RU2103714C1 - Method for automatic control of dynamic object - Google Patents

Abstract

FIELD: automation. SUBSTANCE: method involves use of regulator with controlled integrator and controlled phase- advance filter of input signal of controlled integrator. Also method involves generation of functions for resetting integrator and switching rate of proportional arm of filter using logical combinations of signs of error signal, output signal of controlled integrator, rate of setting signal, difference between rate of setting signal and error rate. Difference of latter rates corresponds to rate of output feedback signal for object. In addition method involves clipping output signal of filter and use of alternating threshold of proportional arm of filter according current signal. Integrator for compensation of constant error constituent is connected in parallel to regulator. This results in possibility of dynamic amplitude-frequency response of linear regulator with decreased equivalent phase delay in working bandwidth Device provides possibility of jump setting of output of controlled integrator when error sign is altered and correction of rates of setting and output rates in whole range. EFFECT: increased dynamic precision. 4 cl, 12 dwg

Description

 The invention relates to the automatic control of astatic systems with non-linear corrective devices and can be used in high-precision drives with various types of executive motors.

 A known method of automatic control of an object, implemented in a controlled Pi-controller [1]. According to this method, to control the ratio of the proportional (P) and integral (I) components of the input signal of the controller, the value of the error rate is used. The lower the speed, the lower the time constant of the integrator and the stronger the influence of the I-controller. The low speed of the error signal is characteristic of the steady state of the system; high speed - for transients.

However, this method is ineffective in steady motion due to the large phase delay (-90 ^o ) and zero drift of the I-controller, and also because of the nonlinear amplitude properties of the controller due to the deterministic dependence of its parameters on the absolute value of the error rate.

 A known method of automatic control of an object, implemented in a servo drive [2]. According to this method, when generating a control signal for an object, the output of the error integrator is used with logical control of the key of the bypass circuit of the output and input of the integrator according to the ratio of the speeds of the master and output signals of the tracking system. Shunting the integrator is equivalent to switching the I-controller to the P-controller. The I-controller is used to increase the dynamic accuracy of the tracking system in steady-state conditions with a small difference in the speeds of the driving output signals, the P-controller is used to reduce the oscillation of transients at a large difference in speeds.

 The reasons for the low efficiency of this method are similar to the previous case, and the nonlinear amplitude properties of the controller are due to the deterministic threshold value of the difference in the absolute values of the speeds for switching the controller.

 The main objective of the methods [1, 2] is to improve the quality of transients in the system due to the weakening of the I-component in the controller. These methods are not intended for the dynamic tracking mode, which is quite common in the practice of servo systems, for a piecewise monotonic driving signal (for example, harmonic or triangular).

A known method of automatic control of an astatic object, implemented in servo systems [3, 4] and servo drive [5]. In all systems, when generating a control signal for an object, the following signals are received and used: the output signal of a PI controller with logically switched feedback of a controlled integrator (UI) and the scaled error and error rate in a phase-ahead filter (FF) with a function U of the form
U = K • ε + T _D • D _ε ,
where ε is the error of the tracking system;
D _ε is the error rate;
K is the coefficient of proportionality;
T _D - the time constant of differentiation.

 The main difference between the systems [3, 4, 5] lies in the law of the formation of the signal of the logical control of the feedback switching UI. On this basis, the prototype, i.e. the closest in technical essence to the proposed method is the method implemented in [5], which uses the sign of the output signal of the MI to obtain the control signal of the switching feedback of the MI, as well as the speed of the reference signal of the system.

 The technical result - increasing the dynamic accuracy of this tracking system - is achieved due to the variability of the structure of the controller and the associated sliding modes. In real sliding modes, there are always self-oscillations with finite amplitude and frequency, the values of which are due to nonlinearities and perturbations of the control object, which impairs the dynamic accuracy of the tracking system. Also, this method does not provide astatism of the amplitude frequency response (AFC) of the PI controller with a reduced equivalent phase delay. A decrease in phase delay is necessary to increase the stability margins and to reduce the overshoot of transients in the servo system in comparison with a system with a linear PI controller.

 The objective of the invention is to increase the dynamic accuracy of a tracking system with an astatic object due to the additional astatism of the frequency response of a pseudo-linear PI controller with a reduced equivalent phase delay in the working frequency domain (another name for such a controller in TAP is non-linear isodrome (NI)).

The problem is solved in that the FF is controlled by logical switching of the coefficient K and one-sided upper limitation of the signal U with a variable level of limitation, after the limitation, the output signal of the FF is fed to the input of the MD with zeroing, to control the zeroing, use the logical function y1, to control the coefficient K use the logical function y2
y1 = (x1 = -x4) AND [(x4 = x2) OR (x4 = x3)],
y2 = (x1 = -x4) AND [(x1 = x2) AND (x1 = x3)],
where x1 is the sign of the output signal of the MD;
x2 is the sign of the speed of the driving signal;
x3 - signal sign of the difference between the speed of the reference signal and the speed of the error signal.

 x4 is the sign of the error signal.

 If the unity of the signal y1 is equal to zero, the output signal of the MI is zeroed, when the unity of the signal y2 is selected, the larger of the two values of the coefficient K is selected, the output signal of the PI controller is summed with the output signal of the additional integrator for compensating the constant error component, and the total signal is fed to the control input of the astatic object.

 Figure 1 shows a functional diagram of a method with MD with zeroing; figure 2 is a functional diagram of the implementation of IA with zeroing; figure 3 - logarithmic amplitude frequency characteristics (LAC) output to the error of the tracking system and LAC linear object with first-order astatism; in FIG. 4 - corresponding logarithmic phase frequency characteristics (LPC) of the output to the error of the tracking system and LPC of a linear object with first-order astatism; in FIG. 5 - qualitative characteristics of the error reference signal and the controller output signal with a harmonic reference signal of the operating frequency in the tracking system; in FIG. 6 - qualitative characteristics of the same signals in an open system; in FIG. 7 - LFCH of the regulator in the tracking system and open system; in FIG. 8 - qualitative characteristics of the driving signal, error and controller output signal with a triangular driving frequency signal in the tracking system; in FIG. 9 is a functional diagram of a method with a UI with zeroing and installation; in FIG. 10 is a functional diagram of the implementation of MI with zeroing and installation; in FIG. 11 - LACH of the output to the error of tracking systems with MI with zeroing and with MI with zeroing and installation; in FIG. 12 - corresponding LPFC of the output to the error of servo systems with MI with zeroing and with MI with zeroing and installation.

 In FIG. 1, the functional diagram includes an object 1 containing a first-order sequential astatic link, an error meter 2 of a driving signal and an output feedback signal, differentiators of a driving signal 3 and an error signal 4, MD 5 with zeroing, an integrator 6 for compensating the constant error component, four determinants signs: the sign of the output signal UI 7, the sign of the speed of the driving signal 8, the sign of the difference between the speed of the driving signal and the speed of the error 9, the sign of the error signal 10, a logic block 11 for generating control signals zeroing the UI and switching the coefficient K ФФ, proportional blocks 12, 13, 14, 15, multiplication blocks 16, 17, 18, logically controlled switch 19 П-circuits ФФ with two values of the coefficient K, block 20 one-way restriction with a controlled level of restriction from above , subtraction element 21, two-input adder 22 and three-input adder 23.

In FIG. 1 and 2, the following designations of parameters are accepted:
g is the reference signal of the tracking system;
y is the feedback output signal;
U _p is the output signal of the controller;
D is the differentiation operator d / dt, where d is the differential, t is time; accordingly 1 / D is the integration operator;
T is the time constant of the MI;
dI is the input signal of the MD;
I is the output signal of the MD;
R - input and logical signal to control the resetting of the MD;
X - coefficient theoretically tending to infinity (in practical implementation, an extremely large coefficient);
K ₀ ; K ₁ - values of the coefficient K ФФ, respectively, for y2 = 0 (K = K ₀ ) and y2 = 1 (K = K ₁ );
K _p - coefficient of the P-regulator;
T _to - time constant of the compensation integrator;
W ₀ - the static part of the transfer function of the object.

Designations K • ε; U; K; T _D ; x1; x2; x3; x4; y1; y2 are given earlier.

 The method is as follows.

 The stage of operation of the automatic control system is preceded by the stage of its synthesis. In engineering practice and TAP of nonlinear systems, one of the most common is the frequency synthesis method, coupled with the method of harmonic linearization of the nonlinearities of the object and the regulator.

First, according to the stability criterion, a frequency synthesis of the servo system without AI is carried out, i.e. P-controller with an integrator of compensation for the DC component of the system error caused by the initial bias and low-frequency zero drift of the object, as well as its static load. The value of T _k is chosen large enough so as not to introduce a noticeable phase delay in the LPF of the controller in the working frequency domain. The cutoff frequency of the open system is determined. According to the criteria of sufficient stability margins and the quality of transients in the system, the cutoff frequency is usually chosen 3 ... 5 times less than the frequency with a phase delay of the open system -180 ^o . Then, the UI branch is additionally connected and the NI parameters are synthesized. At the same time, the coefficient K _{p is} reduced by a factor of 2 ... 3, and the value of T for the MI is selected to be 2 ... 3 times larger than the reciprocal cutoff frequency of the initial system without MI. At the same time, the ratios K ₁ / K ₀ and T _D / T are set greater than unity, but for reasons of stability, no more than the ratio of the frequency with the phase -180 ^o to the cutoff frequency of the initial open system without UI.

This completes the synthesis of the system controller. A correctly synthesized system with an NR and a linear astatic object in the mode of tracking harmonic master signals has a LACH shown in FIG. 3, the LPF shown in FIG. 4, and temporal characteristics in FIG. 5. Upon receipt of all characteristics, the ratios K ₁ / K ₀ and T _D / T were chosen equal to three.

All LACH and LPC charts are performed in the traditional manner: LFC have a dimension of dB, LPC is a degree of degrees ( ^o ), the frequency ε is plotted along the argument axis on a logarithmic scale.

In FIG. 3, the solid line indicates the LACH of the output to the system error 20lg (y / ω) and the dashed line indicates the LACH of the object 20lg (y / U _p ), in FIG. 4, the solid line — the LPF of the ε system error; the dashed line — the LPF of the object φ (y / ε) (y / U _p ).

In the working frequency domain, an additional astatism of the LACH of the output to the error of the corrected system with a reduced equivalent phase delay of the LPF is obvious (in the limit of -160 ^o instead of -180 ^{o of an} astatic object with a linear Pi controller).

In FIG. 5, 6 and 8, the signals g, φ, and U _p have a large spread of amplitudes and are given at different scales for clarity, to summarize, the time argument is transformed into the phase argument of the periodic reference signal through a factor of 360 ^o / T ₀ , T ₀ is the period of the repetition time of the master signal. For the cases of FIG. 5 and 8, the error amplitude ε is significantly smaller than the signal amplitude g, for the case of FIG. 6, the error ε coincides with the signal g.

In reality, an astatic object is non-linear and usually has an entry deadband. The limiting case of a system with such an object is an open system due to the complete insensitivity of the object at the input (an open system can also be obtained by breaking feedback). In an open system with a zero input signal, the error is equal to the reference signal (Fig. 6). At the same time, the astatic LAC of the controller practically does not change (the LAC of the controller is not shown in the figure), and the phase delay of the LPFC of the controller in the working frequency domain due to a change in the error waveform and the controller output signal decreases from -70 ^o to -38 ^o (in Fig. 7 the solid line indicates the LPF of the ε controller of the servo system, the dashed line indicates the LPF of φ (U _p / ε) of the open-loop controller).

Formulas of coefficients q; q 'of the harmonic linearization of NR, as well as their derivatives A _q = (q ² + q' ² ) ^0.5 ; φ (U _p / ε) = arctan (q '/ q) obtained taking into account K _p = 1; T; φ _q and based on the waveforms ω and U _{p of} FIG. 5, 6, correspond to the low-frequency asymptotes of LACH and LFCH:
for tracking system:
ε
for open system:
q = 0.43 / (Tω); A _q = 1.43 / (Tω) q '= - 1.36 / (Tω) φ _q = -72 ^°
Another typical example of a dynamic piecewise monotonous reference signal of a tracking system is a triangular signal. In FIG. 8 shows the characteristics for the case of the signal g of the operating frequency. The signal U _r in the steady motion is mainly formed due to the signal I MD I, much larger than the signal of the PI controller q = 1.27 / (Tω); A _q = 1.62 / (Tω) q '= - 1.00 / (Tω) φ _q = -38 ^° .

The main task of the AM in the dynamic tracking mode of the system for a piecewise monotonic signal in the working frequency domain is to keep the system in aperiodic mode without overshoot at y2 = 0 and at the same time actively reduce the error due to the growth of its own output signal (see Fig. 8). The value y2 = 1 corresponds to the transition of the system into an undesirable state of overshoot, and then, to reduce overshoot and the associated equivalent phase delay of NRs, the PF chain coefficient is increased from K ₀ to K ₁ . A means of reducing the phase delay of the MI is also a one-sided upper restriction of the output signal of the FS with a controlled level of limitation K _p • ε, which allows the differential component K • ε to participate only in reducing the input signal of the MI at the stage of system braking when the error tends to zero.

 The logical condition y1 of zeroing the MD makes it impossible for the system to enter the state of uncontrolled braking and the associated significant additional delay in the case of the opposite sign of the output signal of the MD and the same error signs and any of the speeds of the master or output signals of the system (the speed of the feedback signal is identical to the difference of the speeds of the master signal and error signal).

 An additional integrator compensates for the constant component of the object error. In this case, the NI becomes a regulator with pseudo-linear properties, i.e., frequency characteristics that depend on the frequency and do not depend on the magnitudes of the signal amplitudes.

 Thus, an inextricable set of distinctive features of the proposed method of automatic regulation allows you to achieve a new significant technical result.

 An additional way to combat overshoot and reduce the phase delay of the error of the tracking system with an astatic object is a method of setting the output signal of the IA. It consists in the fact that the output signal of the MI is multiplied by the quotient of dividing the speed of the driving signal by the speed of the output signal of the system, the output signal of the MI is set abruptly equal to the result of this multiplication at the moment of changing the sign of the error signal.

 In the functional diagram of FIG. 9 instead of a zero-zero MI with number 5, a MI with zeroing and setting is shown. The remaining blocks with numbers from 1 to 23 of FIG. 9 are identical to the blocks of FIG. 1, but the circuit of FIG. 9 additionally has a divider 24, a block 25 of a two-sided restriction from zero to one, a multiplication block 26, and a block 27 for generating a logical unit at zero input signal of the block.

In FIG. 9 and 10 are additionally indicated:
S - input and logical signal to control the installation of the output of the MD;
I ₀ - input and signal of the value of the output setting of the MI.

According to the circuit of FIG. 9, the moment of the change of the error sign is fixed by the active logical control signal for setting the output of the MD using block 27. According to the circuit of FIG. 10 first, along the front of the transition of the control signal S to the active state, the value of the setting I ₀ obtained by multiplying the output signal of the IA by a limited coefficient of the ratio of speeds is stored in the memory element of the signal. Memorization is completed at the beginning of the MI installation process by the active signal level S. The installation process (in the particular case, zeroing) of the MI output is accomplished by closing the tracking system with the reference signal of the MI output setting value. This system with an extremely high direct-circuit gain K∞ is closed via a normally open contact of a switch controlled by a combined signal generated by the OR function from the logic signals of setting and zeroing. When zeroing the MD from the active control signal of zeroing R, a zero signal is connected to the input of the installation tracking system. In the absence of active control signals R and S, through the normally closed contact of the switch in normal integration mode, the input signal UI dI is connected to the integrator.

In the dynamic tracking mode for a piecewise monotonic driving signal of the operating frequency, when switching to overshoot and changing the sign of the error, the speeds of the driving and output signals of the system are usually the same in sign, but the speed of the output signal is greater than the speed of the driving signal, and, therefore, the quotient of the speed division will be positive a number greater than or equal to zero but less than one. At the time of zeroing the error and the signal of the P-controller K _p • ε, only the output signal II determines the output velocity of the astatic object. The transition to overshoot indicates an excess of the output speed and, therefore, an excess of the output signal of the MD. By reducing the jump in the output signal of the MI using the coefficient of the ratio of speeds at the time of changing the sign of the error, this excess is partially compensated and the subsequent overshoot is reduced.

 The limitation of the coefficient of the ratio of speeds in the range from zero to unity is also an essential sign. If at the moment of changing the sign of the error the signs of the speeds were opposite, which indicates the proximity of the frequency of the master signal to the system frequency, a zero limit will make the ratio of the speeds zero and the function to set the output signal of the MD will actually become a function of zeroing the MD. In the frequency domain near the cutoff frequency, this also allows one to further reduce the phase delay of the controller due to the attenuation of the component of the ID in the total signal of the NR. Limiting the velocity ratio coefficient to one unit from above guarantees the system the impossibility of accidentally (due to noise and errors of differentiation and division operations) an undesirable increase in the MD signal at the moment of changing the error sign.

 A clear confirmation of what has been said are comparative LACH (Fig. 11) and LPCH (Fig. 12) of the output to the error of servo systems with MD with zeroing (solid lines of characteristics) and MD with zeroing and setting (dashed lines of characteristics). In the entire frequency domain, with almost identical VLF systems, they obtain less delay of the VLF system with MD with zeroing and setting.

 Thus, the combination of additional distinctive features of the method allows to achieve a technical result of an additional reduction in phase delay.

Sources of information:
1. The patent of Germany N 1673601, G 05 B 11/00, 1973.

 2. USSR author's certificate N 794611, G 05 B 11/01, 1981.

 2. Copyright certificate of the USSR N 1352451, G 05 B 11/01, 1987.

 2. USSR Author's Certificate N 1425595, G 05 B 11/01, 1988.

 2. USSR Author's Certificate N 1446600, G 05 B 11/01, 1988.

Claims (2)

1. The method of automatic control of an astatic object, which consists in the following signals being received and used when generating a control signal for the object: the output signal of the PI controller with a logically controlled integrator, the sign of the output signal of the controlled integrator, the speed signal of the reference signal of the tracking system, scaled signals errors and error rates in a phase-reflection filter with a function U of the form
U = K • ε + T _d • D _ε ,
where e is the error of the tracking system;
D _ε is the error rate;
K is the coefficient of proportionality;
T _{d the} time constant of differentiation,
characterized in that the phase-leading filter is controlled by logical switching of the coefficient K and one-sided upper limitation of the signal U with a variable level of limitation K • ε, after limiting the output signal of the phase-shifting filter is fed to the input of a controlled integrator with zeroing the output signal, to control the zeroing, use the logical function y1, to control the switching of the coefficient K, use the logical function y2
y1 (x1 -x4) AND [(x4 x2) OR (x4 x3)]
y2 (x1 -x4) AND (x1 x2) AND (x1 x3),
where x1 is the sign of the output signal of the controlled integrator;
x2 sign of the speed of the driving signal;
x3 sign of the signal of the difference between the speed of the reference signal and the speed of the error signal;
x4 error sign
if the unit of signal y1 is equal to zero, the output signal of the controlled integrator is zero, if the unit of signal y2 is equal, the larger of the two values of the coefficient K is selected, the output signal of the PI controller is summed with the output signal of the additional integrator for compensating the constant error component, and the total signal is fed to the control input of the object.  2. The method according to p. 1, characterized in that the output signal of the controlled integrator is multiplied by the quotient of dividing the speed of the driving signal by the difference between the speed of the driving signal and the speed of the error signal, the output signal of the controlled integrator is jump-set to the result of this multiplication at the time of changing the sign of the error signal of the tracking system.

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