CN115685757A - A Filter-Based Active Disturbance Rejection Predictive Control Method for Pure Time-Delay Systems - Google Patents

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

A Filter-Based Active Disturbance Rejection Predictive Control Method for Pure Time-Delay Systems

technical field

The invention relates to the technical field of control, in particular to a filtering-based active disturbance rejection predictive control method in a pure time-delay system.

Background technique

难以满足系统的控制需求。利用Smith预估器可以消除因时间延迟因素给系统造成的影响，提升系统带宽，但PI-Smith控制对系统模型误差敏感，且抗扰动能力差。In the adaptive optics system, due to factors such as the time-consuming sampling of the wavefront detector and the time-consuming processing of the wavefront, there is a time delay τ of 2 to 3 times the sampling period in the adaptive optics system. Usually, when designing the control method, The adaptive optics system is considered to be a pure time-delay system. The most widely used control method in the wavefront control part of the adaptive optics system is the PI control method, but under the control of this control method, the effective bandwidth of the system is only the sampling frequency

It is difficult to meet the control requirements of the system. Using the Smith predictor can eliminate the influence of the time delay factor on the system and improve the system bandwidth, but the PI-Smith control is sensitive to the system model error and has poor anti-disturbance ability.

Active disturbance rejection control is a control method that can actively resist disturbance and has strong robustness. The extended state observer part can estimate and compensate the disturbance of the applied system, so this control method is introduced into the adaptive In the optical system, the accuracy requirements of the Smith control model are improved, and the system's anti-disturbance ability is improved. However, due to the pure time-delay characteristics of the adaptive optics system, the direct use of ADRC will make the system's anti-noise capability poor at high frequencies. , so that the system has a strong ability to suppress internal and external disturbances.

Contents of the invention

Aiming at the pure time-delay characteristics of the adaptive optical system and the problems that the PI-Smith control method is sensitive to system model errors and poor anti-disturbance ability, the present invention provides a filter-based ADR prediction control method in the pure time-delay system, In order to improve the system's ability to suppress internal and external disturbances, simplify the controller tuning process and improve system performance.

In order to achieve the stated purpose, the solution adopted by the present invention is: a filter-based ADRR prediction control method in a pure time-delay system, the specific implementation steps are as follows:

Step 1: Fit the transfer function of the controlled object, and apply the ADRC predictive control method to the pure time-delay system control;

Step 2: The ADRC estimation control method is applied to the pure time-delay system to form a control system, and the relationship between the input, output and control quantities of the control system is derived, and the form of the control system is simplified;

Step 3: In the structure of the simplified control system, design the filtering link according to the characteristics of the control system;

Step 4: Find the closed-loop transfer function of the control system, and factorize it according to the expected closed-loop bandwidth value;

Step 5: According to the time estimation length requirement of the actual pure time-delay system, use the Routh criterion to select the control parameter range when the control system is stable.

Further, the pure time-delay system is a system in which the system model has a time-delay link and does not contain any inertial link.

Further, the filtering link is a first-order low-pass filter, which is set at the output of the control quantity to correct the control quantity.

Further, the control law part of the ADRC predictive control method uses a PI control structure.

The principle of the present invention is that: ADRC technology is a kind of robust control technology, and the stable immunity of ADRC is used to weaken the requirement of Smith's prediction for the accuracy of given compensation parameters, while increasing the low-pass The filtering link makes the number of poles of the system closed-loop transfer function more than the number of zeros, ensuring the system's anti-noise ability at high frequencies and strong ability to suppress external and internal disturbances.

The advantage of the present invention compared with prior art is:

(1) The present invention has strong robustness, and has a strong ability to suppress internal disturbances and external disturbances of the system;

(2) The present invention adjusts the controller parameters according to the time delay variation range required by the actual system, and only two parameters need to be adjusted, which simplifies the parameter adjustment process.

Description of drawings

Fig. 1 is a simplified structural diagram of a filter-type active disturbance rejection estimation controller applied in an adaptive optics system according to the present invention;

Figure 2 is a control structure diagram of an ADRC applied to an adaptive optics system;

Fig. 3 is a simplified control structure diagram of an ADRC applied to an adaptive optics system;

Figure 4 shows the output response of the system when Smith estimates full compensation;

Figure 5 shows the output response of the system when the system time delay perturbation is the maximum expected value.

Detailed ways

The present invention will be further described below by taking the control of the tilting mirror in the adaptive optics system as an example in conjunction with the accompanying drawings.

Fig. 1 is a simplified structural diagram of the application of the filter-based ADRR prediction control method in the adaptive optics system in a pure time-delay system of the present invention, in the adaptive optics system whose sampling period is h=0.0012 seconds, If the system is regarded as a linear system and the tilted mirror is ideal, the equivalent transfer function of the tilted mirror can be simplified as K=1, and the system model is G(s)=e ^-τs . The ideal time delay in the system is set to be 0.0025 seconds, and the Smith predictor compensation parameter _τ1 selects the ideal delay time as 0.0025 seconds, which is twice the sampling period delay, and the perturbation range of the actual time delay τ of the system is (0,0.008 ) seconds, make the system track the fixed value input r=1.

The specific implementation steps are as follows:

Step 1: Apply the ADRC method to the adaptive optics system control as shown in Figure 2;

Step 2: According to the block diagram of the control system, deduce the relationship between the input quantity r, the output quantity y and the control quantity u of the control system as follows:

u＝G ₁ *[G ₀ *r-(G ₀ +H)*y]

In the formula:

Among them, s is the complex variable after Laplace transform in the time domain to the complex number domain, w ₀ is the bandwidth of LESO, b ₀ is the parameter to be designed, k _p and _ki are the parameters of the control law, and G ₀ is the The characterization of the control law, G ₁ and H reflect the LESO characteristics and the feedback state in the control structure, based on which the simplified control structure diagram shown in Figure 3 can be obtained.

该滤波器G_f(s)不会影响原本的线路增益，只提供大小为w_c的截止频率，用以修正控制量u，此时u被修正为：Step 3: As shown in Figure 1, add a Smith predictor on the basis of Figure 3, and add a first-order low-pass filter at the control output

The filter G _f (s) will not affect the original line gain, but only provides a cut-off frequency of w _c to modify the control variable u. At this time, u is modified as:

u'=u*G _f

Step 4: At this point, the closed-loop transfer function of the control system can be obtained as:

In the formula, the filter G _f is embodied in G′ ₁ :

M can be expanded as:

附近有一个极点与零点相消，且一个极点可以提供系统期望的带宽。因此作出如下设计：According to the pole-zero characteristics of the Bode diagram, we hope that M is

There is a nearby pole that cancels the zero, and a pole can provide the desired bandwidth of the system. Therefore make the following design:

make:

Synthetic division can factor B(s) into:

和k_i→0。记

则根据既约分数求解多项式有理根的原则，可将C(s)因式分解为

此分解方式是保证B(s)在高频处有较强的噪声抑制能力。若令

则可将D(s)因式分解为

由此可得

其中0＜μ＜1。and should be satisfied at this time

and k _i →0. remember

Then according to the principle of solving polynomial rational roots by reducing fractions, the factorization of C(s) can be decomposed into

This decomposition method is to ensure that B(s) has a strong noise suppression ability at high frequencies. Ruoling

Then D(s) can be factored into

Therefore

where 0<μ<1.

Step 5: According to the time estimation length requirement of the actual system, if the system time delay perturbation range is required to be (0, 0.008) seconds, the control parameter range when the system is stable can be selected by using Routh criterion. Through calculation, combined with the value requirements of b ₀ , w _c , and _ki in step 4, it can be concluded that:

成立时，满足劳斯判据，系统具有稳定性。This formula can also be used to judge the output time domain length of the controlled process when the filter-type active disturbance rejection prediction controller is used in the adaptive optics system. and it can be deduced that in

When established, the Routh criterion is met, and the system is stable.

Under this design, the target bandwidth can be obtained by adjusting w ₀ and k _p . From the factorization of B(s), it can be seen that the target bandwidth is about μw ₀ . Then give roughly the value of w ₀ according to the required bandwidth, and then only need to adjust μ to achieve satisfactory dynamic tracking performance.

可得：If it is assumed that the required target bandwidth f _3dB ＝k _p w _c ＝μw ₀ ＝181rad/s, combined with

Available:

0.577<μ<1

181< _w0 <313

满足实际系统需求。If the value is selected within this range, and the parameter matching is reasonable, the system bandwidth and dynamic response performance can be considered. When choosing w ₀ =300, adjust μ to 0.6, as shown in Fig. 4, when Smith estimates full compensation, the output response of the system, it can be seen that the rise time required for the response to rise from 10% of the final value to 90% of the final value is less than One sampling step can be tracked quickly and without overshoot. At the same time, an external step disturbance is applied to the controlled object at 0.2 seconds. It can be seen that the disturbance is suppressed, and the dynamic characteristics of the process of restoring the tracking state are consistent with the transition process. Figure 5 shows the output response of the system when the system time delay perturbation is the maximum expected value of 0.008 seconds. It can be seen that the peak time of the system is 0.024 seconds, and the overshoot

meet the actual system requirements.

The parts not described in detail in the present invention belong to the well-known technology in the art. The above-mentioned embodiments are only descriptions of the preferred implementations of the present invention, and the preferred embodiments do not exhaustively describe all the details, nor limit the invention to the described specific implementations. Without departing from the design spirit of the present invention, various modifications and improvements to the technical solution of the present invention by those skilled in the art shall fall within the scope of protection determined by the claims of the present invention.

Claims (4)

1. an ADRC estimation control method based on filtering in a pure time-delay system, is characterized in that, said method comprises the following steps: Step 1: Fitting the transfer function of the controlled object, applying the ADRC estimation control method to the control of the pure time-delay system; Step 2: Apply the ADRC estimation control method to the pure time-delay system to form a control system, deduce the relationship between the input quantity, output quantity and control quantity of the control system, and convert the form of the control system Do simplification; Step 3: In the structure of the simplified control system, design the filtering link according to the characteristics of the control system; Step 4: Find the closed-loop transfer function of the control system, and factorize it according to the expected closed-loop bandwidth value; Step 5: According to the time estimation length requirement of the actual pure time-delay system, use the Routh criterion to select the control parameter range when the control system is stable. 2. in a kind of pure time-delay system according to claim 1, based on filtering ADRC predictive control method, it is characterized in that: The pure time-delay system is a system in which the system model has a time-delay link and does not contain any inertia link. 3. in a kind of pure time-delay system according to claim 1, based on the ADRC estimation control method of filtering, it is characterized in that: The filtering link is a first-order low-pass filter, which is set at the output of the control quantity to correct the control quantity. 4. in a kind of pure time-delay system according to claim 1, based on filtering ADRC predictive control method, it is characterized in that: The control law part of the ADRC predictive control method uses a PI control structure.

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