CN108873682B - Tilting mirror vibration suppression method based on improved repetitive controller - Google Patents

Abstract

The invention discloses a tilting mirror vibration suppression method based on an improved repetitive controller, which is inserted into a tilting mirror system to suppress vibration. Repetitive control is a learning type strategy that can enhance the error attenuation and optimally correct the system disturbance when the system disturbance frequency is known. Aiming at the problem that the disturbance is amplified under the aperiodic frequency in the traditional repetitive control method, the invention provides an improved repetitive controller which is optimized from a control algorithm, and the disturbance amplification of other frequencies can not be caused on the basis of improving the system disturbance suppression capability. In addition, the method only needs one image sensor, and is low in cost. Meanwhile, the structure is simple, the model is not depended on, the operation and the realization are easy, and the compromise between vibration suppression and noise transmission cannot be caused.

Description

Tilting mirror vibration suppression method based on improved repetitive controller

Technical Field

The invention belongs to the field of photoelectric tracking and control, and particularly relates to a tilting mirror vibration suppression method based on an improved repetitive controller, which is mainly used for improving the disturbance suppression capability of a photoelectric tracking system such as an astronomical telescope system and the like and improving the closed-loop performance of the system.

Background

One of the important technical difficulties to be overcome in the current astronomical telescope system is to suppress vibration so as to obtain high-definition imaging. The repetitive control is a learning type strategy, and can realize optimal correction and effectively improve the disturbance suppression capability of the system when the disturbance frequency of the system is known on the basis of not increasing the number of sensors and not depending on a model. Nevertheless, conventional repetitive control amplifies the disturbance at non-periodic frequencies. The present study aims to invent an improved repetitive controller, which alleviates the disturbance amplification of the repetitive control at the aperiodic frequency, thereby further improving the advantage of the method in disturbance suppression.

Disclosure of Invention

Aiming at the problem that the vibration of a mechanical structure of a large telescope influences the performance of the system, and the vibration cannot be compensated by a classical adaptive optical control system, an improved repetitive controller is provided to further improve the disturbance suppression capability of the system.

In order to achieve the purpose of the invention, the invention provides a tilting mirror vibration suppression method based on an improved repetitive controller, which comprises the following concrete implementation steps:

step (1): an experimental platform under a classical feedback control loop is built, and PSD (position sensing device) is used for detecting the deviation of a target and feeding the deviation back to the control loop;

step (2): design of position controller C (z) with PSD^-1) Completing basic position closed loop to form a feedback control loop;

and (3): constructing an improved repetitive controller structure, realizing the improved repetitive controller structure based on Euler parameterization, and inserting the improved repetitive controller into the feedback control loop of the step (2);

and (4): aiming at the problem that the repetitive control method can amplify the disturbance under the aperiodic frequency, a proper Q filter is designed, so that the disturbance suppression capability and the closed-loop performance of the system are improved.

Wherein, in step (4), in order to relieve the disturbance amplification under the non-periodic frequency, the invention designs a new additional sensitivity function E_IRC(z^-1) It can be expressed as:

wherein E is_IRC(z^-1) Is an abbreviation for an additional sensitivity function, denoted in particular as E_IRC(z^-1)＝1-Q_IRC(z^-1) (ii) a Alpha is a tunable parameter, alpha is an element of 0,1]，z^-NIs a delay link; q (z)^-1L) is a low pass filter, l is a positive integer;

thus, the Q filter Q in the discrete domain_IRC(z^-1) Can be expressed in the following form:

among others, q (z) in the improved repetitive controller of the present invention^-1L) is a MA (moving average) filter of the form:

wherein z is^-lIs a delay link; q (z)^-1L) is a low-pass filter, and q (z)^-1L) can be represented as q (z)^-1,l)＝a_lz^l+a_l-1z^l-1+…+a₀+…+a_l-1z^-l+1+a_lz^-lWherein l is a positive integer, anAnd q (z)^-1L) coefficients in the expression satisfy a_l＝a_l-1＝…＝a₀＝1/(2l+1)。

Compared with the prior art, the invention has the following advantages:

(1) the repetitive control is a learning type strategy, which can enhance the error attenuation under the condition that the disturbance frequency of the system is known, and realize optimal correction, thereby effectively improving the disturbance suppression capability of the system.

(2) The method of the present invention maintains a slight advantage even in the absence of vibration in the PI controller frequency range.

(3) The method can improve the disturbance suppression capability of the system and simultaneously does not cause disturbance amplification of other frequencies.

(4) The method has low dependence on the model and does not result in a compromise between interference suppression and noise propagation in the loop.

(5) The method optimizes the system from the control algorithm, only needs one position sensor, and has low control cost.

(6) The method is easy to operate and implement and has a wide application range.

Drawings

Fig. 1 is a schematic diagram of a classical feedback control experiment platform, wherein 1 is a laser, 2 is a tilting mirror, 3 is a voice coil motor, 4 is a driver, 5 is a controller, and 6 is a position sensor PSD.

Fig. 2 is a block diagram of a classical feedback control system architecture.

Fig. 3 is a control diagram of a tilting mirror vibration suppression method based on an improved repetitive controller proposed in the present invention.

FIG. 4 is an additional sensitivity function E of a conventional repetitive controller_CRC(z^-1) Amplitude-frequency response diagram of (c).

FIG. 5 is an additional sensitivity function E of the improved repetitive controller_IRC(z^-1) Amplitude-frequency response diagram of (c).

FIG. 6 is a graph comparing the interference of a tilting mirror platform under open loop control and integral control.

FIG. 7 is a graph of vibration contrast for a tilted mirror platform with the insertion of a conventional repetitive controller and the improved repetitive controller of the present invention.

Detailed Description

The following detailed description of embodiments of the invention refers to the accompanying drawings.

As shown in fig. 1, fig. 1 is a schematic diagram of a classical feedback control experiment platform, which includes a laser 1, a tilt mirror 2, a voice coil motor 3, a driver 4, a controller 5, and a position sensor PSD 6.

Fig. 3 is a control block diagram of a tilting mirror vibration suppression method based on an improved repetitive controller, wherein a CCD position loop and the repetitive controller are included, and the specific implementation steps for improving the system performance by using the device are as follows:

step (1): an experimental platform under a classical feedback control loop is built, and PSD (position sensing device) is used for detecting the deviation of a target and feeding the deviation back to the control loop;

step (2): design of position controller C (z) with PSD^-1) Completing basic position closed loop to form a feedback control loop;

and (3): constructing an improved repetitive controller structure, realizing an improved repetitive controller structure based on Euler parameterization, and inserting the improved repetitive controller into the feedback control loop of step (2), wherein the improved repetitive controller C_eq(z^-1) Can be expressed in the form of:

wherein, C (z)^-1) Shown is a position controller, Q (z)^-1) Denoted by a low-pass filter, z^-nA delay element is shown which is a delay element,

shown is a control module G (z)^-1) The inverse of (c).

And (4): aiming at the problem that the repetitive control method can amplify the disturbance at the aperiodic frequency, a proper Q filter is designed to solve the problem, so that the disturbance suppression capability and the closed-loop performance of the system are improved.

Q filter Q of Conventional Repetitive Controller (CRC)_CRC(z^-1) A simple low-pass filter can be expressed as:

Q_CRC(z^-1)＝z^-Nq(z^-1,l)

wherein z is^-NIs a delay link; q (z)^-1L) is a low-pass filter, and q (z)^-1L) can be represented as q (z)^-1,l)＝a_lz^l+a_l-1z^l-1+…+a₀+…+a_l-1z^-l+1+a_lz^-lWherein l is a positive integer, q (z)^-1L) coefficient in the expression satisfies 2 (a)_l+a_l-1+…+a₁)+a₀1. We define the extra sensitivity function E of a conventional repetitive controller_CRC(z^-1) In the following form:

E_CRC(z^-1)＝1-z^-Nq(z^-1,l)

additional sensitivity function E for conventional repetitive controllers_CRC(z^-1) The amplitude-frequency response is shown in fig. 4, and it can be seen that the conventional repetitive controller produces a high gain at the periodic frequency to cancel the interference, but the controller also amplifies the gain at other non-periodic frequencies, and in the worst case, 6dB of gain amplification, which is undesirable for the interference suppression control system. In order to relieve the disturbance amplification at the non-periodic frequency, the invention designs a new additional sensitivity function E_IRC(z^-1) It can be expressed as:

E_IRC(z^-1)＝1-Q_IRC(z^-1)

wherein alpha is an adjustable parameter, and alpha belongs to [0,1 ]]. Additional sensitivity of repetitive controller improved with variation of alphaDegree function E_IRC(z^-1) The amplitude-frequency response of (a) is shown in figure 5. When alpha is 0, the amplification effect at the non-periodic frequency is gradually weakened along with the increase of alpha, which is equivalent to the traditional repetitive controller, and the problem originally proposed by the invention is solved. Therefore, the Q filter Q in the discrete domain designed by the invention_IRC(z^-1) Can be expressed in the following form:

among others, q (z) in the improved repetitive controller of the present invention^-1L) is a MA (moving average) filter of the form:

wherein q (z)^-1L) coefficients in the expression satisfy a_l＝a_l-1＝…＝a₀＝1/(2l+1)。

The effectiveness of the present invention is demonstrated below using a tilting mirror platform system as an example.

On the basis of completing the step (1) and the step (2), the vibration interference situation of the tilting mirror platform under the control of an open loop control and a simple integral controller can be measured, as shown in the attached figure 6. While the step (3) and the step (4) are carried out, the traditional repetitive controller and the improved repetitive controller provided by the invention can be respectively inserted into the existing feedback control loop to measure the interference situation in the system under two conditions, as shown in figure 7, it is obvious that the improved repetitive controller provided by the invention has stronger vibration suppression capability, and the effectiveness and the superiority of the method are fully proved.

Claims (1)

1. A tilting mirror vibration suppression method based on an improved repetitive controller, characterized in that: the method comprises the following steps:

step (1): an experimental platform under a classical feedback control loop is built, and PSD (position sensing device) is used for detecting the deviation of a target and feeding the deviation back to the control loop;

step (2): design of position controller C (z) with PSD^-1) Completing basic position closed loop to form a feedback control loop;

and (3): constructing an improved repetitive controller structure, realizing the improved repetitive controller structure based on Euler parameterization, and inserting the improved repetitive controller into a feedback control loop of the step (2):

wherein, C (z)^-1) Shown is a position controller, Q (z)^-1) Denoted by a low-pass filter, z^-nA delay element is shown which is a delay element,

shown is a control module G (z)^-1) The inverse of (1);

and (4): aiming at the problem that the repetitive control method can amplify the disturbance under the aperiodic frequency, a proper Q filter is designed, so that the disturbance suppression capability and the closed-loop performance of the system are improved;

in order to relieve the disturbance amplification at the non-periodic frequency, a new additional sensitivity function E is designed_IRC(z^-1) It can be expressed as:

wherein E is_IRC(z^-1) Is an abbreviation for an additional sensitivity function, denoted in particular as E_IRC(z^-1)＝1-Q_IRC(z^-1) (ii) a Alpha is a tunable parameter, alpha is an element of 0,1]，z^-NIs a delay link; q (z)^-1L) is a low pass filter, l is a positive integer;

thus, the Q filter Q in the discrete domain_IRC(z^-1) Can be expressed in the following form:

Images