CN111025897B - Robust adaptive decoupling control method for aerial remote sensing inertially stabilized platform - Google Patents

Robust adaptive decoupling control method for aerial remote sensing inertially stabilized platform Download PDF

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CN111025897B
CN111025897B CN201910929403.7A CN201910929403A CN111025897B CN 111025897 B CN111025897 B CN 111025897B CN 201910929403 A CN201910929403 A CN 201910929403A CN 111025897 B CN111025897 B CN 111025897B
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周向阳
李娅婷
王维乾
高�浩
何俊峰
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Abstract

The invention discloses a robust self-adaptive decoupling control method for an aerial remote sensing inertially stabilized platform, which comprises the steps of establishing a frame kinetic equation based on the inertially stabilized platform; nonlinear decoupling and robustness improvement are carried out on the stable platform through inverse system feedback linearization; and the model reference adaptive control is used for carrying out suppression method research on residual coupling left by inverse system feedback linearization, completing the decoupling control process and improving the overall control precision of the system. According to the invention, the nonlinear coupling of the stable platform is decoupled through inverse system feedback linearization, so that the defects of a common linear decoupling control method are overcome, and the stable precision of the platform is improved; the robustness of the inertially stabilized platform system can be effectively improved, and the method is suitable for the aerial remote sensing inertially stabilized platform with the coupling moment between the base and the frame.

Description

Robust adaptive decoupling control method for aerial remote sensing inertially stabilized platform
Technical Field
The invention relates to a robust self-adaptive decoupling control method for an aerial remote sensing inertially stabilized platform, which can be used for decoupling control of dynamic coupling between various medium-high precision aerial remote sensing inertially stabilized platform carriers and frames, and is particularly suitable for an inertially stabilized platform with large range and high dynamic.
Background
The aerial remote sensing system has very unique advantages in a large number of aspects such as economic cost, repeatable observability, instantaneity and the like. Therefore, in many developed countries in the west, about 65% or more of the basic urban surveying and planning systems are capable of fully guaranteeing the high-resolution spatial data. And the high-precision control method of the inertially stabilized platform is the key of the imaging stability of the light and small aerial remote sensing system. Compared with the image displayed after the aerial remote sensing is isolated by the stabilizing platform and before the isolation, the aerial remote sensing aerial imaging system has the advantages that the definition is improved, and the distorted image is real and ideal, so that the stabilizing platform is indispensable in the disturbance of the aerial remote sensing aerial imaging system, and the imaging quality of light and small aerial remote sensing is greatly improved due to the existence of the stabilizing platform, the working efficiency of the whole system is indirectly improved, and the cost of image processing is saved. The stability precision is one of the main technical indexes of the inertially stabilized platform, and reflects the inhibition capability of the stabilized platform on the disturbance moment. In summary, the development of aerial remote sensing systems is not independent of the research and development of inertially stable platforms with high-precision control methods.
The inertially stabilized platform mainly comprises three frames, namely a pitching frame, a rolling frame and an orientation frame from inside to outside, and finally achieves vertical ground stabilization and track stabilization of a camera visual axis arranged on the innermost frame (the pitching frame). For the coupling moment, when the platform frame is in the process of rapid rotation, the dynamic coupling between the base and the frame is serious, and at the moment, if an effective decoupling control method is not adopted, the normal control precision of the stable platform is difficult to ensure. The commonly adopted PID control method does not consider the coupling factor to cause the precision to be reduced. Therefore, when a stable platform control system is designed, an effective decoupling control method must be adopted for the problem of dynamic coupling among three frames, so that the control precision of the stable platform is improved.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the defect that the conventional feedback control has insufficient inhibiting capacity on coupling torque between a carrier and a frame is overcome, and the robust adaptive decoupling control method for the aerial remote sensing inertial stabilization platform is provided and used for improving the system stabilization precision.
The technical solution of the invention is as follows: a robust self-adaptive decoupling control method for an aerial remote sensing inertially stabilized platform comprises the following steps:
(1) establishing a frame kinetic equation based on an inertia stable platform;
(2) nonlinear decoupling and robustness improvement are carried out on the stable platform through inverse system feedback linearization;
(3) and the model reference adaptive control is used for carrying out suppression method research on residual coupling left by inverse system feedback linearization, completing the decoupling control process and improving the overall control precision of the system.
The establishment of the inertial stabilization platform frame kinetic equation in the step (1) is divided into the following 3 parts:
the kinematic equation of the pitch frame about the pitch axis is:
Figure BDA0002217432090000021
the kinetic equation of the roll frame assembly around the roll axis is simplified as:
Figure BDA0002217432090000022
the dynamic equation of the azimuth frame assembly around the azimuth axis is simplified as follows:
Figure BDA0002217432090000023
defining: respectively winding the pitch frames around xf,yf,zfThe moment of inertia of three axes is defined as Jfx,Jfy,Jfz(ii) a The roll frame is wound around xr,yr,zrThe moment of inertia of three axes is defined as Jrx,Jry,Jrz(ii) a Azimuth frame is around xa,ya,zaThe moment of inertia of three axes is defined as Jax,Jay,Jaz；
Figure BDA0002217432090000031
The projection of the angular velocity of the orientation frame relative to the inertial space on the x, y and z axes is respectively recorded as
Figure BDA0002217432090000032
Figure BDA0002217432090000033
The projection of the angular velocity of the roll frame relative to the inertia space on the x, y and z axes is respectively marked as
Figure BDA0002217432090000034
θrFor the corners of the roll frame relative to the azimuth frame,
Figure BDA0002217432090000035
the angular velocity of the pitching frame relative to the rolling frame is determined;
Figure BDA0002217432090000036
angular acceleration of the pitch frame relative to the roll frame; mxFor combined moments of forces, M, experienced by the pitch frame assembly along the x-axisyCombined moment, M, to which the roller frame assembly is subjected along the y-axiszIs the resultant moment experienced by the azimuth frame along the z-axis.
In the step (2), a nonlinear decoupling control process is carried out on the stable platform through inverse system feedback linearization, and the process is divided into the following 3 steps:
step 1) firstly establishing a pseudo-linear system equation of an inertially stabilized platform as shown in the formula IV:
Figure BDA0002217432090000037
wherein F represents the complex moment factor, MdRepresenting the comprehensive moment, meanwhile, B represents a coefficient matrix, f (x) is a correlation function, C is the coefficient matrix, u is an input vector of the system, y is an output vector of the system, and x is a state vector of the system.
Step 2) then the inversion system: neglecting the unknown interference outside, and obtaining the inverse system as formula (v).
Figure BDA0002217432090000038
Wherein D is y obtained by second-order derivation
Figure BDA0002217432090000039
Jacobi matrix for u.
Step 3) finally according to the original pseudo-linear system andthe inverse system is connected in series to construct a nonlinear system with feedback linearization for decoupling, and the input of the nonlinear system is
Figure BDA00022174320900000310
Output of
Figure BDA00022174320900000311
Wherein
Figure BDA00022174320900000312
Is the second derivative of y and,
Figure BDA00022174320900000313
is the first derivative of y, so
Figure BDA0002217432090000041
Can be composed of
Figure BDA0002217432090000042
Is integrated at a time.
The control process of suppressing the residual coupling left by the feedback linearization of the inverse system through model reference adaptive control in the step (3) is divided into the following 2 steps:
the goal of stable platform system control is to ultimately ensure
Figure BDA0002217432090000043
When the difference between the actual output value of the stabilized platform and the model predicted output value is 0, y isp(t) is the actual output signal of the stabilization stage, ym(t) is the output signal of the reference model of the stabilized platform.
Step 1) firstly introducing an adaptive error signal delta (t):
δ(t)＝Ap(p)yp(t)-Bm(p)r(t) ⑥
when delta (t) ═ Am(p)e(t)，e(t)＝ym(t)-yp(t), taking the control law function as:
Figure BDA0002217432090000044
in the formula: k (t), Ki(t) (i ═ 0, 1.., n) is a tunable parameter.
Figure BDA0002217432090000045
Step 2) introducing a classical PID controller control law function:
Figure BDA0002217432090000046
and (c) obtaining a decoupling controller of the robust reference adaptive control based on the PID according to a formula (c):
Figure BDA0002217432090000047
in this formula:
Figure BDA0002217432090000048
all the parameters are initial values of parameters which can be adjusted, and the values of the parameters can be obtained by parameter setting or trial and error; wherein the coefficient gamma is greater than 0 and lambda1＞0，λ1＞0，λ3Is greater than 0. The stable platform system can realize the stability by the self-adaptive control of model reference through the formula (R), and achieve the corresponding precision and dynamic performance.
Compared with the prior art, the invention has the advantages that:
(1) according to the invention, the nonlinear coupling of the stable platform is decoupled through inverse system feedback linearization, so that the defects of a common linear decoupling control method are overcome, and the stable precision of the platform is improved;
(2) the decoupling principle of the invention is clear, the decoupling algorithm is simple, and the invention is easy to be realized in DSP programming;
(3) the invention utilizes the measured value of the inertial sensor as the real-time feedback information, and is more intuitive and easy to realize compared with a control method of a software design state observer.
Drawings
FIG. 1 is a flow chart of a decoupling control method of the present invention;
FIG. 2 is a working schematic diagram of an aerial remote sensing triaxial inertially stabilized platform according to the present invention;
FIG. 3 is a schematic diagram of a decoupling control method of the present invention;
FIG. 4 is a graph of the result of angular position feedback simulation after decoupling control of the stable platform system and the inverse system in the present invention.
In the figure: an azimuth frame rate gyro 1, a roll frame rate gyro 2, a roll frame torque motor 3, an azimuth frame torque motor 4, a pitch frame torque motor 5, a pitch frame rate gyro 6, an accelerometer y 7, an accelerometer x 8, a pitch frame 9, a roll frame 10 and an azimuth frame 11.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1, according to the flowchart of the decoupling control method of fig. 1, the specific implementation method of the present invention is as follows.
As shown in fig. 2, the mechanical structure of the aerial remote sensing inertially stabilized platform includes an azimuth frame rate gyro 1, a roll frame rate gyro 2, a roll frame torque motor 3, an azimuth frame torque motor 4, a pitch frame torque motor 5, a pitch frame rate gyro 6, an accelerometer y 7, an accelerometer x 8, a pitch frame 9, a roll frame 10 and an azimuth frame 11. The aerial remote sensing inertial stabilization platform is used for three-axis imaging stabilization, and three-axis frames of the aerial remote sensing inertial stabilization platform are a pitching frame 9, a rolling frame 10 and an azimuth frame 11 respectively. The pitching frame 9 is fixed with a pitching frame rate gyroscope 6 and a pitching frame torque motor 5, and the pitching frame 9 controls the pitching frame torque motor 5 by measuring the pitching frame motion angle and the angular velocity through the pitching frame rate gyroscope 6, so as to maintain the frame stability. The roll frame 10 is fixed with the roll frame rate gyroscope 2 and the roll frame torque motor 3, and the roll frame 10 controls the roll frame torque motor 3 by measuring the motion angle and the angular velocity of the roll frame through the roll frame rate gyroscope 2, so as to maintain the stability of the frame. The azimuth frame 11 is fixed with the azimuth frame rate gyroscope 1 and the azimuth frame torque motor 4, and the azimuth frame 11 measures the azimuth frame motion angle and the angular velocity through the azimuth frame rate gyroscope 1 to control the azimuth frame torque motor 4 and maintain the frame stability.
A robust self-adaptive decoupling control method for an aerial remote sensing inertially stabilized platform is characterized in that based on an established three-frame kinetic equation, a stabilized platform system is decoupled and robustness is improved through an inverse system, then residual coupling left by the inverse system is restrained and researched through model reference self-adaptive control, and the principle of the decoupling control method shown in figure 3 is known, wherein a model reference self-adaptive controller is positioned in a position ring and mainly comprises a position ring front-end controller, a position ring feedback controller and a position ring reference model, wherein the form of the reference model is required to be the same as the structure of a function model of the stabilized platform system, and because the control target of the stabilized platform is to keep the angle position and a set value consistent, the position angle error e is required to be tracked by the system3The angular error is corrected by the action of the control system until it is 0. The schematic diagram mainly comprises an outer ring and an inner ring, wherein the inner ring is a general feedback control system and mainly comprises an original system and an adjustable gain and position ring feedback controller, parameters of a position ring front-end controller are adjusted by the outer ring, and when a controlled system is influenced by interference, an error e is caused3When the difference is not zero, it is desirable that the parameter value of the corresponding adaptive regulator is corrected by the difference between the outputs of the stable platform system and the reference model, so that the difference between the outputs of the reference model and the stable platform system is zero, and finally high-precision control of the stable platform is realized. The method specifically comprises the following steps:
firstly, establishing an inertial stabilization platform frame kinetic equation, which is divided into the following 3 parts:
1) the kinematic equation of the pitch frame about the pitch axis is: mz Mz
Figure BDA0002217432090000061
2) The kinetic equation of the roll frame assembly around the roll axis is simplified as:
Figure BDA0002217432090000071
3) the dynamic equation of the azimuth frame assembly around the azimuth axis is simplified as follows:
Figure BDA0002217432090000072
defining: respectively winding the pitch frames around xf,yf,zfThe moment of inertia of three axes is defined as Jfx,Jfy,Jfz(ii) a The roll frame is wound around xr,yr,zrThe moment of inertia of three axes is defined as Jrx,Jry,Jrz(ii) a Azimuth frame is around xa,ya,zaThe moment of inertia of three axes is defined as Jax,Jay,Jaz；
Figure BDA0002217432090000073
The projection of the angular velocity of the orientation frame relative to the inertial space on the x, y and z axes is respectively recorded as
Figure BDA0002217432090000074
Figure BDA0002217432090000075
The projection of the angular velocity of the roll frame relative to the inertia space on the x, y and z axes is respectively marked as
Figure BDA0002217432090000076
θrFor the corners of the roll frame relative to the azimuth frame,
Figure BDA0002217432090000077
the angular velocity of the pitching frame relative to the rolling frame is determined;
Figure BDA0002217432090000078
angular acceleration of the pitch frame relative to the roll frame; mxFor combined moments of forces, M, experienced by the pitch frame assembly along the x-axisyCombined moment, M, to which the roller frame assembly is subjected along the y-axiszIs the resultant moment experienced by the azimuth frame along the z-axis.
Secondly, nonlinear decoupling is carried out on the stable platform through inverse system feedback linearization, firstly, a nonlinear system decoupling controller with feedback linearization is designed, and the method comprises the following 3 steps:
step 1) firstly establishing a pseudo-linear system equation of an inertially stabilized platform as shown in the formula IV:
Figure BDA0002217432090000079
wherein F represents the complex moment factor, MdRepresenting the comprehensive moment, meanwhile, B represents a coefficient matrix, f (x) is a correlation function, C is the coefficient matrix, u is an input vector of the system, y is an output vector of the system, and x is a state vector of the system.
Step 2) then the inversion system: neglecting the unknown interference outside, and obtaining the inverse system as formula (v).
Figure BDA0002217432090000081
Wherein D is y obtained by second-order derivation
Figure BDA0002217432090000082
Jacobi matrix for u.
Step 3) finally constructing a nonlinear system with feedback linearization according to the original pseudo linear system and inverse system in series for decoupling, wherein the input of the nonlinear system is
Figure BDA0002217432090000083
Output of
Figure BDA0002217432090000084
Wherein
Figure BDA0002217432090000085
Is the second derivative of y and,
Figure BDA0002217432090000086
is the first derivative of y, so
Figure BDA0002217432090000087
Can be composed of
Figure BDA0002217432090000088
Is integrated at a time.
Thirdly, performing complete decoupling control on the inertially stabilized platform by inhibiting residual coupling left by feedback linearization of an inverse system through model reference adaptive control, and finally designing a robust reference adaptive decoupling controller of the inertially stabilized platform, wherein the decoupling controller comprises the following 2 steps:
the goal of stable platform system control is to ultimately ensure
Figure BDA0002217432090000089
When the difference between the actual output value of the stabilized platform and the model predicted output value is 0, y isp(t) is the actual output signal of the stabilization stage, ym(t) is the output signal of the reference model of the stabilized platform.
Step 1) firstly introducing an adaptive error signal delta (t):
δ(t)＝Ap(p)yp(t)-Bm(p)r(t) ⑥
when delta (t) ═ Am(p)e(t)，e(t)＝ym(t)-yp(t), taking the control law function as:
Figure BDA00022174320900000810
in the formula: k (t), Ki(t) (i ═ 0, 1.., n) is a tunable parameter.
Figure BDA00022174320900000811
Step 2) introducing a classical PID controller control law function:
Figure BDA00022174320900000812
and (c) obtaining a decoupling controller of the robust reference adaptive control based on the PID according to a formula (c):
Figure BDA0002217432090000091
in this formula:
Figure BDA0002217432090000092
all the parameters are initial values of parameters which can be adjusted, and the values of the parameters can be obtained by parameter setting or trial and error; wherein the coefficient gamma is greater than 0 and lambda1＞0，λ1＞0，λ3Is greater than 0. The stable platform system can realize the stability by the self-adaptive control of model reference through the formula (R), and achieve the corresponding precision and dynamic performance.
Fourthly, optimizing result of robust reference self-adaptive decoupling controller of inertially stabilized platform
In order to verify the effect of the robust adaptive decoupling control method provided by the invention applied to an inertially stabilized platform, a simulation model of an inertially stabilized platform system is built by using a Matlab/Simulink simulation tool according to a decoupling control method schematic diagram of FIG. 3, wherein simulation parameters and conditions are as follows:
1. the carrier having an amplitude of relative inertia space of
Figure BDA0002217432090000093
The angular motion with the frequency of 1Hz, the three-frame moment of inertia parameters are as follows: j. the design is a squareax＝1.56kg·m2、Jay＝1.56kg·m2、Jaz＝2.38kg·m2；Jfx＝0.24kg·m2、Jfy＝0.24kg·m2、Jfz＝0.46kg·m2；Jrx＝0.65kg·m2、Jry＝0.413kg·m2、Jrz＝1.025kg·m2. Where a represents the azimuth frame, f represents the pitch frame, and r represents the roll frame.
2. The given angle tracking signal in the simulation experiment is a step signal with the amplitude of 1 degree, an unbalanced moment model which is programmed into a module by s-function is added into a stable platform system to serve as the interference amount of the step signal, then simulation is carried out, the simulation time is set to be 30s, the unbalanced moment interference model is added into a model of a stable platform control system, decoupling and simulation are carried out on an inertial stable platform by using a robust reference self-adaptive decoupling control algorithm, and angular position feedback comparison is carried out by using other methods, so that the good decoupling effect of decoupling control on a stable platform frame system is verified.
According to the angular position feedback diagram (shown in fig. 4) under the condition of step response and without decoupling, the overshoot of the azimuth frame is 0.271 degrees when the decoupling is not performed, the adjusting time is 35s, the overshoot of the inverse system decoupling is 0.184 degrees, compared with the overshoot of the azimuth frame when the decoupling is not performed, the overshoot is reduced by 32.1 percent, the adjusting time is 5s, and the overshoot is reduced by 85.7 percent compared with the overshoot of the azimuth frame when the decoupling is not performed.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (1)

1. A robust self-adaptive decoupling control method for an aerial remote sensing inertially stabilized platform is characterized by comprising the following steps:
(1) establishing a frame kinetic equation based on an inertia stable platform;
the establishment of the inertial stabilization platform frame kinetic equation in the step (1) is divided into the following 3 parts:
the kinematic equation of the pitch frame about the pitch axis is:
Figure FDA0002880226680000011
the kinetic equation of the roll frame assembly around the roll axis is simplified as:
Figure FDA0002880226680000012
the dynamic equation of the azimuth frame assembly around the azimuth axis is simplified as follows:
Figure FDA0002880226680000013
defining: respectively winding the pitch frames around xf,yf,zfThe moment of inertia of three axes is defined as Jfx,Jfy,Jfz(ii) a The roll frame is wound around xr,yr,zrThe moment of inertia of three axes is defined as Jrx,Jry,Jrz(ii) a Azimuth frame is around xa,ya,zaThe moment of inertia of three axes is defined as Jax,Jay,Jaz；
Figure FDA0002880226680000019
The projection of the angular velocity of the orientation frame relative to the inertial space on the x, y and z axes is respectively recorded as
Figure FDA0002880226680000014
Figure FDA0002880226680000015
The projection of the angular velocity of the roll frame relative to the inertia space on the x, y and z axes is respectively marked as
Figure FDA0002880226680000016
θrFor the corners of the roll frame relative to the azimuth frame,
Figure FDA0002880226680000017
the angular velocity of the pitching frame relative to the rolling frame is determined;
Figure FDA0002880226680000018
angular acceleration of the pitch frame relative to the roll frame; mxFor combined moments of forces, M, experienced by the pitch frame assembly along the x-axisyCombined moment, M, to which the roller frame assembly is subjected along the y-axiszThe comprehensive moment applied to the azimuth frame along the z-axis;
(2) nonlinear decoupling and robustness improvement are carried out on the stable platform through inverse system feedback linearization;
in the step (2), a nonlinear decoupling control process is carried out on the stable platform through inverse system feedback linearization, and the process is divided into the following 3 steps:
step 1) firstly establishing a pseudo-linear system equation of an inertially stabilized platform as shown in the formula IV:
Figure FDA0002880226680000021
wherein F represents the complex moment factor, MdRepresenting the comprehensive moment, meanwhile, B represents a coefficient matrix, f (x) is a correlation function, C is the coefficient matrix, u is an input vector of the system, y is an output vector of the system, and x is a state vector of the system;
step 2) then the inversion system: neglecting the external unknown interference to obtain the inverse system as shown in formula (v):
Figure FDA0002880226680000022
wherein D is y obtained by second-order derivation
Figure FDA0002880226680000023
Jacobi matrix for u;
step 3) finally constructing a nonlinear system with feedback linearization according to the series connection of the original pseudo linear system and the inverse system for decoupling, wherein the input of the nonlinear system is
Figure FDA0002880226680000024
Output of
Figure FDA0002880226680000025
Wherein
Figure FDA0002880226680000026
Is the second derivative of y and,
Figure FDA0002880226680000027
is the first derivative of y, so
Figure FDA0002880226680000028
Can be composed of
Figure FDA0002880226680000029
The first integration is carried out;
(3) residual coupling left by inverse system feedback linearization is researched by a suppression method through model reference adaptive control, a decoupling control process is completed, and the overall control precision of the system is improved;
the control process of suppressing the residual coupling left by the feedback linearization of the inverse system through model reference adaptive control in the step (3) is divided into the following 2 steps:
step 1) firstly introducing an adaptive error signal delta (t):
δ(t)＝Ap(p)yp(t)-Bm(p)r(t) ⑥
in the formula yp(t) is the actual output signal of the stabilization stage, ym(t) is the output signal of the reference model of the stabilized platform;
when delta (t) ═ Am(p)e(t)，e(t)＝ym(t)-yp(t), taking the control law function as:
Figure FDA0002880226680000031
in which K (t), Ki(t) (i ═ 0, 1.., n) is a tunable parameter;
Figure FDA0002880226680000032
step 2) introducing a classical PID controller control law function:
Figure FDA0002880226680000033
and (c) obtaining a decoupling controller of the robust reference adaptive control based on the PID according to a formula (c):
Figure FDA0002880226680000034
in this formula:
Figure FDA0002880226680000035
all the parameters are initial values of parameters which can be adjusted, and the values of the parameters can be obtained by parameter setting or trial and error; wherein the coefficient gamma is greater than 0 and lambda1＞0，λ2＞0，λ3Is greater than 0; the stable platform system can realize the stability by the self-adaptive control of model reference through the formula (R), and achieve the corresponding precision and dynamic performance.
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