A hybrid control method for fast mirrors based on multivariable extended state observer

Abstract

The present invention discloses a hybrid control method for a fast mirror based on a multivariable extended state observer, and relates to the technical field of precision motion control. The control method comprises the steps of: obtaining the transfer functions of the X and Y axes of a voice coil type fast mirror system by a system identification method, and obtaining a fast mirror model; designing a model-assisted multivariable extended state observer according to the obtained fast mirror model; and designing a hybrid state feedback controller based on the model-assisted multivariable extended state observer. The invention combines an extended state observer with hybrid control, adds known model information to an observer to design a model-assisted multivariable extended state observer, and simultaneously observes the X and Y axes, thereby reducing the estimation error of disturbances in each channel, and is used to improve the decoupling capability and robust performance of the extended state observer.

Description

Technical Field

[0001] The invention relates to the technical field of precision motion control, and in particular to a fast mirror hybrid control method based on a multivariable extended state observer. Background Art

[0002] The fast reflector is installed on platforms such as satellites, aircraft, and ships. The working environment is relatively harsh. Changes in parameters such as temperature and air pressure will cause the model of the fast reflector to change. Multi-source interference in the working environment will also affect the control performance of the fast reflector. As the core component of precise tracking in composite axis control in marine stereoscopic space communication, the control accuracy of the fast reflector determines the tracking accuracy of the entire system. However, in the face of many uncertain interferences in the ocean, how to efficiently ensure that the fast reflector does not affect its precise output under different working conditions is an urgent problem to be solved.

[0003] Active disturbance rejection control is an effective method for dealing with system uncertainty. Its core lies in real-time estimation of disturbances by extending the state observer and designing corresponding control strategies to ensure the stability of the system. This can significantly improve the performance of the fast mirror system in terms of tracking accuracy and anti-interference ability. Active disturbance rejection control can estimate and compensate for disturbances in the system in real time, effectively improving the robustness of the system in the face of external disturbances and inherent uncertainties. Chinese patent CN118938691A discloses an anti-interference control method for decoupling the tracking and stability performance of an airborne optoelectronic system, which establishes a fast mirror dynamics model and designs an extended state observer according to the order of the fast mirror dynamics model, constructs a correction term using the output of the sensor and the error between the output of the extended state observer, and obtains a corrected observer equation; based on the corrected observer equation, the pointing controller of the optoelectronic tracking system driving the fast mirror is designed, which improves the command tracking and disturbance suppression performance of the fast mirror system, and realizes fast response and high-precision control of the fast mirror. However, in an environment with large high-frequency noise or when the working environment changes drastically, such as temperature, air pressure, humidity, etc., the active disturbance rejection control changes the model information of the fast mirror, resulting in inaccurate estimation results.

[0004] When observing a severely coupled multivariable system such as a fast mirror, the traditional Distributed Extended State Observer (DESO) fails to fully utilize the known information of the system, so there will inevitably be certain errors in the estimation of the coupled disturbances on each channel. Summary of the invention

[0005] In order to solve the above problem that the fast mirror model may change due to the change of working environment, resulting in serious degradation of the control performance of the fast mirror system, the present invention provides a hybrid control method of the fast mirror based on a multivariable extended state observer.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions: A hybrid control method for a fast reflector based on a multivariable extended state observer comprises the following steps: S1 adopts a system identification method to obtain the transfer functions of the X-axis and Y-axis of a voice coil type fast reflector system, and obtains a fast reflector model; S2 designs a model-assisted multivariable extended state observer based on the obtained fast reflector model, and observes the X-axis and Y-axis; S3 designs a hybrid control method based on the model-assisted multivariable extended state observer. State feedback controller.

[0007] Furthermore, in S1, the Hankel matrix system identification method based on impulse response is used to identify the system's X-axis transfer function: and the transfer function of the Y axis They are:

[0008] ;

[0009] ;

[0010] In the formula, is the complex frequency domain variable in the Laplace transform domain;

[0011] Due to the existence of external disturbances, the identified fast mirror model is written as:

[0012] ;

[0013] ;

[0014] In the formula, is the actual output of the X-axis; is the actual input of the X-axis; is the disturbance on the X-axis; is the actual output of the Y axis; is the actual input of the Y axis; is the disturbance on the Y axis; is the real gain of X axis; is the real gain of the Y-axis to X-axis coupling; is the actual gain of the X-axis to Y-axis coupling; is the real gain of Y axis; is the actual unknown total disturbance of the X-axis; is the actual unknown total disturbance of the Y axis; The X-axis contains the sum of the unknown total disturbance and the known object information, which is equivalent to the expansion of the disturbance; The Y axis contains the sum of the unknown total disturbance and the known object information, which is equivalent to the expansion of the disturbance;

[0015] According to the fast reflector model information obtained by identification , It is known that , , , ; It is known that , ; , is the self-tuning parameter, .

[0016] Furthermore, in S2, select the state variable: , , , , , , then the state space form of the fast mirror model is:

[0017] ;

[0018] MMESO is designed to:

[0019] ;

[0020] Written in matrix form:

[0021] ;

[0022] In the formula, Tracking output of two channels ; Tracking of two channels ; Tracking disturbances in both channels; is the observer gain matrix of MMESO.

[0023] Furthermore, in order to obtain the observer gain matrix of MMESO and make full use of the known model information, the observer gain is calculated through the X-axis and Y-axis;

[0024] On the X-axis, the transfer function So, the state space of the X-axis differential equation is in the form of:

[0025] ;

[0026] Written in matrix form:

[0027] ;

[0028] in, , , , ; At this time, the observer characteristic equation corresponding to the X-axis is obtained by the pole configuration method:

[0029] ;

[0030] In the formula, for The identity matrix of is the X-axis observer gain matrix; is the observer bandwidth;

[0031] The X-axis observer gain matrix is ​​solved as follows:

[0032] ;

[0033] On the Y axis, the transfer function So, the state space of the Y-axis differential equation is in the form of:

[0034] ;

[0035] Written in matrix form:

[0036] ;

[0037] in, , , , ;

[0038] At this time, the observer characteristic equation corresponding to the Y axis is obtained by the pole configuration method:

[0039] ;

[0040] In the formula, for The identity matrix of is the Y-axis observer gain matrix; is the observer bandwidth;

[0041] The Y-axis observer gain matrix is ​​solved as follows:

[0042] .

[0043] Furthermore, in S3, mixed The specific steps of designing a state feedback controller are:

[0044] Assuming that the state of the system can be directly measured, design a state feedback The controller is:

[0045] ;

[0046] In the formula, is the desired controller;

[0047] The corresponding closed-loop system is:

[0048] ;

[0049] In the formula, , are the specific parameters of the state space equation of the closed-loop system; is an external disturbance;

[0050] Asymptotically stable and closed-loop transfer function of The norm satisfies:

[0051] ;

[0052] In the formula, is the upper bound of the controller norm; for Upper bound of the controller norm;

[0053] If and only if there exists a symmetric positive definite matrix ,matrix , so that:

[0054] ;

[0055] If the matrix inequality has a feasible solution , , then the corresponding The state feedback control law is:

[0056] ;

[0057] Assuming that the state of the system can be directly measured, design a state feedback The controller is:

[0058] ;

[0059] The corresponding closed-loop system is:

[0060] ;

[0061] Asymptotically stable and closed-loop transfer function of The norm satisfies:

[0062] ;

[0063] In the formula, for Upper bound of the controller norm;

[0064] If and only if there exists a symmetric positive definite matrix , and matrix , so that:

[0065] ;

[0066] ;

[0067] ;

[0068] If the above matrix inequality has a feasible solution , and , then the state feedback The control law is:

[0069] .

[0070] Furthermore, in the x-axis, the fast mirror system is described in state space form:

[0071] ;

[0072] In the formula, , , , , , ;

[0073] Combined with status feedback Matrix Inequality and State Feedback of Controllers The matrix inequality of the controller is solved by linear matrix inequality:

[0074] ;

[0075] get and , so the corresponding state feedback control law of the X-axis is:

[0076] ;

[0077] In the Y-axis, the fast-firing mirror system is described in state-space form:

[0078] ;

[0079] In the formula, , , , , , ;

[0080] Combined with status feedback Matrix Inequality and State Feedback of Controllers The matrix inequality of the controller is solved by linear matrix inequality:

[0081] ;

[0082] get and , so the corresponding state feedback control law of the Y axis is:

[0083] .

[0084] The beneficial effect of the present invention is that the present invention combines the extended state observer with the hybrid The control is combined with the known model information to design a model-assisted multivariable extended state observer, which simultaneously observes the X and Y axes, reduces the estimation error of each channel disturbance, and improves the decoupling ability and robustness of the extended state observer. Control as a state feedback controller, respectively and The norm is used to measure the optimal performance and robustness of the system, and the robustness of the system is improved while ensuring the tracking accuracy and anti-interference ability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 Shown is the structural block diagram of the model-assisted multivariable extended state observer controller.

[0086] Figure 2 Mixed Control block diagram.

[0087] Figure 3 Shown is a comparison diagram of spiral signal tracking using MMESO+cascade PD and DESO+cascade PD methods.

[0088] Figure 4The figure shows the tracking error comparison between the MMESO+cascade PD and DESO+cascade PD methods.

[0089] Figure 5 The figure shows the tracking comparison of sinusoidal signals with an X-axis amplitude of 0.1° and a frequency of 10Hz.

[0090] Figure 6 The figure shows the tracking error comparison of a sinusoidal signal with an X-axis amplitude of 0.1° and a frequency of 10Hz.

[0091] Figure 7 The figure shows the tracking comparison of sinusoidal signals with an X-axis amplitude of 0.1° and a frequency of 30Hz.

[0092] Figure 8 The figure shows the tracking error comparison of a sinusoidal signal with an X-axis amplitude of 0.1° and a frequency of 30Hz.

[0093] Fig. 9 The figure shows the tracking comparison of sinusoidal signals with an X-axis amplitude of 0.1° and a frequency of 50Hz.

[0094] Fig.10 The following is a comparison chart of the tracking error of a sinusoidal signal with an X-axis amplitude of 0.1° and a frequency of 50Hz.

[0095] Fig.11 The figure shows the tracking comparison of sinusoidal signals with Y-axis amplitude of 0.1° and frequency of 10Hz.

[0096] Fig.12 The figure shows the tracking error comparison of a sinusoidal signal with a Y-axis amplitude of 0.1° and a frequency of 10Hz.

[0097] Fig.13 The figure shows the tracking comparison of sinusoidal signals with Y-axis amplitude of 0.1° and frequency of 30Hz.

[0098] Fig.14 The figure shows the tracking error comparison of a sinusoidal signal with a Y-axis amplitude of 0.1° and a frequency of 30Hz.

[0099] Fig.15 The figure shows the tracking comparison of sinusoidal signals with Y-axis amplitude of 0.1° and frequency of 50Hz.

[0100] Fig.16 The figure shows the tracking error comparison of a sinusoidal signal with a Y-axis amplitude of 0.1° and a frequency of 50Hz.

[0101] Fig.17 The figure shows the tracking comparison of sinusoidal signals with an X-axis amplitude of 0.04° and a frequency of 30Hz.

[0102] Fig.18 The figure shows the tracking error comparison of a sinusoidal signal with an X-axis amplitude of 0.04° and a frequency of 30Hz.

[0103] Fig.19 The figure shows the tracking comparison of sinusoidal signals with an X-axis amplitude of 0.08° and a frequency of 30Hz.

[0104] Fig. 20 The figure shows the tracking error comparison of a sinusoidal signal with an X-axis amplitude of 0.08° and a frequency of 30Hz.

[0105] Fig.21 The figure shows the tracking comparison of sinusoidal signals with an X-axis amplitude of 0.12° and a frequency of 30Hz.

[0106] Fig. 22 The figure shows the tracking error comparison of a sinusoidal signal with an X-axis amplitude of 0.12° and a frequency of 30Hz.

[0107] Fig.23 The figure shows the tracking comparison of a sinusoidal signal with a Y-axis amplitude of 0.04° and a frequency of 30 Hz.

[0108] Fig.24 The figure shows the tracking error comparison of a sinusoidal signal with a Y-axis amplitude of 0.04° and a frequency of 30Hz.

[0109] Fig.25 The figure shows the tracking comparison of a sinusoidal signal with a Y-axis amplitude of 0.08° and a frequency of 30 Hz.

[0110] Fig.26 The figure shows the tracking error comparison of a sinusoidal signal with a Y-axis amplitude of 0.08° and a frequency of 30Hz.

[0111] Fig. 27 The figure shows the tracking comparison of a sinusoidal signal with a Y-axis amplitude of 0.12° and a frequency of 30 Hz.

[0112] Fig.28 The figure shows the tracking error comparison of a sinusoidal signal with a Y-axis amplitude of 0.12° and a frequency of 30Hz.

[0113] Fig.29 Shown is a comparison chart of X-axis anti-disturbance tracking.

[0114] Fig.30 Shown is a comparison chart of X-axis anti-disturbance tracking error.

[0115] Fig.31 Shown is a Y-axis anti-disturbance tracking comparison chart.

[0116] Fig.32 Shown is a comparison chart of Y-axis anti-disturbance tracking error.

[0117] Fig.33 Shown is the X-axis parameter perturbation +25% tracking comparison chart.

[0118] Fig.34The figure shows the comparison of tracking error of X-axis parameter perturbation +25%.

[0119] Fig.35 Shown is the Y-axis parameter perturbation +25% tracking comparison chart.

[0120] Fig.36 The figure shows the comparison of tracking error of Y-axis parameter perturbation +25%. DETAILED DESCRIPTION

[0121] The present invention discloses a fast mirror hybrid control method based on a multivariable extended state observer. An implementation method of the present invention is described in detail below in conjunction with the accompanying drawings.

[0122] The hybrid control method of the fast reflector based on the multivariable extended state observer comprises the following steps: S1 adopts the system identification method to obtain the transfer function of the X-axis and Y-axis of the voice coil type fast reflector system, and obtains the fast reflector model; S2 designs a model-assisted multivariable extended state observer according to the obtained fast reflector model, and observes the X-axis and Y-axis; S3 designs a hybrid control method based on the model-assisted multivariable extended state observer. State feedback controller.

[0123] Furthermore, in S1, the Hankel matrix system identification method based on impulse response is used to identify the system's X-axis transfer function: and the transfer function of the Y axis They are:

[0124] ;

[0125] ;

[0126] In the formula, is the complex frequency domain variable in the Laplace transform domain;

[0127] Due to the existence of external disturbances, the identified fast mirror model is written as:

[0128] ;

[0129] ;

[0130] In the formula, is the actual output of the X-axis; is the actual input of the X-axis; is the disturbance on the X-axis; is the actual output of the Y axis; is the actual input of the Y axis; is the disturbance on the Y axis; is the real gain of X axis; is the real gain of the Y-axis to X-axis coupling; is the actual gain of the X-axis to Y-axis coupling; is the real gain of Y axis; is the actual unknown total disturbance of the X-axis; is the actual unknown total disturbance of the Y axis; The X-axis contains the sum of the unknown total disturbance and the known object information, which is equivalent to the expansion of the disturbance; The Y axis contains the sum of the unknown total disturbance and the known object information, which is equivalent to the expansion of the disturbance;

[0131] According to the fast reflector model information obtained by identification , It is known that , , , ; It is known that , ; , is the self-tuning parameter, .

[0132] Furthermore, in S2, select the state variable: , , , , , , then the state space form of the fast mirror model is:

[0133] ;

[0134] MMESO is designed to:

[0135] ;

[0136] Written in matrix form:

[0137] ;

[0138] In the formula, Tracking output of two channels ; Tracking of two channels ; Tracking disturbances in both channels; is the observer gain matrix of MMESO.

[0139] Furthermore, in order to obtain the observer gain matrix of MMESO and make full use of the known model information, the observer gain is calculated through the X-axis and Y-axis;

[0140] On the X-axis, the transfer function So, the state space of the X-axis differential equation is in the form of:

[0141] ;

[0142] Written in matrix form:

[0143] ;

[0144] in, , , , ; At this time, the observer characteristic equation corresponding to the X-axis is obtained by the pole configuration method:

[0145] ;

[0146] In the formula, for The identity matrix of is the X-axis observer gain matrix; is the observer bandwidth;

[0147] The X-axis observer gain matrix is ​​solved as follows:

[0148] ;

[0149] On the Y axis, the transfer function So, the state space of the Y-axis differential equation is in the form of:

[0150] ;

[0151] Written in matrix form:

[0152] ;

[0153] in, , , , ;

[0154] Among them, the observer characteristic equation corresponding to the Y axis obtained by the pole configuration method is:

[0155] ;

[0156] In the formula, for The identity matrix of is the Y-axis observer gain matrix; is the observer bandwidth;

[0157] The Y-axis observer gain matrix is ​​solved as follows:

[0158] .

[0159] Furthermore, in S3, mixed The specific steps of designing a state feedback controller are:

[0160] Assuming that the state of the system can be directly measured, design a state feedback The controller is:

[0161] ;

[0162] In the formula, is the desired controller;

[0163] The corresponding closed-loop system is:

[0164] ;

[0165] In the formula, , are the specific parameters of the state space equation of the closed-loop system; is an external disturbance;

[0166] Asymptotically stable and closed-loop transfer function of The norm satisfies:

[0167] ;

[0168] In the formula, is the upper bound of the controller norm; for Upper bound of the controller norm;

[0169] If and only if there exists a symmetric positive definite matrix ,matrix , so that:

[0170] ;

[0171] If the matrix inequality has a feasible solution , , then the corresponding The state feedback control law is:

[0172] ;

[0173] Assuming that the state of the system can be directly measured, design a state feedback The controller is:

[0174] ;

[0175] The corresponding closed-loop system is:

[0176] ;

[0177] Asymptotically stable and closed-loop transfer function of The norm satisfies:

[0178] ;

[0179] In the formula, for Upper bound of the controller norm;

[0180] If and only if there exists a symmetric positive definite matrix , and matrix , so that:

[0181] ;

[0182] ;

[0183] ;

[0184] If the above matrix inequality has a feasible solution , and , then the state feedback The control law is:

[0185] .

[0186] Furthermore, in the x-axis, the fast mirror system is described in state space form:

[0187] ;

[0188] In the formula, , , , , , ;

[0189] Combined with status feedback Matrix Inequality and State Feedback of Controllers The matrix inequality of the controller is solved by linear matrix inequality:

[0190]

[0191] ;

[0192] get and , so the corresponding state feedback control law of the X-axis is:

[0193] ;

[0194] In the Y-axis, the fast-firing mirror system is described in state-space form:

[0195] ;

[0196] In the formula, , , , , , ;

[0197] Combined with status feedback Matrix Inequality and State Feedback of Controllers The matrix inequality of the controller is solved by linear matrix inequality:

[0198] ;

[0199] get and , so the corresponding state feedback control law of the Y axis is:

[0200] .

[0201] In the first step, the transfer functions of the X-axis and Y-axis of the voice coil type fast reflector system are obtained by using the system identification method to obtain the fast reflector model. Figure 1 The figure shows the structure diagram of the model-assisted multivariable extended state observer controller. , , is the desired system closed-loop control bandwidth, , They are the reference inputs for the X-axis and Y-axis respectively. is the actual output of the X-axis, is the actual input of the X-axis, is the actual output of the Y axis, is the actual input of the Y axis, is the disturbance of the system, the static decoupling matrix , Tracking output of two channels , Tracking of two channels , Track the perturbations of both channels.

[0202] The Hankel matrix system identification method based on impulse response is used to identify the system's X-axis transfer function. and the transfer function of the Y axis They are:

[0203] ;

[0204] ;

[0205] In the formula, is the complex frequency domain variable in the Laplace transform domain;

[0206] Considering external disturbances, the identified system model is written in the following differential form:

[0207] ;

[0208] ;

[0209] In the formula, is the actual output of the X-axis; is the actual input of the X-axis; is the disturbance on the X-axis; is the actual output of the Y axis; is the actual input of the Y axis; is the disturbance on the Y axis; is the real gain of X axis; is the real gain of the Y-axis to X-axis coupling; is the actual gain of the X-axis to Y-axis coupling; is the real gain of Y axis; is the actual unknown total disturbance of the X-axis; is the actual unknown total disturbance of the Y axis; The X-axis contains the sum of the unknown total disturbance and the known object information, which is equivalent to the expansion of the disturbance; The Y axis contains the sum of the unknown total disturbance and the known object information, which is equivalent to the expansion of the disturbance;

[0210] According to the fast reflector model information obtained by identification , It is known that , , , ; It is known that , ; , is the self-tuning parameter, .

[0211] The second step is to design a model-assisted multivariable extended state observer based on the obtained fast mirror model, and observe the X-axis and Y-axis simultaneously. Select state variables: , , , , , , the fast mirror model in differential form can be written in state space form:

[0212] ;

[0213] MMESO can be designed as:

[0214] ;

[0215] Rewritten into matrix form:

[0216] ;

[0217] In the formula, Tracking output of two channels ; Tracking of two channels ; Tracking disturbances in both channels; is the observer gain matrix of MMESO.

[0218] In order to obtain the observer gain matrix of MMESO and make full use of the known model information, the observer gain is calculated through the X-axis and Y-axis;

[0219] On the X-axis, the transfer function So, the state space of the X-axis differential equation is in the form of:

[0220] ;

[0221] Rewritten in matrix form:

[0222] ;

[0223] in, , , , At this time, the observer characteristic equation corresponding to the X-axis is obtained by the pole configuration method:

[0224] ;

[0225] In the formula, for The identity matrix of is the X-axis observer gain matrix; is the observer bandwidth;

[0226] The X-axis observer gain matrix is ​​solved as follows:

[0227] ;

[0228] On the Y axis, the transfer function So, the state space of the Y-axis differential equation is in the form of:

[0229] ;

[0230] Written in matrix form:

[0231] ;

[0232] in, , , , ;

[0233] At this time, the observer characteristic equation corresponding to the Y axis is obtained by the pole configuration method:

[0234] ;

[0235] In the formula, for The identity matrix of is the Y-axis observer gain matrix; is the observer bandwidth;

[0236] The Y-axis observer gain matrix is ​​solved as follows:

[0237] .

[0238] The third step is to design a hybrid based on the model-assisted multivariable extended state observer. State feedback controller, such as Figure 2 As shown, Figure 2 Mixed Control block diagram, in the figure and are the observation outputs of MMESO for the X and Y axes respectively, , They are the observed values ​​of the disturbances on the X and Y axes of MMESO respectively.

[0239] mix The specific steps of state feedback controller design are: Assuming that the state of the system can be directly measured, design a state feedback The controller is:

[0240] ;

[0241] In the formula, is the desired controller;

[0242] The corresponding closed-loop system is:

[0243] ;

[0244] In the formula, , are the specific parameters of the state space equation of the closed-loop system; is an external disturbance;

[0245] Asymptotically stable and closed-loop transfer function of The norm satisfies:

[0246] ;

[0247] In the formula, is the upper bound of the controller norm; for Upper bound of the controller norm;

[0248] If and only if there exists a symmetric positive definite matrix ,matrix , so that:

[0249] ;

[0250] If the matrix inequality has a feasible solution , , then the corresponding The state feedback control law is:

[0251] ;

[0252] Assuming that the state of the system can be directly measured, design a state feedback The controller is:

[0253] ;

[0254] The corresponding closed-loop system is:

[0255] ;

[0256] Asymptotically stable and closed-loop transfer function of The norm satisfies:

[0257] ;

[0258] In the formula, for Upper bound of the controller norm;

[0259] If and only if there exists a symmetric positive definite matrix , and matrix , so that:

[0260] ;

[0261] ;

[0262] ;

[0263] If the above matrix inequality has a feasible solution , and , then the state feedback The control law is:

[0264] .

[0265] In the x-axis, the fast mirror system is described in state space form:

[0266] ;

[0267] In the formula, , , , , , ;

[0268] Combined with status feedback Matrix Inequality and State Feedback of Controllers The matrix inequality of the controller is solved by linear matrix inequality:

[0269] ;

[0270] get and , so the corresponding state feedback control law of the X-axis is:

[0271] ;

[0272] In the Y-axis, the fast-firing mirror system is described in state-space form:

[0273] ;

[0274] In the formula, , , , , , ;

[0275] Combined with status feedback Matrix Inequality and State Feedback of Controllers The matrix inequality of the controller is solved by linear matrix inequality:

[0276] ;

[0277] get and , so the corresponding state feedback control law of the Y axis is:

[0278] .

[0279] The fourth step is to first compare the model-assisted multivariable extended state observer with the decentralized extended state observer. The designed MMESO+cascade PD and DESO+cascade PD methods track the same spiral signal at the same time, and compare the tracking performance of the two methods. Figure 3 As shown in the figure, the errors of the two methods are Figure 4 shown. Figure 3 Shown is the comparison of spiral signal tracking using the MMESO+cascade PD and DESO+cascade PD methods, where the red spiral represents the reference input, the green spiral represents the tracking path using the MMESO+cascade PD method, and the blue spiral represents the tracking path using the DESO+cascade PD method. Figure 4 Shown is the tracking error comparison between the MMESO+cascade PD and DESO+cascade PD methods, where the red line represents the error between the MMESO+cascade PD method and the reference input, and the green line represents the error between the DESO+cascade PD method and the reference input.

[0280] Experimental results show that the MMESO designed in the present invention can make full use of the known model information of the system, has simple parameter setting, and has better decoupling capability compared with the traditional distributed ESO.

[0281] Secondly, the tracking performance is experimentally analyzed. Controller with DESO-based hybrid Controller and MMESO+cascade PD method are compared, combined with Figures 5 to 28 As shown in the figure, the red line represents the reference input, the green line represents the tracking path using the MMESO+cascade PD method, and the blue line represents the hybrid based on DESO. The tracking path of the controller, the black line represents the MMESO-based hybrid The tracking path of the controller. Use sine as input signal for both X and Y axes, set the amplitude to 0.1°, and set the frequency to 10Hz, 30Hz, and 50Hz respectively. Compare the tracking status and error of different frequencies with the same amplitude. The tracking status and error of the X axis are as follows: Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 as well as Fig.10 As shown, the Y-axis tracking situation and error are as follows Fig.11 , Fig.12 , Fig.13 , Fig.14 , Fig.15 as well as Fig.16 As shown in the figure, the frequency is set to 30Hz, and the amplitude is set to 0.04°, 0.08°, and 0.12° respectively. The tracking conditions and errors of different amplitudes at the same frequency are compared. The X-axis tracking conditions and errors are shown in the figure. Fig.17 , Fig.18 , Fig.19 , Fig. 20 , Fig.21 as well as Fig. 22 As shown, the Y-axis tracking situation and error are as follows Fig.23 , Fig.24 , Fig.25 , Fig.26 , Fig. 27 as well as Fig.28 Observation Figures 5 to 16 It can be seen that for inputs of different frequencies, the mixed The FSM system controlled by the controller can achieve good tracking performance; observe Figures 17 to 28 It can be seen that for inputs of different amplitudes, the mixed The FSM system controlled by the controller can also achieve good tracking results.

[0282] Again, the anti-disturbance performance experimental analysis. Given an input with an amplitude of 0.1° and a frequency of 30Hz, a sinusoidal disturbance with an amplitude of 0.05° and a frequency of 20Hz is applied to the system to verify the hybrid based on MMESO. The disturbance rejection capability of the controller is compared with the hybrid based on DESO. The controller and the MMESO+cascade PD method are compared. According to the collected experimental data, the anti-disturbance experimental result curves of the X-axis and Y-axis controllers are plotted as follows: Fig.29 , Fig.30 , Fig.31 as well as Fig.32 shown.

[0283] Depend on Fig.29 , Fig.30 , Fig.31 as well as Fig.32 By comparison, the hybrid based on MMESO The control method has the best anti-interference ability compared with the other two methods.

[0284] Finally, the robust performance experiment is analyzed. The FSM system model parameters are perturbed by +25%, and a sine wave with a frequency of 30 Hz and an amplitude of 0.1° is used as the input signal to verify the hybrid based on MMESO. Robust performance of FSM controlled systems and hybrid with DESO based The control method is compared with the MMESO+cascade PD method, and the experimental results are as follows: Fig.33 , Fig.34 , Fig.35 as well as Fig.36 The experimental results show that even if the FSM system model parameters are perturbed by +25%, the hybrid The controlled FSM system can still achieve good tracking performance.

[0285] Step 5, Conclusion. In order to improve the anti-interference ability and robust performance of the fast reflector system, the present invention proposes a hybrid Control strategy: First, the fast mirror system model is obtained through identification and then the model-assisted multivariable extended state observer is designed; then the fast mirror system is combined with state feedback , Control-related principles design hybrid The controller is designed and the state feedback control law of the system is obtained by solving linear inequalities. Finally, the feasibility of the design method is verified through the dSPACE experimental platform and compared with the MESO+ cascade PD and PID methods.

[0286] Experimental results show that for input signals of the same amplitude but different frequencies or the same frequency but different amplitudes, the mixed The controllers have better tracking performance; in terms of anti-disturbance ability, for the given disturbance in the experiment, the mixed The disturbance resistance of the control is significantly better than that of the other two methods; in terms of robustness, when the model parameters are perturbed by +25%, the FSM system can still achieve good tracking performance. The control strategy can effectively improve the tracking and anti-disturbance performance of the fast reflector, and when the model undergoes large changes, it can still ensure good control performance and enhance the robustness of the system.

[0287] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A fast mirror hybrid control method based on a multivariable extended state observer, characterized in that: The following steps are involved: S1 uses the system identification method to obtain the transfer function of the X-axis and Y-axis of the voice coil type fast reflector system and obtain the fast reflector model; S2 designs a model-assisted multivariable extended state observer based on the obtained fast mirror model, and observes the X-axis and Y-axis; S3 designs a hybrid H2 / H based on a model-assisted multivariable extended state observer ∞ State feedback controller; In S1, the Hankel matrix system identification method based on impulse response is used to identify the system's X-axis transfer function G x (s) and the transfer function G of the Y axis y (s) are: Where s is the complex frequency domain variable in the Laplace transform domain; Due to the existence of external disturbances, the identified fast mirror model is written as: In the formula, y1 is the actual output of the X-axis; u1 is the actual input of the X-axis; ω1 is the disturbance of the X-axis; y2 is the actual output of the Y-axis; u2 is the actual input of the Y-axis; ω2 is the disturbance of the Y-axis; b x is the real gain of X axis; b yx is the real gain of the Y-axis to X-axis coupling; b xy is the actual gain of the X-axis to Y-axis coupling; b y is the real gain of Y axis; f ′ 1 is the actual unknown total disturbance of the X-axis; f ′ 2 is the actual unknown total disturbance on the Y axis; f1 is the sum of the unknown total disturbance and known object information on the X axis, which is equivalent to the expansion of the disturbance; f2 is the sum of the unknown total disturbance and known object information on the Y axis, which is equivalent to the expansion of the disturbance; According to the identified fast reflector model information a1 and a0, a 1X =62.52, α 1Y =61.94, a 0X =15550, a 0Y =15430; b0 is known, where b 0X =203031.582, b 0y =203031.582; b1 and b2 are self-tuning parameters, b1=b2=-30000; In S2, select the state variables: x1 = y1, x2 = y2, x5=f1,x6=f2,then the state space form of the fast mirror model is: MMESO is designed to: Written in matrix form: In the formula, Track the output Y of the two channels; Tracking of two channels Track the disturbances of the two channels; L = [l1 l2 L3 l4 l5 l6] T is the observer gain matrix of MMESO; In order to obtain the observer gain matrix of MMESO and make full use of the known model information, the observer gain is calculated through the X-axis and Y-axis; On the X-axis, the transfer function G x (s) The state space of the X-axis differential equation is in the form of: Written in matrix form: in, C x =[1 0 0], E x =[0 0 1] T ; At this time, the observer characteristic equation corresponding to the X-axis is obtained by the pole configuration method: λ(s)=|sI-(A x -L x C x )|=(s+ω0) 3 ; Where I is the 3×3 unit matrix; L x is the X-axis observer gain matrix; ω0 is the observer bandwidth; The X-axis observer gain matrix is ​​solved as follows: On the Y axis, the transfer function G y (s) The state space of the Y-axis differential equation is in the form of: Written in matrix form: in, C y =[1 0 0], E y =[0 0 1] T ; Among them, the observer characteristic equation corresponding to the Y axis obtained by the pole configuration method is: λ(s)=|sI-(A y -L y C y )|=(s+ω0) 3 ; Where I is the 3×3 unit matrix; L y is the Y-axis observer gain matrix; ω0 is the observer bandwidth; The Y-axis observer gain matrix is ​​solved as:

2. The fast mirror hybrid control method based on multivariable extended state observer according to claim 1 is characterized in that: In S3, a mixture of H2 / H ∞ The specific steps of designing a state feedback controller are: Assuming that the state of the system can be measured directly, design a state feedback H ∞ The controller is: u=Kx; In the formula, K is the controller obtained; The corresponding closed-loop system is: Where D 11 , D 12 are the specific parameters of the state space equation of the closed-loop system; w is the external disturbance; Asymptotically stable and closed-loop transfer function T 2z (s)H ∞ The norm satisfies: ‖T wz (s)‖ ∞ <γ ∞ ; Where, γ is the upper bound of the controller norm; ∞ H ∞ Upper bound of the controller norm; If and only if there exists a symmetric positive definite matrix P1 and a matrix P2 such that: If the matrix inequality has a feasible solution P1, P2, then the corresponding H ∞ The state feedback control law is: u=Kx=P2P1 -1 x; Assuming that the state of the system can be measured directly, a state feedback H2 controller is designed as: u=Kx; The corresponding closed-loop system is: Asymptotically stable and closed-loop transfer function T wz The H2 norm of (s) satisfies: ‖T wz (s)‖2<γ2; Where γ2 is the upper bound of the H2 controller norm; If and only if there exist symmetric positive definite matrices P1, Q and P2 such that: AP1+B2P2+(AP1+B2P2) T +B1B1 T <0; Trace(Q)<γ2 2 ; If the above matrix inequality has feasible solutions P1, Q and P2, then the state feedback H2 control law is: u=Kx=P2P1 -1 x。 3. The fast mirror hybrid control method based on multivariable extended state observer according to claim 2 is characterized in that: In the x-axis, the fast mirror system is described in state space form: Where x = [x1x2] T , B d =[0 1] T , B d =[0 1] T , C ∞ =[1 0], Combined with state feedback H ∞ The matrix inequality of the controller and the matrix inequality of the state feedback H2 controller are solved by linear matrix inequality: AP1+BP2+(AP1+BP2) T +B d B d T <0 Trace(Q)<γ2 2 ; P1 and P2 are obtained, so the corresponding state feedback control law of the X-axis is: u=Kx=P2P1 -1 x; In the Y-axis, the fast mirror system is described in state space form: Where x = [x1x2] T , B d =[0 1] T , B d =[0 1] T , C ∞ =[1 0], Combined with state feedback H ∞ The matrix inequality of the controller and the matrix inequality of the state feedback H2 controller are solved by linear matrix inequality: AP1+BP2+(AP1+BP2) T +B d B d T <0 Trace(Q)<γ2 2 ; P1 and P2 are obtained, so the corresponding state feedback control law of the Y axis is: u=Kx=P2P1 -1 x。

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