - -r- '- * W and the next procedure ae periodically repeats.

Claims (1)

SUBJECT OF THE INVENTION Controller with an exponential predictor of the first stage, characterized in that a first sampling member (12) is connected to its vatup, to whose output is connected both the first input of the first summation member (7) and the second input of the second summation member (8) and a third sampling member /4 / a first input of the second summation member (8), wherein a second output of the second summation member (8) is connected to the second input of the first summation member (7) via the first delay member (3), 7) the second input of the fourth summation member (10) and the second delaying member (4) of the fourth summation member (10) connected at the same time and the second input of the fifth summation member A1 are connected, and the output of the first summation member (7) is connected via second amplifier (2) and first input5 213 87 pum of the fourth summation member (10) and through the first amplifier (1) with the third input of the second summation member (8), the output of which is connected to the first input of the third summation member (9) connected by its second input through the second sampling member / 13) with a control input of the controller, wherein the output of the third summation member (9) is connected via a time-amplified gain amplifier (5) to the first input of the fifth summation member (11) whose output is connected via a third of the silencer (6) to the controller output .