CN112666960B - L1 augmentation self-adaption-based control method for rotary wing aircraft - Google Patents
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Abstract
The invention relates to a rotor craft control method based on L1 augmentation self-adaption, which comprises the steps of firstly establishing a rotor craft kinematics and dynamics model, designing cascade PID control rate and L1 augmentation self-adaption control rate, and obtaining total control input of the rotor craft. The method can estimate interference on line in real time, and can effectively realize stable control of the rotor craft and large disturbance by matching with the traditional cascade PID control. Practical engineering application shows that the L1-based augmentation self-adaption combined with the traditional cascade PID control can be easily realized in engineering, and the mode has better robustness, stronger disturbance rejection capability and better self-adaption effect than the traditional cascade PID control.
Description
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle application, relates to a control method of an unmanned aerial vehicle, and particularly relates to a control method of a rotor craft based on L1 augmentation self-adaption.
Background
With the development of science and technology, rotorcraft have been used in many military fields, such as reconnaissance of battlefield environments, and striking of small objects, etc. In the civil field, the rotor craft plays an important role in aerial photography, security, electric power inspection, oil and gas pipeline inspection and the like. In the actual flight process of the rotorcraft, the rotation speed of the rotor motor is controlled to achieve the desired position and attitude, and the control of the rotorcraft is the core of the rotorcraft capable of achieving the flight, so that the rotorcraft is particularly important. The control quality of the rotorcraft is directly related to the completion degree of the operation task, and is the core technical basis of the operation. Because the rotor craft needs to carry out the operation flow under complicated operating mode, need rotor craft can adapt to different operating modes to can all have fine control quality under various different operating modes. The traditional PID control has wide application because of no need of model, but because rotor flight needs to run in complex severe environment, the traditional PID control is difficult to adapt to complex working condition environments, such as windy weather, or sudden release of load, and the like, under the conditions, the traditional PID control is difficult to have very good control quality or one group of controller parameters are difficult to adapt to a plurality of working conditions, and the design structure of the control rate of the traditional PID+L1 augmentation adaptive control is proposed herein, can adapt to complex working conditions, and does not need to set a plurality of groups of parameters, and has very good control quality under each complex working condition. The cascade PID+L1 amplification self-adaptive control structure is provided for enhancing the self-adaptability and the robustness of the PID system so as to adapt to different working conditions, and the structure can adapt to the working conditions wider than a single cascade PID without resetting PID parameters to adapt to different working conditions like a single cascade PID, and can obtain better control quality.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a rotor craft control method based on L1 augmentation self-adaption.
Technical proposal
A rotor craft control method based on L1 augmentation self-adaption is characterized by comprising the following steps:
step 1, establishing a rotorcraft kinematics and dynamics model:
rotorcraft kinematic model:
wherein: m represents the weight of the unmanned aerial vehicle, g represents the gravitational acceleration, U 1 Represent lift, K d Represents the coefficient of resistance and,
wherein: ψ denotes a heading angle, θ denotes a pitch angle, γ denotes a roll angle,
a rotation matrix representing the machine system to the navigation system;
kinetic model of rotorcraft:
step 2, designing cascade PID control rate:
horizontal channel position loop control rate design:
v t ＝K p ·(p t -p)
wherein: p is p t Is the desired location; p is the current position, v t To a desired speed, K p The ratio gain is the position loop;
horizontal channel speed loop control rate design:
a t ＝K v ·(v t -v)
wherein: v t Is the desired speed; v is the current speed, a t For the desired acceleration, ψ is the mean heading angle,θ is pitch angle, γ is roll angle, K v Gain for the speed loop ratio;
θ t ＝arctan(-a x /g)
γ t ＝arctan(a y ·cosθ/g)
wherein: θ t Is a desired pose; θ is the current pose, a y ，a x Representing a horizontal acceleration;
angle ring control rate design:
ω t ＝K θ ·(α t -α)
ω t is the desired angular rate; omega is the current angular rate, K θ For the attitude loop proportional gain, alpha represents the dip angle, i.e. roll and pitch;
angular rate ring control rate design:
Δω＝ω t -ω
wherein: k (K) ω For angular rate loop proportional gain, K I For angular rate loop integral gain, K D For the angular rate loop differential gain,
representing an integral operation, s representing a differential operation; Δω is the target angular rate ω t Difference from the current angular rate ω +.>
S is a differential operation symbol;
step 3, L1 augmentation adaptive control rate:
the L1 augmented adaptive state prediction equation is:
wherein: a state matrix A, a control matrix B, a matrix A SP A 3 x 3 matrix with a determinant of negative values, T representing the period of operation of the controller;
wherein:
representing status error, ++>
Representing an estimated state, x (t) representing a true state;
adaptive rate of L1 adaptation:
output of the adaptive controller:
wherein: the expression of C(s) is
Step 4, general control input of the rotorcraft:
control output u of step 2 b (t) output u of step 3 a (t) adding to obtain the total control output u (t)
u(t)＝u b (t)+u a (t)。
Advantageous effects
According to the L1 augmentation self-adaptive rotor craft control method, interference can be estimated on line in real time, and the method is matched with the traditional cascade PID control, so that stable control of the rotor craft can be effectively achieved, and stable control of large disturbance can be achieved. Practical engineering application shows that the L1-based augmentation self-adaption combined with the traditional cascade PID control can be easily realized in engineering, and the mode has better robustness, stronger disturbance rejection capability and better self-adaption effect than the traditional cascade PID control.
The invention has the beneficial effects that:
(1) Compared with cascade PID, the anti-interference capability is stronger;
(2) Compared with cascade PID, the method has stronger adaptability;
(3) Compared with cascade PID, the method has stronger robustness;
(4) Compared with other modern control theory, the method is easier to realize in engineering, and does not need to finely identify the system model;
the L1 augmentation self-adaptive algorithm is combined with cascade PID, so that the adaptability and the robustness of the system can be enhanced, and the control performance of the rotorcraft is greatly improved.
Drawings
FIG. 1 is a horizontal channel control structure;
FIG. 2 height control structure;
FIG. 3 L1 augments an adaptive control architecture;
fig. 4 basic control rate+l1 augmented adaptive control architecture.
Detailed Description
The invention will now be further described with reference to examples, figures:
the first step, a dynamic and kinematic model of the rotorcraft is given for the rotorcraft as a controlled object; secondly, aiming at a model of the rotorcraft, a control strategy of a traditional cascade PID controller is provided, and the output of an angular rate ring in the PID controller is taken as a basic controller u b (output of the base controller); thirdly, we provide a specific implementation method of the L1 controller, and record the output of the L1 adaptive controller as u a (adaptive controller)An output); fourth, the control input of the model of the rotorcraft is u total The concrete representation method is as follows
u total ＝u a +u b (1)
The steps can be written as
(1) Establishing a six-degree-of-freedom model of the rotor craft;
(2) Aiming at a six-degree-of-freedom model of the rotor craft, a traditional cascade PID control strategy is provided;
(3) Aiming at a six-degree-of-freedom model of the rotorcraft, a specific implementation mode of L1 augmentation self-adaptive control is provided.
(4) And calculating the total control input of the rotorcraft by combining the control output of the cascade PID and the L1 augmentation self-adaptive control output.
The individual implementation steps are described in detail below.
Step 1, establishing a rotorcraft kinematics and dynamics model
The method only describes a traditional PID and L1 augmentation self-adaptive specific control method, does not describe a complex and fine model of the rotorcraft system, and only adopts general system description, for example, engineering researchers want to know the system model of the rotorcraft more deeply, and can refer to related literature data or books for further study.
Taking a four-rotor aircraft as an example, before deriving a six-degree-of-freedom model of the rotor aircraft, it is necessary to perform variable description on some variables that are used later. Definitions for variables to be used later
Table 1 shows the results.
TABLE 1 definition of physical variables
(1) Establishing a rotorcraft kinematics equation
Rotorcraft are subjected mainly to the following forces: gravity; lifting force; resistance.
According to the aerodynamic theory of the rotorcraft, the lift force U 1 Torsion in three directions (U 2 ，U 3 ，U 4 ) The specific calculation method of (1) is related to the rotating speed of the rotorcraft, and the expression is as follows:
the meanings of the respective letters in the formulae are shown in Table 1. According to the stress condition of the rotor craft, the kinematic equation of the rotor craft is obtained by applying Newton's second law:
the third term on the right of the above medium number is a drag term, which is proportional to the speed of the aircraft and has opposite signs.
Wherein the matrix is rotated
Is represented by the expression:
the ψ in the formula (7) represents a heading angle, θ represents a pitch angle, and γ represents a roll angle.
(2) Establishing a kinetic equation for a rotorcraft
The conversion relationship between the angular rate of the rotorcraft and the derivative of the euler angle is as follows:
the following equation holds according to the law of conservation of angular momentum:
the above detailed development is as follows:
then the kinetic equation for the rotorcraft can be derived.
Equations (7) and (11) describe the translational and rotational movement of the rotorcraft in space for the kinematic and kinetic model equations of the rotorcraft.
Step 2, design of cascade PID control rate
For the dynamics and kinematics model of the rotorcraft, the rotorcraft can be controlled by using a traditional cascade PID control mode, and the following description is divided into the following parts:
(1) horizontal position channel control structure
The control structure of the horizontal position channel is shown in fig. 1, and variables used in the figure are as follows:
(1)p t a desired location; p represents the current position, and the onboard integrated navigation systemCalculating to obtain;
(2)v t a desired speed; v represents the current speed and is calculated by an onboard integrated navigation system;
(3)a t a desired acceleration; a represents the current acceleration, and can be calculated by an organic vehicle-mounted integrated navigation system; see fig. 1;
(4)θ t a desired pose; θ represents the current gesture, which can be calculated by the organic-vehicle integrated navigation system;
(5)ω t a desired angular rate; ω represents the current angular rate, which can be obtained by an on-board integrated navigation system.
Desired position p t The expected speed v is obtained by making a difference from the current position p through a position proportion controller t The method comprises the steps of carrying out a first treatment on the surface of the Desired speed v t The expected acceleration a is obtained by making a difference with the current speed v through a speed proportional controller t . The above position loop and speed loop control rates can be described by the following formulas:
horizontal channel position loop control rate design:
v t ＝K p ·(p t -p) (12)
wherein K is p Is the position loop proportional gain.
Horizontal channel speed loop control rate design:
a t ＝K v ·(v t -v) (13)
wherein K is v Proportional gain for speed loop
Desired acceleration a t Theoretical calculation of the desired attitude θ by small disturbance hypothesis t The calculation formula for the conversion from the desired acceleration into the desired attitude is as follows, the condition of the small disturbance assumption being that the rotorcraft has no altitude-directional movement in the equilibrium position, the body has no heading-directional movement and the heading angle ψ≡0 is zero.
Is arranged to obtain
And (3) finishing the formula (15) again to obtain a calculation formula from acceleration to inclination angle:
equation (16) is the equation from acceleration to tilt angle (roll and pitch). According to (16) the desired acceleration a t Converted into the desired inclination angle theta t . Desired inclination angle theta t The error angle is obtained by making a difference with the current inclination angle, and the expected angular rate omega is obtained by the error angle through the gesture proportional controller t . The attitude loop control rate design can be expressed by the following expression:
ω t ＝K θ ·(α t -α) (17)
wherein K is θ For attitude loop proportional gain, α here represents tilt angle (roll and pitch).
Desired angular rate omega t The angular output of the angular rate controller obtained by the angular rate PID controller after the difference is made with the current measured angular rate is recorded as u b (u b Referred to as the base controller output, which is used in the subsequent steps), the horizontal position control architecture shown in fig. 1 describes how the control architecture thought of the tandem PID is transferred to the attitude control, i.e., the outer loop is the position loop and the inner loop is the attitude loop. Thus the output u of the base controller b The calculation formula of (2) is as follows:
wherein K is ω For angular rate loop proportional gain, K I For angular rate loop integral gain, K D For the angular rate loop differential gain,
the integral operation is represented, and s represents the differential operation. Δω is the target angular rate ω t Difference from the current angular rate ω +.>
S is the integral operation symbol and s is the differential operation symbol.
Step 3, L1 augmentation adaptive control rate design
The cascade PID+L1 amplification self-adaptive control structure is provided by combining the traditional cascade PID control structure and the L1 self-adaptive structure, so that the self-adaptability and the robustness of the PID system are enhanced, different working conditions can be adapted to, and the structure can be adapted to the working conditions wider than a single cascade PID without resetting PID parameters like a single cascade PID in order to adapt to different working conditions.
This control method is described below in terms of a gesture control loop:
the angular velocity PID control shown in fig. 1 is outputted as a basic controller control signal in fig. 3, so that fig. 3 can be changed to that shown in fig. 4. The combined controller is now called the base controller by the cascade PID control. For the attitude inner loop controller, we choose the triaxial organism angular rate as the state variable x, and record the output of the cascade PID angular rate PID controller as u b ：
u b Output of PID controller at angular rate (19)
I.e.
Then the L1 augmented adaptive state prediction equation is
The parameter interpretation in the formula (21) can be described in the section L1 augmentation self-adaption, and when the system matrix A is used in actual engineering, the system matrix A needs to be determined by a system identification methodAnd B, matrix A SP The 3×3 matrix with the determinant being negative can be adjusted in the actual use process.
x (t) represents a true value, and actual measured gyroscope data of the integrated navigation system may be used instead.
L1 adaptive self-adaption rate calculation:
t represents the running period of the controller, and in the practical use process, the higher the running frequency of the self-adaptive control rate is, the more the total uncertainty of the system can be estimated in real time
After the uncertainty estimate of the system is obtained, the L1-adaptive control quantity output u can be calculated by the following equation ad The output of the self-adaptive controller is:
the authors have discrete forms of C(s) in actual use:
the above bilinear transformation is:
and (3) making:
f c for the filter cut-off frequency, f s Data sampling frequency, f when the author actually uses s ＝1kHz，f c =5 Hz, different systems may differ slightly.
Redefining and sorting into:
then the real-time usage pair
Performing second order low pass filtering
Wherein the method comprises the steps of
The intermediate variable is w [ n ], w [ n-1] is the value of w [ n ] of the last period, and w [ n-2] is the value of w [ n ] of the last period.
Step 4, calculating the total control input of the rotorcraft
The controller output calculated in step 2 and step 3 is used as the control input u (t) of the actuator of the rotorcraft, and the calculation formula is as follows
u(t)＝u b (t)+u a (t) (32)
Wherein u is b (t) outputting the calculation engineering for the cascade PID angular rate controller as shown in the formula (18) of the step 2, u a (t) outputting it for L1 augmentation adaptive controllerThe calculation process is shown in (24).
When the self-adaptive control system is actually used, the operation period of the angular rate ring is 500HZ, the self-adaptive control self-adaptive rate operation rate of the L1 is 1000Hz, and the higher the operation frequency of the self-adaptive controller is, the faster the estimation of the uncertainty of the system is, and the better the control effect is.
The same applies to the height channel. The authors have greatly improved the wind resistance, attitude stability and overall stability of the rotorcraft after loading by using the control method in horizontal channel inner rings and vertical altitude inner rings.
Claims (1)
1. A rotor craft control method based on L1 augmentation self-adaption is characterized by comprising the following steps:
step 1, establishing a rotorcraft kinematics and dynamics model:
rotorcraft kinematic model:
wherein: m represents the weight of the unmanned aerial vehicle, g represents the gravitational acceleration, U 1 Represent lift, K d Represents the coefficient of resistance and,
wherein: ψ denotes a heading angle, θ denotes a pitch angle, γ denotes a roll angle,
a rotation matrix representing the machine system to the navigation system;
kinetic model of rotorcraft:
step 2, designing cascade PID control rate:
horizontal channel position loop control rate design:
v t ＝K p ·(p t -p)
wherein: p is p t For the desired position, p is the current position, v t To a desired speed, K p The ratio gain is the position loop;
horizontal channel speed loop control rate design:
a t ＝K v ·(v t -v)
wherein: v t For the desired speed, v is the current speed, a t For the desired acceleration, ψ is the heading angle, θ is the pitch angle, γ is the roll angle, K v Gain for the speed loop ratio;
θ t ＝arctan(-a x /g)
γ t ＝arctan(a y ·cosθ/g)
wherein: θ t For the desired pitch angle, θ is the current pitch angle, a x Represents tangential acceleration along the x-axis, a y Represents normal acceleration along the y-axis, gamma t Is the desired roll angle;
angle ring control rate design:
ω t ＝K θ ·(θ t -θ)
ω t for the desired angular rate, ω is the current angular rate, K θ For the proportional gain of the attitude loop, theta t The desired pitch angle is the θ, the current pitch angle;
angular rate ring control rate design:
Δω＝ω t -ω
wherein: k (K) ω For angular rate loop proportional gain, K I For angular rate loop integral gain, K D For the angular rate loop differential gain,
representing an integral operation, s representing a differential operation; Δω is the target angular rate ω t Difference from the current angular rate ω +.>
S is a differential operation symbol;
step 3, L1 augmentation adaptive control rate:
the L1 augmented adaptive state prediction equation is:
wherein: a state matrix A, a control matrix B, a matrix A SP A 3 x 3 matrix with a determinant of negative values, T representing the period of operation of the controller;
wherein: x% (t) represents the state error,
representing an estimated state, x (t) representing a true state;
adaptive rate of L1 adaptation:
output of the adaptive controller:
wherein: the expression of C(s) is
Step 4, general control input of the rotorcraft:
control output u of step 2 b (t) output u of step 3 a (t) adding to obtain the total control output u (t)
u(t)＝u b (t)+u a (t)。
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