CN114527655B - Periodic interference suppression and signal tracking method based on improved FDRC - Google Patents
Periodic interference suppression and signal tracking method based on improved FDRC Download PDFInfo
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Abstract
The invention discloses a periodic interference suppression and signal tracking method based on improved finite-dimension repetitive control, which comprises the following steps: firstly, designing a classical controller to ensure the stability of a closed loop system under the action of a periodic interference signal and a reference signal; then designing an improved finite-dimension repetitive controller, and connecting the controller with an original closed-loop controller in parallel to form a composite controller, so that periodic interference signal suppression and reference signal tracking are realized; and finally, selecting a convergence coefficient according to the phase range of the system function, and designing a compensation link according to the convergence coefficient to improve the stability margin of the system. The invention adopts parallel finite dimension repetitive control, reduces the influence of infinite poles on the stability of the system, and simultaneously solves the problems of poor system stability and the like caused by interference signal amplification and phase lag in a non-harmonic frequency band of the traditional serial finite dimension repetitive control; the parallel structure is adopted, the control system is simple in structure, and parameters are easy to adjust.
Description
Technical Field
The invention belongs to the field of periodic interference suppression and signal tracking, and particularly relates to an improved parallel finite-dimension repetitive control method which is used for suppressing periodic interference signals and tracking periodic reference signals.
Background
Periodic signals are common in rotating machinery systems, uninterruptible power supplies, energy storage converters, such as displacement signals in magnetic levitation motors, machine tools, hard disks, etc., harmonic current signals of uninterruptible power supplies and energy storage converters. In practical systems, it is generally required to suppress a periodic interference signal or track a reference signal, and currently, common methods include iterative control, adaptive control, wave trap, and repetitive control. The iterative control algorithm has poor self-adaptability and robustness and is sensitive to uncertain disturbance; although the adaptive control algorithm does not need an accurate mathematical model, it is difficult to achieve complete compensation for periodic disturbances; the method of designing the wave trap is easy, the calculated amount is small, but the inhibition capability is very limited. The repetitive control is a widely used control method at present, can effectively inhibit periodic interference which has known period, uncertain amplitude and multiple frequency components, and has the advantages of simple structure, small calculated amount, small occupied memory and the like, but the addition of the repetitive controller leads the closed loop system to introduce infinite virtual poles, thereby influencing the stability of the system. In order to improve the stability of the closed-loop system, the improved repetitive control is connected with a low-pass filter in series before a time lag link to filter out high-frequency poles, so that the effect of repetitive control on periodic signals and the stability of the closed-loop system are closely related to the low-pass filter.
Depending on the spectral characteristics of the periodic signal, the periodic signal spectrum is primarily focused on the first few lower harmonic frequencies. High-precision interference suppression and reference signal tracking can be realized by only eliminating main low-order harmonic frequency components. The Finite Dimensional Repetitive Control (FDRC) has a finite number of virtual poles, so that the influence of an infinite number of virtual poles introduced by the repetitive control on the stability of the system is reduced. The conventional finite-dimension repetition usually adopts a serial form, and serial finite-dimension repetition control is connected with an original system controller in series to realize the suppression of periodic interference signals or the tracking of reference signals. However, the serial limited dimension repetitive control has the problems of interference signal amplification, phase lag and the like in a non-harmonic frequency band, and causes the problems of poor system stability, poor inhibition or tracking precision and the like. Therefore, there is a need for improved forms of limited-dimensional repetitive control that achieve high accuracy periodic interference suppression and signal tracking while guaranteeing closed-loop system stability.
Disclosure of Invention
The invention aims to solve the technical problems that: the invention overcomes the defects of the prior art, and discloses an improved method for realizing periodic interference suppression and signal tracking by adopting a mode that a parallel finite-dimension repetitive controller is connected with an original closed-loop controller in parallel to form a composite controller, and design controller parameters according to a root locus method so as to realize periodic interference suppression and reference signal tracking on the basis of guaranteeing the closed-loop stability of a control system.
The technical scheme adopted for solving the technical problems is as follows:
a method for improved finite-dimension repetitive control includes designing a classical controller to ensure stability of an original closed-loop system; then designing an improved finite-dimension repetitive controller, and connecting the controller in parallel with the original closed-loop controller to form a composite controller; and finally, selecting a convergence coefficient according to the phase range of the system function, reasonably designing a compensation link according to the convergence coefficient to improve the stability of the system, and realizing high-precision periodic interference suppression and reference signal tracking.
The specific steps of the invention are as follows:
(1) Classical closed-loop controller design, ensuring the basically stable closed-loop system
Design classical closed loop controller G c And(s) ensuring the stability of the closed loop system under the action of the periodic reference signal R(s) and the interference signal D(s), namely ensuring that all characteristic roots of the closed loop system are on the left half plane of the complex plane.
(2) Improved finite dimension repetitive controller design
Improved finite-dimension repetitive controller C fd (s) modifying the conventional series-form finite-dimension repetitive controller into a parallel-form, wherein the expression is as follows:
wherein C is f,i (s) is an i-th order basic finite dimension repetitive controller; lambda (lambda) i As a convergence coefficient, the value of the convergence coefficient not only determines the convergence speed of the system, but also influences the stability of the system; k (K) i (s) is a compensation link, compensation C f,i (s) the influence of the introduced closed loop virtual pole on the system stability is improved, and the stability margin is improved; m is the order of the finite-dimension repetitive controller and is determined by the system interference suppression precision or the signal tracking precision.
Improved finite-dimension repetitive controller C fd (s) and original closed-loop controller G c (s) are connected in parallel to form a composite controller, so that the periodic interference signal suppression and the reference signal tracking are realized.
Under the action of the periodic reference signal R(s) and the interference signal D(s), the closed loop system error E(s) is as follows:
as is clear from the above, when i is not more than m,
the amplitude gain of the systematic error is 0, indicating that the improved finite-dimension repetitive controller can effectively track and suppress the periodic reference signal R(s) and the interference signal D(s) with the frequency of iΩ.
(3) Parameter design and system stability analysis
Closed loop system incorporates an improved finite-dimension repetitive controller C f,i After(s), the control system introduces m pairs of virtual poles, so that the stability margin of the system is reduced, and the closed loop system is in a critical stable state. To ensure the stability of the closed loop system, K is adopted i And(s) correcting the closed loop system to realize high-precision periodic interference suppression and signal tracking.
According to the root locus method, the improved finite-dimension repeated control parameter design comprises the following steps: first according to the system function R i-1 (s) determination of convergence coefficient lambda for phase-frequency characteristics i Sign, lambda of i The sign selection principle of (2) enables the compensation link to provide a phase compensation angle as small as possible; then according to lambda i Symbol determination compensation element K i (s) let R be i-1 (s)K i (s) satisfying a phase condition capable of ensuring the stability of the closed loop system at ω=iΩ:
compared with the prior art, the invention has the following advantages:
(1) The invention adopts parallel finite dimension repetitive control, avoids the influence of introducing infinite poles on the system stability, and solves the problems of poor system stability and the like caused by interference signal amplification and phase lag in a non-harmonic frequency band in the traditional serial finite dimension repetitive control;
(2) The parallel finite-dimension repetitive controller designed by the invention can reasonably select the order according to the system control precision and the system hardware, and reduce the calculated amount of the control system;
(3) The controller designed by the invention adopts a parallel structure, the original closed-loop controller can not be changed, the control system has simple structure, and the parameters are easy to adjust;
(4) The invention designs the compensation link, can effectively improve the stability margin of the control system and enhance the anti-interference capability of the control system.
Drawings
FIG. 1 is a flow chart of the design of the present invention;
FIG. 2 is a schematic diagram of periodic interference suppression and signal tracking based on improved finite dimensional repetitive control;
FIG. 3 is a graph of parallel finite dimension repetitive control frequency characteristics;
fig. 4 is a series finite-dimension repetitive control frequency characteristic curve.
Detailed Description
The invention is further described with reference to the drawings and specific steps of implementation.
As shown in fig. 1, the specific implementation steps of the present invention are as follows:
(1) Classical closed-loop controller design, ensuring the basically stable closed-loop system
As shown in fig. 2, a classical closed loop controller G is designed c And(s) ensuring the stability of the closed loop system under the action of the periodic reference signal R(s) and the interference signal D(s), namely ensuring that all characteristic roots of the closed loop system are on the left half plane of the complex plane. Wherein R(s) and D(s) are a periodic reference signal and an interference signal respectively, and the period is T; g p (s) is a controlled object transfer function; e(s) is the systematic error.
(2) Improved finite dimension repetitive controller design
Improved finite-dimension repetitive controller C fd (s) modifying the conventional series-form finite-dimension repetitive controller into a parallel-form, wherein the expression is as follows:
wherein C is f,i (s) is an i-th order basic finite dimension repetitive controller; lambda (lambda) i As a convergence coefficient, the value of the convergence coefficient not only determines the convergence speed of the system, but also influences the stability of the system; k (K) i (s) an advanced correction compensation step for the ith-order basic finite-dimension repetitive controller, compensating C f,i (s) the influence of the introduced closed loop virtual pole on the system stability is improved, and the stability margin is improved; m is the order of the finite-dimension repetitive controller, and is determined by the control precision of the system and the system hardware, so that the calculated amount of the control system is reduced.
Ith-order basic finite-dimension repetitive controller C f,i (s) is expressed as:
where Ω=2ρt is the fundamental frequency of the periodic signal.
In order to compare the advantages of the improved parallel finite-dimension repetitive controller provided by the invention, the invention provides K at 200Hz i (s)＝1，m＝5，λ i When=1m, the improved parallel and conventional series finite-dimension repetitive control frequency characteristic curves. As shown in fig. 3, the improved finite dimensional repetitive control is carried out at each harmonic frequency, the amplitude gain is infinite, and the phase is changed by 180 degrees; the amplitude gain at non-harmonic frequencies is almost zero and the phase is approximately an integer multiple of 2 pi. As shown in fig. 4, the amplitude gain at each harmonic frequency is infinity while the amplitude gain at non-harmonic frequencies is not zero by the conventional tandem finite-dimension repetitive controller, i.e., the addition of the tandem finite-dimension repetitive controller amplifies the signal at non-harmonic frequencies while suppressing periodic disturbances and tracking the periodic reference signal. In addition, the series-connection type finite-dimension repetitive control has certain phase lag at the non-harmonic frequency, and has great influence on the stability of a closed-loop system. Therefore, the invention provides improved finite dimensional repetitive controlThe method is superior to the traditional series limited-dimensional repetitive control.
As shown in fig. 2, the improved finite-dimension repetitive controller C fd (s) and original closed-loop controller G c (s) are connected in parallel to form a composite controller. Under the action of the periodic reference signal R(s) and the interference signal D(s), the closed loop system error E(s) is as follows:
as is clear from the formula (3), when i is not more than m,
the amplitude gain of the systematic error is 0, indicating that the improved finite-dimension repetitive controller can effectively track and suppress the periodic reference signal R(s) and the interference signal D(s) with the frequency of iΩ.
(3) Parameter design and system stability analysis
Closed loop system incorporates an improved finite-dimension repetitive controller C f,i After(s), the control system introduces m pairs of virtual poles, so that the stability margin of the system is reduced, and the closed loop system is in a critical stable state. To ensure the stability of the closed loop system, K is adopted i And(s) correcting the closed loop system to realize high-precision periodic interference suppression and reference tracking. Thus lambda is i And K i The parameter design of(s) plays a crucial role in the stability of the closed loop system.
As can be seen from fig. 2, the characteristic equation of the closed loop system after adding the m-order parallel finite dimensional repetitive controller is:
in which Q 0 (s)＝1+G c (s)G p And(s) is a characteristic polynomial of the original closed-loop system.
When the closed loop system joins C f,i (s) when the closed loop system is added with the previous i-1 order finite dimensional repetitive controller and the system is stable, the closed loop system is at the momentThe effective characteristic equation is:
Q i (s)＝[s 2 +(iΩ) 2 ]Q i-1 (s)+λ i G p (s)K i (s)(s+iΩ) 2 ＝0 (5)
in which Q i-1 (s) is a system characteristic polynomial containing a first i-1 order parallel finite dimension repetitive controller, wherein characteristic roots are all positioned on the left half plane of a complex plane, and the expression is as follows:
to ensure the addition of C f,i (s) stability of post-closed loop system, compensation Link K i The design of(s) should ensure that all feature roots of equation (6) lie in the left half plane of the complex plane.
Definition of the definition
As a system function. According to the root locus method, the compensation link K i The design of(s) should be such that the following formula satisfies the phase condition at s= ±ijΩ: />
Wherein arg () represents the argument; l is an integer.
Therefore, the steps of the improved finite-dimension repetitive control parameter design are as follows: first according to the system function R i-1 (s) determination of phase-frequency characteristics lambda i Sign, lambda of i The sign selection principle of (2) enables the compensation link to provide a phase compensation angle as small as possible; then according to lambda i Symbol determination compensation element K i (s) let R be i-1 (s)K i (s) satisfies a phase condition capable of ensuring the stability of the closed loop system at ω=iΩ.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art.
Finally, it should be noted that the above-mentioned embodiments are only for illustrating the technical scheme of the present invention and are not limiting; while the invention has been described in detail with reference to the preferred embodiments, those skilled in the art will appreciate that: modifications may be made to the specific embodiments of the present invention or equivalents may be substituted for part of the technical features thereof; without departing from the spirit of the invention, it is intended to cover the scope of the invention as claimed.
Claims (1)
1. The periodic interference suppression and signal tracking method based on the improved finite-dimension repetition control is characterized by comprising the following steps of:
step one, designing a classical controller G c (s) ensuring the stability of the closed loop system under the action of the periodic reference signal R(s) and the interference signal D(s), namely ensuring that all characteristic roots of the closed loop system are on the left half plane of the complex plane;
step two, designing an improved finite-dimension repetitive controller C fd (s) connecting the controller in parallel with the original closed-loop controller to form a composite controller;
improved finite-dimension repetitive controller C fd (s) to improve the traditional series-form finite-dimension repetitive controller into a parallel-form, the expression is as follows:
wherein C is f,i (s) is an ith order basic finite dimension repetitive controller, lambda i For convergence factor, K i (s) is a compensation link, m is the order of the finite-dimension repetitive controller;
step three, designing parameters of a closed loop system and analyzing the stability of the system, and selecting a convergence coefficient according to the phase range of a system function so as to enable a compensation link to provide a phase compensation angle as small as possible;
the system stability is improved according to the sign design compensation link of the convergence coefficient, and high-precision periodic interference suppression or signal tracking is realized;
for lambda i And K i Parameter design of(s):
the characteristic equation of the closed loop system after the m-order parallel finite-dimension repetitive controller is added is as follows:
in which Q 0 (s)＝1+G c (s)G p (s) is a feature polynomial of the original closed-loop system;
when the closed loop system joins C f,i (s) when the closed loop system is added with the first i-1 order finite dimensional repetitive controller and the system is stable, the equivalent characteristic equation of the closed loop system is as follows:
Q i (s)＝[s 2 +(iΩ) 2 ]Q i-1 (s)+λ i G p (s)K i (s)(s+iΩ) 2 ＝0
wherein Ω is the fundamental frequency of the periodic signal; g p (s) is a controlled object transfer function; q (Q) i-1 (s) is a system characteristic polynomial containing a first i-1 order parallel finite dimension repetitive controller, wherein characteristic roots are all positioned on the left half plane of a complex plane, and the expression is as follows:
definition of the definition
Is a system function; according to the root locus method, the compensation link K i The design of(s) is such that the following satisfies the phase condition at s= ±ijΩ:
wherein arg () represents the argument; l is an integer;
first according to the system function R i-1 (s) determination of phase-frequency characteristics lambda i Is used in the sign of (a),λ i the sign selection principle of (2) enables the compensation link to provide a phase compensation angle as small as possible;
then according to lambda i Symbol determination compensation element K i (s) let R be i-1 (s)K i (s) the phase condition is satisfied at frequency ω=iΩ.
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