CN109814384A - A nested saturation control method and fixed-point tracking control method for aerostats - Google Patents

Abstract

The invention belongs to the technical field of automatic control, and discloses a nested saturation control method for an aerostat, comprising step 1: establishing an improved saturation function μ based on a continuously differentiable standard saturation function σ(r) _i (s), i∈1,n, and then establish the n-order nested control law function; step 2, establish the second-order integral chain system of the controlled variable, take the second-order nested control law function and its corresponding improved saturation For the function μ ₂ (s), the upper limit of the first-order differential of the second-order nested control law function is used as the upper limit of the output variable rate of the corresponding actuator, and the upper limit of the improved saturation function μ ₂ (s) is used as the upper limit. The control quantity corresponds to the upper limit of the output quantity of the actuator, calculate the linear domain size of the improved saturation function μ ₂ (s), and then establish a second-order nested control law function between the controlled quantity and the output quantity of the corresponding actuator Step 3: According to the second-order nested control law function between the controlled quantity and the output quantity of the corresponding actuator, through the control redistribution, the output quantity of the actuator is controlled to complete the control of the controlled quantity.

Description

A nested saturation control method and fixed-point tracking control method for aerostats

technical field

The invention belongs to the technical field of automatic control, and in particular relates to a nested saturation control method for an aerostat, a fixed-point tracking control method and a control system.

Background technique

Stable position tracking and dynamic localization for a class of multi-propeller vector thrust aerostats with input rate and amplitude constraints. The research object is a flat-shaped multi-propeller vector thrust aerostat with no air rudder surface, equipped with four axisymmetrically distributed propellers, and has the ability to move in all directions in space.

Due to energy and weight constraints, the multi-propeller combined aircraft is configured with a small thrust-to-weight ratio, which is about 1/30. Therefore, the magnitude and rate of change of the thrust output by the propellers are strictly constrained. The aerostat has the characteristics of large inertia and large volume, and due to the limited execution capability of the propeller, the saturation of the propeller thrust amplitude and rate is easy to occur during the motion control process. When designing the control system, it is necessary to consider the constraints of the actuator. Through the design of the control system with constraints, it is avoided that the aircraft loses its autonomous control ability due to the saturation of the actuator under extreme flight conditions, and the flight safety of the aircraft is ensured.

Liu Fen, Chen Li, Duan Dengping. Design of anti-saturation controller for multi-propeller aerostat. Journal of Shanghai Jiaotong University, 2017, 51(2): 157 For this type of aerostat, the amplitude constraints and the inconsistencies of the actuators are considered. Symmetric problem, design of anti-saturation compensator based on linear matrix inequality (LMI) under the unified framework of anti-saturation; Method: Chinese Patent, 201410486563. On 2015-01-28, a fault-tolerant controller based on model predictive control was proposed for a four-propeller stratospheric airship, and numerical optimization method was used to consider the constraints of the actuator; Han D, Wang X L, Chen L, et al. Adaptivebackstepping control for a multi-vectored thrust stratospheric airship withthrust saturation in wind.Proc Inst Mech Eng Part G J Aerosp Eng,2016,230(1):45 Based on the backstepping method, the amplitude of the actuator is avoided by adjusting the adaptive term of the controller Saturated, the method requires a lot of online computation to get the adaptive term.

The above research only considers the actuator amplitude constraint, but does not consider the rate constraint, and the controller solution method is a numerical calculation method, which cannot explicitly express the relationship between the controller output and the physical constraints of the actuator.

SUMMARY OF THE INVENTION

The invention provides a nested saturation control method, a fixed-point tracking control method and a control system for an aerostat, and solves the problem that the existing aerostat control system can only limit the amplitude of the output of the actuator, and cannot carry out Output rate change constraints and other issues.

The present invention can be realized through the following technical solutions:

A nested saturation control method for an aerostat comprising the steps of:

Step 1. Based on the continuously differentiable standard saturation function σ(r), establish an improved saturation function μ _i (s), i∈1,n, and then establish an n-order nested control law function;

Step 2: Establish a second-order integral chain system of controlled quantities, take the second-order nested control law function and its corresponding improved saturation function μ ₂ (s), and use the first-order differential of the second-order nested control law function The upper limit of the controlled variable corresponds to the upper limit of the output change rate of the actuator, and the upper limit of the improved saturation function μ ₂ (s) is taken as the upper limit of the controlled variable corresponding to the output of the actuator, and the improved saturation function is calculated. The size of the linear domain of the function μ ₂ (s), and then the second-order nested control law function between the controlled variable and the output of the corresponding actuator is established;

Step 3: Control the output of the actuator through control redistribution according to the second-order nested control law function between the controlled variable and the output of the corresponding actuator to complete the control of the controlled variable.

Further, the expression of the standard saturation function is as follows

Among them, L _σ represents the linear domain of σ(r), α _σ represents the slope in the linear domain of σ(r), S _σ represents the unsaturated domain of σ(r), H ₁ (r), H ₂ (r) represent The nonlinear function part in the unsaturated domain of σ(r), σ ^max represents the saturation value of the standard saturated function σ(r);

The expression of the improved saturation function is as follows

and

in, represents the magnitude constraint of the function μ(s), represents the linear domain of the function μ(s), represents the slope in the linear domain of the function μ(s), represents the unsaturated domain of the function μ(s);

The expression of the n-order nested control law function is set as

U=-μ _n (y _n +μ _n-1 (y _n-1 +...+μ ₁ (y ₁ ))).

Further, the expression of the upper limit of the first-order differential of the second-order nested control law function is as follows

Among them, A ₂ ,A ₃ ,B ₂ ,B ₃ ,C ₂ ,C ₃ ,D ₂ ,D ₃ represent constant parameters, and their expressions are as follows

make It is equal to the upper limit of the output quantity of the actuator corresponding to the controlled quantity, and R ₁ is equal to the upper limit of the output quantity change rate of the controlled quantity corresponding to the actuator, and the linear domain of the improved saturation function μ ₂ (s) is calculated.

Further, the multi-order differential of the improved saturation function μ _i (s) exists, is continuous and has an upper limit, the controlled variable is set as the forward speed or lateral speed of the aerostat, and the corresponding actuator is set as the propeller , and its output is set as the resultant force of the thrust provided by each propeller in the X-axis or Y-axis direction.

A control method for the fixed-point tracking of the multi-vector propeller combined aerostat for the nested saturation control method of the aerostat described above, comprising the following steps:

Step 1: Calculate the distance D between the target position and the current body center position of the aerostat;

Step 2. Establish the forward nested saturation control law function between the forward speed, the component of the distance D on the x-axis and the resultant force of the propeller's vector thrust in the x-axis direction, as well as the lateral speed, the component of the distance D on the y-axis and The laterally nested saturation control law function of the vector thrust of the propeller between the resultant forces in the y-axis direction;

Step 3: Calculate the vector thrust and angle of each propeller required to reach the target position according to the forward and lateral nested saturation control law functions.

Further, the second step includes the following steps:

Step 1. Establish the second-order integral chain system of forward velocity and lateral velocity, as shown below

Among them, x ₁ represents the forward speed u or the side speed v, U=-μ ₂ (y ₂ +μ ₁ (y ₁ )) represents the second-order nested saturation control law function, represents the state transition between y ₁ , y ₂ and x ₁ , x ₂ , represents the slope in the linear domain of the function μ ₂ (s);

Step Ⅱ, utilize the method as claimed in claim 3, the concrete expression of standard saturation function is as follows

in,

Taking σ ^max =2, L _σ =1, α _σ =1, Obtain the expression of the upper limit of the first-order differential of the second-order nested control law function as described below, and then make it equal to the upper limit of the rate of change of the resultant force of the thrust provided by each propeller in the x-axis and y-axis directions, and calculate the corresponding improved saturation Linear domain of the function μ ₂ (s)

Step III. According to the calculated linear domain of the improved saturation function μ ₂ (s) Then establish the forward nested saturation control law function between the forward speed, the component of the distance D on the x-axis and the resultant force of the propeller's vector thrust in the x-axis direction, as well as the lateral speed, the component of the distance D on the y-axis and the propeller's The laterally nested saturation control law function between the resultant force of the vector thrust in the Y-axis direction.

Further, it is characterized by:

Step 1. Establish the three-degree-of-freedom dynamic equation of the aerostat that only considers the plane motion as follows;

Among them, u, v, r represent the flight speed and yaw angular velocity of the aerostat along the x-axis and y-axis in the body coordinate system; Represents the differential of u, v, r, m represents the mass of the aerostat; I _z represents the moment of inertia of the aerostat around the z-axis; m ₁₁ , m ₂₂ represent the additional mass of forward motion and lateral motion, respectively, m ₃₃ represents The additional moment of inertia of the z-axis, F _Ax , F _Ay , N _A means that the aerostat is subjected to aerodynamic forces and moments along the x-axis, y-axis and around the z-axis, F _Tx , F _Ty , N _T means that the propeller is in x, y The resultant thrust in the direction and the resultant moment around the z-axis, F _Ix , F _Iy , and N _I represent the Cordial forces along the x-axis, y-axis and around the z-axis, respectively,

Thus, the relationship between F _Tx , F _Ty , N _T and the vector thrust and angle of a single propeller is obtained as follows

Among them, r _p represents the installation position of each propeller relative to the aerostat body center in the body coordinate system, F _ti represents the vector thrust of a single propeller, μ _ti represents the angle of the vector thrust of a single propeller, i=1,2, 3,4;

Step 2. Using the forward nested saturation control law function and the lateral nested saturation control law function, as well as the relationship between F _Tx , F _Ty , N _T and the vector thrust and rotation angle of a single propeller, calculate the single propeller required to reach the target position. Vector thrust F _ti and angle μ _ti of the propeller.

A control system based on the above-described control method for the fixed-point tracking of multi-vector propeller combined aerostats, comprising a distance comparison module, the distance comparison module is connected with a forward resultant force generation module and a side resultant force generation module, The forward resultant force generation module and the side resultant force generation module are connected with the control distribution module, the control distribution module is connected with the main controller of the aerostat, and the main controller is connected with the distance comparison module through the state measurement module, so The state measurement module is connected with the forward resultant force generation module and the lateral resultant force generation module through the state transformation module;

The state measurement module is used to measure the attitude information of the aerostat, as well as the position and speed information in the geographic coordinate system;

The state transformation module is used to convert the speed information under the geographic coordinate system into the speed information under the body coordinate system;

The distance comparison module is used to receive the position information of the current position of the aerostat body center and the target position under the geographic coordinate system, and calculate the distance information D between the two;

The forward resultant force generation module receives the forward speed and distance information D under the current body coordinate system in the x-axis direction, and uses the forward nested saturation control law function to generate the resultant force of the vector thrust of each propeller in the x-axis direction. ;

The lateral resultant force generation module receives the lateral speed and distance information D in the y-axis direction under the current body coordinate system, and uses the lateral nested saturation control law function to generate the resultant force of the vector thrust of each propeller in the y-axis direction. ;

The control distribution module is used to receive the resultant force of the vector thrust of each propeller in the x-axis and y-axis directions, and combine with the dynamic equation of the aerostat to generate the vector thrust required by each propeller of the aerostat and its corresponding angle .

Further, the forward resultant force generation module includes a forward linear domain calculation module, a forward nested saturation control law generation module connected with the forward linear domain calculation module,

The forward linear domain calculation module is used to make the maximum value of the second-order improved saturation function equal to the magnitude of the resultant force of the vector thrust of each propeller in the x-axis direction based on the second-order nested saturation control law function, and the second-order nested The upper limit of the first-order differential of the saturation control law function is equal to the change rate of the resultant force of the vector thrust of each propeller in the x-axis direction, and the linear domain of the second-order improved saturation function is calculated;

The forward nested saturation control law generation module is used to generate the vector thrust of each propeller in the x-axis direction based on the linear domain of the second-order improved saturation function, the forward speed, and the distance D between the components of the x-axis. The forward nested saturation control law function.

Further, the lateral resultant force generation module includes a lateral linear domain calculation module, a lateral nested saturation control law generation module connected with the lateral linear domain calculation module,

The lateral linear domain calculation module is used to make the maximum value of the second-order improved saturation function equal to the magnitude of the resultant force of the vector thrust of each propeller in the y-axis direction based on the second-order nested saturation control law function, and the second-order nested The upper limit of the first-order differential of the saturation control law function is equal to the change rate of the resultant force of the vector thrust of each propeller in the y-axis direction, and the linear domain of the second-order improved saturation function is calculated;

The laterally nested saturation control law generation module is used to generate the vector thrust of each propeller in the y-axis direction based on the linear domain of the second-order improved saturation function, the lateral velocity, and the distance D between the components of the y-axis. The laterally nested saturation control law function.

The beneficial technical effects of the present invention are:

Based on the standard saturation function, an improved n-order saturation function is established, and then an n-order nested saturation control law function is established, and the upper limit of the first-order differential of the second-order nested saturation control law function is equal to the output change rate of the actuator. The upper limit of the second-order improved saturation function is equal to the output constraint of the actuator, and the linear domain of the second-order improved saturation function is calculated to establish the second-order nested control between the controlled variable and the output of the corresponding actuator The law function, which completes the control system's constraints on the output of the actuator and its rate of change, and provides a fixed-point tracking control method and control system on this basis to avoid the saturation of the propeller thrust amplitude and rate during the motion control process. , loses the ability to control the aerostat, improves the flight safety of the aerostat, provides an analytical calculation method for the control function of the controller, and clearly expresses the physical constraint relationship between the output of the controller and the actuator , easy to adjust, and effectively improve the reliability of the control system. At the same time, the control system of the present invention has better robustness, enhances the anti-interference ability, and can ensure the stability of the system under different initial states and wind disturbance conditions.

Description of drawings

Fig. 1 is the overall control flow schematic diagram of the present invention;

Fig. 2 is the standard saturation function of the present invention and the schematic diagram of the relationship of the improved saturation function;

3 is a schematic diagram of the overall structure of the aerostat of the present invention;

4 is a schematic diagram of the vector thrust decomposition of the multi-vector propeller f _iH component force on the xoy projection of the present invention, wherein, f _ix represents the component force of the f _iH component force on the x-axis, and f _iy represents the f _iH component force on the y-axis. The component force of , i=1,2,3,4;

Fig. 5 is the mapping schematic diagram of the horizontal thrust of the multi-vector propeller of the present invention on the xoy plane;

6 is a schematic diagram of the relationship between the first-order differential upper bound of the control law of the present invention and the linear domain of the improved saturation function;

7 is a schematic diagram showing the comparison of the trajectory tracking effects of the fixed-point tracking control method of the present invention and the PID control method under wind disturbance conditions;

Fig. 8 is the change schematic diagram of the vector thrust and the rate of change thereof using the fixed-point tracking control method of the present invention, wherein, the sign a represents the vector thrust, and the sign b represents the rate of change;

9 is a schematic diagram of the state quantity change of the aerostat using the fixed-point tracking control method of the present invention, wherein marks A, B, C, and D respectively represent the flight speed of the aerostat along the x-axis and the y-axis in the body coordinate system and yaw angular velocity, and the yaw angle in the geographic coordinate system;

Fig. 10 is the vector thrust response curve schematic diagram of each propeller that adopts the control method of fixed-point tracking of the present invention, wherein, mark ①, ②, ③, ④ respectively represent the vector thrust of propellers 1, 2, 3, 4 in Fig. 2;

11 is a schematic diagram of the angle response curve corresponding to the vector thrust of each propeller using the fixed-point tracking control method of the present invention, wherein the signs (1), (2), (3), (4) represent the vectors of the propellers 1, 2, 3, and 4 in FIG. 2, respectively. The angle corresponding to the thrust.

12 is a circuit control block diagram of the control system of the present invention

Detailed ways

The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments.

Considering the characteristics of the rotationally symmetric aerostat and the convenience of calculation, it is assumed that the geographic coordinate system is [X, Y, Z], the body coordinate system is [x, y, z], the origin is the volume center of the body, and the corresponding x-axis, The velocity on the y-axis and z-axis is [u, v, w], the corresponding angular velocity on the x-axis, y-axis, and z-axis is [p, q, r], the conversion between the geographic coordinate system and the body coordinate system The matrix is ψ represents the yaw angle of the aerostat in the geographic coordinate system.

In general, the input amplitude saturation constraints describing the system are as follows:

Among them, U(t) is the control input of the system, U _max , U _min are the upper and lower limits of the input amplitude constraint of the system, respectively, when the input U(t) exceeds the upper or lower limit, it will be limited to U _min or U _max respectively , otherwise its value does not change.

The rate-of-change saturation constraint of the system input can be described by the following formula:

in, is the first derivative of the input U(t), and _dmax is the upper limit of the rate-of-change constraint of the input, that is, the rate of change of the input When it is greater than the upper limit _dmax , its value is limited to _dmax , and when it is less than the lower limit _dmin , it is limited to _dmin , otherwise its value remains unchanged.

The present invention provides a nested saturation control method for an aerostat, as shown in Figure 1, comprising the following steps:

Step 1. Based on the continuously differentiable standard saturation function σ(r), establish an improved saturation function μ _i (s), i∈1,n, and then establish an n-order nested control law function, as shown below;

The expression for the standard saturation function is as follows:

Among them, L _σ represents the linear domain of σ(r), α _σ represents the slope in the linear domain of σ(r), S _σ represents the unsaturated domain of σ(r), H ₁ (r), H ₂ (r) represent The nonlinear function part in the unsaturated domain of σ(r), σ ^max represents the saturation value of the standard saturated function σ(r).

In order to make the standard saturation function σ(r) continuously differentiable, a continuous differentiable function H ₁ (r), H ₂ (r) is used to connect at the function saturation, and the resulting saturation function is both close to the sat(·) function, to describe the amplitude constraint, and can calculate its first derivative to describe the rate constraint.

By changing the parameters of the standard saturation function σ(r), the improved saturation function is obtained, as shown in Figure 2, and its expression is as follows:

and

in, represents the magnitude constraint of the function μ(s), represents the linear domain of the function μ(s), represents the slope in the linear domain of the function μ(s), represents the unsaturated domain of the function μ(s);

The expression of the n-order nested control law function is then set to U=-μ _n (y _n +μ _n-1 (y _n-1 +...+μ ₁ (y ₁ ))).

Using existing theories, such as Xinghua Wang and Aimin Xu, On the divideddifference form of FAA DI BRUNO'S Formula II, Journal of ComputationalMathematics, Vol.25, No.6, 2007, 697-704, an improved saturation function can be proved The k-order differential of μ _i (s) exists and is continuous, and its analytical expression is as follows:

where |f ⁽ⁱ⁾ (t)|≤Qi,i=1,...,k-a+1; B _k,a (Q ₁ ,...,Q _k-a+1 ) is defined by Q ₁ ,...,Q _k-a+1 composed of Bell polynomials,

The above formula shows that the k-order differential of the improved saturation function μ _i (s) has an upper bound, then the n-order nested control law function composed of it has a k-order differential and an upper bound. If the parameters of the saturation function are designed to make The upper bound of the first-order differential of the n-order nested control law function is equal to the limit of the rate of change of the output of the actuator, then the anti-rate saturation design of the control law can be realized.

Step 2: Establish a second-order integral chain system of controlled variables, take the second-order nested control law function and its corresponding improved saturation function μ ₂ (s), and use the upper limit of the first-order differential of the second-order nested control law function As the upper limit of the output change rate of the actuator corresponding to the controlled quantity, the improved saturation function μ ₂ (s) is calculated by taking the upper limit of the improved saturation function μ ₂ (s) as the upper limit of the output quantity of the controlled quantity corresponding to the actuator. The linear domain size of , and then establish a second-order nested control law function between the controlled variable and the output of the corresponding actuator.

The expression for the upper limit of the first-order differential of the second-order nested control law function is as follows

Among them, A ₂ , A ₃ , B ₂ , B ₃ , C ₂ , C ₃ , D ₂ , D ₃ represent constant parameters, and their expressions are as follows:

make It is equal to the upper limit of the output quantity of the actuator corresponding to the controlled quantity, and R ₁ is equal to the upper limit of the output quantity change rate of the controlled quantity corresponding to the actuator, and the linear domain of the improved saturation function μ ₂ (s) can be calculated.

Step 3: According to the second-order nested control law function between the controlled quantity and the output quantity of the corresponding actuator, control the output quantity of the actuator through control redistribution to complete the control of the controlled quantity. The controlled amount can be set as the forward speed or lateral speed of the aerostat, the corresponding actuator is set as the propeller, and the output is set as the resultant force of the thrust provided by each propeller in the x-axis or y-axis direction.

The control method of the invention is based on the standard saturation function, establishes an n-order improved saturation function, further establishes an n-order nested saturation control law function, and sets the upper limit of the first-order differential of the second-order nested saturation control law function equal to the actuator The upper limit of the second-order improved saturation function is equal to the output amount constraint of the actuator, and the linear domain of the second-order improved saturation function is calculated to establish the relationship between the controlled amount and the output of the corresponding actuator. The second-order nested control law function completes the control system's constraints on the output of the actuator and its rate of change, avoids the saturation of the propeller thrust amplitude and rate during the motion control process, and loses the ability to control the aerostat. The flight safety of the aerostat is improved, and the analytical calculation method of the control function of the controller is provided, and the physical constraint relationship between the output of the controller and the actuator is clearly expressed, which is convenient for adjustment and effectively improves the control system. reliability.

The present invention also provides a control method for the fixed-point tracking of the multi-vector propeller combined aerostat as described above for the nested saturation control method of the aerostat. For an elliptical-shaped airship with a propeller, the two propellers are symmetrically distributed at the diameter of the aerostat, as shown in Figure 3, and the schematic diagram of the local coordinate system of the vector thrust of the propeller is shown in Figure 4, which specifically includes the following steps:

Step 1: Calculate the distance D between the target position and the current body center position of the aerostat;

Step 2. Establish the forward nested saturation control law function between the forward speed, the component of the distance D on the x-axis and the resultant force of the propeller's vector thrust in the x-axis direction, as well as the lateral speed, the component of the distance D on the y-axis and The lateral nested saturation control law function of the vector thrust of the propeller between the resultant forces in the y-axis direction is as follows;

Step 1. Establish the second-order integral chain system of forward velocity and lateral velocity, as shown below

Among them, x ₁ represents the forward speed u or the lateral speed v, U=-μ ₂ (y ₂ +μ ₁ (y ₁ )) represents the second-order nested saturation control law function, y ₂ =x ₂ , represents the state transition between y ₁ , y ₂ and x ₁ , x ₂ , represents the slope in the linear domain of the function μ ₂ (s);

Step II, using the method as described above, the specific expression of its standard saturation function is as follows

in,

Taking σ ^max =2, L _σ =1, α _σ =1, Obtain the expression of the upper limit of the first-order differential of the second-order nested control law function as described below, and then make it equal to the upper limit of the rate of change of the resultant force of the thrust provided by each propeller in the x-axis and y-axis directions, and calculate the corresponding improved saturation Linear domain of the function μ ₂ (s)

Step III. According to the calculated linear domain of the improved saturation function μ ₂ (s) Then establish the forward nested saturation control law function between the forward speed, the component of the distance D on the x-axis and the resultant force of the propeller's vector thrust in the x-axis direction, as well as the lateral speed, the component of the distance D on the y-axis and the propeller's The laterally nested saturation control law function between the resultant force of the vector thrust in the Y-axis direction.

The upper limit R1 of the _first -order differential of the second-order nested control law function varies with The transformation curve is shown in Fig. 6. It can be seen that the value of the rate constraint decreases with the increase of the linear domain of the saturation function μ ₂ (s), that is, the smaller the slope of the linear domain of the function μ ₂ (s), the greater the constraint on the rate of change of the control law. powerful.

Here, the upper limit of the forward thrust change rate of the aerostat is taken as 20N·s ^-1 , so R ₁ =20, with For example, get Then the expression corresponding to the control law is: U=-10σ(0.8176u+0.25σ(0.7220x+3.2706u))

Step 3: Calculate the vector thrust and angle of each propeller required to reach the target position according to the forward and lateral nested saturation control law functions.

Specifically as follows:

Step 1. Establish the three-degree-of-freedom dynamic equation of the aerostat that only considers the plane motion as follows;

Among them, u, v, r represent the flight speed and yaw angular velocity of the aerostat along the x-axis and y-axis in the body coordinate system; Represents the differential of u, v, r, m represents the mass of the aerostat; I _z represents the moment of inertia of the aerostat around the z-axis; m ₁₁ , m ₂₂ represent the additional mass of forward motion and lateral motion, respectively, m ₃₃ represents The additional moment of inertia of the z-axis, F _Ax , F _Ay , N _A means that the aerostat is subjected to aerodynamic forces and moments along the x-axis, y-axis and around the z-axis, F _Tx , F _Ty , N _T means that the propeller is in x, y The resultant thrust in the direction and the resultant moment around the z-axis, F _Ix , F _Iy , and N _I represent the Cordial forces along the x-axis, y-axis and around the z-axis, respectively,

According to the mapping of the horizontal thrust on the xoy plane as shown in Figure 5, the relationship between F _Tx , F _Ty , N _T and the vector thrust and angle of a single propeller is obtained as follows

Among them, r _p represents the installation position of each propeller relative to the aerostat body center in the body coordinate system, F _ti represents the vector thrust of a single propeller, μ _ti represents the angle of the vector thrust of a single propeller, i=1,2, 3,4;

Step 2. Using the forward nested saturation control law function and the lateral nested saturation control law function, as well as the relationship between F _Tx , F _Ty , N _T and the vector thrust and rotation angle of a single propeller, calculate the single propeller required to reach the target position. Vector thrust F _ti and angle μ _ti of the propeller.

Through the simulation and verification of the specific example system, the simulation results under two conditions of no wind and wind are given. In order to reflect the advantages of the nested saturation control law, the optimized nested saturation controller and the PID control under saturation constraints are combined. The controller control effects are compared, and the results are shown in Figure 7-11.

The tracking trajectory in a given inertial coordinate system is as follows:

Among them, t represents time, and x _d and y _d represent the vertical and horizontal target positions, respectively.

The tracking situation of the system under a given trajectory is simulated, the given initial displacement velocity is all zero, and the wind field shown in the following formula is added in the x direction.

It can be seen from Figure 7 that the nested saturation control system can quickly track the target trajectory, with a small tracking error and less influence by wind disturbance. It can be seen from Figure 8 that the thrust is limited within the range of ±20N, and The rate of change is also limited within the range of ±20N/s; it can be seen from Figure 9 that the nested saturation control system has a shorter convergence time under wind disturbance, and the overshoot is small in the process of returning to the steady state. It can be seen from Figures 10 and 11 that the thrust and rotation angle of the propeller do not change drastically within the constraints. In contrast, the system under the saturation-constrained PID controller is prone to saturation because of the limited input amplitude and speed, resulting in more intense oscillations in the sudden change of wind field.

From the above simulation results, it can be found that the robustness of the nested saturation control law is better, it can ensure the stability of the system under different initial states and wind disturbance conditions, and can avoid the amplitude and rate saturation of the actuator. The display expresses the relationship between the actuator rate constraints and the tunable parameters of the controller, thereby improving the dynamic performance of the closed-loop system.

The present invention also provides a control system based on the above-mentioned control method for the fixed-point tracking of the multi-vector propeller combined aerostat, as shown in FIG. 12 , including a distance comparison module, the distance comparison module and the forward resultant force The generation module is connected with the lateral resultant force generation module, the forward resultant force generation module and the lateral resultant force generation module are connected with the control distribution module, and the control distribution module is connected with the main controller of the aerostat, and the main controller passes through the state measurement module. Connected with the distance comparison module, the state measurement module is connected with the forward resultant force generation module and the lateral resultant force generation module through the state transformation module.

The state measurement module is used to measure the attitude information of the aerostat, as well as the position and speed information under the geographic coordinate system; the state transformation module is used to convert the speed information under the geographic coordinate system into the speed information under the body coordinate system; The distance comparison module is used to receive the position information of the current position of the aerostat body center and the target position in the geographic coordinate system, and calculate the distance information D between the two; the forward resultant force generation module receives the current airframe coordinate system. The forward speed and distance information D of the component in the x-axis direction, and the forward nested saturation control law function is used to generate the resultant force of the vector thrust of each propeller in the x-axis direction; the lateral resultant force generation module receives the current body coordinate system. The components of the lateral speed and distance information D in the y-axis direction, and the lateral nested saturation control law function is used to generate the resultant force of the vector thrust of each propeller in the y-axis direction; the control distribution module is used to receive the vector thrust of each propeller The resultant forces in the x-axis and y-axis directions, combined with the dynamic equation of the aerostat, generate the vector thrust required by each propeller of the aerostat and its corresponding angle.

Specifically, the forward resultant force generation module includes a forward linear domain calculation module, a forward nested saturation control law generation module connected to the forward linear domain calculation module, and the forward linear domain calculation module is used for second-order embedding based on the forward linear domain calculation module. Set the saturation control law function, so that the maximum value of the second-order improved saturation function is equal to the amplitude of the resultant force of the vector thrust of each propeller in the x-axis direction, and the upper limit of the first-order differential of the second-order nested saturation control law function is equal to the value of each propeller. The rate of change of the resultant force of the vector thrust in the x-axis direction is used to calculate the linear domain of the second-order improved saturation function; the forward nested saturation control law generation module is used to generate each propeller based on the linear domain of the second-order improved saturation function The forward nested saturation control law function between the resultant force of the vector thrust in the x-axis direction and the forward velocity, the distance D in the x-axis component.

The lateral resultant force generation module includes a lateral linear domain calculation module, a lateral nested saturation control law generation module connected to the lateral linear domain calculation module, and the lateral linear domain calculation module is used for the second-order nested saturation control law based on function, the maximum value of the second-order improved saturation function is equal to the magnitude of the resultant force of the vector thrust of each propeller in the y-axis direction, and the upper limit of the first-order differential of the second-order nested saturation control law function is equal to the vector thrust of each propeller in the y-axis direction. The rate of change of the resultant force in the axial direction is used to calculate the linear domain of the second-order improved saturation function; the lateral nested saturation control law generation module is used to generate the vector thrust of each propeller based on the linear domain of the second-order improved saturation function in y The laterally nested saturation control law function between the resultant force in the axial direction and the lateral velocity, the component of the distance D in the y-axis.

Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that these are only examples, and various changes or modifications may be made to these embodiments without departing from the spirit and spirit of the present invention. Therefore, the protection scope of the present invention is defined by the appended claims.

Claims (10)

1. a kind of nested saturation control method for aerostat, it is characterized in that comprising the following steps: Step 1. Based on the continuously differentiable standard saturation function σ(r), establish an improved saturation function μ _i (s), i∈1,n, and then establish an n-order nested control law function; Step 2: Establish a second-order integral chain system of controlled quantities, take the second-order nested control law function and its corresponding improved saturation function μ ₂ (s), and use the first-order differential of the second-order nested control law function The upper limit of the controlled variable corresponds to the upper limit of the output change rate of the actuator, and the upper limit of the improved saturation function μ ₂ (s) is taken as the upper limit of the controlled variable corresponding to the output of the actuator, and the improved saturation function is calculated. The size of the linear domain of the function μ ₂ (s), and then the second-order nested control law function between the controlled variable and the output of the corresponding actuator is established; Step 3: Control the output of the actuator through control redistribution according to the second-order nested control law function between the controlled variable and the output of the corresponding actuator to complete the control of the controlled variable. 2. The nested saturation control method for aerostat according to claim 1, wherein: the expression of the standard saturation function is as follows Among them, L _σ represents the linear domain of σ(r), α _σ represents the slope in the linear domain of σ(r), S _σ represents the unsaturated domain of σ(r), H ₁ (r), H ₂ (r) represent The nonlinear function part in the unsaturated domain of σ(r), σ ^max represents the saturation value of the standard saturated function σ(r); The expression of the improved saturation function is as follows and in, represents the magnitude constraint of the function μ(s), represents the linear domain of the function μ(s), represents the slope in the linear domain of the function μ(s), represents the unsaturated domain of the function μ(s); The expression of the n-order nested control law function is set as U=-μ _n (y _n +μ _n-1 (y _n-1 +...+μ ₁ (y ₁ ))). 3. The nested saturation control method for aerostat according to claim 2, wherein: the expression of the upper limit of the first-order differential of the second-order nested control law function is as follows Among them, A ₂ ,A ₃ ,B ₂ ,B ₃ ,C ₂ ,C ₃ ,D ₂ ,D ₃ represent constant parameters, and their expressions are as follows make It is equal to the upper limit of the output quantity of the actuator corresponding to the controlled quantity, and R ₁ is equal to the upper limit of the output quantity change rate of the controlled quantity corresponding to the actuator, and the linear domain of the improved saturation function μ ₂ (s) is calculated. 4 . The nested saturation control method for aerostats according to claim 1 , wherein the controlled quantity is set as the forward speed or the lateral speed of the aerostat, and the corresponding actuator is set as 4 . The output of the propeller is set as the resultant force of the thrust provided by each propeller in the X-axis or Y-axis direction. 5. a control method for multi-vector propeller combined aerostat fixed-point tracking of the nested saturation control method for aerostat according to claim 1, is characterized in that comprising the following steps: Step 1: Calculate the distance D between the target position and the current body center position of the aerostat; Step 2. Establish the forward nested saturation control law function between the forward speed, the component of the distance D on the x-axis and the resultant force of the propeller's vector thrust in the x-axis direction, as well as the lateral speed, the component of the distance D on the y-axis and The laterally nested saturation control law function of the vector thrust of the propeller between the resultant forces in the y-axis direction; Step 3: Calculate the vector thrust and angle of each propeller required to reach the target position according to the forward and lateral nested saturation control law functions. 6. The control method for multi-vector propeller combined aerostat fixed-point tracking according to claim 5, wherein the step 2 comprises the following steps: Step 1. Establish the second-order integral chain system of forward velocity and lateral velocity, as shown below Among them, x ₁ represents the forward speed u or the side speed v, U=-μ ₂ (y ₂ +μ ₁ (y ₁ )) represents the second-order nested saturation control law function, represents the state transition between y ₁ , y ₂ and x ₁ , x ₂ , represents the slope in the linear domain of the function μ ₂ (s); Step Ⅱ, utilize the method as claimed in claim 3, the concrete expression of standard saturation function is as follows in, Taking σ ^max =2, L _σ =1, α _σ =1, Obtain the expression of the upper limit of the first-order differential of the second-order nested control law function as described below, and then make it equal to the upper limit of the rate of change of the resultant force of the thrust provided by each propeller in the x-axis and y-axis directions, and calculate the corresponding improved saturation Linear domain of the function μ ₂ (s) Step III. According to the calculated linear domain of the improved saturation function μ ₂ (s) Then establish the forward nested saturation control law function between the forward speed, the component of the distance D on the x-axis and the resultant force of the propeller's vector thrust in the x-axis direction, as well as the lateral speed, the component of the distance D on the y-axis and the propeller's The laterally nested saturation control law function between the resultant force of the vector thrust in the Y-axis direction. 7. the control method for multi-vector propeller combined aerostat fixed-point tracking according to claim 5, is characterized in that: Step 1. Establish the three-degree-of-freedom dynamic equation of the aerostat that only considers the plane motion as follows; Among them, u, v, r represent the flight speed and yaw angular velocity of the aerostat along the x-axis and y-axis in the body coordinate system; Represents the differential of u, v, r, m represents the mass of the aerostat; I _z represents the moment of inertia of the aerostat around the z-axis; m ₁₁ , m ₂₂ represent the additional mass of forward motion and lateral motion, respectively, m ₃₃ represents The additional moment of inertia of the z-axis, F _Ax , F _Ay , N _A means that the aerostat is subjected to aerodynamic forces and moments along the x-axis, y-axis and around the z-axis, F _Tx , F _Ty , N _T means that the propeller is in x, y The resultant thrust in the direction and the resultant moment around the z-axis, F _Ix , F _Iy , and N _I represent the Cordial forces along the x-axis, y-axis and around the z-axis, respectively, Thus, the relationship between F _Tx , F _Ty , N _T and the vector thrust and angle of a single propeller is obtained as follows Among them, r _p represents the installation position of each propeller relative to the aerostat body center in the body coordinate system, F _ti represents the vector thrust of a single propeller, μ _ti represents the angle of the vector thrust of a single propeller, i=1,2, 3,4; Step 2. Using the forward nested saturation control law function and the lateral nested saturation control law function, as well as the relationship between F _Tx , F _Ty , N _T and the vector thrust and rotation angle of a single propeller, calculate the single propeller required to reach the target position. Vector thrust F _ti and angle μ _ti of the propeller. 8. A control system based on the control method for multi-vector propeller combined aerostat fixed-point tracking according to claim 6, characterized in that: comprising a distance comparison module, the distance comparison module and the forward resultant force generation module and The lateral resultant force generation module is connected, the forward resultant force generation module and the lateral resultant force generation module are connected with a control distribution module, and the control distribution module is connected with the main controller of the aerostat, and the main controller passes through the state measurement module. is connected with the distance comparison module, and the state measurement module is connected with the forward resultant force generation module and the lateral resultant force generation module through the state transformation module; The state measurement module is used to measure the attitude information of the aerostat, as well as the position and speed information in the geographic coordinate system; The state transformation module is used to convert the speed information under the geographic coordinate system into the speed information under the body coordinate system; The distance comparison module is used to receive the position information of the current position of the aerostat body center and the target position under the geographic coordinate system, and calculate the distance information D between the two; The forward resultant force generation module receives the forward speed and distance information D under the current body coordinate system in the x-axis direction, and uses the forward nested saturation control law function to generate the resultant force of the vector thrust of each propeller in the x-axis direction. ; The lateral resultant force generation module receives the lateral speed and distance information D in the y-axis direction under the current body coordinate system, and uses the lateral nested saturation control law function to generate the resultant force of the vector thrust of each propeller in the y-axis direction. ; The control distribution module is used to receive the resultant force of the vector thrust of each propeller in the x-axis and y-axis directions, and combine with the dynamic equation of the aerostat to generate the vector thrust required by each propeller of the aerostat and its corresponding angle . 9. The control system for fixed-point tracking of a multi-vector propeller combined aerostat according to claim 8, wherein the forward resultant force generation module comprises a forward linear domain calculation module, which is different from the forward linear domain The forward nested saturation control law generation module connected to the calculation module, The forward linear domain calculation module is used to make the maximum value of the second-order improved saturation function equal to the magnitude of the resultant force of the vector thrust of each propeller in the x-axis direction based on the second-order nested saturation control law function, and the second-order nested The upper limit of the first-order differential of the saturation control law function is equal to the change rate of the resultant force of the vector thrust of each propeller in the x-axis direction, and the linear domain of the second-order improved saturation function is calculated; The forward nested saturation control law generation module is used to generate the vector thrust of each propeller in the x-axis direction based on the linear domain of the second-order improved saturation function, the forward speed, and the distance D between the components of the x-axis. The forward nested saturation control law function. 10. The control system for fixed-point tracking of a multi-vector propeller combined aerostat according to claim 8, wherein the lateral resultant force generation module comprises a lateral linear domain calculation module, which is different from the lateral linear domain The laterally nested saturation control law generation module connected to the calculation module, The lateral linear domain calculation module is used to make the maximum value of the second-order improved saturation function equal to the magnitude of the resultant force of the vector thrust of each propeller in the y-axis direction based on the second-order nested saturation control law function, and the second-order nested The upper limit of the first-order differential of the saturation control law function is equal to the change rate of the resultant force of the vector thrust of each propeller in the y-axis direction, and the linear domain of the second-order improved saturation function is calculated; The laterally nested saturation control law generation module is used to generate the vector thrust of each propeller in the y-axis direction based on the linear domain of the second-order improved saturation function, the lateral velocity, and the distance D between the components of the y-axis. The laterally nested saturation control law function.