SU1686461A1 - Spline-interpolator - Google Patents

Abstract

The invention relates to automation and computing, in particular to polynomial and spline approximators, and can be used in automatic control systems when playing a wide class of functional dependencies. The aim of the invention is to expand the scope by altering the accuracy of the calculations and improving the speed. The interpolator is used to reproduce functional dependencies based on a piecewise polynomial spline approximation of third-degree splines with uniform division into approximation segments and can work in real time. The interpolator contains a microprogram control block 1, counters 2. 3, memory blocks 4, 5, multiplication blocks 6-9, adder 10 and the result register 11. 1 il.

Description

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about

The invention relates to automation and computing, in particular, to polynomial and spline approximators, and can be used in automatic control systems for playing a wide class of functional dependencies.

The purpose of the invention is to expand the field of application by changing the accuracy of calculations and improving speed.

The drawing shows a block diagram of an interpolator.

The interpolator contains microprogram control unit 1, counters 2 and 3, memory blocks 4 and 5, multiplication blocks 6-9, adder 10, result register 11.

The principle of the interpolator is based on a piecewise polynomial spline approximation by degree III splines with uniform division into approximation segments.

Calculations are made using the formula

5чЛ1-гхм + 4 хмЛЬг1 х)

where f) the value of the interpolated function at the nodal points;

) is a coefficient depending on the current value of the abscissa;

lX; j - & x-1) -uX; 1 (j 3.N))

4j4 -; Wl- & x / bX; - | (X; lAX, (j.§)}

X - ,, - LH; LH 11-lh; Y | (1-LH; 14-LH;, (,

-I M - Ui -1) In the first interpolation region, 0 2) xi 0 and formula (1) takes the form

Sia f 12 xi2 + fz xi2 + f34 xi2 (2)

Where

2

X; g 1 -ХХ; LЈН-ЬХ; №Х; J V.a XHbX I-bX-,

iz

In the last part of the interpolation

(J N)% 0

p ... t t .... i "...

SIN fn-2 XIN + fN-1 XIN + fN XIN.

(3)

Where

4; N (l-bX; f & yi

2X; N (f- & X-, bO-bX-yuX; j

B, - (.

The xij coefficients are stored in memory block 4, made on ROM. The values of the function f | at the nodal points are successively fed to the input of the memory block 5, with

brane on shift registers. From the outputs of block 5, four values of the function fj-2 arrive in parallel at the inputs of blocks 6-9.

f | -1. f2. fj + 1.

5At the same time to other inputs of blocks

multiplications come from block 4 corresponding values of 1xr, -2; 2x, ij-i: 3xi.j; 4xi, j + i. The generated products are fed to the inputs of the adder 10, the output of which

10, we obtain the values of the spline Si. Register 11 is used to fix these values, and to save information about the value of the function f | at the last nodal point, the value of f fN SMN is rewritten directly from block 5 to register 11 at the end of the calculation process.

The operation of the interpolator begins when the input of the Block 1 of the logic unit level appears at the input.

20 Block 1 generates a signal that resets counter 2, counter 3, block 5 and register 11. Simultaneously with recording fi in block 5, code M is entered in counter 3, which determines the number of calculated values

25 functions within the interpolated interval and forms the lower bits of the address of block 4. The contents of counter 3 are reduced by 1 after each computational value of the function. With a value of O,

30, the interpolation in this region ends. A code M is recorded in counter 3 before each new interpolation segment simultaneously with the recording of the next value of f. Code M also enters block 4 and

35 is the middle part of the address word. Counter 2 forms the leading bits of the address of block 4 and determines the instant of the beginning of the interpolation process, counting at the beginning of the work the number of received values fj arriving at the input of block 5. Starting from the calculation of the third value of fj. At this moment in time, the contents of counter 2 are equal to 2. Under this condition, the value of Si is calculated by formula (2).

45 After finding the values of the function in the first interpolation region, the contents of counter 2 are reduced by 1. With a value of 1 for counter 2, the calculations are made by the formula (1). Following

50 control signal appears after the start signal disappears. The contents of counter 2 become equal to 0. and in the last section of the interpolation calculation is made according to the formula (3).

Claims (1)

55 claims A spline interpolator containing the first and second counters, the first and second memory blocks, the first multiplier block, the accumulator, the result register, the microprogram control block, and the start input the interpolator is connected to the first input of the microprogram control unit; the synchronous input of the interpolator is connected to the second input of the microprogram control unit, the first output of which is connected to the reset inputs of the first and second counters and the result register, the second output with the summing input of the first counter, the output of the first counter connected to the first address input of the first memory block, the output of which is connected to the first information input of the first multiplication unit, the second information input of which is connected to the output second o memory block, the output of the first multiplier is connected to the first input of the adder, the output of which is connected to the first information input of the result register, the output of which is the output of the interpolator, characterized in that, in order to expand the scope by changing the accuracy of the calculations and higher speeds, three multiplication blocks are entered into it, the first and second information inputs of which are connected respectively to the outputs of the first and second memory blocks, and the first and second control inputs from the first and second the gate of the first input unit and multiplying respectively with the third and fourth You are a microprocess control unit moves, the fifth, sixth, seventh, eighth, ninth, tenth and eleventh outputs of which are connected respectively with the first control input of the result register, with the subtracting input of the first counter, with the control input A second memory input, with a second counter recording input, with a second counter subtracting input, with a second control input of the result register, the second information input of which is connected to the output of the second memory block, the second output, tr The second and fourth multiplication blocks are connected respectively to the second, third and fourth inputs of the adder, the input of the number of function values within the interpolator interval is connected to the information input of the second counter and the second address input of the first memory block, the third address input of which is connected to the output of the first counter and to the third input of the firmware control unit, the fourth input of which is connected to the third address input of the first memory block and to the output of the second counter, the input of the value of the interpol function Torus is connected to the information input of the second memory block.