CN113671835A - Inertial stabilization platform sliding mode control method based on fuzzy switching gain adjustment - Google Patents
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Abstract
The invention discloses an inertia stable platform sliding mode control method based on fuzzy switching gain adjustment, which takes an inertia stable platform as a research object, aims at the problem of improving the control precision of the inertia stable platform under a complex multi-source disturbance environment, takes all disturbances of the inertia stable platform as a whole, designs a global rapid terminal sliding mode controller of the inertia stable platform based on sliding mode equivalent control, and realizes that the system state is rapidly and accurately converged to a balance state and does not leave a sliding mode surface; aiming at the problem that robustness and buffeting of a global fast terminal sliding mode controller cannot be simultaneously taken into consideration, fuzzy switching gain adjustment is fused on the basis of sliding mode control, fuzzy rules are designed, switching gain in sliding mode control of an inertially stabilized platform is effectively estimated according to sliding mode arrival conditions, multisource interference influence is weakened or eliminated by utilizing fuzzy switching gain, the buffeting phenomenon is reduced, a good multisource disturbance suppression effect is obtained, and the stability precision of the inertially stabilized platform is obviously improved.
Description
Technical Field
The invention relates to a fuzzy switching gain adjustment-based sliding mode control method for an inertially stabilized platform, which can enhance the suppression capability of the inertially stabilized platform on multi-source disturbance, reduce the influence of buffeting, improve the stabilization precision of the inertially stabilized platform and is suitable for the disturbance suppression of large, medium and small inertially stabilized platform systems.
Background
The airborne aerial remote sensing system has the advantages of high resolution, flexibility, good real-time performance and the like, and plays an increasingly important role in daily life of people. Under the influence of multi-source disturbances such as external environment and internal disturbance of the aircraft, non-ideal motion of the platform of the aircraft on a multi-dimensional space is inevitable, and the non-ideal motion is highlighted in complex forms such as a nonlinear friction disturbance moment, an unbalanced disturbance moment, cross coupling and the like, so that the visual axis of the camera shakes seriously, the camera cannot well perpendicular to the ground, and high-resolution imaging is seriously influenced. At the moment, a high-precision inertially stabilized platform is needed to isolate multi-source disturbance, so that the visual axis of the camera is kept stable.
In order to realize high-precision control of the inertially stabilized platform, all disturbances need to be regarded as a whole, and the total disturbance is restrained, so that the control precision of the inertially stabilized platform is improved. The common sliding mode control can be quickly converged to a control target, the influence of the total disturbance on the stable precision of the inertially stabilized platform is solved, and the convergence to zero in a limited time cannot be realized. Therefore, a global fast terminal sliding mode controller is designed based on sliding mode equivalent control and combined with linear and exponential terminal sliding mode surfaces, and the system state is rapidly and accurately converged to a balance state. In order to enable an inertially stabilized platform system to maintain ideal control performance under a complex environment condition and solve the problem of instability caused by buffeting, fuzzy switching gain adjustment is fused on the basis of global fast terminal sliding mode control, a fuzzy controller is introduced, a global fast terminal sliding mode control method based on fuzzy switching gain adjustment is designed, control signals are softened, the buffeting phenomenon is weakened, and the system stability precision is improved.
In conclusion, with the development and popularization of the aerial remote sensing technology, a wide prospect is provided for high-precision imaging control of the aerial remote sensing system, and research and practice research in the aspect is relatively lacked. The invention starts from the general point, and the research content relates to an inertia stable platform sliding mode control method based on fuzzy switching gain adjustment, and provides guidance and reference for the design of a disturbance suppression method similar to that of an inertia stable platform.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the method is used for improving the suppression capability of the inertially stabilized platform on the multisource disturbance, can reduce the buffeting problem, and is suitable for multisource disturbance suppression of large, medium and small inertially stabilized platform systems.
The technical solution of the invention is as follows: an inertia stabilized platform sliding mode control method based on fuzzy switching gain adjustment comprises the following steps:
step 1: according to the mapping relation of the voltage, current, torque, rotating speed and position change parameters of the inertially stabilized platform, a three-loop control system model of the inertially stabilized platform is established, wherein the three-loop control system model comprises an inner loop which is a current loop and a speed loop, and an outer loop which is a position loop; the first loop of the three-loop control is the current loop of the innermost loop, and the response speed is fastest; the second loop is a rate loop, and the output of the controller in the second loop is the setting of the current loop; the third ring is a position ring, which uses the POS or IMU to acquire the angular position of the frame, and the precision of the ring is the highest;
step 2: based on the three-loop control system in the step 1, PID control is adopted for an inner loop current loop and a speed loop, robustness sliding mode control is adopted for an outer loop position loop, multi-source disturbance is regarded as a whole to be used as sum disturbance, and a global fast terminal sliding mode controller is designed to restrain the sum disturbance; during aerial photography work of the inertial stabilization platform, multi-source disturbance from the inside and the outside of the inertial stabilization platform can influence the stabilization precision of the inertial stabilization platform; the internal disturbance of the inertially stabilized platform mainly comprises unbalanced moment disturbance and friction disturbance; external disturbance of the inertially stabilized platform mainly comprises wind resistance moment disturbance and base angular motion disturbance; taking the main multi-source disturbance inside and outside the inertially stabilized platform as a whole as total disturbance;
and step 3: aiming at the problem that robustness and buffeting of the inertial stabilization platform control system based on the global fast terminal sliding mode control in the step 2 cannot be considered simultaneously, a fuzzy controller is introduced to carry out fuzzy switching gain adjustment on the basis of the global fast terminal sliding mode controller, multi-source disturbance influence is weakened or eliminated by utilizing the fuzzy switching gain, an output signal of the global fast terminal sliding mode controller based on the fuzzy switching gain adjustment is softened, the buffeting phenomenon is reduced, and the stabilization precision of the inertial stabilization platform is improved.
In the step 1, the established three-loop control system model is as follows:
wherein x is1Representing the output angular position thetaout，
For angular velocity, u (t) is input to the three-loop control system, d (t) is input to the three-loop control system, and the angular position error e is defined as thetain-θout，θinIs the reference angular position.
In the step 2, the designed global fast terminal sliding mode controller is as follows:
usw＝G(t)sgn(s)
wherein u is ueq+uswIs an equivalent control law of a sliding mode,
is an equivalent control term, d (t) is the sum perturbation; u. ofswIs a nonlinear control term, g (t) is a switching gain, g (t) max | d (t) | η + η, a control gain parameter η > 0,s is a slip form surface, denoted by
Alpha, beta is constant of slip form surface, p1，p2Are all positive odd numbers, satisfy p1＞p2。
The control law u of the global fast terminal sliding mode controller takes the total disturbance and the parameter perturbation of the inertial stabilization platform into consideration, and the accessibility condition of the sliding mode is met;
design Lyapunov function V (t) 0.5s2And (t) showing that the three-loop control system with the outer loop controlled by the global fast terminal sliding mode has stability, and realizing the suppression of the total disturbance.
In step 3, the fuzzy set design of the sliding mode controller based on fuzzy switching gain adjustment is as follows:
if it is not
The switching gain g (t) should be increased;
if it is not
The switching gain g (t) should be reduced;
according to
And the switching gain variation Δ g (t), where t represents time, and the input and output fuzzy sets of the fuzzy controller are defined as follows:
ΔG(t)＝{NB NM NS ZO PS PM PB}
wherein NB is negative and large, NM is negative and medium, NS is negative and small, ZO is zero, PB is positive and large, PM is positive and small, an input and output membership function of the fuzzy controller is defined according to control requirements, the variation range of the switching gain G (t) is between 0 and 1, and the following 7 fuzzy rules are designed:
when in use
G (t) ═ PB; when in use
If so, then g (t) ═ PM;
when in use
When, g (t) ═ PS; when in use
When so, g (t) is ZO;
when in use
Then g (t) ═ NS; when in use
When, g (t) ═ NM;
when in use
Then g (t) ═ NB;
(N is negative, P is positive, NB NM NS ZO PS PM PB are common expressions of fuzzy sets)
The fuzzy control is used for realizing the change of the switching gain G (t), and the upper bound of G (t) is estimated by an integral method, which is expressed as:
wherein K is a proportionality coefficient and is greater than 0, and is determined empirically. By using
Replacing G (t), and controlling the sliding mode control system u of the inertially stabilized platform based on fuzzy switching gain adjustment to be:
the position ring adopts a composite control scheme combining a global fast terminal sliding mode controller and a fuzzy controller, fuzzy switching gain adjustment is fused on the basis of global fast terminal sliding mode control, fuzzy rules are designed, switching gain is effectively estimated according to sliding mode arrival conditions, and output signals of the global fast terminal sliding mode controller based on the fuzzy switching gain adjustment are softened, so that the global fast terminal sliding mode control system based on the fuzzy switching gain adjustment has robustness and meanwhile the buffeting influence is weakened.
Compared with the prior art, the invention has the advantages that:
(1) the invention is based on the principle of three-ring control, voltage maps current change, current maps torque magnitude, torque magnitude maps change of rotating speed, and the rotating speed maps change of position at the same time.
(2) The invention adopts the principle of sliding mode control, considers all disturbances of the inertially stabilized platform as a whole and designs the global fast terminal sliding mode controller of the inertially stabilized platform. Compared with the state tracking error of the common sliding mode control, the state tracking error can only be asymptotically converged to zero, the global fast terminal sliding mode control comprehensively considers the combination of linearity and an index terminal sliding mode surface, the system state is fast and accurately converged to a balanced state, and the problem that the tracking error cannot be converged to zero within a limited time is solved.
(3) According to the invention, by adopting the inertial stabilization platform sliding mode control method based on fuzzy switching gain adjustment, aiming at the problem that the robustness and the buffeting problem of the control system cannot be simultaneously considered, fuzzy switching gain adjustment is fused on the basis of the sliding mode control platform, and disturbance items are eliminated by using switching gain, so that the buffeting phenomenon is reduced, and in addition, the capability of the system for dealing with uncertain disturbance and the robustness of the system can be enhanced by the sliding mode control based on the fuzzy switching gain adjustment.
Drawings
FIG. 1 is a flow chart of a sliding mode control method based on fuzzy switching gain adjustment in the present invention;
FIG. 2 is a schematic diagram of the operation of the inertially stabilized platform of the present invention;
fig. 3 is a structure diagram of a sliding mode control system based on fuzzy switching gain adjustment in the present invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 2, the mechanical structure of the inertially stabilized platform includes 1 accelerometer y, 2 pitch frame rate gyro, 3 pitch frame gear pair, 4 pitch frame resolver, 5 pitch frame torque motor, 6 azimuth frame torque motor, 7 azimuth frame resolver, 8 roll frame gear pair, 9 roll frame torque motor, 10 roll frame resolver, 11 azimuth frame rate gyro, 12 roll frame rate gyro, and 13 accelerometer x. The inertia stable platform compensates disturbance moment by driving the frame to rotate through motors in three directions, coded discs in three directions are used for measuring relative rotation angles of the frame to realize frame soft locking, angular rate gyroscopes in three directions are respectively used for sensing angular rates of the frame relative to an inertia space, and a two-axis accelerometer is used for sensing local acceleration information of two horizontal frames of pitching and rolling and providing position information for a position ring.
As shown in fig. 1 and 2, according to the sliding mode control method of the inertially stabilized platform based on fuzzy switching gain adjustment of the present invention, firstly, the kinematics relationship of each frame of the inertially stabilized platform is analyzed according to the mechanical structure characteristics of the inertially stabilized platform of fig. 2, and a system dynamics model is established according to the requirements of the control system, and the inertially stabilized platform is approximately regarded as a second-order nonlinear system. Secondly, in order to control the platform more accurately, effectively suppress the total disturbance and weaken buffeting influence, an inertially stabilized platform control system is designed based on three-loop control, and a sliding mode controller based on fuzzy switching gain adjustment shown in fig. 3 is adopted in a position loop of the outermost loop to replace a traditional PID controller. The control signal outputs sliding mode switching gain in real time through the fuzzy controller, estimates the upper bound of the control signal in an integral mode, and then outputs the control signal to the global fast sliding mode controller, so that buffeting is restrained while the advantages of robustness, rapidity and the like of the control signal are guaranteed, and finally the control precision of the inertially stabilized platform is improved. The following are specifically included.
Firstly, modeling and disturbance analysis of an inertially stabilized platform control system are carried out, and the process is divided into the following 2 steps:
step 1) modeling of inertially stabilized platform control system
By adopting an indirect driving mode, the state space equation of the motor and platform load model is expressed as follows:
wherein: rmIs a motor loop resistance, TeIs the armature electromagnetic time constant, CmIs the motor moment coefficient, KsIs PWM power amplification factor, N is transmission ratio, CeAnd J is the rotational inertia of the motor rotor and the load, and the rotational inertia of the motor rotor can be ignored because the rotational inertia of the motor rotor is far smaller than that of the load. The simplified transfer function of the three-loop control system is combined, the controller is designed for convenient analysis, the three-loop control system based on the inertia stable platform can be approximately regarded as a second-order nonlinear system, and the expression is as follows:
wherein x is1Representing the output angular position thetaout，
For angular velocity, u is the system input, d (t) is the external disturbance to the system, defining the angular position error e ═ θin-θout，θinIs the reference angular position.
Step 2) determining disturbance factors of inertially stabilized platform
During aerial photography work of the inertial stabilization platform, multi-source disturbance from the inside and the outside of the inertial stabilization platform can influence the stabilization precision of the inertial stabilization platform; the internal disturbance of the inertially stabilized platform mainly comprises unbalanced moment disturbance and friction disturbance; the external disturbance of the inertially stabilized platform mainly comprises wind resistance moment disturbance and base angular motion disturbance.
Secondly, designing a global fast terminal sliding mode controller, wherein the process comprises the following 3 steps:
step 1) aiming at the state space equation of the inertially stabilized platform system, designing a global fast terminal sliding mode surface as follows:
wherein, alpha and beta are sliding mode surface constants, and p1，p2Are all positive odd numbers, satisfy p1＞p2When the ideal sliding surface is reached, s is 0.
Step 2) designing a controller according to a sliding mode equivalent control method, wherein the equivalent control law is u (t) ueq(t)+usw(t) in which ueqIs an equivalent control term, uswA non-linear control term.
When the system state quantity is in the sliding state, the external disturbance of the system is not considered at first, and the total disturbance d (t) is made to be 0, so that the equivalent control item u can be obtainedeq：
Then, the external disturbances and the parameter perturbation of the system are taken into account to satisfy the accessibility condition of the sliding mode, and the control rate is expressed as:
usw＝G(t)sgn(s)
g (t) is the switching gain, taken as:
G(t)＝max|d(t)|+η
wherein the control gain parameter eta is more than 0
Step 3) carrying out stability analysis on the system, and selecting a Lyapunov function:
y(t)＝0.5s2(t)
taking the first derivative between V (t):
and the accessibility condition of the sliding mode is met.
Thirdly, designing a sliding mode controller based on fuzzy switching gain adjustment, wherein the process comprises the following 3 steps:
step 1) fuzzy set design:
if it is not
The switching gain g (t) should be increased;
if it is not
The switching gain g (t) should be reduced.
According to
And the logic relation between the switching gain variation quantity delta G (t), the input and output fuzzy sets of the fuzzy control system are defined as follows:
ΔG(t)＝{NB NM NS ZO PS PM PB}
wherein NB is negative and large, NM is negative and medium, NS is negative and small, ZO is zero, PB is positive and large, PM is middle, and PS is positive and small.
Step 2), designing a membership function and a fuzzy rule:
and defining an input and output membership function of the fuzzy controller according to the control requirement.
The variation range of the switching gain G (t) is between 0 and 1, and the design fuzzy rule is as follows:
TABLE 1 fuzzy rules
Step 3) sliding mode controller design based on fuzzy switching gain adjustment
The fuzzy control is used for realizing the change of the switching gain G (t), and the upper bound of G (t) is estimated by an integral method, which is expressed as:
wherein K is a proportionality coefficient and is greater than 0, and is determined empirically. By using
Instead of g (t), the control law of the sliding mode control based on the fuzzy switching gain adjustment of the system at this time is as follows:
the position ring adopts a composite control scheme combining a sliding mode controller and a fuzzy controller, fuzzy switching gain adjustment is fused on the basis of global fast terminal sliding mode control, fuzzy rules are designed, effective estimation is carried out on switching gain according to sliding mode arrival conditions, output signals of the controller are softened, and buffeting existing in sliding mode control is reduced.
Fourth, the disturbance experiment result of the sliding mode controller of the inertially stabilized platform based on fuzzy switching gain adjustment
In order to verify the restraining capability of the sliding mode control algorithm based on fuzzy switching gain adjustment on multi-source disturbance, an unbalanced moment interference experiment is carried out. The weight of the simulated load in the experiment is 30 kg, and the simulation is carried out by a conventional pid control method and a sliding mode control method based on fuzzy switching gain adjustment in two groups of experiments. During the experiment, the mass blocks with the mass of 0.5 kg are successively placed on the surface of the rolling frame at the positions 20 cm away from the centers of the rolling shaft and the pitching shaft, and under the condition, the interference of the mass unbalance moment on the rotating shaft after the conversion is 1.0 Nm.
Under the condition of 1.0Nm mass unbalance moment interference, the maximum deviation of a rolling frame under the action of PID control and sliding mode control based on fuzzy switching gain adjustment is-0.104 degree and-0.087 degree respectively; after the weights are removed, the maximum deviation of the rolling frame is 0.131 degrees and 0.096 degrees respectively. Obviously, the sliding mode control based on the fuzzy switching gain adjustment has a faster response speed and a more excellent disturbance rejection capability than the PID control.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (4)
1. An inertia stabilized platform sliding mode control method based on fuzzy switching gain adjustment is characterized by comprising the following steps:
step 1: according to the mapping relation of the voltage, current, torque, rotating speed and position change parameters of the inertially stabilized platform, a three-loop control system model of the inertially stabilized platform is established, wherein the three-loop control system model comprises an inner loop which is a current loop and a speed loop, and an outer loop which is a position loop;
step 2: based on the three-loop control system in the step 1, PID control is adopted for an inner loop current loop and a speed loop, robustness sliding mode control is adopted for an outer loop position loop, multi-source disturbance is regarded as a whole to be used as sum disturbance, and a global fast terminal sliding mode controller is designed to restrain the sum disturbance;
and step 3: aiming at the problem that robustness and buffeting of the inertial stabilization platform control system based on the global fast terminal sliding mode control in the step 2 cannot be considered simultaneously, a fuzzy controller is introduced to carry out fuzzy switching gain adjustment on the basis of the global fast terminal sliding mode controller, multi-source disturbance influence is weakened or eliminated by utilizing the fuzzy switching gain, an output signal of the global fast terminal sliding mode controller based on the fuzzy switching gain adjustment is softened, the buffeting phenomenon is reduced, and the stabilization precision of the inertial stabilization platform is improved.
2. The inertial stabilization platform sliding-mode control method based on fuzzy switching gain adjustment according to claim 1, characterized in that: in the step 1, the established three-loop control system model is as follows:
wherein x is1Representing the output angular position thetaout，
For angular velocity, u (t) is input to the three-loop control system, d (t) is input to the three-loop control system, and the angular position error e is defined as thetain-θout，θinIs the reference angular position.
3. The inertial stabilization platform sliding-mode control method based on fuzzy switching gain adjustment according to claim 1, characterized in that: in the step 2, the designed global fast terminal sliding mode controller is as follows:
usw＝G(t)sgn(s)
wherein u is ueq+uswIs an equivalent control law of a sliding mode,
is an equivalent control term, d (t) is the sum perturbation; u. ofswIs a nonlinear control term, g (t) is a switching gain, g (t) max | d (t) | η + η, and a control gain parameter η>0, s is a sliding mode surface, expressed as
Alpha, beta is constant of slip form surface, p1,p2Are all positive odd numbers, satisfy p1>p2。
4. The method for controlling the inertially-stabilized platform sliding mode based on the fuzzy switching gain adjustment according to claim 1, is characterized in that: in step 3, the fuzzy set design of the sliding mode controller based on fuzzy switching gain adjustment is as follows:
if it is not
The switching gain g (t) should be increased;
if it is not
The switching gain g (t) should be reduced;
according to
And the switching gain variation Δ g (t), where t is time, the input and output fuzzy sets of the fuzzy controller are defined as follows:
ΔG(t)＝{NB NM NS ZO PS PM PB}
wherein NB is negative and large, NM is negative and medium, NS is negative and small, ZO is zero, PB is positive and large, PM is positive and small, an input and output membership function of the fuzzy controller is defined according to control requirements, the variation range of the switching gain G (t) is between 0 and 1, and the following 7 fuzzy rules are designed:
when in use
G (t) ═ PB; when in use
If so, then g (t) ═ PM;
when in use
When, g (t) ═ PS; when in use
When so, g (t) is ZO;
when in use
Then g (t) ═ NS; when in use
When, g (t) ═ NM;
when in use
Then g (t) ═ NB;
the fuzzy control is used for realizing the change of the switching gain G (t), and the upper bound of G (t) is estimated by an integral method, which is expressed as:
wherein K is a proportionality coefficient, and K>0, determined empirically. By using
Replacing G (t), and controlling the sliding mode control system u of the inertially stabilized platform based on fuzzy switching gain adjustment to be:
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