RU2037192C1 - Aiming cosine matrix calculator - Google Patents

Abstract

FIELD: computer engineering. SUBSTANCE: aiming cosine matrix calculator has register storage unit, three character shaping units, six multipliers, two Levy-Chivit parameter shaping units, three subtracters, adder, flip-flop, NOT gate, intermediate-matrix shaping unit, two AND gate units, and two aiming-cosine matrix shaping units functionally interconnected. EFFECT: enlarged functional capability of device due to provision for transfer from one cartesian coordinate system to other throughout entire range of input quantities. 5 cl, 6 dwg

Description

 The invention relates to computer technology and can be used in modeling the dynamics and flight control of aircraft.

A device for calculating the directional cosines of a vector in space, containing eight iterative blocks, each of which includes adders, multipliers, code converters [1]
The disadvantage of this device is the limited scope.

The closest in technical essence to the invention is a device for calculating the matrix of guide cosines through the Rodrigue-Hamilton parameters, comprising a conjugation unit, a register memory unit, a control device unit, four units for calculating variable Rodrigue-Hamilton parameters, respectively, three blocks for calculating diagonal cosines, respectively, and six blocks for calculating off-diagonal cosines, respectively [2]
The disadvantage of this device is the complexity of the technical feasibility of the algorithm for calculating the matrix of guide cosines by integrating the system of kinematic differential equations in the Rodrigue-Hamilton parameters and the lack of technical ability to determine the initial values of the components of the quaternion.

 The purpose of the invention is the expansion of the scope due to the possibility of transition from one Cartesian coordinate system to another in the entire range of input values.

 This goal is achieved by the fact that the first and second blocks for generating the Levi-Civita parameter, the block for generating an intermediate matrix, the first and second blocks for forming the matrix of guide cosines, three blocks for generating a sign, are introduced into the device for calculating the matrix of guide cosines, which contains a register memory block multipliers, three subtractors, the first and second blocks of AND elements, the adder, trigger, and the element NOT, and the register memory block is made in the form of a set of registers for storing codes, three of them are xp the codes of the numbers of the axes of the original coordinate system, six registers for storing the codes of the sines and cosines of the rotation angles and a register for storing the code of the number "6", the first three outputs of the register memory block being connected respectively to the inputs of the first, second and third sign-forming units and to the first inputs of the first , the second and third multipliers, the second inputs of which are connected respectively to the outputs of the first, second and third blocks of the formation of the sign and with the first inputs of the fourth, fifth and sixth multipliers, the second inputs are of the fourth and fifth multipliers are connected to the output of the first Levi-Civita parameter formation unit, the second input of the sixth multiplier is connected to the output of the second Levi-Civita parameter formation, the outputs from the fourth to eighth register memory block are connected respectively to the row inputs of the intermediate matrix forming unit, column inputs which are connected respectively to the outputs of the fourth, fifth and sixth multipliers, the ninth output of the register memory block is connected to the column inputs of the first and second blocks of of the matrix of guide cosines, the tenth output of the register memory block is connected to the input of the decreasing first subtractor, the output of which is connected to the inputs of the decreasing second and third subtracters, the inputs of the subtracted first, second and third subtractors are connected respectively to the outputs of the second, first and third multipliers, the outputs of the first and the second multipliers are connected respectively to the first and second inputs of the first block of the formation of the Levi-Civita parameter, the third input of which is connected to the output of the second At the same time, the outputs of the second and third multipliers are connected respectively to the first and second inputs of the second Levi-Civita parameter generation unit, the third input of which is connected to the output of the third subtracter, the outputs of the fourth and fifth multipliers are connected to the first and second inputs of the adder, the output of which is connected to the control input the first block of AND elements and with the input of the element NOT, the output of which is connected to the control input of the second block of AND elements, the outputs of the intermediate matrix forming unit are connected to information inputs odes of the first and second blocks of AND elements, the outputs of which are connected respectively to the inputs of the rows of the first and second blocks of formation of the matrix of guide cosines, the outputs of which are the outputs of the device.

 In FIG. 1 shows a functional diagram of the proposed device; figure 2 and 3 functional diagrams of the blocks of the formation of the Levi-Civita parameter; figure 4 is a functional block diagram of the formation of the intermediate matrix; in FIG. 5 and 6 are functional diagrams of blocks forming a matrix of guide cosines.

 A device for calculating the matrix of guide cosines contains a register memory block 1, first, second and third sign generation blocks 2-4, first, second and third multipliers 5-7, the first Levi-Civita parameter generation block 8, fourth and fifth multipliers 9 and 10 the first, second, third subtractors 11-13, the second Levi-Civita parameter generation block 14, the sixth multiplier 15, the adder 16, the trigger 17, the HE 18 element, the intermediate matrix formation block 19, the first, second blocks of the elements And 20 and 21, the first block 22 of the formation of the matrix of guide braids inuses, the second block 23 of the formation of the matrix of guide cosines, interconnected functionally.

 The first block 8 of the formation of the Levi-Civita parameter contains the subtractors 24, 25 and 28, the multiplier 26 and the divider 27 into two, interconnected functionally.

 The second block 14 of the formation of the Levi-Civita parameter contains the subtractors 29, 30 and 33, the multiplier 31 and the divider 32 into two, interconnected functionally.

 The intermediate matrix forming unit 19 comprises a multiplier 34, an element HE 35, multipliers 36-40, an element HE 41 and a multiplier 42 interconnected functionally.

 The first block 22 of the formation of the matrix of guide cosines contains a multiplier 43, an element NOT 44, a multiplier 45, an element 46, multipliers 47 and 48, an adder 49, multipliers 50 and 51, an adder 52, a multiplier 53, an adder 54, multipliers 55 and 56, an adder 57 and a multiplier 58, interconnected functionally.

 The second block 23 of the formation of the matrix of guide cosines contains the element NOT 59, the multipliers 60-62, the adder 63, the multipliers 64 and 65, the adder 66, the multipliers 67 and 68, the adder 69, the multipliers 70-72 and the adder 73 are interconnected functionally.

 The principle of operation of the proposed device is based on the calculation of a matrix of guide cosines of dimension 3 x 3 to establish a connection between any rectangular coordinate systems, which is the product of three rotation matrices (plane rotation) around the coordinate axes.

 The type of elementary rotation matrices is determined by the number of the axis around which the rotation is carried out and the rule of reference of angles.

 The device implements the following sequence of actions.

1. The conditional matrix formula is specified
FM P ₁ P ₂ P ₃ ∈ {± 1, ± 2, ± 3} where P ₁ , P ₂ and P _{3 are the} sequence of numbers of the axes of the original coordinate system with their signs, corresponding to the given sequence of introducing elementary rotation angles with respect to the indicated axes and their rule reference frame.

2. Consistently calculated indices
i P ₁ SignP ₁
j P ₂ SignP ₂
k P ₃ SignP ₃
l 6 ij
m 6 jk
∈ _ijl = (ij) (jl) (li) / 2
∈ _jkm = (jk) (km) (mj) / 2
q ₁ = ∈ _ijl SignP ₁
q ₂ = ∈ _ijl SignP ₂
q ₃ = ∈ _ikm SignP ₃ where Sign is a sign extraction operation.

3. The elements of the auxiliary matrix are determined:
U _ij C ₂ Uij U _jl Ul _i U _il C ₁ U _li
U _ji q ₃ S ₃ U _jj C ₁ U _{jl =} q ₁ S ₁
U _li q ₂ S ₂ U _lj C ₂ U _jl U _ll C ₁ C ₂ C ₁ , S ₁ , C ₂ , S ₂ , C ₃ , S ₃ given at the input are the sine and cosine of the nth elementary angle of rotation, respectively, for this n 1,2,3 sequence number of rotation.

4. The elements of the matrix of guide cosines of the transition from the original coordinate system to a given coordinate system are determined
V _mi C ₃ U _ii V _mj U _ij C ₃ + U _ij U _jj V _ml U _ij U _jl + C ₃ U _il
V _ji U _ji U _ii Vjj U _jj C ₃ U _ij U _ji V _jl U _jl C ₃ U _il U _ji
V _ki U _li V _ki U _lj V _kl U _ll
if q ₁ + q ₂ ≠ 0
V _mi C ₃ U _li V _mj U _jj U _ji + C ₃ Ul _j V _ml U _jl U _ji + C ₃ U _ll
V _ji -U _ji U _li V _jj -U _ji U _li + C ₃ U _jj V _jl -U _ji U _ll + C ₃ U _jl
V _ki U _ii V _ki U _ij V _kl U _il
if q ₁ + q ₂ 0
A device for forming a matrix of guide cosines is as follows.

, Sign P₂=

, Sign P₃=

поступают на входы блоков 5,6,7 соответственно, с выходов которых соответственно на вход блока 8 формирования параметра Леви-Чивита и блока 12 поступает код i P₁SignP₁, на вторые входы блоков 11 и 8, а также на первый вход второго блока 14 формирования параметра Леви-Чивита поступает код j P₂SignP₂; на второй вход блока 14 и блока 13 код k P₃SignP₃. Код 6 j на выходе блока 11 в блоке 12 преобразуется к виду l 6 i j и поступает на 3-й вход блока 8, одновременно с этим код 6 j в блоке 13, преобразуясь к виду m 6 j k, поступает на третий вход блока 14. Блоки 8 и 14 формируют на выходах соответственно коды символов Леви-Чивита
∈_ijl= (i-j)(j-l)(l-i)/2 , ∈_jkm= (j-k)(k-m)(m-j)/2, которые с помощью блоков 9, 10 и 15, на вторые входы которых поступают, соответственно, коды SignP₁, SignP₂, SignP₃ преобразуются к виду q₁ ∈_ijlSignP₁, q₂ ∈_ijlSignP₂, q₃ ∈_jkmSignP₃
Преобразованные коды q₁, q₂ и q₃ поступают на вход блока 19 формирования промежуточной матрицы, которые вместе с кодами синусов и косинусов элементарных углов поворота С₁, С₂, S₁, S₂, S₃ используются для формирования на выходе блока 19 кодов элементов промежуточной матрицы U_ii, U_ji, U_li, U_jj, U_jl, U_ll, U_ij, U_il, U_lj.At the moment of its switching on, an pulse is issued to the block 1 by an external start signal, which is a set of registers for storing codes, from 1-3 outputs of which the codes P ₁ , P ₂ are respectively output to the inputs of blocks 2,3,4 and 5,6,7 and P ₃ with their own signs (the numbers of the axes of the original coordinate system, relative to which elementary rotation angles are successively performed; from 4-5 and 7-9 outputs of block 1 to the inputs 4-8 of block 19, codes C ₁ cos φ ₁ , C ₂ cos φ ₂ , S ₁ sin φ ₁ , S ₂ sin φ ₂ , S ₃ sin φ ₃ sines and cosines of elementary rotation angles; from output 6 of block 1 to input S blocks 22 and 23 receives the code C ₃ cos φ ₃ and from the output 10 of block 1 to the input of block 11 code "6"). At the outputs of the blocks 2,3,4, the generated codes are SignP ₁ , SignP ₂ , SignP ₃ , where Sign P ₁ =

, Sign P ₂ =

, Sign P ₃ =

enter the inputs of blocks 5,6,7, respectively, from the outputs of which respectively the input of block 8 of the formation of the Levi-Civita parameter and block 12 receives the code i P ₁ SignP ₁ , to the second inputs of blocks 11 and 8, as well as to the first input of the second block 14 the formation of the Levi-Civita parameter receives the code j P ₂ SignP ₂ ; to the second input of block 14 and block 13, code k P ₃ SignP ₃ . The code 6 j at the output of block 11 in block 12 is converted to the form l 6 ij and goes to the 3rd input of block 8, at the same time the code 6 j in block 13, being converted to the form m 6 jk, goes to the third input of block 14. Blocks 8 and 14 form Levi-Civita character codes at the outputs, respectively
∈ _ijl = (ij) (jl) (li) / 2, ∈ _jkm = (jk) (km) (mj) / 2, which with the help of blocks 9, 10 and 15, the second inputs of which receive, respectively, SignP codes ₁ , SignP ₂ , SignP _{3 are} transformed to the form q ₁ ∈ _ijl SignP ₁ , q ₂ ∈ _ijl SignP ₂ , q ₃ ∈ _jkm SignP ₃
The converted codes q ₁ , q ₂ and q ₃ are input to the intermediate matrix forming unit 19, which, together with the codes of the sines and cosines of the elementary rotation angles C ₁ , C ₂ , S ₁ , S ₂ , S _3, are used to form the output of block 19 codes of elements of the intermediate matrix U _ii , U _ji, U _li , U _jj , U _jl , U _ll, U _ij, U _il , U _lj .

At the same time, codes q ₁ and q ₂ are input to the first summing unit 16. From the output of block 16, the signal is input to the unit of trigger 17 if q ₁ + + q ₂ ≠ 0. Depending on the value of the control signal code, trigger 17 is used by blocks of elements I 20 and 21, the inputs of which are supplied from the outputs of block 19 codes of elements of the intermediate matrix U _ii , U _ji , U _li , U _jj , U _jl , U _ll , U _ij , U _il, U _lj , gives a control action on the functioning of the first block 22 of the matrix of guide cosines, if the signal at the output of the trigger 17 equal to "1" or the start of the second block 23 of the formation of the matrix of guide cosines, if the signal is in The trigger output is "0". At the outputs of blocks 22 and 23, elements of the coordinate transformation matrix V _mi , V _ji , V _mj , V _ki, V _jj , V _kj , V _ml , V _jl , V _{kl are formed} in accordance with the above algorithm.

 Thus, the proposed device provides the implementation of the calculation of the matrix of guide cosines of the transition from one Cartesian coordinate system to another in the entire range of input values compared with known devices of the same purpose.

Claims (5)

 1. DEVICE FOR CALCULATING THE MATRIX OF GUIDING COSINUSES, containing a block of register memory, characterized in that, in order to expand the scope by providing a transition from one Cartesian coordinate system to another in the entire range of input quantities, the first and second blocks of the formation of the Levy parameter are introduced into it Civita, an intermediate matrix forming unit, the first and second blocks for generating a matrix of guide cosines, the first, second and third character forming units, the first, second and third subtracters, the first net multipliers, the first and second blocks of AND elements, the adder, trigger, and the NOT element, and the register memory block is made in the form of a set of registers for storing codes, of which three are storing codes for the codes of the axis numbers of the original coordinate system, six registers for storing codes of sines and cousines of angles rotation and storage register of the code number "6", and the first, second and third outputs of the register memory block are connected respectively to the inputs of the first, second and third blocks of the formation of the sign and the first inputs of the first, second and third multiply Iteli, the second inputs of which are connected respectively with the outputs of the first, second and third blocks of the formation of the sign and with the first inputs of the fourth, fifth and sixth multipliers, the second inputs of the fourth and fifth multipliers are connected with the output of the first block of parameter formation Levy Civita, the second input of the sixth multiplier with the output the second block of the formation of the Levi Civita parameter, the fourth and eighth outputs of the register memory block are connected respectively to the inputs of the rows of the intermediate matrix formation block, the column inputs to connected to the outputs of the fourth, fifth, and sixth multipliers, the ninth output of the register memory block is connected to the column inputs of the first and second blocks of the matrix of guide cosines, the tenth output is connected to the input of the decreasing first subtractor, the output of which is connected to the inputs of the decreasing second and third subtractors, the inputs of the deductible first, second and third subtractors are connected respectively to the outputs of the second, first and third multipliers, the outputs of the first and second multiplier st are connected respectively to the first and second inputs of the first Levi Civita parameter formation block, the third input of which is connected to the output of the second subtracter, the output of the second and third multipliers are connected respectively to the first and second inputs of the Levi Civita parameter formation block, the third input of which is connected to the output of the third the subtractor, the outputs of the fourth and fifth multipliers are connected to the first and second inputs of the adder, the output of which is connected to the input of the trigger, the output of which is connected to the control input the first block of AND elements with the input of the element NOT, the output of which is connected to the control input of the second block of AND elements, the outputs of the intermediate matrix forming unit are connected to the information inputs of the first and second blocks of AND elements, the outputs of the first block of AND elements are connected to the row inputs of the first matrix forming unit guide cosines, the outputs of the second block of elements AND with the inputs of the rows of the second block forming the matrix of guide cosines, the outputs of the first and second blocks of the formation of the matrix of guide cosines Mustache is the output of the device.  2. The device according to claim 1, characterized in that the Levi Civita parameter generating unit comprises first, second and third subtractors, a multiplier and a divider by two, the first input of the block being connected to the input of the reduced first subtractor and the input of the subtracted third subtractor, the second input of the block with the inputs of the subtracted first and second subtractors, the third input with the inputs of the decreasing second and third subtracters, the outputs of the first, second and third subtractors are connected respectively to the second, first and third inputs of the multiplier, the output of which oh connected to the input of the divider into two, the output of which is the output of the unit.  3. The device according to claim 1, characterized in that the intermediate matrix forming unit comprises a first seventh multiplier and the first and second elements NOT, wherein the input of the first row of the intermediate matrix forming unit is connected to the input of the first element NOT and to the first input of the first multiplier, the second input which is connected to the input of the second row of the intermediate matrix forming unit, with the input of the second element NOT and is the first output of the block, the inputs of the third row and the first column of which are connected to the inputs of the sixth multiplier, the inputs the fourth row and second column with the inputs of the fourth multiplier, the inputs of the fifth row and third column with the inputs of the third multiplier, the output of which is the second output of the block, the third output of which is connected to the output of the fourth multiplier and the first input of the fifth multiplier, the output of which is the fourth output of the block, fifth the input of which is connected to its first input, the output of the sixth multiplier is connected to the second inputs of the fifth and seventh multipliers, the first input of the last is connected to the output of the second element NOT, and the output is is the sixth output of the block, the seventh output of which is connected to the output of the second multiplier, the first input of which is connected to the output of the first element NOT, and the second input with the output of the fourth multiplier, the output of the sixth multiplier is the eighth output of the block, the ninth output of which is connected to the output of the first multiplier.  4. The device according to p. 1, characterized in that the first block forming the matrix of guide cosines contains the first tenth multipliers, the first - fourth adders and the first and second elements NOT, and the inputs of the first row and column of the block are connected to the inputs of the first multiplier, the output of which is the first output of the block, the second output of which is connected to the output of the second multiplier, the first input of which is connected to the second input of the first multiplier, and the second input of the second multiplier is connected to the first input of the tenth multiplier and the output of of the first element NOT, the input of which is connected to the input of the second element NOT, the first input of the third multiplier and is the input of the second row of the block, the input of the third row of which is the third output of the block, the fourth output of which is connected to the output of the first adder, the first input of which is connected to the output of the fourth multiplier , the second input of which is connected to the second input of the fifth multiplier and is the input of the fourth row of the block, the input of the fifth row of which is connected to the second inputs of the sixth and third multipliers, the output of the last is single with the second input of the first adder, the input of the block column is connected to the first inputs of the fourth and sixth multipliers, the output of the last is connected to the second input of the second adder, the output of which is the fifth output of the block, the sixth output of which is connected to the input of the sixth row of the block, the input of the seventh row of which is connected with the second inputs of the tenth and eighth multipliers, the output of the latter is connected to the second input of the third adder, the output of which is the seventh output of the block, the eighth output of which is connected to the output of the fourth an adder, the second input of which is connected to the output of the tenth multiplier, and the first input with the output of the ninth multiplier, the first input of which is connected to the second input of the seventh multiplier and is the input of the eighth row of the block, the column input of which is connected to the first input of the eighth and second input of the ninth multiplier, input the first element is NOT connected to the first input of the seventh multiplier, the output of which is connected to the first input of the third adder, the output of the second element is NOT connected to the first input of the fifth multiplier, the output of which is connected with the first input of the second adder, the input of the ninth line of the block is its ninth output.  5. The device according to claim 1, characterized in that the second block forming the matrix of guide cosines contains the first tenth multipliers, the first and fourth adders and the element NOT, the input of the first line of the block being its third output, the input of the second line connected to the input of the element whose output is connected to the first input of the first multiplier, the output of which is the second output of the block, the first output of which is connected to the output of the second multiplier, the first input of which is connected to the input of the column of the block, the third row of which is single with the second inputs of the first and second multipliers, the input of the fourth row of the block is its sixth output, the input of the fifth row is connected to the first input of the sixth multiplier and the second input of the third multiplier, the output of which is connected to the first input of the first adder, the output of which is the fourth output of the block, the fifth output of which is connected to the output of the second adder, the first input of which is connected to the output of the fifth multiplier, the first input of which is connected to the second input of the fourth multiplier and is the input of the sixth row block, the input of the seventh row of which is its ninth output, the input of the eighth line is connected to the first inputs of the ninth and seventh multipliers, the output of the latter is connected to the first input of the third adder, the output of which is the seventh output of the block, the eighth output of which is connected to the output of the fourth adder, the first the input of which is connected to the output of the tenth multiplier, the first input of which is connected to the second input of the eighth multiplier and is the input of the ninth row of the block, the column input of which is connected to the first input of the fourth of the multiplier, the second input of the sixth multiplier, the first input of the eighth multiplier and the second input of the ninth multiplier, the output of which is connected to the second input of the fourth adder, the first input of the third multiplier is connected to the second input of the seventh multiplier and to the input of the element NOT, the output of which is connected to the second inputs of the fifth and the tenth multiplier, the output of the fourth multiplier with the second input of the first adder, the output of the sixth multiplier with the second input of the second adder, and the output of the eighth multiplier with the second input of the third sum atora.