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Pulsed Nonlinear Automatic Control System for Guidance of a Caterpillar
Tractor Unit in Vineyards
Sit M.L.
Institute of Power Engineering Kishinau, Republic of Moldova
Abstract. The automatic guidance systems of tractors for soil cultivation in vineyards have attracted the attention of researchers since the second half of the twentieth century. The purpose of this paper is to investigate the driving quality of an automatic guidance system (AGS) of a caterpillar tractor unit (CTU) consisting of a crawler tractor and a vineyard plow and having an orientation system for grapes. Compared with the known works (in which GPS, LIDAR, and video cameras are used for orientation), the proposed system is the least expensive. For this, the existence of stability of the AGS as a whole in the range of operating speeds of the unit was proved. The dynamic model of the vineyard plow was verified on a three-point hitching system of the tractor, field tests of the AGS were carried out, which confirmed the results of theoretical studies, and suggested directions for further research. The shape and parameters of the modulation characteristic (MC) of the pulse-width modulator (PWM) of the AGS control system, the rational values of the hydraulic drive speeds of the sequential control mechanism of the clutch of the turn and the crawler tractor belt brake, were established, depending on the slope angle and the speed of the unit, ensuring agrotechnical requirements for driving. New solutions, in comparison with the known ones, are the ways of forming the MC of PWM using a new design probe and the associated driver MC of PWM.
Keywords: automatic guidance, caterpillar tractor, pulse-width modulation, control, mechanical probe, field tests.
DOI: 10.5281/zenodo.1217294
Sistemul neliniar cu impulsuri de dirijare automata pentru conducerea tractorului pe senile in randuri ai
vitei de vie Sit M.L.
Insitutul de Energetica Chisinau, Republica Moldova Sistemele de dirijare automata ale agregatului de tractor pentru prelucrarea solului atrage atentia cercetatorilor din a doua jumatate a secolului al XX-lea. Sarcina lucrarilor conexe acestui domeniu de cercetare - constituie in imbunatatirea calitatii conducerii, in reducerea costurilor fortei de munca ale angajatilor, in cresterea sigurantei personalului la operatii de stropire, varsarea erbicidelor etc. Scopul acestei lucrari este de a studia calitatea sistemului automat de conducere (SAC) a tractorului pe senile (GTA), constand dintr -un tractor pe senile si plug pentru prelucrarea solului in randurile vitei de vie si care se orienteaza la tulpinele plantelor. Comparativ cu lucrari cunoscute (care sunt utilizate pentru orientare GPS, LIDAR, camere video), sistemul propus este low-cost. Pentru aceasta, a fost demonstrata existenta stabilitatii SAC in ansamblu in intervalul vitezelor de functionare ale agregatului. Au fost stabilite conditii de stabilitate ale sistemului in intregime in diapazonul de viteze si a rezistentelor de tractiune. Au fost stabiliti indicii statistici de precizie de miscare a agregatului. Au fost efectuate incercari in terenuri, care au confirmat rezultatele calculelor teoretice. Au fost stabiliti forma si parametrii caracteristicii de modulatie a PWM (modulatia duratei impulsurilor) - modulatorul sistemului de conducere, valorile rationale ale vitezelor actionarilor hidraulice in dependenta de conditiile de miscare a agregatului. Rezultatele noi constau in elaborarea modului de formare a caracteristicii de modulatie PWM cu utilizarea sondei de tip nou cu parametrii variabili ai dimensiunilor ale mecanismului sondei, argumentarea teoretica si experimentala a posibilitatii de conducerea precisa a agregatului de tractor, orientat la butucii vitei de vie.
Cuvinte-cheie: sistemul de conducere automata, tractorul pe senile, modulatie in durata a impulsurilor, dirijare, sonda mecanica, teste in teren.
Нелинейная импульсная система автоматического управления для вождения гусеничного
тракторного агрегата на виноградниках Шит М.Л.
Институт энергетики Кишинев, Республика Молдова Аннотация. Системы автоматического вождения тракторных агрегатов для обработки виноградников привлекают внимание исследователей, начиная со второй половины ХХ века. Задача работ, связанных
©Sit M.L., 2018
этим направлением исследований - повысить качество вождения, снизить затраты на оплату труда работников, повысить безопасность работы персонала при опрыскивании и внесении гербицидов, и т.д. Цель данной работы состоит в исследовании, качества вождения системы автоматического вождения (САВ) почвообрабатывающего гусеничного тракторного агрегата (ГТА), состоящего из гусеничного трактора и виноградникового плуга, и имеющей систему ориентации по штамбам винограда. По сравнению с известными работами (где для ориентации используются GPS, LiDAR, видеокамеры) предлагаемая система является самой малозатратной. Для этого было доказано наличие устойчивости САВ в целом в диапазоне рабочих скоростей агрегата. Также были установлены зависимости точности движения агрегата, в виде среднего отклонения от оси междурядья и дисперсии отклонения от оси междурядья в зависимости от среднего значения и дисперсии разброса осей штамбов относительно оси ряда, определяющей направление движения ГТА в зависимости от скорости движения ГТА и тяговой нагрузки. Также была верифицирована динамическая модель виноградникового плуга на трехточечной навесной системе трактора, проведены полевые испытания САУ САВ, подтвердившие результаты теоретических исследований, а также предложены направления дальнейших исследований. Были установлены форма и параметры модуляционной характеристики (МХ) ШИМ-модулятора системы регулирования САВ, рациональные значения скоростей гидроприводов механизма последовательного управления фрикционной муфтой поворота и ленточным тормозом гусеничного трактора в зависимости от угла склона и скорости движения агрегата, обеспечивающие выполнение агротехнических требований при вождении. Новыми решениями, по сравнению с известными, являются способы формирования МХ ШИМ-регулятора с использованием щупа новой конструкции и связанного с ним формирователя МХ ШИМ.
Ключевые слова: автоматическое вождение, гусеничный трактор, широтно-импульсная модуляция, управление, механический щуп, полевые испытания.
Введение
The work relates to the field of the control of moving objects in agriculture, which is referred to as a "precision agriculture" in the West [18]. A huge number of scientific articles are devoted to this area, scientific conferences are regularly held, European grants are allocated for research. In the field of viticulture, the latest known works are [1-7], which describe vineyard robots for determining the quality of the harvest, its harvesting, as well as automatic aggregates consisting of a wheeled tractor and a sprayer. The accuracy of the automatic driving of these types of machines does not meet the high demands that are imposed on tillers. Therefore, the study of automatic systems for driving such aggregates, in particular, on vineyards is of interest.
The purpose of this article is the theoretical and experimental justification of the parameters of the regulator of the automatic driving system of a soil-cultivating machine-tractor unit in vineyards using grape stems as landmarks. Scientific works of S.A. Litinsky, AG. Kechhuashvili [8-9], Yekutieli O. and Garbati-Pegna F. (2002) [13], associated with the development of orientation systems on wire using a low-frequency electromagnetic field generated by electric current in wires or additional wire installed in the lower part of the vine bushes. These systems have not received further distribution due to low
reliability. There are known works on orientation systems using mechanical probes for tractors in vineyards of the author of the present article [10, 11, 12] (1978-1985), Upchurch B.L. [14]. There are known works using a laser scanner to calculate the coordinates of straight lines characterizing the rows of grapes, but for vineyards that are clogged with grass, such a system cannot be acceptable. Lifting the sensors above the level of grass height will increase the level of shading from the branches and leaves of grape plants. The system using DGPS [16] can provide the required accuracy of movement due to the high resolution of the GPS (0.02 m) with respect to the required resolution of the orientation system (0.01 m) (in vineyards, the deviations of the agricultural machine from the center of the row must not exceed 0.08 m, while the resolution of GPS is not less than 0.1 m.), and, in addition, the cheapness of the orientation system using probes, in comparison with all other orientation devices is obvious. However, it can be assumed that the optimal technical solution of the orientation system is in the "hybridization" of the mechanical and laser orientation systems. The VINESCOUT 3D optical navigation system from CLEMENS [15], helps the driver in vineyards while driving a tractor and provides an average tractor deviation value of 0.03 m. A number of reviews are devoted to the problem [19-25].
1. Description of the automatic guidance system
The automatic guidance system consists of a hydraulically actuated electrically operated drive which subsequently acts on the pivoting mechanism - friction clutch and belt brake, as well as a controller and an orientation system made in the form of probes and connected to the controller. The probe of the orientation system was made in the form of a rocking mechanism (Fig .1.1).
The spring pressing the rocker 1 to the stop 4 is not shown. When this circuit is operated, the probe 2 is pulled out from the slotted bar 1, the value of movement of slotted bar 1 being proportional to the overlapping of the probe by the die. When using this scheme, there is no need for an MTA speed sensor, the calculation algorithm is simpler, the delay for the triggering of the MP, which is inherent in the first version of the VO, is eliminated. Inconvenience is the need to rebuild the lengths of parts a1 and L in the transition from one transmission of the tractor to another. When this circuit is operated, the probe 2 is pulled out of the slotted bar 1, and the amount of movement of the slotted bar 1 is proportional to the overlapping of the probe by the die. In the absence of an electronic circuit for changing the duration of the control pulses, it is necessary to rearrange the lengths of the parts a1 and L when changing from one tractor transmission to another.
If you connect a simple lever probe (Fig.1.2.) With a speed-controlled tractor, a slope angle sensor, a traction resistance sensor with a signal multiplier for the duration of the contact between the probe and the grapes stem (Fig. 1.2), then the need for a stylus with the linkage disappears. The probe has its own turn sensor, which produces a signal, the duration of which is proportional to the contact time of the probe and stem in the "straight" stroke of the probe, when the tractor goes forward and the probe is tilted back. When the contact of the probe and the stem ends and the probe returns to its original position, the signal from the probe's turn sensor does not pass to the controller input, since it disconnects from the controller by the character differentiator included in the system. The character differentiator passes a positive signal from the probe position sensor and disconnects the negative signal from the controller.
(return spring of the link not shown). Figure. 1.1. Scheme of the rocking mechanism of the probe movement.
1. Angle meter of the probe. 2. Relay. 3. Differentiator with the signum relay. 4-controller.
Figure.1.2. Lever probe and diagram of its interaction with the controller.
A promising technical solution is that when a bar with sensors is mounted on the probe that allows one to determine what is in front of the sensor: the stem of the grapes or grass. If the sensor has started to deflect, and there is no stem in front of the sensor, only the grass, then the signal of the probe deflection from the reference position does not pass to the regulator.
In Figure 1.3, a photo of a tractor unit with an automatic guidance system is shown. Let us consider the relationship between the duration of the pulses produced by the lever probe and overlapping by the probe of the plant stem. Due to the fact, that the pulse duration is insufficient effectively influencing the rotation mechanism, it is necessary to increase it, which has been realized in the controller circuit.
xt =1 Jl2 ~{l sin^-| x,.| )2 -1 CQS^ + |x|c/g(^ l/v (1.1)
Figure 1.3. Tractor unit with automatic guidance system (AGS) using stems of grapes.
The dependence of the duration of the straight movement of the probe is inversely proportional to the speed of the tractor, depends on the angle of the slope on which the aggregate operates, the height of the probes suspension above the soil surface and depends nonlinearly on the overlapping of the grape's stems by the probes.
t = k •
f (| x\ + h • tga)
(1.2)
The value of the coefficient «k» in (1.2) is determined by the necessity of realization of stability and precision of movement of the tractor unit with respect to the speed of movement.
2. Investigation of the stability of AGS and statistical indicators of the accuracy of movement of the tractor unit with the AGS by a prescribed trajectory
2.1.1. Mathematical model of a tractor as a control object
As an object of regulation of motion along a prescribed trajectory, a caterpillar tillage tractor unit (CTTU) can be represented as a two-dimensional transfer function with two outputs (trajectory of the tractor center of mass and the center of mass of the vineyard plow), and the single control action - the moment of the tractor turning.
The purpose of this part of the study was to determine the tuning parameters of the regulator, in which the accuracy of driving to agrotechnical requirements is ensured (the coordinate of the center of mass of the tiller is considered as an output).
The desired characteristic of the output process is the standard deviation of the coordinate of the center of the masses of the agricultural machine.
kl( MB + Mp )
A?s
1 -A 1 P
TP+1
T2 p2 + T^p + T4
T p2 + T8 p -1
1
T p2 + T p +1
V.
Figure 2.1.1. Transfer function of CTTU, as the object of control of tractor course.
kl(MB + M, ) —<&-
Tp + 1
I A?s
1 P ? T1 P1 + T P + k4 j
T? p1 + T„ P +1
1
T p2 + T p+1
Figure 2.1.2. The simplified block diagram of a tractor unit (consisting of a crawler tractor and a vineyard plow), as a control object in the AGS.
Investigation of the system under influence of random perturbations
the
For the research, the method described in [17] has been applied, which consists in determining the linear statistical equivalent of a closed nonlinear system as a whole. The discrete transfer function of the dynamic part of the ACS has the form:
W ( p ) =
k M (T p +1) e
p2 TP+1)
(2.1)
t - the value of delay in the automatic control system (ACS), T - tractor time constant as the object of control in ACS, T'2= R / v - the gain of the ACS at the heading angle, R - the shoulder of the edge of the probe in front of the center of mass of the tractor, T - the pulse repetition of PWM T = L / v. L - the distance between the stems of plants, v - tractor velocity, M - the turning moment of the tractor, k' = k • v. Performing the D-transformation of expression (2.1) we obtain equation (2.3).
v
k.M (T- T ) k MT ((1 -t) eq + t) K(q) = -—\ 2 ' + --^--'- +...
eq -1
t
(T - T) k,Me T eq
(eq -1)2
(2.3)
It can be demonstrated that the equivalent structural diagram of the ACS has the form (fig.2.1.3).
f
Figure 2.1.3. Simplified block diagram of ACS (upper left graph of PWM modulation characteristic).
f
K
11
k ; m ( t2 - t )
eq - 1
S
K
21
k,MT ((1 -t) eq + t)
iîl—l
K
3]
( T - T2') k'Me T eq
eq - e T
Figure 2.1.4. Equivalent block diagram of ACS.
&
YT
We represent the response of the linear part of fo (x) = k[MT x)®(x) the automatic control system to a sequence of rectangular pulses in the form
F ( x) = kxMT p2 ( x )®( x )
*K] = 1 1LFj (K]% (n,m),
(2.4)
j=0 m=0
where,
F (X) = k'MT
i T
t 1
1 - e T
0( x ),
(2.5)
where p(x) - is PWM modulation characteristics.
We represent the expressions (x), (j = 1,2,3) in the form
r
2
r
O(x) = £Cj • Hv(x), (2.6)
k=0
where, H ( x ) - orthonormal Hermite polynomials and Cj are equal to [18]
Cj =
1
( x-v)
H = M {x}.
Oj ( x )H ( x ) dx
(2.7)
control object and the regulator for the disturbance correlation function of the form:
Rf (t) = ct;2 • cos w •t. (2.6.2)
Parameters of the control object, general for the graphs from one to four:
T = 0.6 s;T = 0.1s; t = 0.2 s;^ = 0.04 m.
The input process (deviation of the axes of the stems from the row axis) is centered, the amplitude characteristic of the PWM is odd, and then the process of the error signal is centered (cj = 0;^ = 0). We confine ourselves to
the first approximation v = 1. Thus, the nonlinear system is replaced by an equivalent linear with coefficients Cj, C2, C? and the statistically linearized model of the automatic control system takes the following form
C3 (t - T )k'Me T eq C2k,M (T - T ) Wl ( q )= 1 (1 2 }\-+ 1 1 .( 2 1 ' +...
eq - e T1
eq -1
C1 (k'MT)((1 -t)eq -T)
(R2 .
(2.8)
A sign above the elements of the formula means the division of the corresponding quantity by T and reduction to a dimensionless time. The equation for calculating the error signal is as follows:
K q ) =
f ( q )
1+ W ( q )
(2.9)
The equation for calculating the dispersion of the center of gravity of a tillage machine has the following form:
1 n
ia) = ~ J (®)W10 (jà)\2 dœ.
(2.10)
œ = œT.
Figure 2.1.5 shows the graphs of the change in the dispersion deviation of the center of masses of the vineyard plow depending on the value of the saturation of the PWM modulation characteristic "c" for various parameters of the
Sets of input data and their corresponding chart numbers are as follows:
1. kM = 0.1c 2m; m2 = 0.04 m; w2 = 0.07 m; T2 = 1.5 s.
2. k[M = 0.2c~2m; m2 = 0.04m;«2 = 0.07m;T2 = 1.0s.
3. k M = 0.3 c-2 m; m2 = 0.02 m; «2 = 0.05 m;T2 = 1.0 s.
4. k M = 0.2 c"2m; m2 = 0.04 m; «2 = 0.07 m;T2 = 1.0 s.
The set of input data (variant 5, fig.2.1.5.).
kM = 0.96 c2 m; m2 = 0.02 m; w2 = 0.05 m;T = 0.6 s;T = 0.31s;
T2 = 1.5 s; t = 0.2 s; af = 0.05 m.
The graphs are shown in Fig. 2.1.5. From the consideration of the figures, it is seen, that for this system, a "fine" adjustment of the regulator is possible in order to obtain the required characteristics of the system operation, depending on the speed of the tractor unit and its traction load.
From the consideration of the graphs in Figure 2.1.5 it follows that the pulse-width automatic control system can fulfill the agrotechnical requirements.
3. Modeling of indicators of accuracy of process of tractor movement with AGS
The task of statistical digital modeling was to determine the dependence of the main adjusting parameters of the automatic control system: the type of modulation characteristic of the PWM regulator and the speed of the servo rod in order to determine the mathematical expectation and variance of the deviation of the mass center of the plow from the straight line.
Determining the trajectory of the tractor unit for various statistical characteristics of the deviation of the trajectory relative to the middle of the vineyard aisle and when driving at different speeds and with different traction resistance to tractor movement.
t
The correlation function of the prescribed trajectory has been experimentally determined and approximated by the following expression:
Re (t) = D • e~hT + D2 • CQSw -T. (3.1)
0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02
^Y
\3
.......... 0
\ k 0 0
0
0,1
0,2
0,3
Figure 2.1.5. Dependences of the mean square deviation of the trajectory of the vineyard plow from the parameters of the ACS regulator.
Resulted from the field experiments, the density distribution of the probabilities of the components of the random process of deviations of axes of stems of plants relative to the straight line was estimated and approximated by the expression (3.2):
f \
P - v = , _• exp
2 -nD
1 2)
- D1( 2)
(3.2)
As was shown in [103], the first component of the random process Y1 (t), described by the
exponential correlation function, has realizations of the following type:
Y (t ) = V sin (f (4)-1 + p),
f (A1(2) ) = -h
(3.3)
where A1 has the Rayleigh distribution law, random initial phase p distributed uniformly in the interval (0, 2n).
The second component of the random process (3.2) is described by expression
Y> (t) = 4 • Sin(f (4)• t + p). (3.4)
The density of distribution of probabilities p (s)of variables 4X(2) is [103]:
pi(2)(s) = D
• exp
f A) = -h • tg
1(2)
(
1 + -
v 2 - DY1(2) j
: 2 /
2 • Dv
exp
/
Dv
(3.3) .(3.4)
We define the degree of the polynomial, approximating criteria of system quality of the automatic guidance system q = 2 . (the integral quadratic criterion is the integral of the square of the deviation of the center of the masses of the tillage trajectory from the straight line characterizing the direction of the row of the vineyard). Then from the formula
N = (1 + q)m , where m = 3 the number of
realizations, characterizing the influence of random perturbations on the precision of the system, will be equal to 27. Values of statistical nodes /uikj, (3.2.3), (3.2.4) ,
will determine the setting on the AGS in the form of random deviations of stems from the straight line. As a result of calculations, the sums
N N
Mi =Y.PikMikf, Di =TPikDik,; , ¿=1 ¿=1
(3.5)
where pik - values of Cristoffel numbers of the i - th realization. Mik , Dik - values of sample
mean and variance i - th realization. After carrying out statistical modeling it was established that the AGS is workable, satisfying the agrotechnical requirements to the quality of driving. After that, field tests were required.
4. The field test result of the automatic guidance system
Equation of the AGS reference trajectory YP (I), where I is the number of the stem in the row,
s
0
along which the tractor unit moves, orienting itself around the grapes, is as follows:
Yp (I ) = || ar (i)| -| a (0|| • • sign(max ar (i) v max a^ (i))
(4.1)
As the results of field experiments have shown, the distribution law of the reference trajectory can be considered normal. Correlation between the deviations of the right and left rows from the straight line is practically absent (the values of the normalized correlation function do not exceed 0.1). If we express the reference trajectory depending on the number of the stem opposite the probe, then the correlation function of the raw will be:
Rxx (n) = D • e + D2 • cos w • n, (4.2)
where
a\ =
2n
( k +1) Lst '
(4.3)
Lst - distance between stems; k - the number of stems per period of a sinusoidal length with a circular frequency w1. For the investigated vineyards: h = 1;k = 5...25;Lst = 1.5m. The sample mean deviation of the rows from the straight line was in the range 0.05 ... 0.08 m, the root-mean-square deviations were 0.05 ... 0.09 m. In the vineyards studied, there was a significant spread of the stems relative to the axis of the row. The quality of guidance of the vineyard tractor unit is determined by the values of the width of the protective zones around the entry points of the grapes bushes into the ground. Table 1 presents statistics of random processes characterizing the guidance of the unit during the cultivation of the vineyard (tractor T-54B, plow PRVN-2,5A). Let us consider the character of the correlation functions of the input effect (spread of the planting of the vine bushes) for the first variant. From the analysis of these data, it is evident, that the system provides tracking of the average value of the control action. The quality of guidance of the vineyard tractor unit is determined by the width of the protective
zones. Let us consider the character of the transformation of the input setting influence (Table 1).
The sample average displacement of the output trajectory is 0.063 m., The right-hand row displacement is 0.061 m, the left - 0.002 m. The comparison of the last two numbers shows the result of the AGS operation - the system provides accurate tracking of the mean value of the control input. The coefficients of amplification of the mean square deviations of the trajectory of the plow, representing the ratio of the variances of the reference trajectory to the trajectory of the plow, are 1.34, 1.16, 1.33 respectively. The values of the asymmetry ( A ) and excess ( ) coefficients of the output trajectory are less than the same values of the reference trajectory, which positively characterizes the smoothing properties of the AGS.
The values of the asymmetry and kurtosis coefficients for the reference and output trajectories indicate the proximity of the law of distribution of the deviation of the trajectories to the normal one.
The proximity of the normalized correlation and dispersion functions of the trajectories of the center of mass of the plow in the shift zone up to n = 10 (the length of the shift along the length is 0.3 m) testifies to the admissibility of using the method of statistical linearization for the investigation of the AGS under random influences. The values of the correlation coefficient of the trajectory of the center of mass of the plow and the protective zones indicate a good quality of tracking by the system of the driving influence.
From the analysis of the correlation functions of the left and right protective zones, determined from the maximum deviation of the stem relative to the axis of the row, it becomes obvious that their correlation coefficients are equal at n = 0 when determined as the time of the first intersection by the correlation function of the abscissa axis.
Table 1. Statistics of random processes during automatic and manual guidance of a tractor unit
Name of the process mx [m] 10-2 [m] 10-2 Ax Ex
Automatic guidance
V=2 m/s
Left row -0.18 5.48 -0.29 0.24
Right row 6.08 6.34 0.43 -0.24
Reference trajectory 3.39 5.51 0.54 1.52
Right protective zone 18.58 7.68 0.087 -0.34
Left protective zone 26.1 8.6 0.087 0.33
Trajectory of the center of mass of the plow 6.77 7.33 0.38 0.86
V=2.4 m/s
Left row -7.1 6.78 -0.34 0.12
Right row 8.14 6.0 -0.047 0.32
Reference trajectory 0.72 8.54 -0.32 -0.68
Right protective zone 28.7 7.7 0.1 0.16
Left protective zone 25.1 9.2 -0.38 0.1
Trajectory of the center of mass of the plow -0.94 7.17 -0.198 -0.673
V=2.4 m/s, склон 8о
Left row -2.73 4.92 0.09 -0.96
Right row 3.76 5.77 -0.59 -0.62
Reference trajectory 1.87 4.06 0.21 -0.77
Right protective zone 29.2 6.36 0.56 -0.12
Left protective zone 16.4 5.62 -0.19 -0.04
Trajectory of the center of mass of the plow 5.55 5.25 -0.678 -0.733
V=1.6 m/s
Left row 4.13 3.26 0.53 0.59
Right row 0.39 4.21 0.28 -0.32
Reference trajectory 1.82 3.6 -0.66 -1.2
Right protective zone 16.64 8.5 0.34 -0.81
Left protective zone 17.9 6.3 -0.05 -1.04
Trajectory of the center of mass of the plow 2.5 6.12 -0.18 -1.13
Manual guidance V=2.4 m/s
Right protective zone 10.5...26.4 9.5.10.1 -0.45.0.92 -0.42.1.3
Left protective zone 16.3...7.5 9.3.11.9 0.73.0.96- 0.025.-0.63
Trajectory of the center of mass of the plow 9.8.14.3 5.6.7.5 0.46.0.42 0.32.-1.1
• the average value of the gain factor for the dispersion of the reference trajectory does not exceed 1.3;
• the average value of the protective zone is not less than 0.18 m;
• the average value of the sample mean standard deviation of the protection zone does not exceed 0.068 m;
• the slope time of the correlation function of the trajectory of the center of gravity of the vineyard plow during automatic guidance is less than in the case of manual one, which is explained by the principle of orientation of the AGS.
The time of slope in the correlation functions of the protection zones for automatic driving is 1.4 ... 2.5 times higher than for manual guidance.
Mean square deviations of the trajectory of the central paw of a plow from a straight line for manual and automatic driving differ insignificantly.
the following conclusions: • AGS ensures agrotechnical requirements;
i
0,8 0,6 0,4 0,2
0 -0,2
-0,4
-0,6
\
\\
V [
n
\ __
5 i0 L ----- 20 25 30 1
35 n
Figure.4.3. Normalized correlation (R) and dispersion (D) functions of the trajectory of the center of the mass of the plow.
Analysis of the statistics of the output processes of the AGS operation made it possible to make
r,d
Conclusion
1. Analysis of the experimentally obtained statistical characteristics of the automatic driving process showed the absence of auto-oscillations in the automatic control system.
2. For a tractor with a turning mechanism in the form of friction clutches and belt brakes, it is possible to use a relay electrohydraulic drive that ensures their sequential activation, and the braking tape should be tightened by a linearly increasing force as a function of the stroke of the servo rod.
Figure 4.1. Normalized correlation (R, solid line) and dispersion (D, dashed line) function of the right-hand protection zone of the row.
Figure 4.2. Normalized correlation (R, solid line) and dispersion (D, dashed line) function of the left-hand protection zone of the row.
2. When working in vineyards with a distance of more than 1 m between stems, it is necessary to install two pairs of probes with the distance between them being equal to half the distance between the stems.
3. Nonlinear pulsed ACS of AGS of the tractor unit in vineyards ensures carrying out of agrotechnical requirements.
4. Using the probe based on the rocking mechanism allows obtaining control signals with a wide range of variation in duration, depending on the speed of the tractor unit.
5. It has been found that the means of increasing the error-rate performance of the AGS should be the limitation of the duration of the control pulses and the frequency of their repetition.
Литература (References)
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About the author.
Sit Mikhail Livovichi - PhD., leading researcher, associate Professor - researcher of the Laboratory of Energy Efficiency and Renewable Energy Sources. Area of scientific interests: automatic control of technological processes, robotics. E-mail: mihail_sit@mail.ru
