CN111338369B - Multi-rotor flight control method based on nonlinear inverse compensation - Google Patents
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Abstract
The invention discloses a multi-rotor flight control method based on nonlinear inverse compensation. The method comprises the following steps: firstly, performing dynamics analysis on a multi-rotor aircraft, and establishing a multi-rotor dynamics equation according to Newton's second law and the theorem of moment of momentum; secondly, establishing an equivalent model of the brushless direct current motor, deducing a relational expression of the motor rotating speed and the force and the moment borne by the multiple rotors, and determining a flight control equation set of the multiple rotors; and finally, establishing inverse mapping of the nonlinear link, establishing a pseudo-linear system through the inverse mapping, and designing the controller based on the inner and outer ring control structure. The multi-rotor flight control method based on the nonlinear inverse compensation has the advantages of high track tracking precision, high response speed and strong anti-interference capability, and can realize stable and accurate control on the position and the attitude of the multi-rotor aircraft.
Description
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to a multi-rotor flight control method based on nonlinear inverse compensation.
Background
The multi-rotor aircraft is an unmanned aircraft which can fly autonomously or remotely by relying on rotors to provide lift. The multi-rotor wing has wide application range, and can be used for aerial photography, rescue, plant protection, monitoring and the like, particularly in the civil field. The flight control system is an inner ring control system which uses information generated by a sensor as a feedback signal in an unmanned aerial vehicle control system to realize the stability or maneuvering action of the unmanned aerial vehicle, and common multi-rotor flight control methods comprise PID (proportion integration differentiation), optimal control, sliding mode control and fuzzy logic control.
At present, a controller is designed by a conventional PID control method widely adopted in engineering, the conventional controller has no great requirement on the precision of a multi-rotor aircraft model, the influence of an uncertain item in the multi-rotor aircraft model is neglected, the approximation is only realized when the multi-rotor aircraft is in a near hovering state, and when the multi-rotor aircraft carries out large-maneuvering flight, the performance of the conventional controller is sharply deteriorated, and potential safety hazards exist. Meanwhile, the conventional controller only provides a feedback channel for the output of the control system, the control law design process is simple, the control precision is low, the control performance is poor, and the strong coupling in the flight process, the uncertainty of a multi-rotor aircraft model and the external interference are difficult to deal with.
Disclosure of Invention
The invention aims to provide a multi-rotor flight control method based on nonlinear inverse compensation, which has high track tracking precision, high response speed and strong anti-interference capability.
The technical solution for realizing the purpose of the invention is as follows: a multi-rotor flight control method based on nonlinear inverse compensation comprises the following steps:
and 3, establishing inverse mapping of the nonlinear link, establishing a pseudo-linear system through the inverse mapping, and designing the controller based on the inner and outer ring control structure.
Compared with the prior art, the invention has the following remarkable advantages: (1) the interference of a nonlinear link and external interference on the flight process can be reduced, and the control precision and the control performance of the multi-rotor aircraft model are improved, so that the flight safety and operability of the multi-rotor aircraft are improved; (2) the multi-rotor-wing tracking system has the advantages of high track tracking precision, high response speed and high anti-interference capability, and can well control the positions and the postures of multiple rotors.
Drawings
Fig. 1 is a flowchart of a method for controlling a multi-rotor flight based on nonlinear inverse compensation according to an embodiment of the present invention.
Fig. 2 is a schematic view of a multi-rotor aircraft according to an embodiment of the present invention.
Fig. 3 is a structural diagram of flight control of a multi-rotor unmanned aerial vehicle based on nonlinear inverse compensation according to an embodiment of the present invention.
Fig. 4 is a pseudo linear segment Γ based on a nonlinear inverse compensation method according to an embodiment of the present invention 2 Structure diagram.
Fig. 5 is a pseudo linear segment Γ based on a nonlinear inverse compensation method according to an embodiment of the present invention 2 A control block diagram of (1).
FIG. 6 shows a pseudo linear segment Γ based on a nonlinear inverse compensation method according to an embodiment of the present invention 1 Structure diagram.
Fig. 7 is a pseudo linear segment Γ based on a nonlinear inverse compensation method according to an embodiment of the present invention 1 A control block diagram of (1).
FIG. 8 is a graph of a desired thrust versus a desired acceleration provided by an embodiment of the present invention.
Fig. 9 is a pseudo linear segment Γ based on a nonlinear inverse compensation method according to an embodiment of the present invention 3 Structure diagram.
Fig. 10 is a pseudo linear segment Γ based on a nonlinear inverse compensation method according to an embodiment of the present invention 3 A control block diagram of (2).
Fig. 11 is a simulation diagram of attitude angle step signal control provided by the embodiment of the present invention, in which (a) is a step signal response curve diagram, and (b) is a step response error curve diagram.
Fig. 12 is a simulation diagram of position step signal control provided by the embodiment of the present invention, in which (a) is a step response curve diagram, and (b) is a step response error curve diagram.
Fig. 13 is a simulation diagram of the "go back" shape trajectory tracking provided by the embodiment of the present invention, in which (a) is a trajectory tracking curve graph and (b) is a trajectory tracking error curve graph.
Fig. 14 is a simulation diagram of plane tracking of the circular trajectory XOY according to the embodiment of the present invention, where (a) is a projection diagram of the trajectory on the XOY plane, and (b) is a Y-direction tracking error curve diagram.
Fig. 15 is a simulation diagram of "go back" type track height tracking according to an embodiment of the present invention, in which (a) is a graph of height tracking and (b) is a graph of height tracking error.
Detailed Description
With reference to fig. 1, the present invention provides a multi-rotor flight control method based on nonlinear inverse compensation, which includes the following steps:
and 3, establishing inverse mapping of the nonlinear link, establishing a pseudo-linear system through the inverse mapping, and designing the controller based on the inner and outer ring control structure.
Further, step 1 said carry on dynamics analysis to many rotor crafts, establish many rotor dynamics equation according to newton's second law and momentum moment theorem, specifically as follows:
first, the following 4 assumptions are made:
(1) the aircraft is a rigid body with six degrees of freedom, and the mass of the aircraft is kept unchanged in the flight process;
(2) the center of mass of the aircraft is positioned on the geometric center line of the aircraft and is positioned at the origin of the coordinate system of the aircraft body;
(3) the external interference and gravity on the aircraft are not influenced by the flight altitude;
(4) the rotor wing is a rigid body;
secondly, establishing a moment equation set, a motion equation set and a position equation set which represent a dynamic model of the multi-rotor aircraft:
the set of moment equations is expressed as follows:
wherein p, q, r represent angular velocities about the body axes x, y, and z, respectively, ofA torque form;
respectively representing roll angular acceleration, pitch angular acceleration and yaw angular acceleration; d p ,D q ,D r Respectively representing the components of the external interference D along the x axis, the y axis and the z axis of the machine system in a moment form; j. the design is a square bx ,J by ,J bz Respectively, the moments of inertia about the x, y, z axes of the machine system, J rotor Represents the moment of inertia of the rotor, and Ω is the sum of the angular speeds of 4 motors; m φ (F)、M θ (F)、M ψ (F) The components of the moment of the combined external force to the center of mass of the multi-rotor wing on the x axis, the y axis and the z axis of the system are respectively;
the set of equations of motion is expressed as follows:
wherein phi, theta and psi are respectively a roll angle, a pitch angle and a yaw angle,
respectively roll angle change rate, pitch angle change rate and yaw angle change rate;
the set of position equations is expressed as follows:
wherein T represents motor tension;
respectively representing the acceleration of the mass center of the aircraft along the x axis, the y axis and the z axis of a ground coordinate system; d x ,D y ,D z Respectively representing the components of the external interference D along the x axis, the y axis and the z axis of the ground coordinate system in the form of force; g represents the gravitational acceleration, m represents the mass of the aircraft; a is nx 、a ny 、a nz Is the acceleration under the navigation coordinate systemX-axis, y-axis and z-axis components.
Further, step 2, establishing an equivalent model of the brushless dc motor, and deriving a relationship between the motor speed and the force and torque applied to the multiple rotors, specifically as follows:
the phase voltage of each phase winding of the brushless direct current motor consists of a resistance voltage drop part and a winding induced potential, wherein the winding induced potential comprises potentials generated by self inductance of the windings and mutual inductance between the windings, and counter electromotive force generated by cutting magnetic lines of force by the windings in a magnetic field;
if the control voltage at two ends of the armature circuit of the motor is u, the winding current is i, and the angular velocity of the rotor is ω, the voltage balance equation of the armature circuit is:
wherein R is a Is the equivalent resistance of the motor, L a Is the equivalent inductance of the motor, k e Is the back electromotive force coefficient, t is the time;
electromagnetic torque T of motor e ＝k t i, where k t Is an electric torque coefficient and a load torque of T m A viscous friction coefficient of B a The moment of inertia of the motor is J rotor Then, the torque balance equation of the motor is:
when the motor is in steady state, di/dt is 0, the voltage balance equation of the armature loop becomes:
thus, under steady state conditions, the mathematical model of the motor is:
because of T m Related to omega, the mathematical model of the motor of the above formula shows nonlinearity, and the mathematical model of the motor of the above formula is corresponding to the rotating speed point omega 0 Linearization was performed to obtain:
wherein A, B and C are constants;
is the time derivative of the motor speed omega.
Further, step 2 determines a multi-rotor flight control equation set, specifically as follows:
selecting variables as control variables according to the motion mechanism of the multi-rotor aircraft, and selecting parameters which can be obtained through a sensor as much as possible as state variables according to the requirement of reducing uncertainty;
the control quantity comprises: u. of 1 ,u 2 ,u 3 ,u 4 The expression is:
wherein u is 1 Is the total tension input, u 2 ,u 3 ,u 4 Respectively roll, pitch, yaw input, T 1 ,T 2 ,T 3 ,T 4 For the pull of four motors, omega 1 ,ω 2 ,ω 3 ,ω 4 At four motor speeds, K T Is the tension coefficient; k Q Is a drag coefficient;
considering external interference, the multi-rotor flight control equation set is as follows:
wherein l bx 、l by The lengths of the force arms of the x axis and the y axis of the body axis respectively,
are the x-axis, y-axis and z-axis components of the acceleration in the navigational coordinate system.
Further, step 3, establishing inverse mapping of the nonlinear link, building a pseudo-linear system through inverse mapping, and designing a controller based on the inner and outer ring control structures, specifically as follows:
the transfer function of the attitude control system is as follows:
R 1 (s) is a gesture input signal, Y 1 (s) is the attitude output signal, H 2 (s)＝diag{h 21 ,h 22 ,h 23 Is the state feedback matrix of the angular velocity control loop, K 2p ＝diag{k 2p1 ,k 2p2 ,k 2p3 Is the proportionality coefficient of the angular velocity control loop, K 1p ＝diag{k 1p1 ,k 1p2 ,k 1p3 Is the proportionality coefficient of the attitude control loop, K 1d ＝diag{k 1d1 ,k 1d2 ,k 1d3 Is the differential coefficient of the attitude control loop;
the transfer function of the position control system is:
wherein, a 1 ＝(H 2 +K 1d K 2p ),a 2 ＝(K 1p K 2p +K 1d K 2p K 4p ),a 3 ＝(K 1d K 2p K 4p +K 1d K 2p K 3p K 4p ),a 4 ＝K 1p K 2p K 3p K 4p ,b 1 ＝K 1d K 2p K 3p K 4p ,b 2 ＝K 1p K 2p K 3p K 4p ，K 3p ＝diag{k 3p1 ,k 3p2 ,k 3p3 Is the proportionality coefficient of the speed control loop, K 4p ＝diag{k 4p1 ,k 4p2 ,k 4p3 Is the proportionality coefficient of the position control loop.
The invention is described in further detail below with reference to the figures and the embodiments.
Examples
The embodiment provides a multi-rotor flight control method based on nonlinear inverse compensation, which comprises the following steps:
s1: firstly, carrying out comprehensive dynamics analysis on a multi-rotor aircraft, and establishing a multi-rotor dynamics equation according to Newton's second law and the theorem of moment of momentum;
s2: then, establishing an equivalent model of the brushless direct current motor, deducing a relational expression of the motor rotating speed and the force and the moment borne by the multiple rotors, and determining a flight control equation set of the multiple rotors;
s3: and finally, establishing inverse mapping of the nonlinear link, establishing a pseudo-linear system through the inverse mapping, and designing the controller based on the inner and outer ring control structure.
According to the multi-rotor flight control method based on the nonlinear inverse compensation, firstly, comprehensive dynamics analysis is carried out on a multi-rotor aircraft, and a multi-rotor dynamics equation is established according to Newton's second law and the theorem of moment of momentum. Secondly, an equivalent model of the brushless direct current motor is established, and a relational expression of the motor rotating speed and the force and the moment borne by the multiple rotors is deduced. And then, a control method based on nonlinear link inverse compensation is provided based on an inner ring control structure and an outer ring control structure, so that the interference of the nonlinear link and the external interference to the flight process can be reduced, the control precision and the control performance of the multi-rotor aircraft model are improved, and the flight safety and the operability of the multi-rotor aircraft model are improved.
First, building a multi-rotor aircraft model based on the multi-rotor aircraft mathematical model and accuracy requirements includes:
a multi-rotor aircraft is shown in figure 2. The inherent parameters are shown in the table 1, and the maximum lifting force provided by a single steering engine is 300 g.
TABLE 1 Multi-rotor intrinsic parameters
The control quantity comprises: u. of 1 ,u 2 ,u 3 ,u 4 . The expression is as follows:
wherein T is 1 ,T 2 ,T 3 ,T 4 Power, omega, supplied to rotors 1, 2, 3, 4, respectively 1 ,ω 2 ,ω 3 ,ω 4 At four motor speeds, K T Is the coefficient of tension.
In this embodiment, based on flight mechanics and aerodynamics principle to according to the control performance requirement, carry out atress analysis to many rotor crafts, and combine the relevant knowledge of kinematics, confirm many rotor crafts mathematical model through following step, many rotor craft kinetic model includes: a set of moment equations, a set of motion equations and a set of position equations representing a multi-rotor aircraft dynamics model;
the set of moment equations is expressed as follows:
wherein p, q, r respectively represent a roll angular velocity, a pitch angular velocity and a yaw angular velocity,
respectively representing roll angular acceleration, pitch angular acceleration and yaw angular acceleration, D p ,D q ,D r Respectively representing the components of the external disturbance D along the x-axis, the y-axis and the z-axis of the body system, in the form of moments. (J) bx ,J by ,J bz ) Are respectively a winder system x, yZ-axis moment of inertia, J rotor Representing the moment of inertia of the rotor, Ω is the sum of the angular speeds of the 4 motors.
The system of equations of motion is represented as follows:
the set of position equations is expressed as follows:
wherein, T represents the pulling force of the motor,
representing the acceleration of the aircraft's centre of mass along the x-, y-and z-axes, respectively, of the ground coordinate system, D x ,D y ,D z Representing the components of the external disturbance D along the x-, y-and z-axes, respectively, of the ground coordinate system, in the form of a force. g denotes the gravitational acceleration and m denotes the mass of the aircraft.
After an initial state is given, the angular acceleration of the multi-rotor aircraft is completely determined by the moment generated by the rotation of the rotors, namely the control of the angular motion can be realized by controlling the moment of the mass center of the multi-rotor; the acceleration of the multiple rotors is not only related to the tension of the rotors, but also related to the attitude angles of the rotors, under the condition of known initial state, the acceleration of the multiple rotors needs to be controlled by controlling the tension and the attitude angles of the rotors, so that the control of the linear motion of the multiple rotors is realized, and the attitude angles cannot be directly controlled, which shows that the coupling and the relation exist between the angular motion and the linear motion. The relationship between multi-rotor angular motion and linear motion is shown in figure 3. Considering external interference, the multi-rotor flight control equation set is as follows:
according to the step 3, the control method based on the nonlinear link inverse compensation is provided based on the inner and outer ring control structure, and comprises the following steps: and (3) establishing inverse mapping of a nonlinear link, establishing a pseudo-linear system through inverse mapping, and designing a controller based on an inner ring control structure and an outer ring control structure.
Setting attitude angle of multiple rotors as state y 1 Angular velocity as a control input v 1 The rotational kinematic link of which can be written as a map T 1 :v 1 →y 1 ：
Wherein:
is provided with
Because of the matrix B 1 Is reversible, so that the link (6) has inverse mapping T 1 -1 :
Link T 1 -1 :
Is the first-order integral inverse mapping of the original link.
Let the angular velocity states of the multiple rotors be y 2 Motor control input is v 2 The rotational dynamics can be written as a map T 2 :v 2 →y 2 ：
Wherein:
is provided with
Because of the matrix B 2 Is reversible, so that the link (10) has inverse mapping T 2 -1 :
Link T 2 -1 :
Is the first order inverse mapping of the original link.
Inverse mapping the first order to T 2 -1 :
Is connected in series with the original ring segment to obtain a composite link with the symbol gamma 2 The structure is shown in FIG. 4.
design link gamma 2 The state feedback controller of (2) is shown in fig. 5.
Wherein:
the transfer function of the link shown in fig. 5 is:
r 2 as links t 2 The physical meaning of which is the desired angular velocity. Introduction of a proportionality coefficient K 2p Is provided with r 2 And link T 1 -1 :
The relationship of (1) is:
r 2 ＝K 2p v 1 ＝diag{k 2p1 ,k 2p2 ,k 2p3 }v 1 (17)
at the following link F 2 On the basis of the link T 1 :v 1 →y 1 Pseudo linear link gamma of 1 As shown in fig. 6.
design link gamma 1 As shown in fig. 7.
r 1 Is the desired pose, PD represents the proportional-derivative element:
wherein, K 1p ＝diag{k 1p1 ,k 1p2 ,k 1p3 },K 1d ＝diag{k 1d1 ,k 1d2 ,k 1d3 }。
The transfer function of the link shown in fig. 8 is:
equation (20) is the attitude control link transfer function based on the inverse mapping method.
For position control, when a desired position is given, a desired acceleration can be obtained from the current position, which can be converted into a desired roll angle φ d And a desired pitch angle θ d Desired yaw angle psi d Given by a control instruction (phi) d ,θ d ,ψ d ) That is, the desired value of the attitude control loop, the attitude can be controlled using an attitude controller. The desired acceleration and desired attitude angle conversion relationship is given in the position control loop.
The attitude of the multiple rotors can be obtained in navigation information, and the expected acceleration a is obtained through a position control equation nd ：
Let the acceleration corresponding to the desired thrust of the multiple rotors be a Td It and the desired acceleration a nd The relationship of (2) is shown in FIG. 8.
Wherein, a Td Desired acceleration a for multiple rotors nd Sum and interference force D n Corresponding to the vector difference of acceleration and gravitational acceleration g, a Td The expression under the inertial system is:
wherein D is n ＝[D x ；D y ；D z ]。
Let the axial unit vector of the desired machine system be [ i ] bd j bd k bd ]Vector k due to the fixed structure of the multiple rotors bd A direction of Td In opposite directions, therefore a Td The expression under the desired regime is:
the current yaw angle psi is obtained by a sensor to obtain a Td Then, let the navigation system be the rotation matrix of the desired system
Substitution into a Td After that
Satisfies the following conditions:
wherein:
from the orthogonality of the rotation matrix, the desired attitude angle is derived:
due to the limited range of attitude adjustability of the multiple rotors, clipping of the desired attitude is required. To maintain stability, limit its desired roll angle φ d And a desired pitch angle θ d Comprises the following steps:
at this time, the clipping processing is performed on equation (26) so as to satisfy:
the translational kinetic equation of the multi-rotor is as follows:
wherein, | a T And | is the magnitude of the acceleration corresponding to the motor thrust. Setting the position state of multiple rotors as y 3 Control input is v 3 The rotation dynamics link can be written as a mapping T 3 :v 3 →y 3 ：
Wherein:
is provided with
In the case of a known yaw angle command, the link T 3 There is an inverse mapping T 3 - 1 :
link T 3 -1 :
Is a second order inverse mapping of the original link, where the output v 3 The physical meaning of (A) is a desired thrust and a desired Euler angle, and r 1 The relationship of (1) is:
inverse mapping the second order to T 3 -1 :
Connected in series with its original ring segment to obtain a complete composite system, denoted by the symbol Γ 3 The structure is shown in FIG. 9.
design system gamma 3 As shown in fig. 10:
wherein:
the transfer function of the system shown in fig. 10 is:
wherein, a 1 ＝(H 2 +K 1d K 2p ),a 2 ＝(K 1p K 2p +K 1d K 2p K 4p ),a 3 ＝(K 1d K 2p K 4p +K 1d K 2p K 3p K 4p ),a 4 ＝K 1p K 2p K 3p K 4p ,b 1 ＝K 1d K 2p K 3p K 4p ,b 2 ＝K 1p K 2p K 3p K 4p 。
The external interference is set to be zero, and the attitude controller parameters obtained through parameter setting are shown in table 2. Assuming that the initial state of the multiple rotors is zero, the desired attitude angle is 30 °. Using the parameters of table 2, an attitude response curve is obtained as shown in fig. 11(a), and an error curve is obtained as shown in fig. 11 (b). As can be seen from the simulation curve, the step response errors of all attitude angles approach to 0, overshoot is avoided, and the yaw angle adjusting time (5%) reaching the steady state at the latest is about 0.42s, which indicates that the steady state performance and the dynamic performance of the system both meet the design index, and the dynamic characteristic of the actual attitude angle is matched with the theoretical analysis conclusion, so that the attitude controller is effective.
The external interference is set to be zero, and the parameters of the position controller obtained through parameter setting are shown in table 3. Let the initial state of the multiple rotors be zero and the expected position be [ x ] nd ,y nd ,alt]＝[5m,5m,5m]. Using the parameters of table 3, a position response curve is obtained as shown in fig. 12(a), and an error curve is obtained as shown in fig. 12 (b). As can be seen from the simulation curves, the step response error approaches 0 for all positions,the state regulation time without overshoot and reaching the steady state at the latest is about 3.08s, which indicates that the steady state performance and the dynamic performance of the system both meet the design index, and therefore, the designed position controller has a good control effect.
TABLE 2 attitude control parameters
TABLE 3 position control parameters
The following analyzes the tracking characteristics of the control system. A set of position instructions (0,0,0) → (0,0,5) → (5,0,5) → (5,5,5) → (0,5,5) → (0,0,5) is designed to form a 'return' font track, and the design instruction running time is 25 s. The trajectory tracking curve is shown in fig. 13(a), and the tracking error graph 13 (b). From the above simulation curves, it can be seen that the multi-rotor ensemble is able to track trajectory commands. And the tracking effect in the horizontal direction is consistent with the response characteristic of the step signal, and before the next command is switched, the multiple rotors reach the current command position without overshoot. As can be seen from fig. 14(a) and 14(b), in the XOY plane, the multi-rotor trajectory substantially conforms to the command trajectory, and the tuning time in the y direction is 3.09s, which meets the design requirements. As can be seen from fig. 15(a) and 15(b), the multi-rotor is stable in the height direction as a whole, and small fluctuation occurs when the command is switched (the horizontal direction changes more sharply), and the amplitude of the fluctuation does not exceed 0.081 m. And (4) conclusion: the controller can meet the requirement of tracking the 'return' font track instruction.
In this embodiment, a multi-rotor aircraft simulation model is established according to a resolvable nonlinear link compensation controller, adjustment parameters of a nonlinear inverse compensation controller are adjusted until control performance meets control requirements, and preliminary verification is performed on the multi-rotor aircraft simulation model based on the nonlinear inverse compensation controller, where the control performance includes: response time overshoot, interference rejection capability.
Claims (1)
1. A multi-rotor flight control method based on nonlinear inverse compensation is characterized by comprising the following steps:
step 1, performing dynamics analysis on a multi-rotor aircraft, and establishing a multi-rotor dynamics equation according to a Newton second law and a momentum moment theorem;
step 2, establishing an equivalent model of the brushless direct current motor, deducing a relational expression of the motor rotating speed and the force and the moment borne by the multiple rotors, and determining a flight control equation set of the multiple rotors;
step 3, establishing inverse mapping of a nonlinear link, establishing a pseudo-linear system through the inverse mapping, and designing a controller based on an inner ring control structure and an outer ring control structure;
step 1, performing dynamics analysis on the multi-rotor aircraft, and establishing a multi-rotor dynamics equation according to Newton's second law and the theorem of moment of momentum, wherein the method specifically comprises the following steps:
first, the following 4 assumptions are made:
(1) the aircraft is a rigid body with six degrees of freedom, and the mass of the aircraft is kept unchanged in the flight process;
(2) the center of mass of the aircraft is positioned on the geometric center line of the aircraft and is positioned at the origin of the coordinate system of the aircraft body;
(3) the external interference and gravity on the aircraft are not influenced by the flight height;
(4) the rotor wing is a rigid body;
secondly, establishing a moment equation set, a motion equation set and a position equation set which represent a dynamic model of the multi-rotor aircraft:
the set of moment equations is expressed as follows:
wherein, p, q and r respectively represent angular velocities around an x axis, a y axis and a z axis of a body axis, and are in a moment form;
respectively representing roll angular acceleration, pitch angular acceleration and yaw angular acceleration; d p ,D q ,D r Respectively representing the components of the external interference D along the x axis, the y axis and the z axis of the machine system in a moment form; j. the design is a square bx ,J by ,J bz Respectively, the moments of inertia about the x, y, z axes of the machine system, J rotor Representing the moment of inertia of the rotor, Ω is the sum of the angular speeds of the 4 motors; m φ (F)、M θ (F)、M ψ (F) The components of the moment of the combined external force on the center of mass of the multi-rotor wing on the x axis, the y axis and the z axis of the aircraft system are respectively;
the set of equations of motion is expressed as follows:
wherein phi, theta and psi are respectively a roll angle, a pitch angle and a yaw angle,
respectively roll angle change rate, pitch angle change rate and yaw angle change rate;
the set of position equations is expressed as follows:
wherein T represents motor tension;
respectively representing the acceleration of the mass center of the aircraft along the x axis, the y axis and the z axis of a ground coordinate system; d x ,D y ,D z Respectively representing the components of the external interference D along the x axis, the y axis and the z axis of the ground coordinate system in the form of force; g represents the gravitational acceleration, m represents the mass of the aircraft; a is nx 、a ny 、a nz Is the x-axis, y-axis and z-axis components of the acceleration in the navigation coordinate system;
step 2, establishing an equivalent model of the brushless direct current motor, and deducing a relational expression of the motor rotating speed and the force and the moment received by the multiple rotors, wherein the relational expression is as follows:
the phase voltage of each phase winding of the brushless direct current motor consists of a resistance voltage drop part and a winding induced potential, wherein the winding induced potential comprises potentials generated by self inductance of the windings and mutual inductance between the windings, and counter electromotive force generated by cutting magnetic lines of force by the windings in a magnetic field;
if the control voltage at two ends of the armature circuit of the motor is u, the winding current is i, and the angular velocity of the rotor is ω, the voltage balance equation of the armature circuit is:
wherein R is a Is the equivalent resistance of the motor, L a Is the equivalent inductance of the motor, k e Is the back electromotive force coefficient, t is the time;
electromagnetic torque T of motor e ＝k t i, where k t Is an electric torque coefficient and a load torque of T m A viscous friction coefficient of B a The moment of inertia of the motor is J rotor Then, the torque balance equation of the motor is:
when the motor is in a steady state, di/dt is 0, equation (4) becomes:
thus, under steady state conditions, the mathematical model of the motor is:
because of T m Related to omega, the expression (7) shows nonlinearity, and the pair of the expression (7) is at the rotating speed point omega 0 Linearization was performed to obtain:
wherein A, B and C are constants;
is the time derivative of the motor speed omega;
step 2, determining a multi-rotor flight control equation set, which specifically comprises the following steps:
selecting variables as control variables according to the motion mechanism of the multi-rotor aircraft, and selecting parameters which can be obtained through a sensor as much as possible as state variables according to the requirement of reducing uncertainty;
the control quantity comprises: u. u 1 ,u 2 ,u 3 ,u 4 The expression is:
wherein u is 1 Is the total tension input, u 2 ,u 3 ,u 4 Respectively roll, pitch, yaw input, T 1 ,T 2 ,T 3 ,T 4 For the pull of four motors, omega 1 ,ω 2 ,ω 3 ,ω 4 At four motor speeds, K T Is the tension coefficient; k Q Is a coefficient of resistance;
considering external interference, the multi-rotor flight control equation set is as follows:
wherein l bx 、l by Respectively the x-axis of the body axisAnd the length of the force arm of the y-axis,
the components of the acceleration in the x axis, the y axis and the z axis of the navigation coordinate system are shown;
step 3, establishing inverse mapping of the nonlinear link, establishing a pseudo-linear system through inverse mapping, and designing a controller based on an inner ring control structure and an outer ring control structure, wherein the controller specifically comprises the following steps:
the transfer function of the attitude control system is:
R 1 (s) is a gesture input signal, Y 1 (s) is the attitude output signal, H 2 (s)＝diag{h 21 ,h 22 ,h 23 Is the state feedback matrix of the angular velocity control loop, K 2p ＝diag{k 2p1 ,k 2p2 ,k 2p3 Is the proportionality coefficient of the angular velocity control loop, K 1p ＝diag{k 1p1 ,k 1p2 ,k 1p3 Is the proportionality coefficient of the attitude control loop, K 1d ＝diag{k 1d1 ,k 1d2 ,k 1d3 Is the differential coefficient of the attitude control loop;
the transfer function of the position control system is:
wherein, a 1 ＝(H 2 +K 1d K 2p ),a 2 ＝(K 1p K 2p +K 1d K 2p K 4p ),a 3 ＝(K 1d K 2p K 4p +K 1d K 2p K 3p K 4p ),a 4 ＝K 1p K 2p K 3p K 4p ,b 1 ＝K 1d K 2p K 3p K 4p ,b 2 ＝K 1p K 2p K 3p K 4p ，K 3p ＝diag{k 3p1 ,k 3p2 ,k 3p3 Is the proportionality coefficient of the speed control loop, K 4p ＝diag{k 4p1 ,k 4p2 ,k 4p3 Is the proportionality coefficient of the position control loop.
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