SU851425A1 - Non-linear interpolator - Google Patents

Description

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The invention relates to automation and computer technology and can be used, for example, in numerical control stations, in air traffic control systems, etc.

An interpolator is known that contains memory registers, a delay element, digital-to-analogue converters, and a SI integrator.

Also known interpolator containing. pulse generator, counter, addressing unit, memory block, digital-to-analog converters, keys, integrators, and output adder C23.

A common drawback of the known interpolators is the reduced accuracy.

Closest to the present invention is a nonlinear interpolator containing a first adder connected by an output to the output of a nonlinear interpolator and a number of groups of keys whose outputs are connected to the inputs of the second adder, and the signal inputs of the key of each group are combined and connected to the corresponding outputs of the block a memory connected by an input to the first output of a cohp, a left counter connected by an input to the output of a pulse generator, and each i-th one. output (1: i N, where N is the number of counter bits) to the i-ro control input of each key group, and the outputs of the corresponding keys are also connected to the first input of the first adder and to the corresponding inputs of the additional group.

10 solder adders, and the outputs of the second and additional adders. Through the corresponding control e1 1e, the voltage dividers are connected to the remaining inputs of the first adder, and

15 control inputs of the voltage dividers are connected to the outputs of the code converters connected to the outputs from the generator of a linearly varying code.

20

The disadvantage of the prototype is the complexity of the technical implementation while ensuring the specified requirements for the accuracy of the joint interpolation of the function and its derivatives.

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The purpose of the invention is to simplify the non-linear interpolator with increasing accuracy of the joint interpolation of a function and its derivatives.

This goal is achieved by the fact that a nonlinear interpolator containing the first adder connected to the output of the nonlinear interpolator and groups of keys whose outputs are connected to the inputs of the second cyivanaTopa, and the signal inputs of the keys of each group are combined and connected to the corresponding outputs of the memory block connected by an input to the first output of a ring counter connected by an input to the output of a pulse generator, and each i-th output (1 /. i N) to the control input of the i-ro key of each group of keys contains an Integrato group The signal inputs of each of them are connected to the output of the previous integrator, and the output is connected to the signal input of the next integrator, the signal input of the integrator hepBoro is connected to the output of the second adder, the inputs of the initial conditions of the follower integrators and the first input of the first adder co are unified with the corresponding Dimi the outputs of the memory block, the zeroing inputs of all the integrators are connected to the output of the ring counter, and the output of the last integrator to the second input of the first adder.

The drawing shows a block diagram of a non-linear interpolator.

The device contains a first adder 1, connected by an output to the output of a nonlinear interpolator, and a series of groups of switches 2, the outputs of which are connected to the inputs of the second adder 3. The signal inputs of keys 2 of each group are combined and connected to the corresponding outputs of memory block 4 connected input with the first output of the ring counter 5, which is connected by the input to the output of the generator 6 pulses, and each i-th output (1: IN, where N is the number of bits of the counter) to the control input of the 1st key 2 of each group of keys, adder 3 is connected to by the input of the first integrator 7, from the groups of integrators 7, 7,. . . , the signal input of each of which is connected to the output of the previous integrator, and the output - to the signal input of the subsequent integrator. Inputs for setting initial conditions of integrators,.,. and the first input of the adder 1 is connected to the corresponding outputs of the memory block 4, and the zero inputs of all the integrators 7 7 f ... are connected to the first output of the counter, and the output of the last of the integrators is connected to the second input of the adder 1.

In the proposed non-linear interpolator, the interpolation of functions is carried out according to its values and the values of its derivatives at specified times of Hermitic splines with additional defect nodes one. Interpolint is formed as a sum;

2N weighted basic spline functions. The basic spline function is defined in such a way that all values of be and its derivatives, the curvature of one (its own for each function), are equal to zero at the interpolation nodes, and in additional (N-1) nodes it is ensured that it is continuous with the output 4 Nl) -ro order inclusive. The N-th output of the basic spline function is piecewise constant. The values of the interpolated function and its derivatives are weighting coefficients when summing up the Nth derivatives of the basis functions. Thus, an N-a derivative of interpolation is formed. For obtaining the interpolation of the original function, the corresponding multiple integration is performed. In this case, the value of the interpolated function and its derivatives in the first interpolation node are used as initial conditions for the integration. In accordance with the specified keys 2 must form 2N groups of N keys 2 .; (where 1 is 4J4.2N. 1 4 i iN, j is the group number, i is the key number) in each group of keys. The number of integrators is also chosen equal to N.

The nonlinear interpolator works as follows.

Upon receipt of pulses from the output of the generator 6 to the input of the counter 5, the N outputs of the latter result in N sequences of rectangular pulses controlling the operation of the keys 2. From the first N outputs of block 4 memory, the voltages are proportional to the values of the interpolated function and its derivatives in the first interpolation node. The remaining N outputs of block 4 receive voltages proportional to the values of the interpolated function and its derivatives in the next interpolation node. The indicated voltages through the corresponding groups of keys 2J are fed to the inputs of the second adder 3, where they are combined with constant weights (weighting factors The determination of terms is calculated during construction and depends on N). The cyND ' iaTOpa 3 output forms the N-a derivative of the interpolated fu | 3 sections, which is fed to the input of a group of N series-connected integrators 7, pre-zeroed by a pulse from the first output of the counter 5. The inputs of the initial conditions of the integrators 7 and the first input of the adder 1 are supplied with voltage from the output; memory block 4 specifying the initial integration conditions. The output of the adder 1 is removed, the voltage corresponding to the interpolated function.

Thus, the proposed nonlinear interpolator allows more

in a simple way to form the required interpolated function while increasing the accuracy of joint interpolation of a function and its derivatives. The latter is achieved by the fact that at the output of adder 1, a function is formed, the values of which, together with its derivatives up to the (N-1) -th order, inclusively coincide with the corresponding values of the interpolated function at specified points in time. v.

Claims (3)

1. USSR author's certificate No. 404097, cl. G 06 G 7/28, 1970. 2.AJBTopcKoe USSR certificate No. 546899, cl. G 06 G 7/26, 1974. 3. USSR author's certificate 5 according to application number 2817306 / 18-24, cl. O 06 G 7/26, 16.07. (prototype).