CN114384804A - Method for counteracting influence of zero point of transfer function of closed loop system when tracking instruction is zero - Google Patents
Method for counteracting influence of zero point of transfer function of closed loop system when tracking instruction is zero Download PDFInfo
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Abstract
A method for counteracting the zero influence of the closed loop system transfer function when the tracking instruction is zero, a controller and a control object form a closed loop system according to a negative feedback mode to obtain an equivalent actual closed loop system transfer function, the numerator of the actual closed loop system transfer function is compared with the numerator of the expected closed loop system transfer function, and a polynomial to be counteracted on the actual closed loop system transfer function numerator is determined; and correcting the zero signal by a tracking instruction correction signal to be used as an input signal of the pre-filter, wherein the denominator of the equivalent transfer function of the pre-filter can counteract a polynomial to be counteracted on the actual closed-loop system transfer function numerator, so that the modified closed-loop system transfer function numerator is the numerator of the expected closed-loop system transfer function, and a finite zero point does not exist. The invention can solve the problem that the pre-filter for offsetting the undesirable finite zero point of the transfer function of the closed loop system cannot function because the output value is zero when the tracking instruction is zero.
Description
Technical Field
The invention relates to the technical field of automatic control, in particular to a method for counteracting the zero influence of a closed loop system transfer function when a tracking instruction is zero.
Background
In automatic control system design, it is generally desirable that the closed loop system transfer function from the tracking command to the control object output be a typical second order element without a finite zero. When the controller is introduced in the form of closed loop feedback, the closed loop system transfer function typically has a finite zero associated with the control parameter, and the transient performance of the system is affected by the location of the finite zero.
In practical engineering design, a pre-filter is usually connected in series before a control command enters a closed-loop control system, and poles of the pre-filter are used for offsetting an undesirable limited zero point of a transfer function of the original closed-loop system.
For an automatic control system with an expected output of zero, the tracking command is zero, and the output of the pre-filter in the method is also zero, so that the capability of adjusting the closed-loop transfer function is lost, and the undesirable limited zero point of the closed-loop system transfer function cannot be offset.
There is no description in the relevant literature as to how to cancel the finite zero point of the closed loop system transfer function when the tracking command is zero.
Disclosure of Invention
In view of the problems in the prior art, the present invention aims to provide a method for canceling the zero influence of the transfer function of a closed loop system when a tracking command is zero. The invention can solve the problem that the pre-filter for offsetting the undesirable finite zero point of the transfer function of the closed loop system cannot function because the output value is zero when the tracking instruction is zero.
In order to achieve the technical purpose, the technical scheme provided by the invention is as follows:
in one aspect, the present invention provides a method for canceling zero influence of a transfer function of a closed loop system when a tracking command is zero, including:
the controller and the control object form a closed-loop system according to a negative feedback mode to obtain an equivalent actual closed-loop system transfer function, and the molecules of the actual closed-loop system transfer function are compared with the molecules of the expected closed-loop system transfer function to determine a polynomial to be counteracted on the actual closed-loop system transfer function molecules;
generating a tracking instruction, wherein the tracking instruction is a zero signal;
generating a tracking instruction correction signal which is a constant value signal;
generating a feedback signal correction signal, wherein the feedback signal correction signal is a constant value signal;
correcting a zero signal by a tracking instruction correction signal to be used as an input signal of a pre-filter, wherein the denominator of an equivalent transfer function of the pre-filter can counteract a polynomial to be counteracted on a transfer function numerator of an actual closed-loop system, so that the numerator of the corrected closed-loop system transfer function is the numerator of an expected closed-loop system transfer function, and a finite zero point does not exist;
subtracting the corrected feedback signal from the output signal of the pre-filter to be used as an input signal of the controller;
the output signal of the controller is used as the input signal of a control object, and the control object outputs a feedback signal;
and the feedback signal is corrected by the feedback signal correction signal to be the corrected feedback signal.
Further, the signal magnitude of the tracking command correction signal is equal to the output value of the control object at the initial time of the operation of the controller.
Further, the signal magnitude of the feedback signal correction signal is equal to the output value of the control object at the initial time of the controller operation.
Further, the signal magnitude of the tracking command modification signal is equal to the signal magnitude of the feedback signal modification signal.
Further, in the present invention, the tracking command minus the tracking command correction signal is used as the input signal to the pre-filter.
Further, in the present invention, the feedback signal minus the feedback signal correction signal is used as the corrected feedback signal.
In another aspect, the present invention provides an apparatus for canceling zero effect of a transfer function of a closed loop system when a tracking command is zero, including:
the tracking instruction generation module is used for generating a tracking instruction, and the tracking instruction is a zero signal;
the tracking instruction corrector is used for generating a tracking instruction correction signal, and the tracking instruction correction signal is a constant signal;
the pre-filter input signal generating module is used for subtracting the tracking instruction correction signal from the tracking instruction to be used as an input signal of the pre-filter;
the denominator of the equivalent transfer function of the pre-filter can offset a polynomial to be offset on the numerator of the actual closed-loop system transfer function, so that the numerator of the corrected closed-loop system transfer function is the numerator of the expected closed-loop system transfer function, and a finite zero point does not exist;
the controller and the control object form a closed-loop system in a negative feedback mode to obtain an equivalent actual closed-loop system transfer function, and a polynomial to be counteracted on the actual closed-loop system transfer function molecule is determined by comparing the actual closed-loop system transfer function molecule with the expected closed-loop system transfer function molecule;
a feedback signal modifier for generating a feedback signal modification signal, the feedback signal modification signal being a constant signal;
the corrected feedback signal generating module is used for subtracting the feedback signal correction signal from the feedback signal to obtain a corrected feedback signal;
and the controller input signal generation module is used for subtracting the corrected feedback signal from the output signal of the pre-filter to be used as an input signal of the controller.
Compared with the prior art, the invention has the advantages that:
through the technical scheme provided by the invention, when the tracking command is zero, the pre-filter for offsetting the undesirable finite zero point of the transfer function of the closed-loop system can still normally function.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a schematic structural diagram of an embodiment of the present invention;
fig. 2 is a schematic structural diagram of another embodiment of the present invention.
Detailed Description
For the purpose of promoting a clear understanding of the objects, aspects and advantages of the embodiments of the invention, reference will now be made to the drawings and detailed description, wherein there are shown in the drawings and described in detail, various modifications of the embodiments described herein, and other embodiments of the invention will be apparent to those skilled in the art. The exemplary embodiments of the present invention and the description thereof are provided to explain the present invention and not to limit the present invention.
In an embodiment of the present invention, a method for canceling zero influence of a transfer function of a closed loop system when a tracking command is zero is provided, including:
the controller and the control object form a closed-loop system according to a negative feedback mode to obtain an equivalent actual closed-loop system transfer function, and the molecules of the actual closed-loop system transfer function are compared with the molecules of the expected closed-loop system transfer function to determine a polynomial to be counteracted on the actual closed-loop system transfer function molecules;
generating a tracking instruction, wherein the tracking instruction is a zero signal;
generating a tracking instruction correction signal which is a constant value signal;
generating a feedback signal correction signal, wherein the feedback signal correction signal is a constant value signal;
correcting a zero signal by a tracking instruction correction signal to be used as an input signal of a pre-filter, wherein the denominator of an equivalent transfer function of the pre-filter can counteract a polynomial to be counteracted on a transfer function numerator of an actual closed-loop system, so that the numerator of the corrected closed-loop system transfer function is the numerator of an expected closed-loop system transfer function, and a finite zero point does not exist;
subtracting the corrected feedback signal from the output signal of the pre-filter to be used as an input signal of the controller;
the output signal of the controller is used as the input signal of a control object, and the control object outputs a feedback signal;
and the feedback signal is corrected by the feedback signal correction signal to be the corrected feedback signal.
Referring to fig. 1, in one embodiment, there is provided an apparatus for canceling the zero effect of a closed loop system transfer function when a tracking command is zero, comprising:
the tracking instruction generation module 6 is used for generating a tracking instruction, and the tracking instruction is a zero signal;
a tracking command corrector 5 for generating a tracking command correction signal, which is a constant signal;
a pre-filter input signal generation module 7, configured to subtract the tracking instruction correction signal from the tracking instruction to obtain an input signal of the pre-filter;
the system comprises a pre-filter 1, a closed loop system and a closed loop system, wherein the denominator of an equivalent transfer function of the pre-filter can offset a polynomial to be offset on an actual closed loop system transfer function numerator, so that the modified closed loop system transfer function numerator is the numerator of an expected closed loop system transfer function, and a finite zero point does not exist;
the controller 2 and the control object 3 form a closed-loop system according to a negative feedback mode to obtain an equivalent actual closed-loop system transfer function, and a polynomial to be counteracted on the actual closed-loop system transfer function molecules is determined by comparing the molecules of the actual closed-loop system transfer function with the molecules of the expected closed-loop system transfer function;
a feedback signal modifier 4 for generating a feedback signal modification signal, which is a constant signal;
the corrected feedback signal generating module 9 is configured to subtract the feedback signal correction signal from the feedback signal to obtain a corrected feedback signal;
and a controller input signal generation module 8, configured to subtract the corrected feedback signal from the output signal of the pre-filter as an input signal of the controller.
Referring to FIG. 2, in one embodiment, a method is provided for canceling the zero effect of the closed loop system transfer function when the tracking command is zero. The embodiment is a closed-loop control system which adopts a proportional-derivative controller and takes a control object as a second-order integral link.
In an embodiment, the equivalent transfer function of the control object 3 is
And at the initial time of the operation of the controller 2, the output value of the controlled object 3 is 1. The closed-loop control system design objective is to cause the control object 3 to change from 1 to 0 and then remain at 0 in accordance with the desired transient response.
The controller 2 adopts a proportional-derivative controller, the proportional-derivative controller is adopted to control the control object 3, the numerator of the equivalent transfer function of the controller is 4s +8 in the example, and the equivalent transfer function of the controller 2 is
After the controller 2 and the controlled object 3 form a closed-loop control system in a negative feedback manner, the numerator of the transfer function of the closed-loop system is 4s + 8. However, the desired closed loop system transfer function numerator is 8. The denominator 12 of the pre-filter transfer function is taken to be 4s +8 and the numerator 11 of the pre-filter transfer function is taken to be 8, so that the steady-state gain of the pre-filter is 1, i.e. the transfer function of the pre-filter 1 is set to be
The polynomial 4s +8 on the numerator of the original closed-loop control system transfer function is cancelled by the denominator 12 of the prefilter transfer function.
In order to make the pre-filter function when the tracking command is zero, the tracking command is corrected to 1 by a tracking command corrector 5. The tracking command correction signal outputted from the tracking command corrector 5 is set to a constant value, and the magnitude of the tracking command correction signal is equal to the output value of the control target at the initial time of the operation of the controller, and is 1 in this example. When the tracking command is zero, the input of the prefilter 1 is: the zero signal subtracts the tracking command correction signal output by the tracking command corrector, namely 0-1, and is always-1.
In order to correct the deviation caused by the tracking command corrector, the feedback signal correction signal output by the feedback signal corrector 4 is set to a constant value, which is also equal to the output value of the control object at the initial time of the controller operation, in this case 1. The output signal of the controlled object 3 is subtracted by the feedback signal correction signal outputted from the feedback signal corrector to obtain a corrected feedback signal.
The inputs to the controller 2 are: the corrected feedback signal is subtracted from the output of the pre-filter 1.
According to the above arrangement, the numerator of the equivalent transfer function of the closed-loop control system after the modification is 8, the finite zero point no longer exists, and the same holds true when the tracking command is zero.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A method for canceling the effect of a zero point of a transfer function of a closed loop system when a tracking command is zero, comprising:
the controller and the control object form a closed-loop system according to a negative feedback mode to obtain an equivalent actual closed-loop system transfer function, and the molecules of the actual closed-loop system transfer function are compared with the molecules of the expected closed-loop system transfer function to determine a polynomial to be counteracted on the actual closed-loop system transfer function molecules;
generating a tracking instruction, wherein the tracking instruction is a zero signal;
generating a tracking instruction correction signal which is a constant value signal;
generating a feedback signal correction signal, wherein the feedback signal correction signal is a constant value signal;
correcting a zero signal by a tracking instruction correction signal to be used as an input signal of a pre-filter, wherein the denominator of an equivalent transfer function of the pre-filter can counteract a polynomial to be counteracted on a transfer function numerator of an actual closed-loop system, so that the numerator of the corrected closed-loop system transfer function is the numerator of an expected closed-loop system transfer function, and a finite zero point does not exist;
subtracting the corrected feedback signal from the output signal of the pre-filter to be used as an input signal of the controller;
the output signal of the controller is used as the input signal of a control object, and the control object outputs a feedback signal;
and the feedback signal is corrected by the feedback signal correction signal to be the corrected feedback signal.
2. The method of claim 1, wherein the magnitude of the tracking command correction signal is equal to the output value of the control object at the initial time of controller operation.
3. The method of claim 1, wherein the feedback signal modification signal has a signal magnitude equal to the output value of the control object at the initial time of controller operation.
4. A method of canceling closed loop system transfer function zero effects when a tracking command is zero as in claim 1 or 2 or 3 wherein the signal magnitude of the tracking command correction signal is equal to the signal magnitude of the feedback signal correction signal.
5. The method of canceling zero effects of a closed loop system transfer function when a tracking command is zero as in claim 4 wherein the tracking command minus a tracking command correction signal is used as an input signal to the prefilter.
6. The method of canceling zero influence of a closed loop system transfer function when a tracking command is zero of claim 4 wherein the feedback signal minus the feedback signal correction signal is the corrected feedback signal.
7. The method of canceling closed-loop system transfer function zero effects when a tracking command is zero according to claim 1 or 2 or 3 or 5 or 6, wherein the equivalent transfer function of the control object is
And at the initial time of the controller operation, the output value of the control object is 1.
8. The method of canceling zero effect of transfer function of closed loop system when tracking command is zero as claimed in claim 7 wherein said controller is a proportional derivative controller and the equivalent transfer function of the controller is
9. The method of canceling closed-loop system transfer function zero effects when the tracking command is zero of claim 8, wherein the closed-loop system transfer function numerator is expected to be 8, thereby setting the equivalent transfer function of the pre-filter to be equal to
The denominator 4s +8 of the pre-filter transfer function is used to offset the polynomial 4s +8 on the numerator of the actual closed-loop system transfer function equivalent to the control object.
10. An apparatus for canceling the effect of a zero point of a transfer function of a closed loop system when a tracking command is zero, comprising:
the tracking instruction generation module is used for generating a tracking instruction, and the tracking instruction is a zero signal;
the tracking instruction corrector is used for generating a tracking instruction correction signal, and the tracking instruction correction signal is a constant signal;
the pre-filter input signal generating module is used for subtracting the tracking instruction correction signal from the tracking instruction to be used as an input signal of the pre-filter;
the denominator of the equivalent transfer function of the pre-filter can offset a polynomial to be offset on the numerator of the actual closed-loop system transfer function, so that the numerator of the corrected closed-loop system transfer function is the numerator of the expected closed-loop system transfer function, and a finite zero point does not exist;
the controller and the control object form a closed-loop system in a negative feedback mode to obtain an equivalent actual closed-loop system transfer function, and a polynomial to be counteracted on the actual closed-loop system transfer function molecule is determined by comparing the actual closed-loop system transfer function molecule with the expected closed-loop system transfer function molecule;
a feedback signal modifier for generating a feedback signal modification signal, the feedback signal modification signal being a constant signal;
the corrected feedback signal generating module is used for subtracting the feedback signal correction signal from the feedback signal to obtain a corrected feedback signal;
and the controller input signal generation module is used for subtracting the corrected feedback signal from the output signal of the pre-filter to be used as an input signal of the controller.
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