阅读说明：本技术 有源串联校正电路及其方法 (Active series correction circuit and method thereof ) 是由 唐静 于 2020-12-03 设计创作，主要内容包括：一种有源串联校正电路,设置有比例微分单元和惯性积分单元,比例微分单元的输入端与惯性积分单元的输出端连接,或者比例微分单元的输出端与惯性积分单元的输入端连接；其中比例微分单元设置有运算放大器U-1,运算放大器U-1的反向输入端连接电阻R-1,电阻R-1的另一端为比例微分环节信号输入端,在电阻R-1的两端还并联有电容C-1,在运算放大器U-1的输出端和反向输入端之间并联有电阻R-2,运算放大器U-1的正向输入端接地；惯性积分单元设置有运算放大器U-2,运算放大器U-2的反向输入端连接电阻R-3,电阻R-3的另一端为惯性积分环节信号输入端,在运算放大器U-2反向输入端和输出端之间并联有电阻R-4,在电阻R-4的两端跨接有电容C-2,运算放大器U-2的正向输入端接地。(An active series correction circuit is provided with a proportional differential unit and an inertia integral unit, wherein the input end of the proportional differential unit is connected with the output end of the inertia integral unit, or the output end of the proportional differential unit is connected with the input end of the inertia integral unit; wherein the proportional differential unit is provided with an operational amplifier U 1 Operational amplifier U 1 Is connected with the resistor R 1 Resistance R 1 The other end of the resistor is a proportional differential link signal input end and is connected with a resistor R 1 Both ends of the capacitor C are connected in parallel 1 In an operational amplifier U 1 Between the output end and the reverse input end of the resistor R 2 Operational amplifier U 1 The positive input end of the transformer is grounded; the inertia integration unit is provided with an operational amplifier U 2 Operational amplifier U 2 Is connected with the resistor R 3 Resistance R 3 The other end of the second loop is an inertia integral link signal input end which is arranged at an operational amplifier U 2 A resistor R is connected in parallel between the reverse input end and the output end 4 At the resistance R 4 Across which a capacitor C is connected 2 Operational amplifier U 2 The positive input terminal of (a) is grounded.)

1. An active series correction circuit, characterized by: the device is provided with a proportional differential unit and an inertia integral unit, wherein the input end of the proportional differential unit is connected with the output end of the inertia integral unit, or the output end of the proportional differential unit is connected with the input end of the inertia integral unit;

wherein the ratio is microIs provided with an operational amplifier U in units₁The operational amplifier U₁Is connected with the resistor R₁The resistance R₁The other end of the resistor is a proportional differential link signal input end, and the resistor R is arranged at the other end of the resistor R₁Both ends of the capacitor C are connected in parallel₁In the operational amplifier U₁Between the output end and the reverse input end of the resistor R₂The operational amplifier U₁The positive input end of the transformer is grounded;

the inertia integration unit is provided with an operational amplifier U₂The operational amplifier U₂Is connected with the resistor R₃The resistance R₃The other end of the operational amplifier is an inertia integral link signal input end, and the operational amplifier U is connected with the other end of the operational amplifier₂A resistor R is connected in parallel between the reverse input end and the output end₄At the resistance R₄Across which a capacitor C is connected₂The operational amplifier U₂The positive input terminal of (a) is grounded.

2. The active series correction circuit of claim 1, wherein: in the operational amplifier U₁Is connected to the positive input terminal via a resistor R₅Back ground, said operational amplifier U₂Is connected to the positive input terminal via a resistor R₆And then grounded.

3. The active series correction circuit of claim 2, wherein: the resistor R₅Has a value of R₅＝R₁//R₂Said resistance R₆Is taken as R₆＝R₄//R₃。

4. The method of claim 1, wherein:

the proportional differential unit has the calculation formula as follows:

proportional differential transfer function:

G_D(s)＝-k_D(T_Ds+1)

whereinT_D＝R₁C₁；

The calculation formula of the inertia integral unit is as follows:

inertial integral link transfer function:

whereinT_I＝R₄C₂；

The calculation method of the active series correction circuit comprises the following steps:

transfer function of active series correction circuit:

τ₁、τ₂and the value of k is determined by an automatically controlled tandem correction method; (s.tau.)₁+1) is the same as the denominator of the established controlled object transfer function; (s.tau.)₂+1) determined by the transfer function of the controlled object, the proposed overshoot and the adjustment time index; k is determined by the static error coefficient of the transfer function of the control object and the proposed static error coefficient index;

the denominator of the correction element is generated by an inertia circuit, tau₂＝R₄C₂Through τ₂Selecting appropriate R₄And C₂；

The correction element molecules are generated by a differentiating circuit, tau₁＝R₁C₁Through τ₁Selecting appropriate R₁And C₁；

Molecule of calibration device (sC)₁R₁+1) is the denominator of the actual controlled object transfer function. So that C of the correcting device₁R₁Is a fixed value;

for convenience of adjustment, let R₄＝R₃So that R₃Can be prepared from R₄Determining;

the proportionality coefficient is:

due to R₄＝R₃Therefore, it isSince it has already been through tau₁Select R₁So that R₂From k and R₁Jointly determining;

calculating tau by series correction theory due to modeling error₁And τ₂And the values of the capacitance and resistance parameters of the series correction circuit cannot meet the index requirements of the control system, and further adjustment is needed. When in series connection with the positive electrodeAfter the circuit is connected with the controlled object in series, the parameter value of each circuit of the series correction circuit is adjusted, and the adjusting method comprises the following steps:

if the overshoot of the output step response waveform is larger than the required overshoot index, then R is decreased simultaneously₃And R₄(ii) a The overshoot of the output step response waveform is smaller than the required overshoot index, and R is simultaneously increased₃And R₄；

If the adjustment time of the output step response waveform is longer than the required adjustment time, R is decreased simultaneously₃And R₄(ii) a If the adjustment time of the output step response waveform is shorter than the required adjustment time, R is simultaneously increased₃And R₄；

When the overshoot of the output step response waveform and the adjustment time are adjusted, please ensure R₃And R₄Varying together, i.e. ensuring R₃＝R₄；

If the static error of the output step response waveform is smaller than the desired static error, R is increased₂A value; if the static error of the output step response waveform is greater than the desired static error, R is decreased₂The value is obtained.

Technical Field

The invention relates to the technical field of automatic control, in particular to an active series correction circuit and method for a controlled object of a second-order under-damping system or approximate second-order under-damping.

Background

The series correction transfer function isWherein tau is₁，τ₂Is built on the transfer function of the controlled object. I.e. the parameters of the transfer function of the controlled object and the performance index to be achieved₁And τ₂The value is obtained. Tau is₁And τ₂The values determine the parameters of the individual circuit components of the series correction circuit.

The parameters of the actual transfer function of the controlled object are not accurate, especially the model developed by theoretical analysis method, for example, the controlled object has a resistance theoretical value of 5 Ω, but it may have 5% error, and in addition, the errors of the circuit board, the wire end, etc., so the transfer function built by the controlled object with the resistance of 5 Ω has an error with the actual transfer function of the controlled object. However, errors also exist in the modeling process of other parts of the controlled object, so that the tau of the series correction model derived in the way₁And τ₂There is a larger deviation, and further there is a deviation in the series correction function derived from the controlled object transfer function and the control index and in the components in the circuit thereof.

The conventional descriptions include: development and development of the Pashuang-automatic control principle virtual laboratory [ D ]. university of Shandong, 2007.

The transfer function of the correction device is:

wherein

T＝R₄C₁

Such correction circuits do not adjust well. In the series correction, the value of τ s +1 is constant because τ s +1 is to be offset from the denominator of the transfer function of the controlled object, and the denominator of the transfer function of the controlled object is constant. Since the actual transfer function is found to have errors, Ts +1 needs to be adjusted during actual operation, i.e. T is a value that needs to be adjusted during actual operation, but from thisT＝R₄C₁In the formula, T is adjusted to cause tau to change, then tau s +1 is changed, and the controlled object cannot be eliminatedThe denominator of (c) is contrary to the derivation theory of tandem correction.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides the series correction circuit which not only meets the composition of each parameter of the series correction function, but also can make up the defect of the transfer function establishment of the controlled object by adjusting the parameter of the series correction circuit; the overshoot and the regulation time index of the controlled object can reach the index requirement through the regulation of R3 and R4 in the series correction circuit provided by the invention, and the static error index can reach the index requirement through the regulation of the series correction circuit R2 provided by the invention. The specific technical scheme is as follows:

an active series correction circuit, characterized by: the device is provided with a proportional differential unit and an inertia integral unit, wherein the input end of the proportional differential unit is connected with the output end of the inertia integral unit, or the output end of the proportional differential unit is connected with the input end of the inertia integral unit;

wherein the proportional differential unit is provided with an operational amplifier U₁The operational amplifier U₁Is connected with the resistor R₁The resistance R₁The other end of the resistor is a proportional differential link signal input end, and the resistor R is arranged at the other end of the resistor R₁Both ends of the capacitor C are connected in parallel₁In the operational amplifier U₁Between the output end and the reverse input end of the resistor R₂The operational amplifier U₁The positive input end of the transformer is grounded;

the inertia integration unit is provided with an operational amplifier U₂The operational amplifier U₂Is connected with the resistor R₃The resistance R₃The other end of the operational amplifier is an inertia integral link signal input end, and the operational amplifier U is connected with the other end of the operational amplifier₂A resistor R is connected in parallel between the reverse input end and the output end₄At the resistance R₄Across which a capacitor C is connected₂The operational amplifier U₂The positive input terminal of (a) is grounded.

Preferably, the method comprises the following steps: in the operational amplifier U₁Is connected to the positive input terminal via a resistor R₅Is connected toGround, the operational amplifier U₂Is connected to the positive input terminal via a resistor R₆And then grounded.

Preferably, the method comprises the following steps: the resistor R₅Has a value of R₅＝R₁//R₂Said resistance R₆Is taken as R₆＝R₄//R₃。

A calibration method for an active series calibration circuit,

wherein the proportional differential unit has a calculation formula as follows:

proportional differential transfer function: g_D(s)＝-k_D(T_Ds+1)

WhereinT_D＝R₁C₁；

The calculation formula of the inertia integral unit is as follows:

inertial integral link transfer function:

whereinT_I＝R₄C₂；

The calculation method of the active series correction circuit comprises the following steps:

active series correction circuit transfer function:

τ₁、τ₂and the value of k is determined by an automatically controlled tandem correction method. (s.tau.)₁+1) is the same as the denominator of the established controlled object transfer function; (s.tau.)₂+1) determined by the transfer function of the controlled object, the proposed overshoot and the adjustment time index; k is determined by the static error coefficient of the transfer function of the controlled object and the proposed static error coefficient index.

The denominator of the correction element is generated by an inertia circuit, tau₂＝R₄C₂Through τ₂Selecting appropriate R₄And C₂。

The correction element molecules are generated by a differentiating circuit, tau₁＝R₁C₁Through τ₁Selecting appropriate R₁And C₁。

Molecule of calibration device (sC)₁R₁+1) is the denominator of the actual controlled object transfer function. So that C of the correcting device₁R₁Is a fixed value. For convenience of adjustment, let R₄＝R₃So that R₃Can be prepared from R₄And (4) determining.

The proportionality coefficient is:

due to R₄＝R₃Therefore, it isSince it has already been through tau₁Select R₁So that R₂Can be formed by k and R₁And (4) jointly determining.

Calculating tau by series correction theory due to modeling error₁And τ₂And the values of the capacitance and resistance parameters of the series correction circuit cannot meet the index requirements of the control system, and further adjustment is needed. When the series correction circuit is connected with a controlled object in series, the parameter value of each circuit of the series correction circuit is adjusted, and the adjusting method comprises the following steps:

if the overshoot of the output step response waveform is larger than the required overshoot index, then R is decreased simultaneously₃And R₄(ii) a The overshoot of the output step response waveform is smaller than the required overshoot index, and R is simultaneously increased₃And R₄；

If the adjustment time of the output step response waveform is longer than the required adjustment time, R is decreased simultaneously₃And R₄(ii) a If the adjustment time of the output step response waveform is shorter than the required adjustment time, R is simultaneously increased₃And R₄；

When the overshoot of the output step response waveform and the adjustment time are adjusted, please ensure R₃And R₄Varying together, i.e. ensuring R₃＝R₄；

If the static error of the output step response waveform is smaller than the desired static error, R is increased₂A value; if the static error of the output step response waveform is greater than the desired static error, R is decreased₂The value is obtained.

The invention has the beneficial effects that: through a resistance R₃Resistance R₄Regulating overshoot and regulation time of output step response waveform, and resistor R₂The static error of the output step response waveform is adjusted, and the controlled object is connected with the series correction circuit of the invention, so that the static error, the overshoot and the adjusting time of the output step response waveform can meet the requirements of control indexes.

Drawings

Fig. 1 is a schematic circuit structure diagram according to a first embodiment of the invention.

FIG. 2 shows a circuit without resistor R according to an embodiment of the present invention₅And R₆Schematic structural diagram of (1).

Fig. 3 is a schematic circuit diagram of a second embodiment of the invention.

FIG. 4 shows a circuit with a resistor R according to a second embodiment of the present invention₅And R₆Schematic structural diagram of (1).

Detailed Description

The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings, will make the advantages and features of the invention easier to understand by those skilled in the art, and thus will clearly and clearly define the scope of the invention.

The first embodiment is as follows:

as shown in fig. 1 and 2: an active series correction circuit is provided with a proportional differential unit and an inertia integral unit, wherein the input end of the proportional differential unit is connected with the output end of the inertia integral unit;

wherein the proportional differential unit is provided with an operational amplifier U₁The operational amplifier U₁Is connected with the resistor R₁The resistance R₁The other end of the resistor R is a signal input end of a proportional differential unit₁Both ends of the capacitor C are connected in parallel₁In the operational amplifier U₁Between the output end and the reverse input end of the resistor R₂The operational amplifier U₁Is connected to the positive input terminal via a resistor R₅Grounding;

the inertia integration unit is provided with an operational amplifier U₂The operational amplifier U₂Is connected with the resistor R₃The resistance R₃The other end of the operational amplifier is a signal input end of an inertia integration unit, and the operational amplifier U is connected with the other end of the operational amplifier U₂A resistor R is connected in parallel between the reverse input end and the output end₄At the resistance R₄Across which a capacitor C is connected₂The operational amplifier U₂Is connected to the positive input terminal via a resistor R₆And (4) grounding. Wherein the resistance R₅Has a value of R₅＝R₁//R₂Resistance R₆Is taken as R₆＝R₄//R₃。

The correction method of the active series correction circuit comprises the following steps of:

transfer function of the proportional differential element: g_D(s)＝-k_D(T_Ds+1)

WhereinT_D＝R₁C₁；

The calculation formula of the inertia integral unit is as follows:

transfer function of inertia integral element:

whereinT_I＝R₄C₂；

The calculation method of the active series correction circuit comprises the following steps:

transfer function of active series correction circuit:

τ₁、τ₂and the value of k is determined by an automatically controlled tandem correction method. (s.tau.)₁+1) is the same as the denominator of the established controlled object transfer function; (s.tau.)₂+1) determined by the transfer function of the controlled object, the proposed overshoot and the adjustment time index; k is determined by the static error coefficient of the transfer function of the controlled object and the proposed static error coefficient index.

The denominator of the correction element is generated by an inertia circuit, tau₂＝R₄C₂Through τ₂Selecting appropriate R₄And C₂；

The correction element molecules are generated by a differentiating circuit, tau₁＝R₁C₁Through τ₁Selecting appropriate R₁And C₁；

Molecule of calibration device (sC)₁R₁+1) is the denominator of the actual controlled object transfer function. So that C of the correcting device₁R₁Is a fixed value.

For convenience of adjustment, let R₄＝R₃So that R₃Can be prepared from R₄And (4) determining.

The proportionality coefficient is:

due to R₄＝R₃Therefore, it isSince it has already been through tau₁Select R₁So that R₂From k and R₁And (4) jointly determining.

Calculating tau by series correction theory due to modeling error₁And τ₂And the values of the capacitance and resistance parameters of the series correction circuit cannot meet the index requirements of the control system, and further adjustment is needed. When the series correction circuit is connected with a controlled object in series, the parameter value of each circuit of the series correction circuit is adjusted, and the adjusting method comprises the following steps:

if the overshoot of the output step response waveform is larger than the required overshoot index, then R is decreased simultaneously₃And R₄(ii) a The overshoot of the output step response waveform is smaller than the required overshoot index, and R is simultaneously increased₃And R₄；

If the adjustment time of the output step response waveform is longer than the required adjustment time, R is decreased simultaneously₃And R₄(ii) a If the adjustment time of the output step response waveform is shorter than the required adjustment time, R is simultaneously increased₃And R₄；

When the overshoot of the output step response waveform and the adjustment time are adjusted, please ensure R₃And R₄Varying together, i.e. ensuring R₃＝R₄；

If the static error of the output step response waveform is smaller than the desired static error, R is increased₂A value; if the static error of the output step response waveform is greater than the desired static error, R is decreased₂The value is obtained.

Example two: as shown in fig. 3 and 4: in the same case as the other structure and embodiment, as a modification, the proportional differential element signal output terminal of the proportional differential unit is connected to the inertia integral element signal input terminal of the inertia integral unit.