CN115685757A - Active disturbance rejection pre-estimation control method based on filtering in pure time lag system - Google Patents
Active disturbance rejection pre-estimation control method based on filtering in pure time lag system Download PDFInfo
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Abstract
The invention relates to an active disturbance rejection estimation control method based on filtering in a pure time lag system. The invention provides a method for applying linear active disturbance rejection control to an adaptive optical system, wherein Smith estimation compensates the influence of time lag on the dynamic response characteristic of the system, and a low-pass filtering link is added, so that the number of poles of a closed-loop transfer function of the system is more than the number of zeros. In addition, a method for setting parameters under active disturbance rejection estimation control based on filtering is provided according to analysis of frequency domain characteristics of a control system. The control can ensure the anti-noise capability of the system at high frequency, has stronger inhibition capability on both external disturbance and internal disturbance of the system, and the proposed parameter setting mode only needs to configure two parameters, thereby simplifying the parameter adjusting process of the control method.
Description
Technical Field
The invention relates to the technical field of control, in particular to an active disturbance rejection prediction control method based on filtering in a pure time lag system.
Background
In adaptive optics systems, due wavesThe time delay tau of 2-3 times of sampling period exists in the adaptive optics system due to factors such as the sampling time consumption of the front detector and the wave front processing time consumption, and the adaptive optics system is generally regarded as a pure time lag system when the control method is designed. The most widely used control method of the wavefront control part of the adaptive optics system is a PI control method, but under the control of the control method, the effective bandwidth of the system is only that of the sampling frequency
It is difficult to meet the control requirements of the system. The Smith predictor can eliminate the influence on the system caused by time delay factors and improve the bandwidth of the system, but the PI-Smith control is sensitive to the error of a system model and has poor disturbance rejection capability.
The active disturbance rejection control is a control method which can actively reject disturbance and has strong robustness, wherein the extended state observer part can estimate and compensate the disturbance quantity of an applied system, so that the control method is introduced into an adaptive optical system, the requirement of Smith control on the accuracy of a model is improved, and the disturbance rejection capability of the system is improved. However, due to the dead time lag characteristic of the adaptive optical system, the anti-noise capability of the system at a high frequency position is poor by directly using the active disturbance rejection control, so that an active disturbance rejection estimation control method based on filtering is provided, the control quantity of the system is corrected, and the system has strong capability of inhibiting internal disturbance and external disturbance.
Disclosure of Invention
Aiming at the problems of sensitivity to system model errors, poor disturbance rejection capability and the like of a pure time lag characteristic and a PI-Smith control method of an adaptive optical system, the invention provides a filtering-based active disturbance rejection estimation control method in the pure time lag system, so as to improve the capability of the system for inhibiting internal disturbance and external disturbance, simplify the parameter adjusting process of a controller and improve the system performance.
In order to realize the purpose, the invention adopts the scheme that: an active disturbance rejection estimation control method based on filtering in a dead time lag system comprises the following specific implementation steps:
step 1: fitting a transfer function of a controlled object, and applying an active disturbance rejection estimation control method to pure time lag system control;
step 2: the active disturbance rejection pre-estimation control method is applied to a dead time delay system to form a control system, deduces a relational expression among input quantity, output quantity and control quantity of the control system, and simplifies the form of the control system;
and step 3: in the structure of a simplified control system, a filtering link is designed according to the characteristics of the control system;
and 4, step 4: solving a closed-loop transfer function of the control system, and factorizing the closed-loop transfer function according to an expected closed-loop bandwidth value;
and 5: and selecting a control parameter range when the control system is stable by utilizing a Laus criterion according to the time pre-estimation length requirement of the actual pure time lag system.
Furthermore, the dead time lag system is a system with a time delay link in a system model and does not include any inertia link.
Further, the filtering element is a first-order low-pass filter, which is disposed at the controlled variable output for modifying the controlled variable.
Furthermore, a control law part of the active disturbance rejection estimation control method uses a PI control structure.
The principle of the invention is as follows: the active disturbance rejection control technology is a control technology with strong robustness, the stable disturbance rejection of active disturbance rejection control is used for weakening the requirement of Smith estimation on the accuracy of given compensation parameters, and meanwhile, a low-pass filtering link is added, so that the number of poles of a closed-loop transfer function of a system is more than the number of zeros, and the anti-noise capability of the system at high frequency and the strong inhibition capability of external disturbance and internal disturbance are ensured.
Compared with the prior art, the invention has the advantages that:
(1) The method has strong robustness and has strong capability of inhibiting internal disturbance and external disturbance of the system;
(2) According to the invention, the controller parameters are set according to the time delay variation range required by the actual system, only two parameters need to be adjusted, and the parameter adjusting process is simplified.
Drawings
FIG. 1 is a simplified block diagram of a filtered active disturbance rejection predictor controller applied in an adaptive optics system according to the present invention;
FIG. 2 is a diagram of an active disturbance rejection controller applied to a control structure of an adaptive optics system;
FIG. 3 is a simplified control block diagram of the ADRC applied to the adaptive optics system;
FIG. 4 is the output response of the system when Smith estimates full compensation;
FIG. 5 is a graph of the output response of the system at a maximum expected value of the system time delay perturbation.
Detailed Description
The present invention will be further described with reference to the accompanying drawings by taking the control of the tilting mirror in the adaptive optics system as an example.
As shown in fig. 1, which is a simplified structure diagram of an adaptive optical system to which the filtering-based active disturbance rejection estimation control method in a dead time lag system is applied, if the system is considered as a linear system and the tilted mirror is ideal, the equivalent transfer function of the tilted mirror can be simplified to K =1, and the system model is G(s) = e -τs . Setting the ideal time delay in the system to be 0.0025 s, and compensating parameter tau of Smith predictor 1 The ideal delay time of 0.0025 seconds, i.e., a two times sample period delay, is selected so that the perturbation range of the system actual time delay τ is (0,0.008) seconds, and the system tracks a constant value input r =1.
The method comprises the following concrete steps:
step 1: the active disturbance rejection control method is applied to adaptive optics system control as shown in fig. 2;
step 2: according to a control system block diagram, a relation among an input quantity r, an output quantity y and a control quantity u of the control system is deduced as follows:
u＝G 1 *[G 0 *r-(G 0 +H)*y]
in the formula:
where s is a complex variable of the time domain after laplace transformation to a complex domain, and w 0 Bandwidth of LESO, b 0 For the parameter to be designed, k p And k i To control law parameters, G 0 For the characterization of the control laws in the control structure, G 1 H reflects the characteristics of the LESO and the feedback status in the control structure, from which a simplified control structure diagram as shown in fig. 3 can be derived.
And 3, step 3: as shown in FIG. 1, a Smith predictor is added on the basis of FIG. 3, and a first-order low-pass filter is added at the output of the control quantity
The filter G f (s) does not affect the original line gain, but only provides a magnitude of w c Is used to correct the control quantity u, in which case u is corrected to:
u′＝u*G f
and 4, step 4: the closed loop transfer function of the control system can be obtained as follows:
filter G in the formula f Body is G' 1 The method comprises the following steps:
m can be expanded to:
according to the pole-zero characteristic of Bode diagram, we hope that M is in
There is a pole nearby that cancels the zero, and a pole can provide the desired bandwidth of the system. Therefore, the following design is made:
order:
comprehensive division can factor B(s) into:
and should satisfy at this time
And k i → 0. Note the book
Then C(s) can be factorized into
The decomposition mode ensures that B(s) has stronger noise suppression capability at high frequency. If make
D(s) can be factorized into
Thus, can obtain
Wherein, mu is more than 0 and less than 1.
And 5: according to the time estimated length requirement of an actual system, if the time delay perturbation range of the system is required to be (0, 0.008) seconds, the control parameter range when the system is stable can be selected by utilizing the Laus criterion. By calculation in combination with step 4 to b 0 、w c 、k i The following can be obtained by the value requirement of (2):
the formula can also estimate the output time domain length of the controlled process when the filter type active disturbance rejection estimation controller is used for the self-adaptive optical system. And can be derived as follows
When the system is established, the Laus criterion is met, and the system has stability.
In this design, adjust w 0 And k p The target bandwidth is obtained, which is approximately μ w as known from the factorization of B(s) 0 . Then gives roughly w according to the required bandwidth 0 Then only mu needs to be adjusted to achieve satisfactory dynamic tracking performance.
Assuming a desired target bandwidth f 3dB ＝k p w c ＝μw 0 =181rad/s, binding
The following can be obtained:
0.577＜μ＜1
181＜w 0 ＜313
the value is selected within the range, and the system bandwidth and the dynamic response performance can be considered when the parameter matching is reasonable. When selecting w 0 If "= 300, μ is adjusted to 0.6, and if the predicted complete compensation for Smith in fig. 4 is predicted, the output response of the system, it can be seen that the response requires less than one sample step to rise from 10% to 90% of the final value, which can be fast and noneOvershoot tracking is carried out, meanwhile, an external step disturbance is applied to the controlled object at 0.2 second, the disturbance can be seen to be restrained, and the dynamic characteristic of the process of recovering the tracking state is kept consistent with that of the transition process. FIG. 5 shows the output response of the system with a system time delay perturbation of 0.008 seconds at the maximum desired value, which shows that the peak time of the system is 0.024 seconds and the overshoot is
And the actual system requirements are met.
Parts of the invention not described in detail are well known in the art. The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and the preferred embodiments are not exhaustive and do not limit the invention to the precise embodiments described. Various modifications and improvements of the technical solution of the present invention may be made by those skilled in the art without departing from the spirit of the invention, and the technical solution is intended to be covered by the scope of the invention defined by the appended claims.
Claims (4)
1. An active disturbance rejection pre-estimation control method based on filtering in a pure time lag system is characterized by comprising the following steps:
step 1: fitting a transfer function of a controlled object, and applying an active disturbance rejection estimation control method to the control of the dead time lag system;
and 2, step: the active disturbance rejection pre-estimation control method is applied to the pure time-lag system to form a control system, a relational expression among the input quantity, the output quantity and the control quantity of the control system is deduced, and the form of the control system is simplified;
and 3, step 3: in the structure of a simplified control system, a filtering link is designed according to the characteristics of the control system;
and 4, step 4: solving a closed loop transfer function of the control system, and factorizing the closed loop transfer function according to an expected closed loop bandwidth value;
and 5: and selecting a control parameter range when the control system is stable by utilizing a Laus criterion according to the time pre-estimation length requirement of the actual pure time lag system.
2. The active disturbance rejection prediction control method based on filtering in a dead time lag system according to claim 1, wherein:
the dead time lag system is a system with a time delay link in a system model and does not contain any inertia link.
3. The active disturbance rejection estimation control method based on filtering in the dead time lag system according to claim 1, wherein:
the filtering element is a first-order low-pass filter which is arranged at the output of the control quantity and used for correcting the control quantity.
4. The active disturbance rejection prediction control method based on filtering in a dead time lag system according to claim 1, wherein:
and the control law part of the active disturbance rejection estimation control method uses a PI control structure.
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| CN117234089A (en) * | 2023-11-10 | 2023-12-15 | 成都铂升科技有限公司 | Unmanned aerial vehicle actuator time lag dynamic compensation control method based on interference observer |
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| CN107908107A (en) * | 2017-11-13 | 2018-04-13 | 大连理工大学 | Disturbance rejection control method of the time lag sampling system based on fallout predictor |
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| CN117234089B (en) * | 2023-11-10 | 2024-01-23 | 成都铂升科技有限公司 | Unmanned aerial vehicle actuator time lag dynamic compensation control method based on interference observer |
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