CN111324138A - Four-rotor attitude designated time performance-guaranteeing output feedback control method - Google Patents
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Abstract
The invention discloses a feedback control method for performance guarantee output of a quadrotor attitude designated time, which relates to the field of automatic control of aircrafts, and comprises the following steps of firstly, establishing a quadrotor unmanned aerial vehicle attitude power/kinematics model based on Euler angle description; secondly, constructing an Extended State Observer (ESO) to carry out online observation and compensation on lumped interference including parameter uncertainty and external interference; and then designing a boundary performance function with arbitrarily-assigned attitude adjusting time, and finally constructing an attitude loop virtual control law and an angular velocity loop actual control law so as to realize prior adjustment of attitude response transient and steady-state performance. The invention has the following advantages: (1) the method can ensure that the four-rotor attitude maneuver control meets the requirement of a preset performance index, and the convergence speed can be randomly specified through the time constant of a performance profile; (2) and by introducing the extended state observer technology, the interference accurate estimation and compensation in the output feedback sense can be realized.
Description
Technical Field
The invention relates to the field of automatic control of aircrafts, in particular to a four-rotor attitude specified time guarantee performance output feedback control method which is applied to finite time guarantee performance control of four-rotor attitude from any initial value to a target value under the condition of not depending on angular rate measurement.
Background
In recent years, with the rapid development of MEMS sensing technology, information network technology, and control technology, the design, development, and practice of quad-rotor unmanned aerial vehicles have gained unprecedented attention. Compare in fixed wing unmanned aerial vehicle, the quad-rotor exhibits following performance advantages: the multifunctional vertical take-off and landing device has the advantages of simple structure, low manufacturing cost, easiness in maintenance, portability and easiness in operation of the device body, and has remarkable performances of maneuverability, environmental durability, hovering property, vertical take-off and landing property and the like, thereby having remarkable military and civil dual-purpose values. The four-rotor is a high-nonlinearity under-actuated coupling system with Multiple Input Multiple Output (MIMO), and meanwhile, the four-rotor dynamics comprise various uncertain disturbance sources including parameter variation, model mismatch, environmental interference and the like. In addition, due to limited loading or simple configuration requirements, part of the conditions (such as angular rate) are often not measurable or the measurement accuracy cannot meet the requirements of closed-loop feedback control. Therefore, the method has more practical value on solving the problem of controlling the four-rotor track/attitude under the condition of not measuring the speed.
The existing four-rotor attitude control method usually only can realize final consistency and boundedness of attitude tracking errors in the output feedback meaning by means of a tracking differentiator or a state observer, and is less concerned about the problem of attitude control performance conservation under the condition of unknown interference. Although the prior adjustment of the performance of the controlled object can be realized by the current preset performance control, the system state can only be ensured to be converged to the preset target in infinite time due to the adoption of the function profile in the form of exponential decay, and the harsh requirement of rapid convergence in actual engineering is difficult to meet. The disclosed control method (such as limited or fixed time control) capable of realizing any specified convergence time has the advantages that the convergence time is strictly dependent on the initial value of the system state and the controller parameters, and the estimation on the upper bound of the convergence time is strongly conservative, so that the engineering application is severely limited. Furthermore, the above control strategies do not enable a priori adjustment of the steady-state behavior of the system. Based on the analysis of the existing results, it is necessary to study a finite-time performance-preserving control method for the attitude of the four-rotor wing from an arbitrary initial value to a target value without depending on the angular rate measurement condition.
Disclosure of Invention
The invention provides a feedback control method for the performance-guaranteed output of specified time of four-rotor attitude, which aims to solve the problem of performance-guaranteed control of the four-rotor attitude from any initial value to a target value under the condition of no dependence on angular rate measurement.
The invention is realized by the following technical scheme: a feedback control method for performance-guaranteeing output of four-rotor attitude designated time comprises the following steps:
(1) establishing a quadrotor unmanned aerial vehicle attitude dynamic/kinematic model based on Euler angle description:
wherein, theta is [ phi, theta, psi ═ phi]TExpressing Euler angles in a body coordinate system, and respectively expressing a rolling angle, a pitching angle and a yaw angle in the attitude of the quad-rotor unmanned aerial vehicle by phi, theta and psi; omega-omegaφ,Ωθ,Ωψ]TDenotes the angular velocity vector, Ωφ,Ωθ,ΩψRespectively representing a rolling angular velocity, a pitch angular velocity and a yaw angular velocity; j ═ diag (J)φ,Jθ,Jψ) Representing a positive definite inertia matrix; ii ═ diag (k)φ,kθ,kψ) Representing an uncertain damping matrix, k, in an attitude loopi(i ═ Φ, θ, ψ) represents a damping coefficient; k ═ diag (l, l, c) denotes a symmetric constant matrix, l denotes the distance of each motor to the four rotor centroids, c denotes the moment coefficient; u ═ Uφ,uθ,uψ]TRepresenting the rotation torque input by the attitude angle of the quad-rotor unmanned aerial vehicle; d ═ dφ,dθ,dψ]TRepresenting an unknown bounded external disturbance applied to the pose kinematics;
for convenience of controller design, the following symbolic variables are introduced:
X1＝Θ，
K2＝J-1K，dΘ＝-J-1ΠΩ+J-1d represents lumped interference in the quad-rotor drone attitude loop, including parametric uncertainty in the system and unknown bounded external interference; through these transformations, the quad-rotor drone attitude dynamics model is written in a compact form as follows:
(2) aiming at the uncertain attitude model of the four rotors given in the step (1), an Extended State Observer (ESO) is constructed to carry out online observation and compensation on lumped interference:
the following four-rotor attitude extended state observer is constructed:
wherein,
w0represents the bandwidth of the extended state observer, satisfies w0> 0, and w0Is the only parameter to be adjusted in the extended state observer;
estimated values of the angular rate and the aggregate interference of the quadrotors respectively;
(3) designing a boundary performance function with arbitrarily-assigned attitude adjusting time, and respectively constructing an attitude loop virtual control law and an angular velocity loop actual control law by combining the interference estimation given in the step (2) so as to realize the prior adjustment of attitude response transient and steady-state performance:
definition of Xid(i ═ phi, theta, psi) is given a sufficiently smooth attitude command, the actual attitude angle being X1＝[Xφ1,Xθ1,Xψ1]TAnd then the attitude tracking error of the quad-rotor unmanned aerial vehicle is ei1＝Xi1-XidTo ensure that the attitude tracking error meets the following performance constraints:
wherein,
ai(t) is a performance function whose convergence time can be arbitrarily specified:
wherein r isi∈(0,1),ai0,ai∞,TiFor specifying the adjustment parameters of the temporal performance profile by adjusting the time TiMay be such that the performance function ai(t) specifying time convergence;
next, an error transfer function S is usedi(. h) can convert constrained attitude tracking errors into unconstrained tracking errors:
wherein z isi(t) is the converted tracking error,
is the normalized error;
based on the converted tracking error, constructing a virtual control law of the attitude subsystem as follows:
wherein k isi1Is the control gain of the attitude loop;
definition of
Taking into account the speed states andlumped disturbances are not measurable, and the actual controller for the angular velocity subsystem is designed as follows:
wherein k is2Is a control gain matrix of the angular velocity loop.
The feedback control method provided by the invention mainly comprises the following processes: firstly, establishing a four-rotor unmanned aerial vehicle attitude dynamic/kinematic model based on Euler angle description; secondly, constructing an Extended State Observer (ESO) to carry out online observation and compensation on lumped interference including parameter uncertainty and external interference; and then designing a boundary performance function with arbitrarily-assigned attitude adjusting time, and finally constructing an attitude loop virtual control law and an angular velocity loop actual control law so as to realize prior adjustment of attitude response transient and steady-state performance.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a performance-guaranteeing output feedback control method for specified time of four-rotor attitude, which provides a performance profile capable of specifying convergence time at will, not only can guarantee attitude error performance-guaranteeing constraint, but also can control the four-rotor attitude to reach a stable state from any initial state according to the specified convergence time, namely the four-rotor attitude maneuver control can be guaranteed to meet the requirement of a preset performance index, and the convergence speed can be specified at will through the time constant of the performance profile; furthermore, the technology of controlling the preset performance and expanding the state observer is integrated, the performance-preserving tracking of the four-rotor attitude at any time under the output feedback framework is realized, and the technology of expanding the state observer is introduced, so that the interference accurate estimation and compensation under the output feedback meaning can be realized.
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FIG. 1 is a flow chart of a four-rotor attitude time-assigned performance-preserving output feedback control method of the present invention.
Detailed Description
The present invention is further illustrated by the following specific examples.
A feedback control method for performance-guaranteeing output of four-rotor attitude designated time is disclosed, and the flow is shown in figure 1, and comprises the following steps:
(1) establishing a quadrotor unmanned aerial vehicle attitude dynamic/kinematic model based on Euler angle description:
wherein, theta is [ phi, theta, psi ═ phi]TExpressing Euler angles in a body coordinate system, and respectively expressing a rolling angle, a pitching angle and a yaw angle in the attitude of the quad-rotor unmanned aerial vehicle by phi, theta and psi; omega-omegaφ,Ωθ,Ωψ]TDenotes the angular velocity vector, Ωφ,Ωθ,ΩψRespectively representing a rolling angular velocity, a pitch angular velocity and a yaw angular velocity;
representing a positive definite inertia matrix; Π biag (0.0024,0.0024,0.0024) Nms2Representing an uncertain damping matrix, k, in an attitude loopi(i ═ Φ, θ, ψ) represents a damping coefficient; k ═ diag (l, l, c) denotes a symmetric constant matrix, l ═ 0.4m denotes the distance of each motor to the center of mass of the quadrotors, c ═ 0.05 denotes the moment coefficient; u ═ Uφ,uθ,uψ]TRepresenting the rotation torque input by the attitude angle of the quad-rotor unmanned aerial vehicle; d ═ dφ,dθ,dψ]T＝[0.2(sin(t)+sin(0.5t)),0.2(cos(0.5t)-cos(0.8t)),0.2(sin(t)sin(0.5t))]TRepresenting an unknown bounded external disturbance applied to the pose kinematics;
for convenience of controller design, the following symbolic variables are introduced:
X1＝Θ，
K2＝J-1K，dΘ＝-J-1ΠΩ+J-1d represents lumped interference in the quad-rotor drone attitude loop, including parametric uncertainty in the system and unknown bounded external interference; by these changes, the quadricycleThe wing drone attitude dynamics model is written in a compact form as follows:
(2) aiming at the uncertain attitude model of the four rotors given in the step (1), an Extended State Observer (ESO) is constructed to carry out online observation and compensation on lumped interference:
the following four-rotor attitude extended state observer is constructed:
wherein,
w020 denotes the bandwidth of the extended state observer, satisfying w0> 0, and w0Is the only parameter to be adjusted in the extended state observer;
estimated values of the angular rate and the aggregate interference of the quadrotors respectively;
(3) designing a boundary performance function with arbitrarily-assigned attitude adjusting time, and respectively constructing an attitude loop virtual control law and an angular velocity loop actual control law by combining the interference estimation given in the step (2) so as to realize the prior adjustment of attitude response transient and steady-state performance:
definition of Xid＝[20sin(3t),30sin(t),sin(2t)]Given a sufficiently smooth gesture command. Actual attitude angular response is X1＝[Xφ1,Xθ1,Xψ1]TAnd then the attitude tracking error of the quad-rotor unmanned aerial vehicle is ei1＝Xi1-Xid；
The initial state of the system is set to X1(0)＝[4,2,2]T，X2(0)＝[0,0,0]T；
To ensure that the attitude tracking error meets the following performance constraints:
wherein,
ai(t) is a performance function whose convergence time can be arbitrarily specified:
wherein r isi＝0.6,ai0＝6,ai∞＝0.1,Ti5 is the regulating parameter of the specified time performance section, and the time T is adjustediMay be such that the performance function ai(t) specifying time convergence;
next, an error transfer function S is usedi(. h) can convert constrained attitude tracking errors into unconstrained tracking errors:
wherein z isi(t) is the converted tracking error,
is the normalized error;
based on the converted tracking error, constructing a virtual control law of the attitude subsystem as follows:
wherein k isi14 is the control gain of the attitude loop;
definition of
Considering that the speed state and the collective disturbance are not measurable, the actual controller of the angular velocity subsystem is designed as follows:
wherein k is2The diag (8,8,8) is a control gain matrix of the angular velocity loop.
The scope of the invention is not limited to the above embodiments, and various modifications and changes may be made by those skilled in the art, and any modifications, improvements and equivalents within the spirit and principle of the invention should be included in the scope of the invention.
Claims (1)
1. A four-rotor attitude designated time performance-guaranteeing output feedback control method is characterized by comprising the following steps: the method comprises the following steps:
(1) establishing a quadrotor unmanned aerial vehicle attitude dynamic/kinematic model based on Euler angle description:
wherein, theta is [ phi, theta, psi ═ phi]TExpressing Euler angles in a body coordinate system, and respectively expressing a rolling angle, a pitching angle and a yaw angle in the attitude of the quad-rotor unmanned aerial vehicle by phi, theta and psi; omega-omegaφ,Ωθ,Ωψ]TDenotes the angular velocity vector, Ωφ,Ωθ,ΩψRespectively representing a rolling angular velocity, a pitch angular velocity and a yaw angular velocity; j ═ diag (J)φ,Jθ,Jψ) Representing a positive definite inertia matrix; ii ═ diag (k)φ,kθ,kψ) Representing an uncertain damping matrix, k, in an attitude loopi(i ═ Φ, θ, ψ) represents a damping coefficient; k ═ diag (l, l, c) denotes a symmetric constant matrix, l denotes the distance of each motor to the four rotor centroids, c denotes the moment coefficient; u ═ Uφ,uθ,uψ]TRepresenting the rotation torque input by the attitude angle of the quad-rotor unmanned aerial vehicle; d ═ dφ,dθ,dψ]TRepresentation applied in gesture kinematicsUnknown bounded external interference;
for convenience of controller design, the following symbolic variables are introduced:
X1＝Θ，
K2＝J-1K，dΘ＝-J-1ΠΩ+J-1d represents lumped interference in the quad-rotor drone attitude loop, including parametric uncertainty in the system and unknown bounded external interference; through these transformations, the quad-rotor drone attitude dynamics model is written in a compact form as follows:
(2) aiming at the uncertain attitude model of the four rotors given in the step (1), an Extended State Observer (ESO) is constructed to carry out online observation and compensation on lumped interference:
the following four-rotor attitude extended state observer is constructed:
wherein,
w0represents the bandwidth of the extended state observer, satisfies w0> 0, and w0Is the only parameter to be adjusted in the extended state observer;
estimated values of the angular rate and the aggregate interference of the quadrotors respectively;
(3) designing a boundary performance function with arbitrarily-assigned attitude adjusting time, and respectively constructing an attitude loop virtual control law and an angular velocity loop actual control law by combining the interference estimation given in the step (2) so as to realize the prior adjustment of attitude response transient and steady-state performance:
definition of Xid(i ═ phi, theta, psi) is given a sufficiently smooth attitude command, the actual attitude angle being X1＝[Xφ1,Xθ1,Xψ1]TAnd then the attitude tracking error of the quad-rotor unmanned aerial vehicle is ei1＝Xi1-XidTo ensure that the attitude tracking error meets the following performance constraints:
wherein,σ∈(0,1),
ai(t) is a performance function whose convergence time can be arbitrarily specified:
wherein r isi∈(0,1),ai0,ai∞,TiFor specifying the adjustment parameters of the temporal performance profile by adjusting the time TiMay be such that the performance function ai(t) specifying time convergence;
next, an error transfer function S is usedi(. h) can convert constrained attitude tracking errors into unconstrained tracking errors:
wherein z isi(t) is the converted tracking error,
is the normalized error;
based on the converted tracking error, constructing a virtual control law of the attitude subsystem as follows:
wherein k isi1Is the control gain of the attitude loop;
definition of
Considering that the speed state and the collective disturbance are not measurable, the actual controller of the angular velocity subsystem is designed as follows:
wherein k is2Is a control gain matrix of the angular velocity loop.
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| CN113238572A (en) * | 2021-05-31 | 2021-08-10 | 上海海事大学 | Preset-time quadrotor unmanned aerial vehicle attitude tracking method based on preset performance control |
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| CN113759949B (en) * | 2021-09-22 | 2024-07-26 | 北京理工大学 | Flexible frame unmanned aerial vehicle control method and device and electronic equipment |
| CN114355959A (en) * | 2021-10-08 | 2022-04-15 | 湖北隆感科技有限公司 | Attitude output feedback control method, device, medium and equipment of aerial robot |
| CN114355959B (en) * | 2021-10-08 | 2024-04-19 | 湖北隆感科技有限公司 | Attitude output feedback control method, device, medium and equipment for aerial robot |
| CN114019848A (en) * | 2021-10-14 | 2022-02-08 | 南京航空航天大学 | Input-limited mechanical system performance-guaranteeing self-adjustment control method |
| CN114019848B (en) * | 2021-10-14 | 2024-04-30 | 南京航空航天大学 | Self-regulating control method for security of mechanical system with limited input |
| CN116300994A (en) * | 2022-12-30 | 2023-06-23 | 西北工业大学 | Four-rotor unmanned aerial vehicle attitude control method based on unknown system dynamics estimator |
| CN116300994B (en) * | 2022-12-30 | 2023-08-22 | 西北工业大学 | Four-rotor unmanned aerial vehicle attitude control method based on unknown system dynamics estimator |
| CN116225043A (en) * | 2023-05-09 | 2023-06-06 | 南京信息工程大学 | Four-rotor unmanned aerial vehicle preset performance control method based on interference observer |
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