RU2012029C1 - Non-linear correcting device - Google Patents

Abstract

FIELD: automatic control systems. SUBSTANCE: device has three units 1, 2, 3 for signal scaling, two adders 4, 5, two multipliers 6, 7, normally-closed switch 8, three units 9, 10, 11 for determination of signal sign, unit 12 for determination of positive sign of signal, unit 13 for determination of negative sign of signal, two logical one shapers 14, 15, differentiating unit 16, integrator 17 having resetting unit, exponential function unit 18. Device design decreases effect of integration errors on frequency characteristics of device, transmission coefficient change depending on sign of speed of output signal absolute value when input and output signals have same signs. In addition effect of alteration in order of integration on integration errors is decreased. EFFECT: increased functional capabilities. 4 dwg

Description

 The invention relates to the field of automatic control and can be used as a correction device in automatic control systems.

Known non-linear corrective device (NKU) with amplitude-frequency characteristic, like an integrator, but with a small phase delay [1]. The disadvantages of NKU are the magnitude of the adjustable phase delay (of the order of minus 18 ^° ), the unchanged first slope of the logarithmic amplitude-frequency characteristic (LFC) and the absence of dependence of the transmission coefficient of the device on the sign of the speed of the input signal module.

 The closest in technical essence to the invention is a non-linear integrator with zero phase shift, containing two channels for converting the input signal of the device, a unit for multiplying the output signals and an integrator, the first channel containing a scaling unit of the input signal, the output of which is the output of the first channel and connected to the input of the block multiplying the output signals of the channels, the second channel contains an input signal differentiator, blocks for determining the signs of the input signal and its time derivative, a multiplier of the output signals of the character determination units, the output signal of the multiplier corresponds to the sign of the speed of the input signal module of the device [2]. The disadvantage of this device is the narrowness of its functionality, expressed in the invariability of the phase-frequency characteristic (PFC) (zero phase shift) and the first slope of the LAC, in the unregulated dependence of the transmission coefficient of the device on the sign of the speed of the input signal module, and also in the absence of a mechanism for compensating for cumulative integration errors, manifested in the drift of the output signal of the analog integrator or errors of the selected method of numerical integration for digital systems.

 The purpose of the invention is to expand the functionality of the device by reducing the influence of integration errors on the frequency characteristics of the device, changing the transmission coefficient of the device depending on the sign of the speed of the input signal module, subject to the condition of coincidence of the signs of the input and output signals of the device, varying the order of integration.

 In FIG. 1 shows a functional diagram of the GCC; in FIG. 2 - graphs of the qualitative temporal dependences of the signals for the frequency case of NKU with zero phase shift; in FIG. 3 - graphs of the qualitative temporal dependences of the signals for the frequency case of the switchgear with phase delay and a constant output signal of the integrator with a negative sign of the speed of the module of the input signal of the switchgear; in FIG. 4 - graphs of the qualitative temporal dependences of the signals for the frequency case of the switchgear with phase advance. The input signal of the NKU on the graphs is harmonic, without a constant component.

 The device contains blocks 1,2,3 with the corresponding coefficients K, K +, K-, adders 4,5, multiplication blocks 6,7, disconnect key 8, signal sign determination blocks 9,10,11, signal positive sign determination block 12 , a block 13 for determining the negative sign of the signal, formers 14.15 pulses with a zero input signal, a differentiator 16, an integrator 17 with a zeroing device, a block 18 for generating a power function with a constant positive exponent.

 By x (t) and y (t) are designated the input and output signals of the NCC, f '(t) and f (t) are the input and output signals of the integrator, respectively, F (t) is the output signal of the power-generating unit and the second channel transforms the input signal of the NKU, t is the time variable, D is the differentiation operator, l / D is the integration operator, r is a constant positive exponent of the power function.

 Analysis of the proposed solution in comparison with the prototype revealed distinctive features, therefore, the proposed solution has a novelty criterion.

 An analysis of the proposed solution in comparison with other analogues revealed the presence of an integrator in the second channel of the NKU circuit and a device for resetting the output signal of the integrator, but unlike the proposed solution, there is no power-generating function block and the dependence of the NKU transmission coefficient on the sign of the input signal module speed. These differences, together with similar features, lead to a new technical result - the expansion of functionality. Therefore, the proposed solution has the criterion of inventive step.

 In accordance with FIG. 1 device operates as follows.

The input signal x (t) is applied to the inputs of several branches of the device. At the output of the branch, consisting of series-connected units of differentiation by time 16 and determining the sign of signal 9, a signal of the sign of the speed of the input signal of the NKU is formed. As a result of multiplying in block 6 the speed sign and the sign of the input NKU signal itself, defined in block 10, the sign of the speed of the module of the input NKU signal is formed. Depending on the polarity of this signal, it is passed either through a branch consisting of blocks 12.2 (a positive sign of the speed of the input signal module of the GCC) or through a branch consisting of blocks 13.3 and a disconnect switch 8 (a negative sign of the speed of the module. At the output the adder 4 generates an integrator 17 f ^' (t) input signal, which is a scaled signal of the speed sign of the module of the input signal of the low-voltage switchgear. Depending on the polarity of the signal f ^' (t), the integrator output signal f (t) either increases or decreases. to a positive degree in the power function generating unit 18, and the obtained signal F (t) is multiplied in the multiplying unit 7 with the input low-voltage switch input signal scaled in block 1. As a result of the multiplication, the output low-voltage switch signal y (t) is generated. the signal of the switchgear and when the signals f (t), F (t), y (t) are reset, the signal f '(t) is also reset.This condition is realized in the proposed structure of the switchgear using the adder 5, blocks 10 and 11 determine the signs of the input and output signals NKU, driver 14 pulses at zero m signal, disconnecting (normally closed) key 8. When zeroing the output signal of the switchgear at the output of block 11, a circuit of the signal polarity occurs. When the signals of blocks 10 and 11 are mixed, the output of the adder 5 produces a zero signal, from the action of which the pulse shaper 14 controls the disconnecting switch 8, which breaks the circuit between the block 3 and the adder 4. The negative signal to the integrator’s input then ceases to be received, and a positive signal can be received through block 2 and the other input of the adder 4. As soon as the integrator output signal becomes positive and the signs of the input and output signals of the low-voltage switchgear begin to match again, a nonzero signal is generated at the output of the adder 5 Al, the driver 14 of the pulse removes the control signal and the key 8 again closes the signal path of the negative sign of the speed of the input signal module NKU. The zeroing of the output signal of the integrator 17 also occurs from the action of the control signal of the pulse shaper 15 with a zero input signal of the switchgear.

{ K1·[sign(x)·sign(dx/dt)] } ·dt, f(t)≥ 0
y(t_o) = F(t_o) = f(t_o) = 0 при x(t_o) = 0 где К - постоянный положительный коэффициент блока масштабирования входного сигнала устройства;
К1 - постоянный коэффициент блока масштабирования выделенного отрицательного или положительного знака скорости модуля входного сигнала устройства (на фиг. 1 этому коэффициенту соответствует К- и К+, причем К- может быть любым по величине и знаку, К+ обязательно положительным);
t_o - момент времени срабатывания устройства обнуления выходного сигнала интегратора при нуле входного сигнала НКУ.Mathematically, the operation of the device can be described by the following system of equations:
y (t) = K * x (t) * F (t);
F (t) = [f (t)] ^r , r>0;
f (t) =

{K1 · [sign (x) · sign (dx / dt)]} dt, f (t) ≥ 0
y (t _o ) = F (t _o ) = f (t _o ) = 0 for x (t _o ) = 0 where K is a constant positive coefficient of the scaling unit of the input signal of the device;
K1 is the constant coefficient of the scaling unit of the selected negative or positive sign of the speed of the input module of the device (in Fig. 1, this coefficient corresponds to K- and K +, and K- can be of any size and sign, K + is necessarily positive);
t _o is the instant of operation of the device to zero the output signal of the integrator when the input signal of the switchgear is zero.

 GCC can be used in various places of the corrected automatic control system, especially in the error channel of the tracking system.

 Due to the operation of the device to reset the integrator output signal, the integrator output signal f (t) is periodically reset with the integration errors contained in it. Due to this, the influence of integration errors on the frequency characteristics of the device is reduced, the independence of the characteristics from the initial conditions for the inclusion of the integrator in the work is realized, and a small phase shift of the switchgear is provided. In a digital implementation of NKU, the integrator with a zeroing device can be made in the form of a pulse generator and a counter with a zeroing input, which is connected to the output of the zeroing pulse shaper 15 at zero input signal of the NKU. In the analogue version, the switchgear integrator can be implemented using an operational amplifier with a capacity in the feedback circuit. In this case, the integrator zeroing device is a closing (normally open) key connected in parallel with the capacitor, the key control input is connected to the output of the zeroing pulse shaper 15.

 By changing the transmission coefficient of the device depending on the sign of the speed of the input module of the NKU module, subject to the condition for the signs of the input and output signals of the device to match, the dynamic properties of the corrected system change as the module of the input signal of the NKU increases and decreases. In particular, in the case of a harmonic input signal of the GCC for various calculated ratios of the coefficients K- and K +, this leads to the appearance of a small (maximum up to two to three tens of degrees) equivalent phase shift of the first harmonic of the output signal of the relative harmonic input signal of the GCC. This phase shift is regulated depending on the ratio of the values of the coefficients K- and K + and can be either positive or negative, in the particular case of equality of the coefficients, an NKU with a zero phase shift is obtained.

 The condition for coincidence of the signs of the input and output signals is necessary to prevent the possibility of loss of stability of the tracking system in which the GCC is used.

 Analysis of the frequency characteristics of the low-voltage switchgear shows that they correspond to the LACH of the integrating link (with an exponent r = 1), but with a small phase shift. By choosing the exponent r of the power-generating unit, the order of integration (astatism) of the device changes. Due to this, the slope of the LAHF of the harmonically linearized transfer function of the NCC changes: in comparison with r = 1, the slope of the LAHC increases for r> 1, and for r <1 it decreases. The dynamic properties of the adjusted automatic control system change accordingly. This property is confirmed by mathematical calculations, the results of modeling the characteristics of the switchgear on a computer and the test results of the prototype.

 In the absence of a constant component in the input harmonic signal, the NCC has pseudo-linear properties, i.e., its frequency characteristics are independent of the amplitude of the input harmonic effect and depend only on the cyclic frequency ω raised to the power r.

The calculations of the harmonic linearization coefficients of the proposed NKU are carried out using the calculations of certain integrals, which in general form (for arbitrary values of r, K-, K + are made only through the recurrence relations of the integrals with decreasing degree of the integrand. Therefore, in general form it is impossible to obtain the final mathematical expressions of the calculated integrals The numerical values of the integrals can be obtained by calculation for specific values of r, K-, K +. It is also possible to obtain complete mathematics of the transmission coefficient formulas K _NKU and phase F _NKU for special cases of r, K-, K +.

As examples, we consider three particular, most characteristic and used cases of NKU:
1) with a zero phase shift at K- = K +, a) r = 1, b) r = 2;
2) with phase delay and a constant output signal of the integrator with a negative sign of the speed of the module of the input signal of the switchgear, for which K- = 0 is selected, a) r = 1, b) r = 2;
3) with a phase lead at K- >> K +, a) r = 1, b) r = 2.

In these cases, the transmission coefficient K _NKU and phase F _NKU in the absence of a constant component in the input harmonic signal, respectively, is
1a) K _NKU = 1.104 * K * (K + / ω);
F _NKU = 0 ^about ;
1b) K _NKU = 1,322 * K * (K + / ω); 2
F _NKU = 0 ^about ;
2a) K _NKU = 1,360 * K * (K + / ω);
F _NKU = -10.6 ^about ;
2b) 2
_NKU = 1.974 * K * (K + / ω);
F _NKU = -16.2 ^about ;
3a)
_NKU = 0.606 * K * (K + / ω);
F _NKU = +24.4 ^about ;
3b) 2
_NKU = 0.701 * K * (K + / ω);
F _NKU = +19.5 ^about .

 Implementation of the proposed NKU is possible in analog, analog-digital, digital forms and in the form of a program that works in real time.

 The use in the automatic control systems of the proposed NKU with significantly expanded functional capabilities will improve their dynamic properties.

Claims (1)

 A NONLINEAR CORRECTIVE DEVICE, comprising an integrator, a first multiplying unit, the output of which is the output of the device, and the first input of which is connected to the output of the first scaling unit, the input of which is the input of the device and connected to the differentiator, the first sign determining unit and the second multiplier, the second input which is connected to the output of the second block determining the sign, the input of which is connected to the input of the device, characterized in that, it introduced the third block sign, blocks for determining the positive and negative signs of the signal, two scaling blocks, a disconnecting key, two pulse shapers at a zero input signal, two adders, a power-generating function block, the output of the second multiplier connected to the inputs of the blocks for determining the positive and negative signs of the signals, outputs which through the corresponding scaling units are connected respectively to the first input of the first adder and the information input of the disconnecting key, the output of which is connected nen with the second input of the first adder, and the control input with the output of the first pulse shaper at a zero input signal, the input of which is connected to the output of the second adder, the first input of which is connected to the output of the second sign determination unit, the second input to the output of the third sign determination unit, the input of which is connected to the output of the first multiplier, the output of the first adder is connected to the input of the integrator, the zeroing input of which is connected to the output of the zeroing pulse shaper at a zero input signal, the input of which connected to the input of the device, the output of the integrator through the block forming the power function is connected to the second input of the first block multiplication.

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