RU2034695C1 - Variable structure control system - Google Patents

Abstract

FIELD: machine engineering. SUBSTANCE: system includes in addition the second module unit 18, the first functional generator 19, the fourth multiplying unit 20, the third relay unit 21, the second functional generator 24, the fourth adder 25, the third functional generator 26, providing identification of a parameter, being varied, and tuning of parameters of a unit for changing a structure of the control system. EFFECT: enhanced reliability of the control system. 1 cl, 1 dwg

Description

 The invention relates to automatic control systems, namely, control systems with a variable structure and is intended to control objects with a significant change in the moment of inertia brought to the shaft of the actuator motor, in particular for controlling manipulating robots.

 Known control systems with a variable structure, containing a mismatch meter, a preamplifier, an actuator, a gearbox and a structure change unit, consisting of a rectifier, a multiplication unit, a phase-ahead filter and a relay element (AS USSR No. 470783).

 Also known is a system with a variable structure, containing a series-connected mismatch meter, a preliminary amplifier, a rectifier, a pulse-width modulator, a non-contact DC motor, the output of which through a gearbox is connected to the input of the mismatch meter, and a relay element whose output is connected to the input of a non-contact motor direct current, on the shaft of which a tachogenerator is installed, connected through a correction device to the first input of the comparison element, the input to torogo connected to the output pre-amplifier, and the output to the input of the relay element (AS USSR N 463097).

 In these systems, the settings of the structure change unit (LSI) are constant. The result of this is either a disruption of the sliding process and the occurrence of overshoot with increasing load parameters, or the delay of transients with a decrease in this load (reduced moments of inertia of the drive motors).

 A variable structure control system is also known, comprising a first mismatch meter, a first amplifier, a rectifier, a second amplifier, a first multiplication unit, to the second input of which, through a comparison element and a first relay element, the output of the first amplifier is connected, a DC motor whose output shaft is connected to a speed sensor and a position sensor, the output of which is connected to the second input of the first mismatch meter, and the output of the speed sensor is connected to the input of the third amplifier, as well as holding a serially connected motor current sensor, a second mismatch meter, an integrator, a division unit, to the second input of which a speed sensor output is connected, a fourth amplifier and a second multiplication unit, the output of which is connected to the second input of the comparison element, and the second input of the second multiplication unit is connected to the output the third amplifier, and the output of the adder is connected to the second input of the second mismatch meter, the output of the external torque disturbance meter is connected to its first input, the output of the speed sensor is connected to the second input of the adder through the fifth amplifier, and the output of the speed sensor is connected to the third input of the adder through the second relay element.

 This device in its technical essence is the closest to the offer.

 The main disadvantage of the prototype system is the decrease in the quality of transients when the sliding mode of operation is disrupted, which occurs as a result of the inaccuracy of the division operation. This is due to the fact that due to errors in adjusting the system parameters, as well as due to the influence of interference when the system approaches a steady state (speed tends to zero), a situation such as "division by zero" and, as a consequence, unpredictable in magnitude and sign speed feedback coefficient.

 The problem that is solved in the present invention is to prevent the disruption of the working sliding mode and improving the quality of transients. The technical result is achieved by the fact that the control system with a variable structure, containing in series a mismatch meter, a first module unit, a first multiplication unit, to the second input of which a mismatch meter output, an amplifier, is connected through a second multiplication unit, a first adder and a first relay element, a direct current electric motor, a gearbox, the output shaft of which is mechanically connected to the control object and a position sensor, the output of which is connected to the second m input of the mismatch meter, as well as a series-connected speed sensor, the input of which is connected to the shaft of the DC motor, a second relay element, a second adder, to the second and third inputs of which are connected the motor current sensor and the output of the speed sensor, and the integrator, as well as the third a multiplication unit, the output of which is connected to the second input of the first adder, in addition, the output of the speed sensor through the second unit block connected in series, the first functional converter The indexer, the fourth multiplication unit, to the second input of which the speed sensor output is connected through the third relay element, is connected to the first input of the third multiplication unit, the integrator output is connected to the second input of the third unit of the module, as well as the output of the third module unit through the third adder connected in series , to the second input of which the output of the second module block is connected, the second functional converter, the fourth adder, the second input of which is connected to the output of the first functional converter azovatelya and a third function generator connected to the second input of the second multiplier block.

 In the proposed system, in contrast to the prototype, additional blocks and communications are implemented that implement non-linear adjustable speed feedback. In addition, blocks and communications were introduced to adjust the transmission coefficient of the mismatch signal, which was not in the prototype. In this regard, we can assume that the proposed system meets the criterion of "novelty."

 There are known control systems in which tuning (including non-linear) of transmission coefficients in direct and feedback channels is performed (see, for example, chapter 3 of Bortsov’s monograph by Yu.A. Polyakhova ND Putova VV Electromechanical systems with adaptive and modal management. L. Energoatomizdat, 1984). However, the sliding mode, the positive properties of which are used in the proposed solution, is not an operating mode for them. Known systems with a variable structure in which nonlinear adjustments of transmission coefficients are used when generating a structure switching signal (see, for example, patent application N 4331114 / 24-160419). In them, as in the prototype, division blocks are used to estimate the moment of inertia. However, for the reasons noted above, this leads to a significant distortion or loss of information necessary for control when the system approaches the equilibrium state (and, accordingly, to a deterioration in the quality of processes).

 The authors are not currently aware of systems with a variable structure, except for the proposed solution, in which, when evaluating the variable moment of inertia and further performing non-linear tuning, division blocks are not used. The introduction of fine tuning significantly improves system performance.

 The drawing shows a structural diagram of the proposed control system with a variable structure.

 The variable structure control system comprises a mismatch meter 1 connected in series, a first unit of module 2, a first multiplication unit 3, to the second input of which a mismatch meter 1 output is connected, a first adder 5 and a first relay element 6, an amplifier 7 , DC motor 8, gear 9. The output shaft of gear 9 is mechanically connected to the control object 10 and position sensor 11, the output of which is connected to the second input of the meter 1, the first input of which is the input of the system. The system also contains series-connected speed sensor 12, the input of which is connected to the shaft of the DC motor 8, the second relay element 13, the second adder 14, to the second and third inputs of which are connected, respectively, the current sensor 15 of the motor 8 and the output of the speed sensor 12, and the integrator 16 , as well as the third block of multiplication 17. The output of the latter is connected to the second input of the first adder 5. In the system, the output of the speed sensor 12 is additionally through the second block of module 18 connected in series, the first functional the second converter 19, the fourth multiplication unit 20, to the second input of which the output of the speed sensor 12 is connected via the third relay element 21, is connected to the first input of the third multiplication unit 17. The output of the integrator 16 is connected to the second input of the third multiplication unit 17. In addition, the output of the third block of module 22 through series-connected third adder 23, to the second input of which the output of the second block of module 18 is connected, the second functional converter 24, the fourth adder 25, the second input of which oedinen with the output of the first function converter 19, and the third function generator 26 is coupled to a second input of the second multiplier block 4.

 The system operates as follows. After a reference signal is supplied to its input, the output signal from the first mismatch meter 1 after conversion in blocks 2, 3, 4, 5 and 6 is amplified by an amplifier 7 and fed to the input of a DC motor 8. The output shaft of the electric motor 7 and, accordingly, the gearbox shaft 9 begin to accelerate, as a result, the control object 10 is rotated, fulfilling the resulting mismatch.

-K

где i_д ток электродвигателя 8, М_ст момент сухого трения, K_вт- коэффициент вязкого трения, К_м моментный коэффициент двигателя,

- скорость вращения вала двигателя. Известно, что в значительном числе случаев для электродвигателя постоянного тока справедливо соотношение
I

= K_мi_д-M_стsign

-K

(1) где I момент инерции, приведенный к валу двигателя. Считаем, что I является кусочно-постоянной или медленно-изменяющейся величиной. Такое допущение справедливо, например, для простейших роботов, манипулирующих объектами различной массы, неизменной во время рабочего цикла. Тогда интегрирование (1) дает
I

=

(K_мi_д-M_стsign

-K_втα_д)dt
(2)
В связи с этим на выходе интегратора 16 формируется сигнал I

, поскольку на его вход подается сигнал с выхода второго сумматора 14, соответствующий подынтегральной функции в (2). Выходной сигнал интегратора 16 через третий блок модуля (БМЗ) 22 подается на вход третьего блока умножения (БУЗ) 17. На другой вход БУЗ 17 поступает сигнал ДС 12, преобразованный в БМ2 18, первом функциональном преобразователе (ФП1) 19, реализующем извлечение квадратного корня, и БУ4 20. Ко второму входу БУ4 20 подключен РЭЗ 21, реализующий функцию sign X. Поэтому на выходу БУЗ 17 сигнал имеет вид

I

sign

Cигнал

I

суммируясь в третьем сумматоре 23 с сигналом

через ФП2 24, также вычисляющем функцию квадратный корень, подается на четвертый сумматор 25, где складывается с сигналом

, поступающим с ФП1 19. В результате при соответствующей настройке коэффициентов на выходе четвертого сумматора 25 формируется сигнал

+

(где К₃ коэффициент передачи третьего сумматора 23 по первому входу), который через ФПЗ 26 подается на вход БУ2 4. ФПЗ 26 реализует функцию
F(x)

при $\genfrac{}{}{0ex}{}{\text{x}}{\text{x}}$ $\genfrac{}{}{0ex}{}{\text{>}}{\text{≅}}$ $\genfrac{}{}{0ex}{}{\text{Δ}}{\text{Δ}}$
(3) где Δ- малая положительная константа. Из (3) видно, что ФПЗ 26 отличается от линейного усилителя тем, что при близком к нулю входном сигнале на его выходе формируется сигнал малой, но ненулевой величины Δ. Это требуется лишь для того, чтобы обеспечить прохождение сигнала рассогласования ε через БУ2 4 на первый сумматор 5. В связи с отмеченным, выходной сигнал четвертого сумматора 25 мало искажается в ФПЗ 26 и через БУ2 4 подается на вход первого сумматора 5, ко второму входу которого подключен выход БУ3 17. На выходе первого сумматора 5 формируется сигнал
S

+

-K

I

sign

(4) где K₁ коэффициент передачи по второму входу первого сумматора 5. Изменение структуры системы происходит при изменении знака сигнала S, т.е. при условии

+

-K

I

sign

= 0
(5)
Покажем, что при надлежащем выборе параметров K₁ и K₃ в системе возникает скользящий режим, описываемый (4) и (5), и следовательно, обеспечивается монотонный переходной процесс.Simultaneously with the speed sensor (DS) 12, the rotation speed signal of the motor shaft 8 through the second relay element (RE2) 13, which implements the sign X function, is fed to the input of the second adder 14. A current sensor 15 of the motor 8 is connected to the second input of the last one. To the third input of the second the adder 14 is connected to the output of the DC 12. With proper selection of the transmission coefficients at the inputs of the second adder 14, a signal K _m i _d -M _st sign is generated at its output

-K

where i _{d the} current of the electric motor 8, M _st moment of dry friction, K _W - coefficient of viscous friction, K _{m the} moment coefficient of the motor,

- the speed of rotation of the motor shaft. It is known that in a significant number of cases for the DC motor, the relation
I

= K _m i _d -M _st sign

-K

(1) where I is the moment of inertia reduced to the motor shaft. We consider that I is a piecewise constant or slowly varying quantity. This assumption is true, for example, for simple robots that manipulate objects of various masses, which is constant during the work cycle. Then integration (1) gives
I

=

(K _m i _d -M _st sign

-K _W α _d ) dt
(2)
In this regard, the signal I is formed at the output of the integrator 16

, since the signal from the output of the second adder 14 corresponding to the integrand in (2) is supplied to its input. The output signal of the integrator 16 through the third block of the module (BMZ) 22 is fed to the input of the third multiplication block (BUZ) 17. At the other input of the BUZ 17, the signal DS 12 is converted to BM2 18, the first functional converter (FP1) 19, which implements the square root , and BU4 20. A REZ 21 is connected to the second input of BU4 20, which implements the sign X function. Therefore, at the output of BUZ 17, the signal has the form

I

sign

Signal

I

summing in the third adder 23 with the signal

through FP2 24, also calculating the square root function, is fed to the fourth adder 25, where it is added to the signal

received from FP1 19. As a result, with the appropriate adjustment of the coefficients at the output of the fourth adder 25, a signal is generated

+

(where K _{3 is} the transmission coefficient of the third adder 23 at the first input), which through FPZ 26 is fed to input BU2 4. FPZ 26 implements the function
F (x)

at $\genfrac{}{}{0ex}{}{\text{x}}{\text{x}}$ $\genfrac{}{}{0ex}{}{\text{>}}{\text{≅}}$ $\genfrac{}{}{0ex}{}{\text{Δ}}{\text{Δ}}$
(3) where Δ is a small positive constant. It can be seen from (3) that FPZ 26 differs from a linear amplifier in that, with an input signal close to zero, a signal of a small but nonzero value Δ is formed at its output. This is only necessary to ensure that the mismatch signal ε passes through the BU2 4 to the first adder 5. In connection with the above, the output signal of the fourth adder 25 is slightly distorted in the FPZ 26 and fed through the BU2 4 to the input of the first adder 5, to the second input of which connected output BU3 17. At the output of the first adder 5, a signal is generated
S

+

-K

I

sign

(4) where K _{1 is} the transmission coefficient for the second input of the first adder 5. The system structure changes when the signal S changes, i.e. provided

+

-K

I

sign

= 0
(5)
We show that, with the proper choice of the parameters K ₁ and K ₃ , a sliding mode arises in the system described by (4) and (5), and therefore a monotonic transient is ensured.

которая не равна нулю при движении изображающей точки системы вплоть до попадания в начало координат
(1+

ε-K

I

sign

= 0
(6)
При отработке скачкообразного задающего воздействия или ненулевых начальных условий выполняются соотношения ε -α_д/K_p

-

/K_p, где K_p коэффициент передачи редуктора 9. Поэтому (6) можно переписать так
(1+

ε+K₁K

I

0
(7) или, с учетом того, что I > 0,
ε +

0
(8)
Предположим, что электрической постоянной времени двигателя 8 можно пренебречь и его передаточная функция по скорости имеет вид W(P) K_д/(T_дP+1), где T_д RI/K_MK_ω (R и K_ω- соответственно сопротивление якорной цепи и коэффициент противоЭДС двигателя). Для возникновения и существования скользящего режима требуется, чтобы линия переключения (8) располагалась на фазовой плоскости в секторе между осью абсцисс и вырожденной устойчивой траекторией (см. монографию Теория систем с переменной структурой (Под ред. С.В. Емельянова. М. Наука, 1970). Для этого нужно настроить коэффициенты K₁ и K₃ согласно соотношениям
K₃ 4KK_дK_pR/K_мK_ω (9)
K₁≥2R/K_pK_мK_ω (10) где "К" коэффициент передачи усилителя 7. Коэффициент K₁ не следует выбирать значительно больше правой части (10), так как это ведет к затягиванию переходных процессов.Equation (5) can be rewritten in another form, after dividing its value

which is not equal to zero when the system imaging point moves up to the origin
(1+

ε-K

I

sign

= 0
(6)
When working out a jump-like driving action or non-zero initial conditions, the relations ε-α _d / K _p

-

/ K _p , where K _{p is} the gear ratio of gear 9. Therefore (6) can be rewritten as
(1+

ε + K ₁ K

I

0
(7) or, given that I> 0,
ε +

0
(8)
Suppose that the electric time constant of engine 8 can be neglected and its speed transfer function has the form W (P) K _d / (T _d P + 1), where T _d RI / K _M K _ω (R and K _ω are the resistance, respectively anchor chain and engine counter-emf coefficient). For the emergence and existence of a sliding regime, it is required that the switching line (8) be located on the phase plane in the sector between the abscissa axis and a degenerate stable trajectory (see the monograph Theory of Systems with Variable Structure (Ed. By S.V. Emelyanov. M. Nauka, 1970). To do this, you need to adjust the coefficients K ₁ and K ₃ according to the ratios
K ₃ 4KK _d K _p R / K _m K _ω (9)
K ₁ ≥2R / K _p K _m K _ω (10) where "K" is the gain of the amplifier 7. The coefficient K ₁ should not be chosen much larger than the right-hand side of (10), since this leads to a delay of transients.

 Thus, in the proposed system due to the organization of the sliding mode of operation, the monotonic nature of transients is ensured (this follows from the solution of differential equation (8)). The most significant advantage of the system, in contrast to the prototype, is that the structure switching signal is generated in the form (4) and therefore does not require the use of division blocks, thus eliminating the prototype disadvantages mentioned above.

Claims (1)

 CONTROL SYSTEM WITH A VARIABLE STRUCTURE, containing a mismatch meter in series, a first module block, a first multiplication block, to the second input of which a mismatch meter output, an amplifier, a DC motor, a gearbox are connected to the mismatch meter, a first adder and a first relay element the output shaft of which is mechanically connected with the control object and the position sensor, the output of which is connected with the second input of the mismatch meter, and sequentially connected speed sensor, the input of which is connected to the DC motor shaft, the second relay element, the second adder, to the second and third inputs of which are connected the motor current sensor and the output of the speed sensor and integrator, as well as the third multiplication unit, the output of which is connected to the second the input of the first adder, characterized in that in addition the output of the speed sensor through series-connected the second block of the module, the first functional converter, the fourth block multiplication, to the second input of which the speed sensor output is connected through the third relay element, is connected to the first input of the third multiplication block, to the second input of which the integrator output is connected through the third module block, and the output of the third module block through the third adder connected in series, to the second input which is connected to the output of the second module block, the second functional converter, the fourth adder, the second input of which is connected to the output of the first functional converter, and the third function The alial converter is connected to the second input of the second multiplication unit.