CN111045324A - Active disturbance rejection control method based on advanced correction - Google Patents

Active disturbance rejection control method based on advanced correction Download PDF

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CN111045324A
CN111045324A CN201911240678.6A CN201911240678A CN111045324A CN 111045324 A CN111045324 A CN 111045324A CN 201911240678 A CN201911240678 A CN 201911240678A CN 111045324 A CN111045324 A CN 111045324A
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disturbance
extended state
disturbance rejection
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魏伟
左敏
张志远
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Beijing Technology and Business University
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Abstract

The invention discloses an active disturbance rejection control method based on advanced correction, which comprises the following steps: designing a conventional second-order linear extended state observer for a first-order controlled object; acquiring a total disturbance estimation value after advanced correction and optimization on the basis of a conventional second-order linear extended state observer; establishing a new active disturbance rejection control law; the number of adjustable parameters is reduced, and meanwhile, the non-difference estimation of slope disturbance is realized; the parameters of the phase lead active disturbance rejection controller are adjusted until satisfactory control performance is obtained. According to the technical scheme, besides constant value interference, time-varying interference such as slope interference and sine interference is estimated with high precision; the performance of estimating time-varying disturbance can be enhanced only by adding the advanced correction part without changing the internal structure of the extended state observer, and the improvement process is simple and practical.

Description

Active disturbance rejection control method based on advanced correction
Technical Field
The invention belongs to the technical field of advanced control, particularly relates to an active disturbance rejection control technology in the advanced control technology, and particularly designs an active disturbance rejection control method based on advanced correction.
Background
The industrial production process is often accompanied by the influence of a plurality of interferences and various uncertain factors, and the core problem to be solved by the automatic control system is how to make the system still operate according to the preset target under the influence of disturbance. Although the modern control theory based on the state variable description greatly expands the application field of classical control and obtains rich theoretical results, the modern control theory excessively depends on a mathematical model of a controlled object, and the popularization and the use of the modern control theory in the industrial production process are restricted. To date, PID control is still widely used in industrial fields.
In fact, neither an accurate mathematical model of the controlled object can be established, nor uncertain factors such as internal dynamics and external disturbances of the controlled object can be obtained. Therefore, finding a control technology which can get rid of the dependence of modern control on model information and has better control effect than PID is important for industrial control. In recent years, a new and practical active disturbance rejection control technology has been developed. Different from the identification model, the method regards the dynamic change inside the system and the external uncertain disturbance as the total disturbance of the system, estimates the total disturbance in real time by using the information of the control quantity and the actual output quantity of the system and dynamically compensates in the control law, thereby eliminating the influence of uncertain factors existing in the control process and obtaining the satisfactory control performance. Such an auto-disturbance rejection control technique based on disturbance estimation and compensation, which has a small dependence on model information, is favored by more and more researchers and engineers in the engineering technical field. The method is widely applied to the fields of aerospace, motion control, process control and the like. However, since the derivative information of the total disturbance is not obtained, it is generally considered that the derivative of the total disturbance is zero when designing the extended state observer. This results in that the conventional extended state observer only has a good estimation effect on constant disturbance, and a phase lag problem exists when estimating time-varying disturbances such as slope and sine, which affects the estimation accuracy of total disturbance, and further affects the final control effect.
The conventional extended state observer has phase lag when estimating time-varying disturbance such as slope and sine, and the accuracy of estimating the time-varying disturbance by the extended state observer is directly influenced. Therefore, in order to improve the capability of the extended state observer to estimate the time-varying disturbance, the phase lag of the observer to estimate the total disturbance needs to be reduced as much as possible, so that the estimation speed and the accuracy of the observer are improved.
Disclosure of Invention
In order to solve the problem that a Linear Extended State Observer (LESO) of a conventional Linear Active Disturbance Rejection Control (LADRC) has a poor estimation time-varying disturbance effect, the invention provides a new extended state observer improvement method, namely, the phase of the estimated time-varying disturbance of the extended state observer is improved by utilizing advanced correction in the classical control theory, so that a disturbance estimation value can more closely follow the total disturbance on the phase, the estimation speed and the accuracy of the total disturbance are improved, and a desired control effect is obtained. For convenience of description, the improved auto-disturbance rejection controller of the present invention is referred to as a phase-lead based auto-disturbance rejection controller (PLADRC), and the corresponding extended state observer is referred to as a phase-lead based ESO. The specific technical scheme of the invention is as follows:
an active disturbance rejection control method based on lead correction is characterized by comprising the following steps:
s1: designing a conventional second-order linear extended state observer for a first-order controlled object;
for a first order system:
Figure BDA0002306126760000021
wherein u is a control signal including interference compensation and applied to the controlled object, y is a system output signal,
Figure BDA0002306126760000027
as the first derivative of the system output y, b0For the controller parameters, f (y, w) is the total disturbance of the system, including the internal dynamic and external disturbance of the system, w is the external disturbance of the system, and f (y, w) is expanded to the state variable x of the system2F (y, w), the equation of state for system (1) can be found:
Figure BDA0002306126760000022
wherein x is1,x2Is a variable of the state of the system,
Figure BDA0002306126760000023
are respectively system state variables x1，x2The first derivative of (a) is,
Figure BDA0002306126760000024
is the first derivative of the total disturbance f (y, w) of the system;
establishing a linear extended state observer:
Figure BDA0002306126760000025
z1to output an estimate, z2For the total disturbance estimate value,
Figure BDA0002306126760000026
are each z1，z2First derivative of β1And β2To expand the state observer gain, observer parameters β are selected1And β2Real-time estimation of each state variable in the formula (2) is realized;
the control law is designed as follows:
u0＝k1(r-z1) (4)
u＝(u0-z2)/b0(5)
u0for control signals without interference compensation r is the given signal, i.e. the desired output signal of the system, k1For the gain of the proportional controller, neglecting z2For the estimation error of f (y, w), the system (1) is simplified to a single integrator structure:
Figure BDA0002306126760000031
according to a bandwidth parameterization method, the following configuration is carried out on parameters of the active disturbance rejection controller:
Figure BDA0002306126760000032
wherein, ω iscFor controller bandwidth, ωoSimplifying auto-disturbance rejection control parameter setting to omega for observer bandwidthc,ωoAnd b0Setting;
s2: according to
Figure BDA0002306126760000033
The relation of (1) is that the total disturbance estimated value z after advanced correction and optimization is obtained on the basis of a conventional second-order linear extended state observer2pl(ii) a Constructing a linear extended state observer based on advanced correction:
Figure BDA0002306126760000034
wherein z is2plIs z2The phase lag and amplitude attenuation degree of the intermediate frequency band are both less than z by the total disturbance estimation after advanced correction optimization2For substituting for z2As a new total disturbance estimate, TdIs a lead time constant, and gamma is a frequency multiplication coefficient;
s3: by z2plIn place of z2Establishing a new active disturbance rejection control law; the control law of the linear active disturbance rejection controller based on the advanced correction optimization is correspondingly adjusted as follows:
Figure BDA0002306126760000035
s4: let Td＝2/(ωo(1- γ)), reducing the number of adjustable parameters while achieving a robust estimation of the slope perturbation;
s5: adjusting parameter b of phase lead active disturbance rejection controller0,ωc,ωoAnd γ until the desired control effect is achieved.
The invention has the beneficial effects that:
1. besides constant interference, the method has better estimation precision on time-varying interference such as slope, sine and the like;
2. the performance of estimating time-varying disturbance can be enhanced only by adding an advanced correction part without changing the internal structure of the extended state observer, and the improvement process is simple and practical;
3. the adjustable parameters are few, the physical significance is clear, and the setting is convenient;
4. the design process is simple and easy to master, and the design method is suitable for the active disturbance rejection controllers of all orders and has good universality.
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In order to illustrate embodiments of the present invention or technical solutions in the prior art more clearly, the drawings which are needed in the embodiments will be briefly described below, so that the features and advantages of the present invention can be understood more clearly by referring to the drawings, which are schematic and should not be construed as limiting the present invention in any way, and for a person skilled in the art, other drawings can be obtained on the basis of these drawings without any inventive effort. Wherein:
FIG. 1 is a system block diagram of the present invention;
FIG. 2(a) is a comparison of set values before and after modification and their following;
FIG. 2(b) is a comparison of total disturbance and total disturbance estimate before and after improvement;
FIG. 3 is a graph of the estimated bias for improving forward and backward sinusoidal disturbances.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
FIG. 1 is a block diagram of a control architecture of the present invention. r is a given signal, i.e. the desired output signal of the system, d is an unknown disturbance, z2plIs z2Total disturbance optimized by look-ahead correctionEstimate, GpIs a controlled object.
In general, consider a first order system:
Figure BDA0002306126760000041
where u is a control signal applied to the controlled object including interference compensation, b0Is the controller parameter, y is the system output signal,
Figure BDA0002306126760000042
as the first derivative of the system output y, b0For the controller parameters, f (y, w) is the total disturbance of the system, including the internal dynamic and external disturbance of the system, w is the external disturbance of the system, and f (y, w) is expanded to the state variable x of the system2F (y, w), the equation of state for system (1) can be found:
Figure BDA0002306126760000043
wherein x is1,x2Is a variable of the state of the system,
Figure BDA0002306126760000044
are respectively system state variables x1，x2The first derivative of (a) is,
Figure BDA0002306126760000051
is the first derivative of the total disturbance f (y, w) of the system; (ii) a
A Linear Extended State Observer (LESO) was established:
Figure BDA0002306126760000052
z1to output an estimate, z2For the total disturbance estimate value,
Figure BDA0002306126760000053
are each z1，z2To the first order ofDerivative, selecting appropriate observer parameters β1And β2And realizing real-time estimation of each state variable in the formula (2).
The control law is designed as follows:
u0＝k1(r-z1) (4)
u＝(u0-z2)/b0(5)
u0for control signals without interference compensation, z is ignored2For the estimation error of f (y, w), the system (1) can be simplified to a single integrator structure:
Figure BDA0002306126760000054
according to a bandwidth parameterization method, the following configuration is carried out on parameters of the active disturbance rejection controller:
Figure BDA0002306126760000055
wherein, ω iscFor controller bandwidth, ωoSimplifying auto-disturbance rejection control parameter setting to omega for observer bandwidthc,ωoAnd b0And (4) setting.
Obtaining z according to formula (3)2The transfer function of (c):
Figure BDA0002306126760000056
wherein s is a laplace operator. According to formula (2) there are:
Figure BDA0002306126760000057
disturbance observation transfer function of united (8) and (9) linear extended state observer
Figure BDA0002306126760000058
Figure BDA0002306126760000059
Substituting formula (7) into:
Figure BDA00023061267600000510
formally, the disturbance observation transfer function φ1(s) is similar to a second order system. In the time domain, the contradiction that the adjustment time and the over-adjustment can not be adjusted and optimized simultaneously exists; in the frequency domain, the problems of serious amplitude attenuation and phase lag of the middle frequency range exist. These are the key to constraining the linear extended state observer to estimate the effects of time-varying disturbances.
Therefore, the invention provides a method for improving the frequency characteristic of a frequency band in a disturbance observation transfer function by using advanced correction, reducing the phase lag and amplitude attenuation degree of the frequency band in the disturbance observation transfer function, and improving the precision of estimating time-varying disturbance by an extended state observer, which comprises the following specific implementation steps:
order to
Figure BDA0002306126760000061
Conversion to time domain form:
Figure BDA0002306126760000062
according to the lead correction theory in the classical control, the frequency multiplication ratio gamma is inversely proportional to the maximum lead angle of the correction network, namely the smaller the gamma is, the larger the lead phase angle the lead correction network can provide. In addition, the maximum lead phase angle provided by the primary lead correction network is 60 degrees, and gamma is between 0 and 1.
Further, a linear-lead-based extended state observer (PLESO) based on the advance correction is constructed:
Figure BDA0002306126760000063
wherein z is2plIs z2Optimized by lead correctionThe phase lag and amplitude attenuation degree of the intermediate frequency band are both less than z in the total disturbance estimation2For substituting for z2As a new total disturbance estimate, TdIs the lead time constant and gamma is the frequency multiplication coefficient.
The control law of the linear active disturbance rejection controller (PLADRC) based on the lead-time based optimization is correspondingly adjusted as follows:
Figure BDA0002306126760000064
the ability of the PLESO to estimate unit steps, unit slopes and unit sinusoidal perturbations is analyzed as follows:
A. let the total perturbation be the unit step signal 1(t), i.e. f (y, w) is 1/s,
combining equations (7), (10) and (12) to obtain the perturbation-observed transfer function after the lead correction
Figure BDA0002306126760000065
Figure BDA0002306126760000066
New total disturbance estimate z2pl(s) response to unit step perturbation:
Figure BDA0002306126760000071
to z2pl(s) performing a pull-type inverse transformation:
Figure BDA0002306126760000072
PLESO estimation of the Steady State deviation e of the Total disturbance2The (∞) satisfies:
Figure BDA0002306126760000073
the PLESO still has better estimation capability on step disturbance, and the steady state estimation deviation is 0.
B. Let the total disturbance be a unit slope disturbance 1 · t, i.e. f (y, w) ═ 1/s2，
A combination formula (16) is adopted to obtain the total disturbance estimation z'2pl(s) response to unit slope perturbation:
Figure BDA0002306126760000074
to z'2pl(s) performing a pull-type inverse transformation:
Figure BDA0002306126760000075
PLESO estimates the steady state deviation e 'of the total disturbance'2The (∞) satisfies:
Figure BDA0002306126760000076
let formula (22) be zero and readily available
Figure BDA0002306126760000077
Therefore, if the time constant T is advanceddWhen the value is taken according to the formula (23), PLESO can realize the non-difference estimation of slope disturbance, and the estimation deviation e' of the linear extended state observer to unit slope disturbance is calculated in the same way2(∞)：
Figure BDA0002306126760000078
In contrast, it follows that LESO will have 2/ω when estimating unit slope perturbationoThe improved estimation deviation of the PLESO to the unit slope disturbance can be converged to zero, and the estimation capability to the slope time-varying disturbance is improved.
C. Let the total disturbance be a unit sinusoidal disturbance sint, i.e. f (y, w) is 1/(s)2+1)，
The total disturbance estimate z' at this time is obtained by combining equation (16)2pl(s) the response to a unit sinusoidal perturbation is:
Figure BDA0002306126760000081
when T is analyzedd＝2/[ωo(1-γ)]And then, the estimated deviation condition of the ESO to the unit sine disturbance before and after the improvement:
bringing formula (23) into formula (25):
Figure BDA0002306126760000082
PLESO estimates the steady state deviation e' of the total disturbance2The (∞) satisfies:
Figure BDA0002306126760000083
wherein, it is made
Figure BDA0002306126760000084
Figure BDA0002306126760000085
Then
Figure BDA0002306126760000086
Figure BDA0002306126760000087
For the initial phase of the steady state estimated deviation of PLESO to the total disturbance of the sinusoid, in particular, when γ is 1, equation (25) is changed to
Figure BDA0002306126760000091
Pledo is equivalent to conventional LESO, in other words, conventional LESO is a special case when the doubling ratio γ of pledo is 1.
The estimated deviation of PLESO to unit sinusoidal disturbance at t → ∞ can be made from equation (26) as the co-multiplication ratio γ of the observer bandwidth ω to the unit sinusoidal disturbanceoThe relationship of (A) is shown in FIG. 3.
From fig. 3 it can be seen that the same observer bandwidth ω isoUnder the condition, the estimation deviation of the PLESO to the unit sinusoidal disturbance is smaller than that of the conventional LESO (gamma is 1), and the more gamma is towards 0, the smaller the estimation deviation of the PLESO to the unit sinusoidal disturbance is.
FIG. 2 is a comparison of the estimation of constant and time varying disturbances before and after improvement, wherein for the purpose of comparison, the controlled object is a single integrator, G p1/s. The total disturbance in the system is now equal to the external disturbance. To verify the estimation effect on the time-varying disturbance before and after the improvement, a composite disturbance as shown in fig. 2(b) is added to the system: a step disturbance with the amplitude of 1 is given at t 1-2s, a unit slope disturbance with the initial value of 1 is given at t 2-3s, and a trigonometric disturbance with the value of 0.5cos (2t-6) +1.5 is given at t 3-10 s. The parameters of the conventional active disturbance rejection controller in the simulation are set as follows: b0＝1,ωc＝20,ωoThe improved parameters of the active disturbance rejection controller (40) are obtained, except that the newly added frequency multiplication ratio gamma is 0.0001, and the rest adjustable parameters b0,ωc,ωoAll in accordance with conventional active disturbance rejection controllers.
As can be seen from fig. 2(a), PLADRC has faster response to step and ramp disturbances, smaller maximum drop and shorter recovery time.
FIG. 2(b) is a comparison of the extended state observer before and after the improvement to estimate the composite total disturbance. As can be seen from the figure, the estimated phase of the improved PLESO to the ramp and sine time-varying total disturbance is advanced from that of the conventional extended state observer, and the estimation precision of the time-varying disturbance is obviously improved.
The method of the invention is also suitable for high-order controlled objects.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, "above" or "below" a first feature means that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact with each other via another feature therebetween. Also, the first feature being "on," "above" and "over" the second feature includes the first feature being directly on and obliquely above the second feature, or merely indicating that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature includes the first feature being directly under and obliquely below the second feature, or simply meaning that the first feature is at a lesser elevation than the second feature.
In the present invention, the terms "first", "second", "third", and "fourth" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. The term "plurality" means two or more unless expressly limited otherwise.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. An active disturbance rejection control method based on lead correction is characterized by comprising the following steps:
s1: designing a conventional second-order linear extended state observer for a first-order controlled object;
for a first order system:
Figure FDA0002306126750000011
wherein u is a control signal including interference compensation and applied to the controlled object, y is a system output signal,
Figure FDA0002306126750000012
as the first derivative of the system output y, b0For the controller parameters, f (y, w) is the total disturbance of the system, including the internal dynamic and external disturbance of the system, w is the external disturbance of the system, and f (y, w) is expanded to the state variable x of the system2F (y, w), the equation of state for system (1) can be found:
Figure FDA0002306126750000013
wherein x is1,x2Is a variable of the state of the system,
Figure FDA0002306126750000014
are respectively system state variables x1，x2The first derivative of (a) is,
Figure FDA0002306126750000015
Figure FDA0002306126750000016
is the first derivative of the total disturbance f (y, w) of the system;
establishing a linear extended state observer:
Figure FDA0002306126750000017
z1to output an estimate, z2For the total disturbance estimate value,
Figure FDA0002306126750000018
are respectively z1，z2First derivative of β1And β2For observation of the dilated stateGain of observer β1And β2Real-time estimation of each state variable in the formula (2) is realized;
the control law is designed as follows:
u0＝k1(r-z1) (4)
u＝(u0-z2)/b0(5)
u0for control signals without interference compensation r is the given signal, i.e. the desired output signal of the system, k1For the gain of the proportional controller, neglecting z2For the estimation error of f (y, w), the system (1) is simplified to a single integrator structure:
Figure FDA0002306126750000019
according to a bandwidth parameterization method, the following configuration is carried out on parameters of the active disturbance rejection controller:
Figure FDA00023061267500000110
wherein, ω iscFor controller bandwidth, ωoSimplifying auto-disturbance rejection control parameter setting to omega for observer bandwidthc,ωoAnd b0Setting;
s2: according to
Figure FDA00023061267500000111
The relation of (1) is that the total disturbance estimated value z after advanced correction and optimization is obtained on the basis of a conventional second-order linear extended state observer2pl(ii) a Constructing a linear extended state observer based on advanced correction:
Figure FDA0002306126750000021
wherein z is2plIs z2The phase lag and amplitude attenuation degree of the intermediate frequency band are both less than z by the total disturbance estimation after advanced correction optimization2For substituting for z2As a new total disturbance estimate, TdIs a lead time constant, and gamma is a frequency multiplication coefficient;
s3: by z2plIn place of z2Establishing a new active disturbance rejection control law; the control law of the linear active disturbance rejection controller based on the advanced correction optimization is correspondingly adjusted as follows:
Figure FDA0002306126750000022
s4: let Td＝2/(ωo(1- γ)), reducing the number of adjustable parameters while achieving a robust estimation of the slope perturbation;
s5: adjusting parameter b of phase lead active disturbance rejection controller0,ωc,ωoAnd γ until the desired control effect is achieved.
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CN108205259A (en) * 2016-12-19 2018-06-26 中国航天科工飞航技术研究院 Multiplex control system and its design method based on linear extended state observer
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Application publication date: 20200421