Airship attitude anti-disturbance control method for inertia uncertainty and center of mass offset

Abstract

The application discloses an airship attitude anti-interference control method for inertia uncertainty and center of mass offset. The method comprises the following steps: firstly, a nonlinear attitude dynamics model of the airship is established through Newton-Euler equation; then, a reference attitude controller is designed, and when inertia parameters and center of mass offset parameters are known, the airship gradually tracks an expected attitude; finally, the reference controller is extended into an adaptive controller, unknown inertia and center of mass offset parameters in the airship model are estimated, and the asymptotic convergence of the attitude tracking error under parameter uncertainty is ensured. The application realizes high-precision tracking control of the airship attitude under unknown inertia and center of mass offset, and can be used for flight tasks such as stratosphere airship residence, cruising, taking off and landing.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aerostat control, and particularly relates to a method for airship attitude anti-interference control aiming at inertia uncertainty and center of mass offset, which is suitable for a stratospheric airship system for completing tasks such as hovering, cruising, taking off and landing. BACKGROUND

[0002] In order to improve the level of weather monitoring and forecasting, high-density and high-precision weather observation data must be obtained. Using a stratospheric airship as an observation platform to carry meteorological detection load equipment for tracking and detecting weather can obtain meteorological data for a long time, at close range and in multiple directions, and is expected to improve the ability to resist various weather disasters. As a key device for this observation means, the flight control system design of the stratospheric airship is one of the core technologies for realizing the entire meteorological detection task.

[0003] The lifting of the airship is mainly realized by the inflation and deflation of the gas bag. The gas bag will change the inertia and center of mass offset of the airship when inflating or deflating gas. The volume change of the airship caused by the diurnal temperature difference will also have a great impact on the inertia of the airship body. The conventional fixed gain control method is difficult to adapt to the changes of the system structure parameters, and therefore it is inevitable to cause the decline of the attitude control precision, the instability of the airship attitude control system, and great difficulties for the airship to carry out the task.

[0004] In order to cope with the problems of inertia parameter changes and center of mass offset changes during flight, and to enable the airship to actively adapt to the changes of the structure parameters, thereby improving the attitude control precision of the airship and safely and efficiently completing the track tracking task, the airship control algorithm must consider the influence of the above-mentioned complex dynamics structure and configuration parameter changes on the airship attitude control system during the design process, so as to improve the tracking performance and reliability of the airship.

[0005] Chinese patent application CN201710753415.X proposes a stratospheric airship height control method in a wind field based on model prediction, but there is a problem: the proposed method assumes that the inertia of the airship is known and constant, and cannot adapt to the scene of structural changes; Chinese patent applications CN201711281786.9 and CN202110834786.7 propose airship track tracking control methods, but both have a problem: the proposed method uses a sign function, which has a high requirement for the bandwidth of the actuator and is difficult to apply to engineering practice.

[0006] Therefore, the above patent applications do not consider the airship attitude control problem under the condition of inertia and center of mass offset uncertainty. SUMMARY

[0007] In order to overcome the defects of the prior art, for the airship system, the present application provides an airship attitude anti-interference control method for inertia uncertainty and center of mass offset. The method can cope with the uncertainty problems of rotational inertia and center of mass offset, and realize high-precision airship attitude tracking control.

[0008] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0009] The airship attitude anti-interference control method for inertia uncertainty and center of mass offset comprises the following steps:

[0010] Firstly, a nonlinear attitude dynamics model of the airship is established;

[0011] Secondly, a reference attitude controller is designed based on backstepping method;

[0012] Thirdly, the reference controller is extended to an adaptive controller.

[0013] Further, the first step comprises:

[0014] Firstly, the attitude kinematics equation of the airship is established:

[0015] ,

[0016] In the formula, is the Euler angle representing the attitude of the airship, wherein respectively represent the roll, pitch and yaw angles of the airship, represents the transpose of the vector , represents the first order derivative of the vector with respect to time, is a state transition matrix, represents the angular velocity of the airship under the body axis system, wherein respectively represent the roll, pitch and yaw angular velocities of the airship under the body axis system.

[0017] Based on Newton Euler equation, the attitude dynamics equation of the airship is modeled as a nonlinear attitude dynamics model through force analysis:

[0018] ,

[0019] In the formula, is the first order derivative of the angular velocity of the airship under the body axis system with respect to time, is the resultant moment of the inertial moment and the gravitational moment, is a control distribution matrix, is the attitude control moment of the airship, wherein respectively are the projections of the attitude control moment of the airship on the body XYZ axis, the resultant moment of the inertial moment and the gravitational moment And control distribution matrix The expression is as follows:

[0020] ,

[0021] ,

[0022] In the formula, , , , , , , , , ; The product of inertia of the airship about the XZ plane of the airframe is represented by Ix, The moment of inertia of the airship about the XYZ axis of the airframe is represented by Ix; The mass of the airframe is represented by m; The offset of the center of mass of the airship along the Z axis of the airframe is represented by h; All are unknown parameters.

[0023] The resultant moment of the inertial moment and the gravitational moment is represented by M, Characterized as the following linear parameterization form:

[0024] ,

[0025] In the formula, the vector Is an unknown parameter, and the matrix Is a function of the known state.

[0026] Further, the second step includes:

[0027] According to the airship nonlinear attitude system model established in the first step, a reference attitude controller is designed based on the backstepping method to track the expected attitude angle .

[0028] Step 2.1, define the attitude tracking error , define the energy function , derive the energy function With respect to time, we get:

[0029]

[0030] In the formula, The first order derivative of the expected attitude angle With respect to time, the expected angular velocity is designed as:

[0031] ,

[0032] In the formula, a control gain of the attitude error, The superscript -1 denotes the inverse operation, and the derivative of the attitude error with respect to time satisfies:

[0033] ,

[0034] The energy function The first-order derivative with respect to time is expressed as:

[0035] ,

[0036] Step 2.2, define the angular velocity tracking error as , define the second energy function , take the derivative of the energy function with respect to time, and obtain:

[0037]

[0038] Here, the airship attitude control torque is designed as the reference controller , which satisfies:

[0039] ,

[0040] In the formula, and respectively represent the nominal values of parameters and , is a control gain of the angular velocity error, and the derivative of the angular velocity error with respect to time satisfies:

[0041] ,

[0042] When the nominal value of the parameter is consistent with the actual value of the parameter, that is, , the derivative of the angular velocity error with respect to time satisfies:

[0043] ,

[0044] At this time the first-order derivative with respect to time is simplified as:

[0045] ,

[0046] According to the Lyapunov stability theory, the error system converges asymptotically, and the actual attitude of the airship asymptotically tracks the expected attitude.

[0047] Further, the third step includes:

[0048] The reference controller obtained in the second step is extended to an adaptive controller, and the expression is as follows:

[0049] ,

[0050] In the formula, is the reference controller obtained in the second step, is the adaptive controller to be designed.

[0051] When the nominal value of the parameter is inconsistent with the actual value of the parameter, that is, ,the derivative of the angular velocity error with respect to time satisfies:

[0052] ,

[0053] The adaptive controller to be designed is designed as:

[0054] ,

[0055] In the formula, represents the estimated value of the unknown parameter , and the derivative of the angular velocity error with respect to time satisfies:

[0056] ,

[0057] In the formula, is the estimation error of the parameter , is the estimation error of the parameter .

[0058] The following Lyapunov function is selected:

[0059] ,

[0060] In the formula, and are the estimated gains of the parameters and the parameter , respectively, and the first-order derivative of with respect to time is calculated as:

[0061] ,

[0062] The adaptive law of the parameters and the parameter is:

[0063]

[0064] Then we have:

[0065]

[0066] Therefore, all the signal and parameter estimation values in the system are bounded, and the attitude tracking error converges asymptotically.

[0067] Compared with the prior art, the present application has the beneficial effects that:

[0068] The present application is mainly aimed at unmanned airship systems, and compared with the traditional attitude control method, the present application has the advantage of strong adaptive ability. By designing an adaptive control algorithm, the present application solves the problem that the existing method is difficult to cope with the changes of structural parameters such as moment of inertia and center of mass offset, and realizes high-precision attitude control of the airship. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 The flowchart of the airship attitude anti-interference control method for inertia uncertainty and center of mass offset of the present application.

[0070] Figure 2 The airship coordinate system and motion parameter diagram in the present application. DETAILED DESCRIPTION

[0071] The present application will be further described below according to the drawings and examples. The specific implementation of the system and method will be described by taking an unmanned airship as an example. As shown in Figure 2 , represents the body coordinate system of the airship, is the geometric center of the airship, located at the origin of the body coordinate system, is the center of gravity of the airship, located along the Z-axis direction of the body coordinate system at the geometric center, is the angular velocity of the airship around the body coordinate system of the airship.

[0072] As shown in Figure 1 , it is the flowchart of the airship attitude anti-interference control method for inertia uncertainty and center of mass offset of the present application, and the specific implementation steps are as follows:

[0073] Step 1. Establish the nonlinear attitude dynamics model of the airship:

[0074] First, the attitude kinematics equation of the airship is established:

[0075] ,

[0076] In the formula, is the Euler angle representing the attitude of the airship, wherein respectively represent the roll, pitch and yaw angles of the airship, represents the transpose of the vector , denotes the vector denotes the first order derivative of the vector is the state transition matrix, denotes the angular velocity of the airship under the body axis system, where denotes the roll, pitch and yaw angular velocities of the airship under the body axis system, respectively.

[0077] Based on Newton-Euler equation, the airship attitude dynamics equation is modeled as a nonlinear attitude dynamics model through force analysis:

[0078] ,

[0079] where, denotes the first order derivative of the angular velocity of the airship under the body axis system with respect to time, is the resultant moment of the inertial moment and the gravitational moment, is the control distribution matrix, is the airship attitude control moment, where are the projections of the airship attitude control moment on the body XYZ axis, the resultant moment of the inertial moment and the gravitational moment and the control distribution matrix are expressed as follows:

[0080] ,

[0081] ,

[0082] where, , , , , , , , , ; denotes the inertia product of the airship with respect to the body XZ plane, denotes the inertia moment of the airship on the body XYZ axis; is the mass of the body; is the offset of the airship mass center along the body Z axis; let be unknown parameters.

[0083] The resultant moment of the inertial moment and the gravitational moment is characterized as the following linear parameterization form:

[0084] ,

[0085] where, the vector is an unknown parameter, and the matrix is a function of the known states.

[0086] Step 2. Design the baseline attitude controller based on backstepping method:

[0087] According to the nonlinear attitude system model of airship established in Step 1, the baseline attitude controller is designed to track the desired attitude angle based on backstepping method .

[0088] Step 2.1, define the attitude tracking error , define the energy function , take the derivative of the energy function with respect to time, we get:

[0089]

[0090] where represents the desired attitude angle , and the first order derivative of the desired attitude angle with respect to time is designed as the desired angular velocity:

[0091] ,

[0092] where is the control gain of the attitude error, and the superscript -1 represents the inverse operation, then the derivative of the attitude error with respect to time satisfies:

[0093] ,

[0094] Further, the first order derivative of the energy function with respect to time is expressed as:

[0095] ,

[0096] Step 2.2, define the angular velocity tracking error as , define the second energy function , take the derivative of the energy function with respect to time, we get:

[0097]

[0098] Here, the attitude control moment of the airship is designed as the baseline controller , which satisfies:

[0099] ,

[0100] where and represent the nominal values of the parameters and , respectively,​ is the control gain of the angular velocity error, then the derivative of the angular velocity error with respect to time satisfies:

[0101] ,

[0102] When the nominal value of the parameter coincides with the actual value of the parameter, i.e. ,the derivative of the angular velocity error with respect to time satisfies:

[0103] ,

[0104] At this time the first order derivative with respect to time is simplified as:

[0105] ,

[0106] According to the Lyapunov stability theory, the error system asymptotically converges, and the actual attitude of the airship asymptotically tracks the expected attitude.

[0107] Step 3. Extend the benchmark controller to an adaptive controller:

[0108] The benchmark controller obtained in step 2 is extended to an adaptive controller, and the expression is as follows:

[0109] ,

[0110] In the formula, is the benchmark controller designed through step 2, is the adaptive controller to be designed.

[0111] When the nominal value of the parameter does not coincide with the actual value of the parameter, i.e. ,the derivative of the angular velocity error with respect to time satisfies:

[0112] ,

[0113] The adaptive controller to be designed is designed as:

[0114] ,

[0115] In the formula, denotes the estimated value of the unknown parameter , at this time the derivative of the angular velocity error with respect to time satisfies

[0116] ,

[0117] where is the estimation error of the parameter is the estimation error of the parameter

[0118] The following Lyapunov function is chosen:

[0119] ,

[0120] where and are the estimation gains of the parameters and respectively, and the first order derivative with respect to time is:

[0121] ,

[0122] The adaptive laws of the parameters and are:

[0123]

[0124] Then we have:

[0125]

[0126] Therefore, all the signal and parameter estimation values in the system are bounded, and the attitude tracking error converges asymptotically.

[0127] The above-described specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above-described specific embodiments are merely examples of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.​​

Claims

1. A method for airship attitude disturbance rejection control against inertia uncertainty and center of mass offset, characterized in that, The method comprises the following steps: Firstly, a nonlinear attitude dynamics model of the airship is established; Secondly, a benchmark attitude controller is designed based on the backstepping method; Thirdly, the benchmark attitude controller is extended to an adaptive controller; The first step comprises: Firstly, an attitude kinematics equation of the airship is established: ， In the formula, Euler angles characterizing the attitude of an airship, where These represent the roll, pitch, and yaw angles of the airship, respectively. Representing vectors transpose, Representing vectors The first derivative with respect to time Here is the state transition matrix. This represents the angular velocity of the airship along its hull axis, where These represent the roll, pitch, and yaw angular velocities of the airship under its hull axis, respectively. Based on the Newton-Euler equation, the attitude dynamics equation of the airship is modeled as a nonlinear attitude dynamics model through force analysis: ， In the formula, Let be the first derivative of the airship's angular velocity with respect to time in the hull axis system. It is the resultant torque of the inertial torque and the gravitational torque. To control the distribution matrix, For the attitude control torque of the airship, where These are the projections of the airship attitude control torque onto the XYZ axes of the airship system, and the resultant torque of the inertial torque and the gravitational torque, respectively. and control distribution matrix The expression is as follows: ， ， wherein , , , , , , , , ; denotes the product of inertia of the airship with respect to the XZ plane of the body system, denotes the moment of inertia of the airship about the Z axis of the body system; is the mass of the body; is the offset of the center of mass of the airship along the Z axis of the body system; and are unknown parameters; The resultant moment of the inertia moment and the gravitational moment is characterized in the following linear parameterization: ， where the vector is an unknown parameter, and the matrix is a function of the known state; The second step comprises: According to the airship nonlinear attitude system model established in the first step, a benchmark attitude controller is designed to track the desired attitude angle based on the backstepping method ; Step 2.1, define pose tracking error , define energy function , derive energy function Taking the derivative with respect to time, we get: wherein denotes the desired orientation angle The desired angular velocity is designed as the first derivative with respect to time ， wherein is a control gain for the attitude error, the superscript -1 denotes the inverse operation, and the derivative of the attitude error with respect to time satisfies: ， Further energy function The first derivative with respect to time is expressed as: ， Step 2.

2. Define the angular velocity tracking error as , define the second energy function , take the derivative of the energy function with respect to time, we get: Controlling the attitude of an airship is designed as a reference controller satisfies: ， wherein and denote nominal values of the parameters and , is a control gain for the angular velocity error, then the derivative of the angular velocity error with respect to time satisfies: ， When the nominal value of the parameter coincides with the actual value of the parameter, i.e. , the derivative of the angular velocity error with respect to time satisfies: ， At this time The first derivative with respect to time simplifies to: ， According to the Lyapunov stability theory, the error system is asymptotically convergent, and the actual attitude of the airship asymptotically tracks the expected attitude; The third step comprises: The benchmark controller obtained in the second step is extended to an adaptive controller, and the expression is as follows: ， wherein is the reference controller designed through the second step, is the adaptive controller to be designed; When the parameter nominal value does not coincide with the parameter actual value, i.e. , the derivative of the angular velocity error with respect to time satisfies: ， The adaptive controller to be designed is is designed as: ， wherein denotes an estimate of the unknown parameter at time t, when the derivative of the angular velocity error with respect to time satisfies: ， wherein is the estimated error of the parameter is the estimated error of the parameter is the estimated error of the parameter is the estimated error of the parameter The following Lyapunov function is selected: ， where and are the estimated gains of the parameters and the parameter respectively, and the first order derivative with respect to time is calculated as dt ， Design parameters and parameters The adaptive law for is Therefore, all the signals and parameter estimation values in the system are bounded, and the attitude tracking error is asymptotically convergent. ​

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