Robust exponential stabilization control method for preventing instability of full-attitude inertial stabilized platform

Abstract

The present invention discloses a robust exponential stabilization control method for preventing instability of a full-attitude inertial stabilization platform, which belongs to the field of inertial measurement systems. Specifically, the method comprises the following steps: for a full-attitude inertial stabilization platform of a four-axis three-frame fiber optic gyroscope to be measured, firstly measuring the state quantity of the platform; then, using the state quantity, deriving a state model of the three channels of the platform body of the inertial stabilization platform; and designing a control law to simplify the state model of the three channels of the platform body of the inertial stabilization platform; then, discretizing the simplified three-channel state model to obtain the state quantity and the disturbance quantity after discretization at time k; finally, inputting the state quantity and the disturbance quantity into the state model of the inertial stabilization platform, simulating the platform to be subject to uncertainty or external interference, and designing a robust controller that satisfies exponential stability, thereby preventing instability of the full-attitude inertial stabilization platform. The present invention improves the dynamic and static performance and anti-interference capability of the stabilization loop, and ultimately effectively improves the anti-instability capability of the entire stabilization loop.

Description

Technical Field

[0001] The present invention belongs to the field of inertial measurement systems, and in particular relates to a robust exponential stabilization control method for preventing instability of a full-attitude inertial stabilization platform. Background Art

[0002] Inertial platform stability control systems are subject to uncertainty and interference due to the influence of multiple physical fields such as force, heat, and magnetism. Traditional correction methods have poor control dynamic performance and anti-interference performance. Therefore, it is extremely important to study the stability control of the inertial platform in this system and improve its anti-interference ability.

[0003] In addition, the wear of components during long-term use of the equipment and the different working environments of the equipment will lead to changes in system parameters, which will have a significant impact on a type of controller designed based on platform parameters when performing high-performance and stable control. Therefore, the control system needs to regularly adjust the parameters of some controllers or even all parameters.

[0004] The long-term adaptability and robustness of inertial stabilization platform control systems are also highly practical issues. Maintaining inertial reference stability, steady-state accuracy, and dynamic response directly impacts the system's accuracy. However, the presence of various multi-physics environments, including mechanical, thermal, and magnetic, as well as external disturbances, can affect the stability and dynamic response of inertial stabilization platforms, potentially leading to overall system instability.

[0005] To this end, the stabilization loop controller needs to possess anti-interference capabilities and robust stability. Research on the anti-instability control and anti-interference capabilities of the inertial platform stabilization loop is extremely important. Traditional corrective control has poor dynamic performance and anti-interference performance. There is an urgent need to propose a robust exponential stabilization control method that can ensure that when the initial state value is non-zero, the stabilization loop control system can still achieve rapid response and be insensitive to parameter changes and disturbances, while taking into account object parameter fluctuations and disturbances. This makes the stabilization loop robust and anti-instability.

[0006] Therefore, the anti-instability control method of the inertial platform stabilization loop is crucial to achieving the long-term adaptability and robust performance of the inertial platform control system. Summary of the Invention

[0007] Considering the uncertainty and interference of multiple physical fields, such as force, heat, and magnetism, in the inertial platform's stabilization loop, a robust exponential stabilization control method is proposed to prevent instability of a full-attitude inertial stabilization platform. This method ensures strong robustness throughout the entire system process when the initial state value is non-zero. By weakening the influence of initial conditions on dynamic performance, robust exponential stabilization can be achieved to prevent instability at any position of the inertial platform, improving the high-dynamic tracking performance of the control system for the four-axis, three-frame, full-attitude inertial stabilization platform.

[0008] The robust exponential stabilization control method for preventing instability of the full-attitude inertial stabilization platform has the following specific steps:

[0009] Step 1: measuring the state quantity of the full-attitude inertial stabilization platform of the four-axis three-frame fiber optic gyroscope to be tested;

[0010] The inertial stabilization platform includes: a platform body and inner and outer frames and a follower frame, which are used to keep the platform body oriented in the inertial space, wherein the platform body is a central circular platform, the platform body is connected to the inner frame of the outer layer through an axis, the inner frame is connected to the outer frame of the outer layer through an axis, the outer frame is connected to the follower frame of the outer layer through an axis, and the follower frame is connected to the bullet (arrow) through an axis;

[0011] When the platform rotates, the fiber optic gyroscope will output a corresponding rotation signal, which, combined with the output results of the disturbance observer that takes into account the parameter uncertainty, nonlinearity and other interferences in the stability loop, is fed back to the robust controller, so that the motors of the platform or the inner and outer frame torque can operate to adjust the control torque and restore the inertial stable platform to stability; the follower frame is sensitive to the inner frame angle. Once the inner frame rotates, it will drive the torque motor of the follower frame axis to work, causing the inner frame to move in the opposite direction until the inner frame angle is 0.

[0012] The state variables include the gyroscope output shaft angle β (x) , β (y) , β (z) and its angular velocity And the platform rotates around the three platform axes x p 、y p and z p The corresponding angular velocity ω xp 、ω yp 、ω zp ,

[0013] The final state equation is:

[0014] Step 2: Using the state variables, derive the state model of the three channels of the inertial stabilized platform;

[0015] The derivation results are as follows:

[0016] The state equation of the platform x channel is:

[0017] The state equation of the y channel of the platform is:

[0018] z-channel equation of state for the stage

[0019] Among them, u x 、u y 、u zΔf is the control input on the x, y, and z channels of the platform, that is, the feedback torque of the motor on the corresponding channel. x , Δf y , Δf z A is the external interference torque on the x, y, and z channels of the platform; x 、A y 、A z are the corresponding channel state coefficient matrices; B x 、B y 、B z are the control input coefficient matrices of the corresponding channels; C x 、C y 、C z is the output coefficient matrix of the corresponding channel.

[0020] Step 3: Design the control law and simplify the state model of the three channels of the inertial stabilized platform;

[0021] The control law is: u(t) = Kx(t); where K∈R 1×n is the feedback gain matrix to be designed.

[0022] Then, the state model of the three channels of the platform is unified into the following form:

[0023]

[0024] Where x(t)=x x (t), w(t)=Δf x ;

[0025] When x(t)=x y (t), w(t)=Δf y ;

[0026] When x(t)=x z (t), w(t)=Δf z ;

[0027] I is the identity matrix.

[0028] Step 4: Discretize the simplified three-channel state model to obtain the state quantity x(k) after the discretization of x(t) at time k and the disturbance quantity w(k) after the discretization of w(t);

[0029] The discretization formula is:

[0030] get:

[0031]

[0032] T is the discretization period;

[0033] Step 5. Input the state quantity and disturbance quantity into the state model of the inertial stabilization platform to simulate the platform being subject to uncertainty or external interference, design a robust controller that meets exponential stability, and realize the anti-instability of the full-attitude inertial stabilization platform.

[0034] Feedback gain matrix The design is as follows:

[0035] If there exists a symmetric positive definite matrix P∈R n×n

[0036]

[0037] in

[0038] The obtained feedback gain matrix is Make the system (1) satisfy the specified H ∞ The mean square exponential stability of the performance index γ improves the steady-state and dynamic tracking accuracy of the four-axis three-frame full-attitude inertial stabilized platform control system.

[0039] The robust controller realizes the anti-instability of the full-attitude inertial stabilization platform. The proof process is as follows:

[0040] First, define the robust control optimization objective function:

[0041] J(K)=x T (k)x(k)-γ 2 w T (k)w(k)

[0042] Then, select the Lyapunov function V(k) and define ΔV(k)=V(k+1)-V(k). Then the mean square exponential stability condition of the system is:

[0043]

[0044] Where V(k)=x T (k)Px(k); intermediate variable ξ(k)=[x T (k) w T (k)] T ,

[0045] Further we get: E{ΔV(k)} <E{-αV(k)-(x T (k)x(k)-γ 2 w T (k)w(k)}

[0046] Then we can get

[0047]

[0048] And k→∞, s is a custom variable, J(s) is the robust control optimization objective function, its independent variable takes the value corresponding to s, k0 is the initial moment at time k, and V(k0) is the value of the Lyapunov function at the initial moment;

[0049] From the above formula, we can see that even if there is a disturbance w, the robust device still satisfies exponential stability:

[0050]

[0051] Available

[0052]

[0053] Compared with existing products, the advantages of the present invention are:

[0054] 1) Compared with the traditional correction control dynamic performance and anti-interference performance, the robust exponential stabilization control method for preventing instability of the full-attitude inertial stabilization platform of the present invention takes into account parameter fluctuations and system disturbances, so that the stabilization loop control system has the advantages of rapid response and insensitivity to parameter changes and disturbances, and the stabilization loop has adaptive anti-instability and disturbance suppression capabilities.

[0055] 2) The robust exponential stabilization control method for preventing instability of the full-attitude inertial stabilization platform of the present invention takes into account the certain uncertainty of the inertial platform stabilization loop system model, and designs a robust control method that satisfies exponential stability when the initial state value is not zero to ensure the strong robustness of the system throughout the entire process.

[0056] 3) The robust exponential stabilization control method for preventing instability of the full-attitude inertial stabilization platform of the present invention takes into account the parameter uncertainty, nonlinearity and interference in the stabilization loop, reduces the steady-state error of the stabilization loop and improves the dynamic performance of the system, weakens the influence of the initial conditions on the dynamic performance, and achieves the steady-state and dynamic tracking accuracy and anti-instability success rate of the four-axis three-frame full-attitude inertial stabilization platform control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Flowchart of the robust exponential stabilization control method for preventing instability of the full-attitude inertial stabilization platform of the present invention;

[0058] Figure 2 This is a structural diagram of the four-axis three-frame full-attitude platform to be tested according to the present invention;

[0059] Figure 3 This is a working principle diagram of the full attitude stabilization circuit of the present invention;

[0060] Figure 4Schematic diagram of the gyroscope output shaft output angle stabilization control according to the present invention;

[0061] Figure 5 Schematic diagram of gyroscope output shaft angular velocity stabilization control according to the present invention;

[0062] Figure 6 Schematic diagram of the angular velocity stabilization control of the table body rotating around the table body axis according to the present invention. DETAILED DESCRIPTION

[0063] The following is a complete and detailed description of the embodiments of the present invention in conjunction with the examples and drawings.

[0064] Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0065] Taking into account the uncertainty and interference of inertial measurement system parameters caused by the complex environment of multiple physical fields such as force, heat and magnetism, the present invention studies the robust exponential stabilization control method for preventing instability of the full-attitude inertial stabilization platform, improves the dynamic and static performance and anti-interference ability of the stabilization loop, and ultimately effectively improves the anti-instability ability of the entire stabilization loop.

[0066] like Figure 1 As shown, the specific steps are:

[0067] Step 1: measuring the state quantity of the full-attitude inertial stabilization platform of the four-axis three-frame fiber optic gyroscope to be tested;

[0068] In practical applications, vibrations from the platform base, errors in system modeling (including parameter uncertainty and nonlinear uncertainties), airflow disturbances, load variations, and equipment cabling can all affect the stability of inertial stabilized platforms. These disturbances not only reduce system accuracy but can also affect its stability. The presence of disturbances also prevents fixed-parameter control methods from maintaining fast response and high system accuracy over time. Therefore, robust controllers with adaptive and disturbance rejection capabilities are needed to prevent instability.

[0069] As a new type of angular velocity sensor, fiber optic gyroscopes (FOGs) have significant advantages over traditional mechanical gyroscopes and are therefore widely used in various fields. In this system, FOGs, as inertial elements that sense the angular velocity of the platform, play a key role in stabilizing the inertial measurement system.

[0070] Measure the state of the stable platform of the inertial measurement system, including the gyroscope output shaft angle β (x) , β (y) , β(z) and its angular velocity And the platform rotates around the three platform axes x p 、y p and z p The corresponding angular velocity ω xp 、ω yp 、ω zp , the final state equation is:

[0071] While single-axis stabilized systems don't require consideration of gyroscope rectification and coupling, they must be considered in full-attitude inertial stabilized platforms. When modeling the system, uncertainties such as unknown external excitations, nonlinearities, and parameter variations can be described as unknown input disturbances. In many cases, the system is subject to disturbances or unmeasurable inputs, making the study of stabilization loop control with unknown input disturbances crucial.

[0072] Aiming at the problem of stable control of fiber optic gyro inertial navigation system platform under disturbance, based on the existing stability loop composition and working principle of inertial navigation system, the design method of robust controller of stability loop is further studied to optimize the static accuracy and high dynamic response characteristics of the anti-instability control loop, so as to achieve a more stable inertial navigation system platform loop with good robust performance.

[0073] Step 2: Using the state variables, derive the state model of the three channels of the inertial stabilized platform;

[0074] In order to facilitate the analysis of the control characteristics of the stabilization loop, the channel models of the three-axis stabilization loop are simplified. Since they are close to zero in the full attitude stabilization loop, the influence of the related terms can be ignored.

[0075] The platform state equation is derived below:

[0076] ① Stage x channel state equation

[0077] The dynamic equation of the four-axis platform frame system is:

[0078]

[0079] in,

[0080] J xx =J xp +J yp1 sin 2 θ zk +J xp1 cos 2 θ zk +J xp2 cos 2 θ zk

[0081] I yy =J yp +J xp1 sin 2 θ zk +J yp1 cos 2 θ zk +J xp2 cos 2 θ zk

[0082] I zz =J zp

[0083] I y'y' =(J yp3 +J yp2 )

[0084] I xy =(J xp1 -J yp1 +J xp2 )sinθ zk cosθ zk

[0085] I xz =(-J xp2 -J zp1 )tanθ yk cosθ zk

[0086] I yz =(J xp1 -J yp1 +J xp2 )sinθ zk cosθ zk

[0087] I y'x =(J zp2 +J xp1 +J xp +J yp3 )cosθ zk sinθ yk tanθ xk -(J yp3 +J yp2 )sinθ zk

[0088] I y'y =(J zp2 +J xp1 +J yp +J yp3 )sinθ zk sinθ yktanθ xk +(J yp3 +J yp2 )cosθ zk

[0089] J y'z =(J zp1 +J zp2 +J yp3 )cosθ yk tanθ xk

[0090] Where θ zk is the relative angle between the inner frame and the platform, θ yk is the relative angle of the outer frame to the inner frame, θ xk is the relative angle of the follower frame to the outer frame, θ yk’ J is the relative angle of the base (rocket body) to the follower frame, xp , J yp , J zp The platform body (including the gyroscope housing) is x p ,y p , z p Moment of inertia of the shaft, J xp1 , J yp1 , J zp1 The platform body (including the gyroscope housing) is x p1 ,y p1 , z p1 Moment of inertia of the shaft, J xp2 , J yp2 , J zp2 The platform body (including the gyroscope housing) is x p2 ,y p2 , z p2 Moment of inertia of the shaft, J xp3 , J yp3 , J zp3 The platform body (including the gyroscope housing) is x p3 ,y p3 , z p3 The moment of inertia of the shaft.

[0091]

[0092]

[0093] Where M Dx2 is the feedback torque of the outer frame shaft torque motor, M Dy1 is the feedback torque of the inner frame shaft torque motor, M Dzp is the feedback torque of the body shaft torque motor, M Dy3 is the feedback torque of the follower frame shaft torque motor, M xp2For the outer frame x p2 External moment on the shaft, M yp1 For the inner frame y p1 External moment on the shaft, M zp For the platform z p External moment on the shaft, M yp3 is the follower frame y p3 External torque on the shaft,

[0094]

[0095]

[0096]

[0097] M 1z =-(J yp -J xp )ω yp ω zp

[0098]

[0099] Where ω xp ,ω yp ,ω zp They are respectively the body around x p 、y p 、z p Absolute angular velocity of the axis; ω xp1 ,ω yp1 ,ω zp1 The carrier, follower frame, outer frame and inner frame are wound around x p1 、y p1 、z p1 Absolute angular velocity of the axis; ω xp2 ,ω yp2 ,ω zp2 The carrier, the follower frame and the outer frame are respectively wound around x p2 、y p2 、z p2 Absolute angular velocity of the axis; ω xp3 ,ω yp3 ,ω zp3 The carrier and the follower frame revolve around x p3 、y p3 、z p3 The absolute angular velocity of the axis.

[0100] M Gx , M Gy , M Gz is the reaction torque of the gyroscope on the platform:

[0101] M Gy' =MGx cosθ zk sinθ yk tanθxk+M Gy sinθ zk sinθ yk tanθ xk

[0102] Let the coefficient matrix Then we can get another form of the four-axis platform frame system dynamic equation:

[0103]

[0104] Available

[0105]

[0106] because

[0107]

[0108]

[0109] Control torque M required for a single axis Dx It can be distributed to each torque motor through the conversion matrix, so the control torque is simplified to:

[0110]

[0111] The state equation of the platform x channel can be derived from the above formula and the x-axis gyroscope dynamic equation:

[0112]

[0113] Right now

[0114]

[0115] The control torque of the z-axis is also considered as the interference torque, so the specific expression of the interference torque is:

[0116]

[0117] C g is the resistance torque coefficient, I y is the moment of inertia of the gyro output axis pointing to the y-axis, H is the moment of inertia of the sensitive axis, θ xk is the positive rotation angle of the follower frame relative to the outer frame, θ yk is the positive rotation angle of the outer frame relative to the inner frame, θ zk It is the positive rotation angle of the inner frame relative to the platform body.

[0118] ② The state equation of the platform y channel

[0119]

[0120] Then get

[0121]

[0122] Control torque M required for a single axis Dy Can be distributed to each torque motor through the conversion matrix, M Dy It can be written as:

[0123]

[0124] The state equation of the y-channel can be derived from the above formula and the y-axis gyroscope dynamic equation as follows:

[0125]

[0126] Right now

[0127]

[0128] The specific expression of the interference torque is:

[0129]

[0130] ③ Stage z-channel state equation

[0131] Similarly, from formula (12) we can get

[0132]

[0133] The state equation of the z channel can be derived from the above formula and the z-axis gyroscope dynamic equation as follows:

[0134]

[0135] Right now

[0136]

[0137] Among them, u x 、u y 、u z Δf is the control input on the x, y, and z channels of the platform, that is, the feedback torque of the motor on the corresponding channel. x , Δf y , Δf z A is the external interference torque on the x, y, and z channels of the platform; x 、A y 、A z are the corresponding channel state coefficient matrices; B x 、B y 、B zare the control input coefficient matrices of the corresponding channels; C x 、C y 、C z is the output coefficient matrix of the corresponding channel.

[0138] Step 3: Design the control law and simplify the state model of the three channels of the inertial stabilized platform;

[0139] The control law is: u(t) = Kx(t); where K∈R 1×n is the feedback gain matrix.

[0140] Then, the state model of the three channels of the platform is unified into the following form:

[0141]

[0142] Where x(t)=x x (t), w(t)=Δf x ;

[0143] When x(t)=x y (t), w(t)=Δf y ;

[0144] When x(t)=x z (t), w(t)=Δf z ;

[0145] I is the identity matrix.

[0146] Step 4: Discretize the simplified three-channel state model to obtain the discretized state quantity x(k) and the discretized disturbance quantity w(k) at time k.

[0147] The discretization formula is:

[0148]

[0149] get:

[0150]

[0151] T is the discretization period;

[0152] Step 5. Input the state quantity and disturbance quantity into the state model of the inertial stabilization platform to simulate the platform being subject to uncertainty or external interference, design a robust controller that meets exponential stability, and realize the anti-instability of the full-attitude inertial stabilization platform.

[0153] According to the inertial measurement system model, a robust controller that satisfies exponential stability is designed. When the initial state value is not zero, the robustness of the entire system is guaranteed, the steady-state error of the stabilization loop is reduced, and the dynamic performance of the system is improved. Considering the parameter uncertainty, nonlinearity and interference in the stabilization loop, a robust control method that satisfies exponential stability is proposed, which weakens the influence of the initial conditions on the dynamic performance, so as to achieve the steady-state and dynamic tracking accuracy and anti-instability success rate of the four-axis three-frame full-attitude inertial stabilization platform control system, and obtain the feedback gain matrix The design method is as follows:

[0154] If there exists a symmetric positive definite matrix P∈R n×n

[0155]

[0156] in

[0157] The obtained feedback gain matrix is Make the system (1) satisfy the specified H ∞ The mean square exponential stability of the performance index γ improves the steady-state and dynamic tracking accuracy of the four-axis three-frame full-attitude inertial stabilized platform control system.

[0158] The robust controller realizes the anti-instability of the full-attitude inertial stabilization platform. The proof process is as follows:

[0159] First, define the robust control optimization objective function:

[0160] J(K)=x T (k)x(k)-γ 2 w T (k)w(k)

[0161] Then, select the Lyapunov function V(k) and define ΔV(k)=V(k+1)-V(k). Then the mean square exponential stability condition of the system is:

[0162]

[0163] Where V(k)=x T (k)Px(k); intermediate variable ξ(k)=[x T (k) w T (k)] T ,

[0164] Further we get: E{ΔV(k)} <E{-αV(k)-(x T (k)x(k)-γ 2 w T (k)w(k)}

[0165] Then we can get

[0166]

[0167] And k→∞, s is a custom variable, J(s) is the robust control optimization objective function, its independent variable takes the value corresponding to s, k0 is the initial moment at time k, and V(k0) is the value of the Lyapunov function at the initial moment;

[0168] From the above formula, we can see that even if there is a disturbance w, the robust device still satisfies exponential stability:

[0169]

[0170] Available

[0171]

[0172] Example:

[0173] The specific design process of the robust exponential stabilization control method for preventing instability of the full-attitude inertial stabilization platform is as follows:

[0174] The first step is to build a schematic diagram of the structure of the four-axis three-frame full-attitude inertial stabilization platform to be tested. Figure 2 As shown, the inertial stabilization platform includes: a platform body and inner and outer frames and a follower frame, which are used to keep the platform body oriented in the inertial space, wherein the platform body is a central circular platform, the platform body is connected to the inner frame of the outer layer through an axis, the inner frame is connected to the outer frame of the outer layer through an axis, the outer frame is connected to the follower frame of the outer layer through an axis, and the follower frame is connected to the bullet (arrow) through an axis; the state quantity of the stable platform of the inertial measurement system is measured;

[0175] The second step is to derive the platform state equations for each channel of the three-axis stabilization loop.

[0176] The working principle of the full attitude stabilization circuit is as follows Figure 3 As shown, the table body and the inner and outer frames of the fiber optic gyroscope inertial stabilization platform are used to keep the table body oriented in the inertial space. When the table body rotates, the fiber optic gyroscope will output a corresponding rotation signal, which is fed back to the robust controller together with the output result of the disturbance observer that takes into account the parameter uncertainty, nonlinearity and other disturbances in the stabilization loop, so that the motor operation of the table body or the inner and outer frames adjusts the control torque to restore the fiber optic gyroscope stabilization platform to stability; the follower frame is sensitive to the inner frame angle. Once the inner frame rotates, it will drive the torque motor of the follower frame axis to work, causing the inner frame to move in the opposite direction until the inner frame angle is 0.

[0177] The third step is to design a robust controller that satisfies exponential stability.

[0178] When the system has model uncertainty or is subject to large external disturbances, a robust controller that satisfies exponential stability is designed to reduce steady-state error and enhance robustness.

[0179] In the fourth step, experiments are conducted to verify the effectiveness of the proposed robust exponential stabilization control technology scheme for anti-instability of the full-attitude inertial stabilized platform.

[0180] For the fiber optic gyroscope experimental device used, the light source is a broad spectrum light source with a wavelength of λ (1550nm) and an output power of I in (2mW), optical path loss is α (3.2dB), gyroscope output axis angle β (x) and its angular velocity and the platform around the platform axis x p The angular velocity of rotation ω xp The acquisition is achieved by a high-speed sampling platform consisting of a reconfigurable Virtex-5 SX95T FPGA, high-speed PCI and PXI-e buses.

[0181] The high-speed sampling platform monitors the nanosecond state variables of the fiber optic gyroscope and inputs the data into the anti-instability robust exponential stability controller to realize the inertial stability platform control. Taking the x-axis of formula (6) as an example, according to the system parameters, it can be known that A x The specific parameters of Δf are The discretization period of the digital system is T = 0.01s. According to Theorem 1, the feedback gain matrix is ​​obtained Figure 4 , Figure 5 and Figure 6 The test results are shown below. The output axis rotation angle β of the x-axis inertial platform gyroscope is (x) and its angular velocity and the platform around the platform axis x p The angular velocity of rotation ω xp After being disturbed, steady-state recovery can be achieved within 0.1s, which meets the expected indicators.

[0182] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A robust exponential stabilization control method for preventing instability of a full-attitude inertial stabilization platform, characterized in that: Specifically include: Step 1: measuring the state quantity of the full-attitude inertial stabilization platform of the four-axis three-frame fiber optic gyroscope to be tested; Step 2: Using the state variables, derive the state model of the three channels x, y and z of the inertial stabilization platform; Step 3: To analyze the control characteristics of the stabilization loop and design the control law, the state model of the three channels of the inertial stabilization platform is simplified. The control law is: u(t) = Kx(t); where K∈R 1×n The feedback gain matrix to be designed is as follows: If there exists a symmetric positive definite matrix P∈R n×n in is the corresponding platform channel state coefficient matrix when x(t) takes different state equations; I is the unit matrix; feedback gain matrix B x is the control input coefficient matrix of the stage x channel; T′ is the discretization period; α is the optical path loss; Then the feedback gain matrix is ​​obtained Make the system meet the specified H ∞ The mean square exponential stability of the performance index γ improves the steady-state and dynamic tracking accuracy of the four-axis three-frame full-attitude inertial stabilization platform control system; Then, the state model of the three channels of the platform is unified into the following form: Step 4: Discretize the simplified three-channel state model to obtain the state quantity x(k) after the discretization of x(t) and the disturbance quantity w(k) after the discretization of w(t) at time k; Step 5. Input the state quantity and disturbance quantity into the state model of the inertial stabilization platform to simulate the platform being subject to uncertainty or external interference, design a robust controller that meets exponential stability, and realize the anti-instability of the full-attitude inertial stabilization platform.

2. The anti-instability robust exponential stabilization control method for an all-attitude inertial stabilized platform according to claim 1, characterized in that: The inertial stabilization platform includes: a platform body and inner and outer frames and a follower frame, which are used to keep the platform body oriented in the inertial space, wherein the platform body is a central circular platform, the platform body is connected to the inner frame of the outer layer through an axis, the inner frame is connected to the outer frame of the outer layer through an axis, the outer frame is connected to the follower frame of the outer layer through an axis, and the follower frame is connected to the projectile / arrow through an axis; When the platform rotates, the fiber optic gyroscope will output a corresponding rotation signal, which, combined with the output results of the disturbance observer that takes into account the parameter uncertainty and nonlinear interference in the stabilization loop, is fed back to the robust controller, so that the motors of the platform or the inner and outer frame torques can operate to adjust the control torque and restore the inertial stabilized platform to stability; the follower frame is sensitive to the inner frame angle. Once the inner frame rotates, it will drive the torque motor of the follower frame axis to work, causing the inner frame to move in the opposite direction until the inner frame angle is 0.

3. The anti-instability robust exponential stabilization control method for an all-attitude inertial stabilized platform according to claim 1, characterized in that: In step 1, the state quantity includes the gyroscope output shaft angle β (x) , β (y) , β (z) and its angular velocity And the platform rotates around the three platform axes x p 、y p and z p The corresponding angular velocity ω xp 、ω yp 、ω zp , The final state equation is:

4. The method for controlling the instability of an inertial stabilized platform according to claim 1, wherein: In the step 2, the state equation of the platform x channel is: The state equation of the y channel of the platform is: z-channel equation of state for the stage Among them, u x 、u y 、u z is the control input on the x, y, and z channels of the platform, that is, the feedback torque of the motor on the corresponding channel; Δf x , Δf y , Δf z A is the external interference torque on the x, y, and z channels of the platform; x 、A y 、A z are the corresponding channel state coefficient matrices; B x 、B y 、B z are the control input coefficient matrices of the corresponding channels; C x 、C y 、C z is the output coefficient matrix of the corresponding channel.

5. The anti-instability robust exponential stabilization control method for an all-attitude inertial stabilized platform according to claim 1, characterized in that: In the step 3, the state model is simplified, when x(t)=x x (t), w(t)=Δf x ; When x(t)=x y (t), w(t)=Δf y ; When x(t) = x z (t), w(t)=Δf z .

6. The method for controlling the instability of a full-attitude inertial stabilized platform with robust exponential stabilization according to claim 1, wherein: In step 4, the discretization formula is: get:

7. The method for controlling the instability of a full-attitude inertial stabilized platform with robust exponential stabilization according to claim 1, wherein: In step 5, the robust controller achieves the anti-instability of the full-attitude inertial stabilization platform. The proof process is as follows: First, define the robust control optimization objective function: J(K)=x T (k)x(k)-γ 2 w T (k)w(k) Then, select the Lyapunov function V(k) and define ΔV(k)=V(k+1)-V(k). Then the mean square exponential stability condition of the system is: Where V(k)=x T (k)Px(k); intermediate variable ξ(k)=[x T (k) w T (k)] T , Further we get: E{ΔV(k)} <E{-αV(k)-(x T (k)x(k)-γ 2 w T (k)w(k)} Then we can get And k→∞, s is a custom variable, J(s) is the robust control optimization objective function, its independent variable takes the value corresponding to s, k0 is the initial moment at time k, and V(k0) is the value of the Lyapunov function at the initial moment; From the above formula, we can see that even if there is a disturbance w, the robust controller still satisfies exponential stability: We can get:

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