CN106325291B - Sliding mode control law and ESO (electronic stability program) based four-rotor aircraft attitude control method and system - Google Patents
Sliding mode control law and ESO (electronic stability program) based four-rotor aircraft attitude control method and system Download PDFInfo
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Abstract
The invention relates to the technical field of automatic control, in particular to a method and a system for controlling the attitude of a four-rotor aircraft based on a sliding mode control law and ESO (electronic stability and attitude optimization). The invention provides a four-rotor aircraft attitude control method based on a sliding mode control law and ESO (electronic stability and safety engineering), which comprises the steps of utilizing the sliding mode control method to realize the control of three attitude angle loops of a four-rotor; the real-time estimation of the total disturbance of the system is realized by utilizing the ESO; the sliding mode control model is combined with the ESO to control the posture of the four-rotor aircraft. Compared with the existing attitude control method, the attitude control method of the four-rotor aircraft has the advantages that the attitude stability of the four-rotor aircraft can be realized, the good tracking performance on the attitude angle instruction is realized, and the anti-jamming capability is stronger compared with the common sliding mode control.
Description
Technical Field
The invention relates to the technical field of automatic control, in particular to a method and a system for controlling the attitude of a four-rotor aircraft based on a sliding mode control law and ESO (electronic stability and attitude optimization).
Background
The four-rotor unmanned aerial vehicle has wide application in the fields of military, industry and civilian use, and has wide application prospect in the fields of investigation and monitoring, electronic interference, weapon attack, traffic monitoring, forest fire prevention, geological exploration, disaster search and rescue, aerial photography and mapping and the like. The applications all need high-precision automatic flight control, wherein attitude control is the most basic control requirement for stable flight of the four-rotor aircraft. The attitude motion of the four-rotor aircraft has strong coupling, multivariable and nonlinearity. Uncertain and the like, and is easily interfered by the outside, so the attitude control is a key technology and a difficult point of the flight control.
At present, for attitude control of four rotors, there are several control methods:
1. the control method based on learning comprises the following steps: and designing the attitude controller of the four-rotor aircraft based on fuzzy control, a neural network adaptive algorithm and robust neural network control. Although the controller does not need a four-rotor motion model, a large amount of experiments and flight data are needed to train the system, the algorithm is complex, the requirement on hardware is high, most of research stays in a simulation stage, and the controller is not practically applied.
2. The linear control method comprises the following steps: and designing a four-rotor attitude controller based on a PID (proportion integration differentiation) and LQ (Linear-Quadrature-quality) control method. This type of linear controller is simpler to implement, but its controller performance can drop significantly when the quad-rotor aircraft is out of nominal conditions or maneuvers over a wide range. At present, an attitude control method designed based on the active disturbance rejection theory exists, but the attitude control method is not realized in hardware.
3. The model-based nonlinear control method comprises the following steps: the four-rotor controller is designed based on feedback linearization, a backstepping method and sliding mode control, the control method needs to depend on an accurate model, and the control performance and the motion range of the four-rotor can be enhanced by the method on the premise that model parameters can be obtained. For example, sliding mode control has better robustness, but since such controllers do not observe system interference in real time, the control effect is not ideal when the interference is large.
Therefore, it is necessary to provide an attitude control method that can achieve a high-quality attitude control of a quad-rotor aircraft with low implementation difficulty and low requirements on hardware systems, and can effectively enhance the system disturbance capability.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a four-rotor aircraft attitude control based on a sliding mode control law and an ESO (electronic stability and attitude optimization), which comprises the following steps:
deducing a four-rotor aircraft dynamic model according to model parameters, constructing a sliding mode surface according to the four-rotor aircraft dynamic model, and acquiring a sliding mode control law according to the sliding mode surface so as to realize control of three attitude angle loops of the four-rotor aircraft;
constructing an ESO according to control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four rotors, and estimating total system disturbance in real time by using the ESO;
and combining the sliding mode control law with the ESO to realize the control of the posture of the four-rotor aircraft.
According to the attitude control method of the four-rotor aircraft based on the sliding mode control law and the ESO, the ESO (EXtended State Observer, ESO for short, Chinese means: an EXtended State Observer) is used for realizing real-time estimation of total disturbance of the system, and is combined with sliding mode control, so that not only can the attitude stability of the four-rotor aircraft be realized, but also the attitude angle instruction has good tracking performance, and the method has stronger anti-jamming capability compared with common sliding mode control.
Further, the four-rotor aircraft dynamics model parameters include moment of inertia Jx、Jy、Jz(ii) a Coefficient of lift cT(ii) a Coefficient of torque cQ(ii) a The time constant T of the motor.
Further, acquiring the sliding mode control model comprises the following steps: (1) considering the quadrotors as rigid bodies, the nonlinear dynamic equation of the posture of the quadrotor aircraft is as follows:
wherein: phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotary inertia of the four rotors along the directions of x, y and z axes;
(2) rewriting the nonlinear dynamical equation into the form of a state space:
wherein, U is the input vector, and X is the state vector, and the specific expression is as follows:
the state variables are as follows:
inputting a vector: u ═ U1 U2 U3]T＝[τφ τθ τψ]T
(3) The conversion matrix between the attitude angle change rate and the body angular rate is used as an identity matrix under the condition of hovering or small-angle flight,
obtaining the sliding mode control model:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotational inertia of the four rotors along the directions of the x axis, the y axis and the z axis respectively.
Further, in the process of deducing a four-rotor aircraft dynamic model according to model parameters and constructing a sliding mode surface according to the four-rotor aircraft dynamic model,
the slip form surface of the structure is
The obtained sliding mode control law is as follows:
wherein the content of the first and second substances,
wherein sign represents a sign function, which is replaced by an approximate continuous saturation function sat(s); the functional expression is:
sat(s) ═ s/(| s | + e) e ∈ [0,1], where e is 0.5;
constructing a second-order filter:
Thus, an expression in the time domain is obtained:
the damping ratio xi is 0.8, natural frequency omega is selectedn＝4.375。
Further, in the process of constructing the ESO based on the control inputs and outputs of the roll angle loop, the pitch angle loop and the yaw angle loop of the four rotors,
wherein the content of the first and second substances,
b0to control the quantity coefficient by 1/JxSelecting a predetermined parameter beta01,β02,β03And ai(i is 1,2), let a1＝0.5,a2＝0.25。
Further, in the process of combining the sliding mode control law and the ESO,
similarly, the control output of the other two attitude loops is obtained as follows:
wherein z is3φ,z3θ,z3ψThe ESO of the roll angle loop, the pitch angle loop and the yaw angle loop respectively obtain the expanded state quantity.
The invention also provides a four-rotor aircraft attitude control system based on the sliding mode control law and the ESO, which comprises the following steps:
the attitude angle loop control unit is used for deducing a four-rotor aircraft dynamic model according to model parameters, constructing a sliding mode surface according to the four-rotor aircraft dynamic model, and acquiring a sliding mode control law according to the sliding mode surface so as to realize control of three attitude angle loops of the four-rotor aircraft;
the system total disturbance real-time estimation unit is used for constructing an ESO (electronic stability and safety) according to the control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four rotors and estimating the total disturbance of the system in real time by using the ESO;
and the four-rotor aircraft attitude control unit is used for adopting the sliding mode control law and the ESO to be combined so as to realize the control of the four-rotor aircraft attitude.
Further, the four-rotor aircraft dynamics model parameters include moment of inertia Jx、Jy、Jz(ii) a Coefficient of lift cT(ii) a Coefficient of torque cQ(ii) a The time constant T of the motor.
Further, the acquisition of the sliding mode control model by the attitude angle loop control unit comprises the following steps:
(1) considering the four rotors as rigid bodies, the nonlinear dynamic equation of the attitude of the four-rotor aircraft is as follows:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotary inertia of the four rotors along the directions of x, y and z axes;
(2) rewriting the nonlinear dynamical equation into the form of a state space:
wherein, U is the input vector, and X is the state vector, and the specific expression is as follows:
the state variables are as follows:
inputting a vector: u ═ U1 U2 U3]T＝[τφ τθ τψ]T
(3) Attitude angle changeThe conversion matrix between the transformation rate and the body angular rate is used as an identity matrix under the condition of hovering or small-angle flight,
obtaining the sliding mode control model:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotational inertia of the four rotors along the directions of the x axis, the y axis and the z axis respectively.
Further, in the process that the attitude angle loop control unit deduces a four-rotor aircraft dynamic model according to model parameters, constructs a sliding mode surface according to the four-rotor aircraft dynamic model, and acquires a sliding mode control law according to the sliding mode surface,
the slip form surface of the structure is
The obtained sliding mode control law is as follows:
wherein the content of the first and second substances,
wherein sign represents a sign function, which is replaced by an approximate continuous saturation function sat(s); the functional expression is:
sat(s) ═ s/(| s | + e) e ∈ [0,1], where e is 0.5;
constructing a second-order filter:
Thus, an expression in the time domain is obtained:
the damping ratio xi is 0.8, natural frequency omega is selectedn＝4.375。
Further, in the process of constructing the ESO according to the control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four rotors by the system total disturbance real-time estimation unit,
wherein the content of the first and second substances,
b0to control the quantity coefficient by 1/JxSelecting a predetermined parameter beta01,β02,β03And ai(i is 1,2), let a1＝0.5,a2＝0.25。
Further, in the process of combining the sliding mode control law and the ESO by the attitude control unit of the four-rotor aircraft,
similarly, the control output of the other two attitude loops is obtained as follows:
wherein z is3φ,z3θ,z3ψThe ESO of the roll angle loop, the pitch angle loop and the yaw angle loop respectively obtain the expanded state quantity.
By adopting the technical scheme, the method has the following beneficial technical effects:
1) the real-time estimation of the total disturbance of the system is realized by utilizing the ESO;
2) and ESO is combined with a sliding mode control law, so that the attitude stability of the four-rotor aircraft can be realized, the tracking performance of the attitude angle instruction is good, and the anti-jamming capability is stronger compared with that of the common sliding mode control.
Drawings
FIG. 1 is a schematic diagram illustrating an attitude control flow of a sliding-mode ESO-based quad-rotor aircraft according to the present invention;
fig. 2 schematically shows a structural schematic diagram of the sliding mode control model of the present invention in combination with an ESO;
FIG. 3 is a diagram schematically illustrating a second order low pass filter structure in the sliding mode control model according to the present invention;
FIG. 4 illustrates an exemplary four-rotor roll angle response curve comparison of the present invention;
FIG. 5 illustrates an exemplary quad-rotor pitch response curve comparison of the present invention;
FIG. 6 is a graphical comparison of the yaw response curves of the four rotors of the present invention;
FIG. 7 schematically illustrates attitude loops ESO interference estimates of the present invention;
FIGS. 8-1 and 8-2 illustrate exemplary roll angle comparison plots for two control methods of the present invention;
FIGS. 9-1 and 9-2 schematically illustrate actual pitch curve comparison for two control methods of the present invention;
FIGS. 10-1 and 10-2 are graphs illustrating a comparison of attitude angle curves for two control methods under external disturbance according to the present invention;
fig. 11 is a schematic diagram schematically illustrating the logical structure of the attitude control system of a four-rotor aircraft based on sliding-mode control law and ESO according to the present invention.
Detailed Description
The present invention will be described in further detail below with reference to specific embodiments and with reference to the attached drawings.
As shown in fig. 1, the present invention provides a sliding-mode control law and ESO based attitude control of a quad-rotor aircraft, comprising:
s110: the method comprises the steps of obtaining a sliding mode control model according to dynamic model parameters of the quadrotor aircraft, constructing a sliding mode surface according to the sliding mode control model, and obtaining a sliding mode control law according to the sliding mode surface so as to control three attitude angle loops of the quadrotor aircraft;
s120: establishing an ESO according to the roll angle, the pitch angle or the yaw angle of the four rotors, and estimating the total disturbance of the system in real time by using the ESO;
s130: and a sliding mode control model is combined with the ESO to realize the control of the posture of the four-rotor aircraft.
The specific process of the attitude control method of the four-rotor aircraft based on the sliding mode control law and the ESO is that before the sliding mode control model is obtained, model parameters are obtained through an experimental test method; wherein the actually measured parameter includes the moment of inertia Jx,Jy,Jz(ii) a Coefficient of lift cT(ii) a Coefficient of torque cQ(ii) a The time constant T of the motor.
In step S110, the step of obtaining the sliding mode control model includes:
(1) the four rotors are regarded as rigid bodies, the gyroscopic effect generated by the rotation motion is ignored, and the obtained nonlinear dynamic equation of the attitude of the four-rotor aircraft is as follows:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle; p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively; tau isφ,τθ,τψControl moments in the directions of the three body shafts respectively; j. the design is a squarex,Jy,JzThe rotational inertia of the four rotors along the directions of the x axis, the y axis and the z axis respectively.
(2) The above equation is rewritten in the form of a state space:
wherein, U is an input vector, X is a state vector, and the specific expression is as follows:
the state variables are as follows:
inputting a vector:
U＝[U1 U2 U3]T＝[τφ τθ τψ]T
(3) the conversion matrix between the attitude angle change rate and the body angular rate can be regarded as an identity matrix under the condition of hovering or small-angle flight, namely
This results in a control model:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotational inertia of the four rotors along the directions of the x axis, the y axis and the z axis respectively.
Constructing a slip form surface according to a slip form control model:
constructing an extended Lyapunov function:
order to
Wherein k is1,k2>0, sign stands for sign function.
The sliding mode control law is thus:
wherein:
the sign function is replaced by a continuous saturation function sat(s), sat(s) s/(| s | + e) e ∈ [0,1], and e is 0.5.
Constructing a second-order filter:
From this, an expression of this equation in the time domain is obtained:
the damping ratio xi is 0.8, natural frequency omega is selectedn＝4.375。
In the embodiment of the present invention, the specific structure of the second-order filter is shown in fig. 3.
In step S120 shown in fig. 1, the specific structure of the ESO is implemented as follows:
the specific structural implementation of the ESO is illustrated by taking the roll angle channel of a four-rotor as an example. The roll angle phi equation of the four rotors is written in the form of:
wherein, b0To control the quantity coefficient by 1/Jx；ω2(t) is the amount of external interference;
is the sum of various perturbation effects (including modeled, unmodeled dynamics, and external perturbations). Make the total disturbance quantity
Expanded state variables, i.e. x, considered unknown3A, the equation becomes a linear system of the form:
then, a nonlinear extended state observer is established for the system:
wherein the content of the first and second substances,
selecting an appropriate parameter beta01,β02,β03And ai(i is 1,2), and a is usually taken out1＝0.5,a20.25, the extended state observer output ziCan well estimate each state quantity x of the original systemiWherein z is3→x3F (·) + ω (t), although the specific functional expression of f (·) and ω (t) is unknown, but in the expanded state z3The total disturbance a of the system can be estimated well.
Similarly, the other two angular loops, namely the pitch angle theta and the yaw angle psi, adopt the same algorithm processing, so that the dynamic compensation linearization of each channel can be realized.
In step S130, taking the roll angle Φ loop as an example, based on the sliding mode control law and the ESO combination, the formula is as follows:
similarly, the control outputs of the other two attitude loops can be obtained as follows:
wherein z is3φ,z3θ,z3ψThe ESO of the roll angle loop, the pitch angle loop and the yaw angle loop respectively obtain the expanded state quantity. The principle of the combination of ESO and sliding mode control model, also referred to as sliding mode controller, of the present invention is shown in detail in the implementation shown in fig. 2.
In the present invention, the simulation verification and the test flight verification are performed in the following embodiments.
In order to verify the controller designed herein and its anti-jamming effect, the attitude initial value of the quad-rotor aircraft is set to (phi, theta, psi) at (30 °, -45 °, -15 °). When 0s<t<At 6s, phid＝θd＝ψd0 °; when 6s<t<At 20s, phid＝θd＝ψd10 °; when 20s<t<Phi at 30sd＝θd＝ψdSin (t) (unit: degrees); when 9.5s<t<External interference of 0.008 Nm is applied to three attitude loops at the same time at 10.5s, and 14.5s<t<External disturbances of-0.008N · m were applied simultaneously to the three attitude loops at 15.5 s.
The parameters of the sliding mode control model part are adjusted to alpha through debugging1＝α2＝α3＝1,k1＝k3＝k5＝2.5,k2＝k4＝3,k6Parametric reference to the extended state observer part [19 ]]H is the sampling step, here 0.004, and the parameter β01,β02,β03Is determined by the sampling step h (the same beta can be used regardless of the controlled object, if the step is constant01,β02,β03) Here take beta01＝β02＝β03The same ESO parameters are used for the three attitude loops, 80.
To better illustrate the superiority of the present controller, the results will be compared to those of a sliding mode controller alone, with the same initial conditions, tracking commands and external disturbances. The simulation results are shown in fig. 4 to 6.
Fig. 4-6 are comparison graphs of simulation curves of each circuit of attitude control of a four-rotor aircraft. Compared to sliding mode control alone and with ESO. As can be seen from the figure, in the whole process, the two control methods can enable the attitude angle of the four rotors to quickly respond and track the attitude command; however, in the time periods of 9.5s < t <10.5s and 14.5s < t <15.5s, due to the action of system disturbance, the attitude angle change amount of the sliding mode control with the ESO is smaller compared with that of the sliding mode control alone, and the algorithm has strong anti-interference performance; in addition, fig. 4 and 6 show that the roll angle and yaw angle response times are shorter with sliding mode control with ESO.
Fig. 7 shows attitude loop ESO interference estimates. As can be seen from fig. 7, when the tracking command is quickly responded and subjected to external interference, the value of ESO is not zero, and other time periods are zero, indicating that it is possible to estimate the disturbance sum in real time.
In the embodiment of the invention, during test flight, the whole four-rotor hardware platform performs equal-altitude mode test flight outdoors, can be stabilized at a specified height, and simultaneously, the attitude control uses the controller designed herein, and the remote controller gives an attitude instruction. In order to better illustrate the superiority of the controller, the test flight results of a rolling angle loop and a pitching angle loop are compared with the test flight results of a single sliding mode controller; in order to better explain the interference resistance of the controller, 108g objects were mounted on the two attitude angle circuits in the trial flight as applied external disturbance torques, and the results were compared. The actual results are shown in fig. 8 to 10.
It should be noted that fig. 8 and fig. 9 are actual comparison graphs of the roll angle and the pitch angle under the two control methods, respectively. From fig. 8-1 and fig. 9-1, it can be seen that the actual tracking error of the roll angle reaches 5.5 degrees at most when the sliding mode control is carried out alone, and the fluctuation near zero degree is +/-5.7°To (c) to (d); the actual tracking error of the pitch angle reaches 4.5 degrees at most, and the fluctuation near zero degree is +/-5.1 degrees; based on sliding mode and ESO control, the actual tracking error of the roll angle reaches 4.6 degrees to the maximum, and the fluctuation near zero degree is +/-5.7°To (c) to (d); the actual tracking error of the pitch angle reaches 2 degrees at most, and the actual tracking error of the pitch angle is zeroNear fluctuation is +/-3°To (c) to (d); the tracking performance of the control method based on the sliding mode and the ESO is more accurate, and the actual fluctuation range is smaller.
In the embodiment of the invention, the actual curve comparison diagram of the attitude angles of the two control methods under the external disturbance moment is shown in the figure 10-1 and the figure 10-2. It can be seen from fig. 10-1 that under the constant roll torque disturbance, the roll angle curve based on sliding mode and ESO control shakes significantly less, and the shaking range can be maintained below 1.2 °; under the interference of constant pitching moment, the range of the pitch angle curve controlled by the sliding mode and the ESO deviating from the zero-degree line is smaller, and the pitch angle is larger than zero, which shows that the controller has the capability of compensating external interference and has stronger anti-interference capability.
The method for controlling the attitude of the four-rotor aircraft based on the sliding-mode control law and the ESO corresponds to the method for controlling the attitude of the four-rotor aircraft based on the sliding-mode control law and the ESO, and the invention also provides a system for controlling the attitude of the four-rotor aircraft based on the sliding-mode control law and the ESO.
Fig. 11 shows a logic structure of a attitude control system of a quad-rotor aircraft based on a sliding-mode control law and an ESO according to an embodiment of the present invention, and as shown in fig. 11, a logic structure 1100 of an attitude control system of a quad-rotor aircraft based on a sliding-mode control law and an ESO according to the present invention includes: attitude angle loop control unit 1110, total system disturbance real-time estimation unit 1120, and quad-rotor attitude control unit 1130.
The attitude angle loop control unit 1110 is configured to derive a four-rotor aircraft dynamic model according to model parameters, construct a sliding mode surface according to the four-rotor aircraft dynamic model, and obtain a sliding mode control law according to the sliding mode surface, so as to control three attitude angle loops of the four-rotor aircraft;
the system total disturbance real-time estimation unit 1120 is used for constructing an ESO according to the control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four rotors, and estimating the system total disturbance in real time by using the ESO;
and a quad-rotor aircraft attitude control unit 1130 configured to combine the sliding mode control law with the ESO to control the attitude of the quad-rotor aircraft.
Further, the four-rotor aircraft dynamics model parameters include moment of inertia Jx、Jy、Jz(ii) a Coefficient of lift cT(ii) a Coefficient of torque cQ(ii) a The time constant T of the motor.
Further, the acquisition of the sliding mode control model by the attitude angle loop control unit 1110 includes the following steps:
(1) considering the four rotors as rigid bodies, the nonlinear dynamic equation of the attitude of the four-rotor aircraft is as follows:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotary inertia of the four rotors along the directions of x, y and z axes;
(2) rewriting the nonlinear dynamical equation into the form of a state space:
wherein, U is the input vector, and X is the state vector, and the specific expression is as follows:
the state variables are as follows:
inputting a vector: u ═ U1 U2 U3]T＝[τφ τθ τψ]T
(3) The conversion matrix between the attitude angle change rate and the body angular rate is used as an identity matrix under the condition of hovering or small-angle flight,
obtaining the sliding mode control model:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p,q,rthe components of the body angular velocity omega on the x, y and z axes of the body coordinate system are respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotational inertia of the four rotors along the directions of the x axis, the y axis and the z axis respectively.
Further, in the process that the attitude angle loop control unit 1110 deduces a four-rotor aircraft dynamic model according to model parameters, constructs a sliding mode surface according to the four-rotor aircraft dynamic model, and obtains a sliding mode control law according to the sliding mode surface,
the slip form surface of the structure is
The obtained sliding mode control law is as follows:
wherein the content of the first and second substances,
wherein sign represents a sign function, which is replaced by an approximate continuous saturation function sat(s); the functional expression is:
sat(s) ═ s/(| s | + e) e ∈ [0,1], where e is 0.5;
constructing a second-order filter:
Thus, an expression in the time domain is obtained:
the damping ratio xi is 0.8, natural frequency omega is selectedn＝4.375。
Further, the system total disturbance real-time estimation unit 1120 is used for constructing the ESO in the process of controlling input and output of the roll angle loop, the pitch angle loop and the yaw angle loop of the four rotors,
wherein, the first and second guide rollers are arranged in a row,
b0to control the quantity coefficient by 1/JxSelecting a predetermined parameter beta01,β02,β03And ai(i is 1,2), let a1＝0.5,a2＝0.25。
Further, in the process of combining the sliding mode control law with the ESO, quad-rotor aircraft attitude control unit 1130,
similarly, the control output of the other two attitude loops is obtained as follows:
wherein z is3φ,z3θ,z3ψThe ESO of the roll angle loop, the pitch angle loop and the yaw angle loop respectively obtain the expanded state quantity.
The invention realizes the real-time estimation of the total disturbance of the system by utilizing the ESO; and ESO is combined with a sliding mode control law, so that the attitude stability of the four-rotor aircraft is realized, and meanwhile, the four-rotor aircraft has good tracking performance on an attitude angle instruction and has stronger anti-jamming capability compared with the common sliding mode control.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A four-rotor aircraft attitude control method based on a sliding mode control law and ESO is characterized by comprising the following steps:
deducing a four-rotor aircraft dynamic model according to the four-rotor aircraft dynamic model parameters, constructing a sliding mode surface according to the four-rotor aircraft dynamic model, and acquiring a sliding mode control law according to the sliding mode surface so as to realize control of three attitude angle loops of the four-rotor aircraft;
in the process of deducing a four-rotor aircraft dynamic model according to model parameters and constructing a sliding mode surface according to the four-rotor aircraft dynamic model,
the slip form surface of the structure is
The obtained sliding mode control law is as follows:
wherein the content of the first and second substances,
s2a slip form surface configured for a slip form controller to construct a roll angle circuit;
wherein sign represents a sign function, which is replaced by an approximate continuous saturation function sat(s); the functional expression is:
sat(s) ═ s/(| s | + e) e ∈ [0,1], where e is 0.5;
constructing a second-order filter:
thus, an expression in the time domain is obtained:
the damping ratio xi is 0.8, natural frequency omega is selectedn＝4.375，
Constructing an ESO according to control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four rotors, and estimating total system disturbance in real time by using the ESO;
and combining the sliding mode control law with the ESO to realize the control of the posture of the four-rotor aircraft.
2. The sliding-mode control law and ESO-based quadrotor attitude control method according to claim 1, wherein the quadrotor kinetic model parameters include moment of inertia Jx、Jy、Jz(ii) a Coefficient of lift cT(ii) a Coefficient of torque cQ(ii) a The time constant T of the motor.
3. The sliding-mode control law and ESO based quadrotor aircraft attitude control method according to claim 1, wherein obtaining the sliding-mode control model comprises the steps of:
(1) considering the quadrotors as rigid bodies, the nonlinear dynamic equation of the posture of the quadrotor aircraft is as follows:
wherein phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotary inertia of the four rotors along the directions of x, y and z axes;
(2) rewriting the nonlinear dynamical equation into the form of a state space:
wherein, U is the input vector, and X is the state vector, and the specific expression is as follows:
the state variables are as follows:
x1＝φ x3＝θ x5＝ψ
inputting a vector: u ═ U1 U2 U3]T＝[τφ τθ τψ]T
(3) The conversion matrix between the attitude angle change rate and the body angular rate is used as an identity matrix under the condition of hovering or small-angle flight,
obtaining the sliding mode control model:
4. the attitude control method for a four-rotor aircraft based on sliding-mode control law and ESO according to claim 1, wherein in the process of constructing the ESO according to the control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four-rotor aircraft,
wherein the content of the first and second substances,
b0to control the quantity coefficient by 1/JxSelecting a predetermined parameter beta01,β02,β03And aiI is 1,2, let a1＝0.5,a2＝0.25。
5. The method for controlling attitude of a four-rotor aircraft based on sliding-mode control law and ESO according to claim 1, wherein during the combination of the sliding-mode control law and the ESO,
similarly, the control output of the other two attitude loops is obtained as follows:
wherein z is3φ,z3θ,z3ψRespectively a roll angle loop and a pitch angle loopAnd the ESO of the yaw angle circuit.
6. A system for controlling attitude of a quadrotor aircraft based on a sliding-mode control law and an ESO, for performing the method for controlling attitude of a quadrotor aircraft based on a sliding-mode control law and an ESO according to claim 1, the system comprising: the attitude angle loop control unit is used for deducing a four-rotor aircraft dynamic model according to model parameters, constructing a sliding mode surface according to the four-rotor aircraft dynamic model, and acquiring a sliding mode control law according to the sliding mode surface so as to realize control of three attitude angle loops of the four-rotor aircraft;
the system total disturbance real-time estimation unit is used for constructing an ESO (electronic stability and safety) according to the control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four rotors and estimating the total disturbance of the system in real time by using the ESO;
and the four-rotor aircraft attitude control unit is used for adopting the sliding mode control law and the ESO to be combined so as to realize the control of the four-rotor aircraft attitude.
7. The sliding-mode control law and ESO based quad-rotor aircraft attitude control system according to claim 6, wherein the quad-rotor aircraft dynamical model parameters include moment of inertia Jx、Jy、Jz(ii) a Coefficient of lift cT(ii) a Coefficient of torque cQ(ii) a The time constant T of the motor.
8. The sliding-mode control law and ESO based quadrotor aircraft attitude control system according to claim 6, wherein the acquisition of the sliding-mode control model by the attitude angle loop control unit comprises the steps of:
(1) considering the quadrotors as rigid bodies, the nonlinear dynamic equation of the posture of the quadrotor aircraft is as follows:
wherein: phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle;
p, q and r are components of the body angular velocity omega on x, y and z axes of the body coordinate system respectively;
τφ,τθ,τψcontrol moments in the directions of the three body shafts respectively;
Jx,Jy,Jzthe rotary inertia of the four rotors along the directions of x, y and z axes;
(2) rewriting the nonlinear dynamical equation into the form of a state space:
wherein, U is the input vector, and X is the state vector, and the specific expression is as follows:
the state variables are as follows:
x1＝φ x3＝θ x5＝ψ
inputting a vector: u ═ U1 U2 U3]T＝[τφ τθ τψ]T
(3) The conversion matrix between the attitude angle change rate and the body angular rate is used as an identity matrix under the condition of hovering or small-angle flight,
obtaining the sliding mode control model:
9. the four-rotor aircraft attitude control system based on the sliding-mode control law and the ESO according to claim 6, wherein the attitude angle loop control unit derives a four-rotor aircraft dynamic model according to model parameters, constructs a sliding mode surface according to the four-rotor aircraft dynamic model, and obtains the sliding-mode control law according to the sliding mode surface,
the slip form surface of the structure is
The obtained sliding mode control law is as follows:
wherein the content of the first and second substances,
wherein sign represents a sign function, which is replaced by an approximate continuous saturation function sat(s); the functional expression is:
sat(s) ═ s/(| s | + e) e ∈ [0,1], where e is 0.5;
constructing a second-order filter:
thus, an expression in the time domain is obtained:
the damping ratio xi is 0.8, natural frequency omega is selectedn＝4.375；
The real-time estimating unit of the total disturbance of the system constructs ESO according to the control input and output of a roll angle loop, a pitch angle loop and a yaw angle loop of the four rotors,
wherein the content of the first and second substances,
b0to control the quantity coefficient by 1/JxSelecting a predetermined parameter beta01,β02,β03And aiI is 1,2, let a1＝0.5,a2＝0.25；
In the process of combining the sliding mode control law and the ESO by the attitude control unit of the four-rotor aircraft,
similarly, the control output of the other two attitude loops is obtained as follows:
wherein z is3φ,z3θ,z3ψThe ESO of the roll angle loop, the pitch angle loop and the yaw angle loop respectively obtain the expanded state quantity.
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