CN112666960A - L1-based augmented self-adaptive rotor craft control method - Google Patents
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Abstract
The invention relates to a rotorcraft control method based on L1 augmentation self-adaptation, which comprises the steps of firstly establishing a rotorcraft kinematics and dynamics model, designing cascade PID control rate and L1 augmentation self-adaptation control rate, and obtaining the total control input of the rotorcraft. The method can estimate the interference in real time on line, and can effectively realize the stable control of the rotor wing aircraft and the stable control of large disturbance by matching with the traditional cascade PID control. Practical engineering application shows that the method can be easily realized in engineering by combining L1-based augmentation self-adaptation with traditional cascade PID control, and compared with the traditional cascade PID control, the method has the advantages of better robustness, stronger disturbance resistance and better self-adaptation effect.
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 rotorcraft based on L1 augmentation self-adaption.
Background
With the development of scientific technology, the rotary wing aircraft has been applied to many military fields, such as the investigation of battlefield environment, the striking of small targets and the like. In the civil field, the rotor craft plays an important role in aerial photography, security, power inspection, oil and gas pipeline inspection and the like. The rotary-wing aircraft can achieve the expected position and attitude by controlling the rotating speed of the rotary-wing motor in the actual flying process, and the control of the rotary-wing aircraft is the core of the rotary-wing aircraft capable of achieving the flying, so the control is particularly important. The control quality of the rotor craft is directly related to the completion degree of the operation task, and is the core technical foundation of the operation. Because rotor craft's needs carry out the operation flow under the operating mode of complicacy, need rotor craft can adapt to different operating modes to can both have fine control quality under various different operating modes. Traditional PID control, because need not be based on the model, have extensive application, but because rotor flight needs to be in complicated abominable environment operation, traditional PID control is difficult to adapt to complicated operating mode environment, for example strong wind weather, or the condition such as sudden release of load, traditional PID control is under this kind of environment, it is difficult to have fine control quality or a set of controller parameter is difficult to adapt to a plurality of operating modes, this paper proposes traditional PID + L1 augmentative adaptive control's control rate design structure, can adapt to complicated operating mode, and need not set multiunit parameter, all have fine control quality under each complicated operating mode. The cascade PID + L1 augmented adaptive control structure is provided to enhance the adaptivity and robustness of a 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, does not need to re-adjust PID parameters to adapt to different working conditions like the 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 rotorcraft control method based on L1 augmentation self-adaption.
Technical scheme
A rotorcraft control method based on L1 augmented adaptive is characterized by comprising the following steps:
step 1, establishing a rotor craft kinematics and dynamics model:
rotorcraft kinematics model:
wherein: m represents the weight of the unmanned aerial vehicle, g represents the acceleration of gravity, U1Denotes lift, KdThe coefficient of resistance is expressed as a function of,
three directional accelerations are shown.The machine system is connected with the navigation system rotation matrix;
wherein: ψ represents a heading angle, θ represents a pitch angle, γ represents a roll angle,a rotation matrix representing the machine system to the navigation system;
kinetic model of rotorcraft:
the rate of acceleration of the three-axis angle,representing the three-axis angular rate. I isxx,Iyy,IzzRepresenting the three-axis inertia, and L representing the distance from the center of the rotor to the center of mass of the aircraft; u shape1Representing lift, U2Torsion, U, representing the direction of roll3Torsion indicating pitch direction, U4A torque force representing a heading direction;
step 2, designing cascade PID control rate:
designing the control rate of a horizontal channel position loop:
vt=Kp·(pt-p)
wherein: p is a radical oftIs a desired position; p is the current position, vtTo the desired speed, KpIs the position loop proportional gain;
designing the control rate of a horizontal channel speed loop:
at=Kv·(vt-v)
wherein: v. oftA desired speed; v is the current speed, atFor desired acceleration,. psi.vProportional gain for the velocity loop;
θt=arctan(-ax/g)
γt=arctan(ay·cosθ/g)
wherein: thetatIs a desired pose; theta is the current attitude, ay,axRepresents a horizontal acceleration;
designing the control rate of an angle ring:
ωt=Kθ·(αt-α)
ωtis the desired angular rate; ω is the current angular rate, KθFor attitude ring proportional gain, α represents the tilt angle, i.e., roll and pitch;
design of angular rate loop control rate:
Δω=ωt-ω
wherein: kωFor angular rate loop proportional gain, KIFor angular rate loop integral gain, KDIn order to be the angular rate loop differential gain,represents an integral operation, s represents a differential operation; Δ ω is the target angular rate ωtThe difference from the current angular rate co,is an integral operation sign, and s is a differential operation sign;
step 3, L1 expands the adaptive control rate:
the state prediction equation of the L1 augmented adaptive is:
wherein: state matrix A, control matrix B, matrix ASPIs a 3 x 3 matrix with the determinant being negative, and T represents the period of controller operation;
wherein:which is indicative of a state error,representing the estimated state, x (t) representing the true state;
l1 adaptive adaptation rate:
output of adaptive controller:
wherein: the expression of C(s) is
And 4, inputting the total control of the rotor craft:
control output u of step 2b(t) and the output u of step 3a(t) adding to obtain the total control output u (t)
u(t)=ub(t)+ua(t)。
Advantageous effects
According to the L1-based augmented self-adaptive rotor aircraft control method, interference can be estimated on line in real time, and the method is matched with the traditional cascade PID control, so that not only can stable control over the rotor aircraft be effectively realized, but also stable control over large disturbance can be realized. Practical engineering application shows that the method can be easily realized in engineering by combining L1-based augmentation self-adaptation with traditional cascade PID control, and compared with the traditional cascade PID control, the method has the advantages of better robustness, stronger disturbance resistance and better self-adaptation effect.
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 robustness is stronger;
(4) compared with other modern control theories, the method is easier to realize in engineering, and a system model does not need to be finely identified;
the L1 augmented adaptive algorithm can enhance the adaptability and robustness of the system by combining with cascade PID, so that the control performance of the rotorcraft is greatly improved.
Drawings
FIG. 1 is a horizontal channel control structure;
FIG. 2 is a height control structure;
fig. 3L 1 expands the adaptive control architecture;
fig. 4 basic control rate + L1 augments the adaptive control structure.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
firstly, aiming at a controlled object which is a rotor aircraft, a dynamics and kinematics model of the rotor aircraft is given; in the second step, aiming at the model of the rotorcraft, a control strategy of a traditional cascade PID controller is given, and the output of an angular rate loop in the PID controller is used as a basic controller ub(output of base controller); thirdly, a concrete implementation method of the L1 controller is given, and the output of the L1 self-adaptive controller is recorded as ua(adaptive controller output); fourth, the control input for the model of the rotorcraft is utotalThe concrete expression method is as follows
utotal=ua+ub (1)
The above 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 a rotor craft, a traditional cascade PID control strategy is provided;
(3) and aiming at a six-degree-of-freedom model of the rotor craft, a specific implementation mode of L1 augmented adaptive control is provided.
(4) The total control input of the rotorcraft is calculated by combining the control output of the cascade PID and the augmented adaptive control output of L1.
The various implementation steps are described in detail below.
Step 1, establishing a rotorcraft kinematics and dynamics model
The patent of the method only explains the specific control method of the traditional PID combined with the L1 augmentation self-adaptation, does not make complicated and fine model description on 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 relevant literature data or books for further research.
Taking a four-rotor aircraft as an example, before deriving a six-degree-of-freedom model of the rotor aircraft, some variables to be used subsequently need to be subjected to variable description. The variables used subsequently are defined in
Shown in table 1.
Table 1 physical variable definitions
Establishing a rotorcraft kinematic equation
Rotorcraft are subjected mainly to several forces: gravity; a lifting force; resistance force.
According to the aerodynamic theory of rotorcraft, lift U1Three directional torsion (U)2,U3,U4) The specific calculation method of (2) is related to the rotating speed of the rotorcraft, and the expression is as follows:
the meanings of the letters in the formula are shown in Table 1. According to the stress condition of the rotor craft, applying Newton's second law to obtain the kinematic equation of the rotor craft:
the third term on the right of the middle sign in the above formula is a resistance term which is proportional to the speed of the aircraft and has opposite signs.
ψ in equation (7) represents a heading angle, θ represents a pitch angle, and γ represents a roll angle.
Second, establish the dynamic equation of the rotor craft
The conversion relationship between the angular rate of a rotorcraft and the differential of the euler angle is as follows:
the following equation holds true according to the law of conservation of angular momentum:
the above formula is developed in detail as follows:
then the equations of dynamics for the rotorcraft can be derived.
Equations (7) and (11) are kinematic and dynamic model equations of a rotorcraft that describe translational and rotational motion of the rotorcraft in space.
Step 2, designing cascade PID control rate
For a dynamics and kinematics model of a rotorcraft, the rotorcraft can be controlled by using a traditional cascade PID control mode, and the following sections are introduced to the traditional cascade PID:
horizontal position channel control structure
The control structure of the horizontal position channel is shown in fig. 1, and the variables used in the figure are as follows:
(1)pta desired position; p represents the current position and is calculated by an airborne integrated navigation system;
(2)vta desired speed; v represents the current speed and is calculated by an airborne integrated navigation system;
(3)ata desired acceleration; a represents the current acceleration and can be calculated by an airborne integrated navigation system; see FIG. 1;
(4)θta desired pose; theta represents the current attitude and can be obtained by calculation of an airborne integrated navigation system;
(5)ωta desired angular rate; ω represents the current angular rate, which can be obtained by the onboard integrated navigation system.
Desired position ptObtaining the expected speed v through the position proportional controller by making difference with the current position pt(ii) a Desired velocity vtObtaining the expected acceleration a through a speed ratio controller by making difference with the current speed vt. The position loop and velocity loop control rates described above can be described by the following equations:
designing the control rate of a horizontal channel position loop:
vt=Kp·(pt-p) (12)
wherein KpIs the position loop proportional gain.
Designing the control rate of a horizontal channel speed loop:
at=Kv·(vt-v) (13)
wherein KvProportional gain for velocity loop
Desired acceleration atObtaining the expected attitude theta through theoretical calculation of small perturbation hypothesistCalculation of the desired attitude from the desired accelerationThe formula is as follows, the condition for the small disturbance assumption is that the rotorcraft has no movement in the altitude direction at equilibrium, the airframe has no movement in the heading direction and the heading angle ψ ≈ 0 is zero.
Is finished to obtain
And (5) finishing the formula (15) again to obtain a calculation formula from the acceleration to the inclination angle:
equation (16) is the equation from acceleration to pitch (roll and pitch). According to (16), the desired acceleration a can be passedtConversion to a desired inclination angle thetat. Desired inclination angle thetatObtaining an error angle by making a difference with the current inclination angle, and obtaining an expected angular rate omega by the error angle through an attitude proportional controllert. The attitude loop control rate design can be expressed by the following expression:
ωt=Kθ·(αt-α) (17)
wherein KθFor the attitude ring proportional gain, α here denotes the tilt angle (roll and pitch).
Desired angular rate ωtObtaining angular output of the angular rate controller recorded as u through the angular rate PID controller after making difference with the current measured angular rateb(ubReferred to as the base controller output, which will be used in subsequent steps), the horizontal position control structure shown in fig. 1 describes how to transfer to the attitude control through the control structure thinking of the cascade PID, i.e., the outer ring is the position ring and the inner ring is the attitude ring. Thus the output u of the basic controllerbThe calculation formula of (a) is as follows:
wherein KωFor angular rate loop proportional gain, KIFor angular rate loop integral gain, KDIn order to be the angular rate loop differential gain,denotes an integral operation, and s denotes a differential operation. Δ ω is the target angular rate ωtThe difference from the current angular rate co,is the sign of the integral operation and s is the sign of the derivative operation.
Step 3, L1 augmented adaptive control rate design
A cascade PID + L1 augmented adaptive control structure is provided by combining a traditional cascade PID control structure and an L1 adaptive structure, so that the adaptivity and robustness of a PID system are enhanced, different working conditions are adapted, the structure can be adapted to the working conditions wider than a single cascade PID, and the PID parameters do not need to be re-adjusted to adapt to different working conditions like the single cascade PID.
This control method is described below in an attitude control loop:
the output is controlled by the angular velocity PID shown in fig. 1 as the basic controller control signal in fig. 3, and thus fig. 3 may become as shown in fig. 4. The controller combined by the cascaded PID control is now referred to as the base controller. For the attitude inner ring controller, the angular rate of a three-axis machine body is selected as a state variable x, and the output of an angular rate PID controller of a cascade PID is recorded as ub:
ubAngular rate PID controller output (19)
Namely, it is
Then the state prediction equation for the L1 augmented adaptation is
The parameter interpretation in the formula (21) is described in the section of L1 augmented adaptive, and when the practical engineering is used, the system matrixes A and B need to be determined by a system identification method, and the matrix ASPThe matrix is a 3 x 3 matrix with the determinant being negative, and can be adjusted in the actual process.
x (t) represents the true value and may be replaced with actual measured gyroscope data of the integrated navigation system.
L1 adaptive adaptation rate calculation:
t represents the running period of the controller, and the total uncertainty of the system can be estimated in real time when the running frequency of the adaptive control rate is higher in the actual use process
After obtaining the uncertainty estimate of the system, the adaptive control output u of L1 can be calculated by the following equationadI.e. the output of the adaptive controller:
the discrete form of C(s) actually used by the authors is:
the above equation is bilinear as:
order:
fcis the filter cut-off frequency, fsFor data sampling frequency, when the author actually uses fs=1kHz,fcDifferent systems may differ slightly by 5 Hz.
Redefined and arranged as:
Wherein
The intermediate variable is wn, wn-1 is the value of wn in the previous cycle, and wn-2 is the value of wn in the previous cycle.
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 actuating mechanism of the rotorcraft, and the calculation formula is
u(t)=ub(t)+ua(t) (32)
Wherein u isb(t) the calculation project of the output of the cascade PID angular rate controller is shown in a step 2, a formula (18), ua(t) the calculation process of the output of the augmented adaptive controller of L1 is shown in (24).
When the method is actually used, the operation cycle of the angular rate loop is 500HZ, the operation rate of the L1 self-adaptive control self-adaptive rate is 1000Hz, the higher the operation frequency of the self-adaptive controller is, the faster the estimation on the uncertainty of the system is, and the control effect is better.
The same applies to the height channel. By using the control method for the horizontal channel inner ring and the vertical direction height inner ring, the wind resistance, the posture stability and the overall stability of the rotor craft after the load is put on are greatly improved.
Claims (1)
1. A rotorcraft control method based on L1 augmented adaptive is characterized by comprising the following steps:
step 1, establishing a rotor craft kinematics and dynamics model:
rotorcraft kinematics model:
wherein: m represents the weight of the unmanned aerial vehicle, g represents the acceleration of gravity, U1Denotes lift, KdThe coefficient of resistance is expressed as a function of,
three directional accelerations are shown.The machine system is connected with the navigation system rotation matrix;
wherein: ψ represents a heading angle, θ represents a pitch angle, γ represents a roll angle,a rotation matrix representing the machine system to the navigation system;
kinetic model of rotorcraft:
the rate of acceleration of the three-axis angle,representing the three-axis angular rate. I isxx,Iyy,IzzRepresenting the three-axis inertia, and L representing the distance from the center of the rotor to the center of mass of the aircraft; u shape1Representing lift, U2Torsion, U, representing the direction of roll3Torsion indicating pitch direction, U4A torque force representing a heading direction;
step 2, designing cascade PID control rate:
designing the control rate of a horizontal channel position loop:
vt=Kp·(pt-p)
wherein: p is a radical oftIs a desired position; p is the current position, vtTo the desired speed, KpIs the position loop proportional gain;
designing the control rate of a horizontal channel speed loop:
at=Kv·(vt-v)
wherein: v. oftA desired speed; v is the current speed, atFor desired acceleration,. psi.vProportional gain for the velocity loop;
θt=arctan(-ax/g)
γt=arctan(ay·cosθ/g)
wherein: thetatIs a desired pose; theta is the current attitude, ay,axRepresents a horizontal acceleration;
designing the control rate of an angle ring:
ωt=Kθ·(αt-α)
ωtis the desired angular rate; ω is the current angular rate, KθFor attitude ring proportional gain, α represents the tilt angle, i.e., roll and pitch;
design of angular rate loop control rate:
Δω=ωt-ω
wherein: kωFor angular rate loop proportional gain, KIFor angular rate loop integral gain, KDIn order to be the angular rate loop differential gain,represents an integral operation, s represents a differential operation; Δ ω is the target angular rate ωtThe difference from the current angular rate co,is an integral operation sign, and s is a differential operation sign;
step 3, L1 expands the adaptive control rate:
the state prediction equation of the L1 augmented adaptive is:
wherein: state matrix A, control matrix B, matrix ASPIs a 3 x 3 matrix with the determinant being negative, and T represents the period of controller operation;
wherein:which is indicative of a state error,representing the estimated state, x (t) representing the true state;
l1 adaptive adaptation rate:
output of adaptive controller:
wherein: the expression of C(s) is
And 4, inputting the total control of the rotor craft:
control output u of step 2b(t) and the output u of step 3a(t) adding to obtain the total control output u (t)
u(t)=ub(t)+ua(t)。
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