CN113625732B - Incremental feedback inverse angular velocity control law design method based on angular acceleration estimation - Google Patents
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Abstract
The invention discloses an incremental feedback inverse angular velocity control law design method based on angular acceleration estimation, which is used for improving the robustness of an advanced aircraft to interference and solving the problem that an angular acceleration signal is difficult to acquire in traditional incremental feedback inverse flight control. And according to the existing aerodynamic parameters, the angular acceleration is estimated in real time by combining an adaptive algorithm, and then an estimated angular acceleration signal is fed back to design an incremental feedback inverse flight control law. The estimated angular acceleration signal has the characteristics of small noise and high instantaneity, so that the flight control law of the incremental feedback inverse method based on the angular acceleration estimation inherits the advantage of robustness of the traditional incremental feedback inverse control, and meanwhile, the method has the advantages of simple structure, good noise resistance and low delay sensitivity, and therefore has important value for improving the robustness and control performance of an advanced aircraft flight control system.
Description
Technical Field
The invention belongs to the technical field of aircraft control, and particularly relates to a design method of an aircraft angular speed control law.
Background
In the actual flight process, the aircraft is subjected to interference of various disturbances, such as sensor noise, atmospheric turbulence, abrupt center of gravity change and the like, and the existence of the disturbances has higher requirements on the control law of the aircraft, namely the control law of the aircraft must have strong robustness to weaken the interference of the disturbances in the flight process, ensure the normal flight of the aircraft and achieve certain control quality. The angular speed flight controller is used as the basis of flight control, and the performance of the angular speed flight controller is directly related to the maneuvering quality and maneuvering performance of the advanced aircraft, so that the design of the angular speed control law by adopting a strong robustness control method has important significance for improving the flight performance of the advanced aircraft and improving the fault tolerance.
The angular velocity flight control law based on incremental feedback inversion has satisfactory control performance and robustness to model uncertainty and interference, but the method is too dependent on the accuracy and instantaneity of the feedback angular acceleration signal. In practical application, the angular acceleration sensor is expensive to manufacture and is not popular, thus preventing the method from being applied to a practical flight control system. For the acquisition of the angular acceleration signal, the conventional methods include an angular velocity difference method and a polynomial fitting method. The former calculates the triaxial angular acceleration by differentiating the measured angular velocity of the gyroscope, and the low-pass filter is necessarily adopted to filter the measured noise of the gyroscope, but the filter can delay the angular acceleration signal while weakening the influence of the noise, so that oscillation can be caused, and the stability of the flight control system can be damaged. In addition, due to the inherent characteristics of the digital difference, the difference further amplifies the noise influence in the process of acquiring the angular acceleration, and the filtering effect of the filter is further reduced. The latter polynomial fitting method is difficult to meet the applicability of control law in a large envelope range, and has poor universality.
In order to exert robustness of the incremental feedback inverse control, it is necessary to ensure real-time performance of the angular acceleration signal. This is currently difficult to achieve from a hardware level.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an incremental feedback inverse angular velocity control law design method based on angular acceleration estimation, which is used for improving the robustness of an advanced aircraft to interference and solving the problem that an angular acceleration signal is difficult to acquire in the traditional incremental feedback inverse flight control. And according to the existing aerodynamic parameters, the angular acceleration is estimated in real time by combining an adaptive algorithm, and then an estimated angular acceleration signal is fed back to design an incremental feedback inverse flight control law. The estimated angular acceleration signal has the characteristics of small noise and high instantaneity, so that the flight control law of the incremental feedback inverse method based on the angular acceleration estimation inherits the advantage of robustness of the traditional incremental feedback inverse control, and meanwhile, the method has the advantages of simple structure, good noise resistance and low delay sensitivity, and therefore has important value for improving the robustness and control performance of an advanced aircraft flight control system.
The technical scheme adopted by the invention for solving the technical problems comprises the following steps:
Step 1: according to aerodynamic parameters obtained by wind tunnel experiments or calculation software, an aircraft angular velocity motion equation is established:
Wherein J represents a moment of inertia matrix, and p, q and r represent roll, pitch and yaw angular velocities respectively; l, M and N represent roll, pitch and yaw moments, respectively, and the correspondence between L, M and N and the respective corresponding moment coefficients C l、Cm and C n is as follows:
wherein Q is dynamic pressure, S is airfoil area, b and Respectively representing the extended length and average aerodynamic chord length of the aircraft;
step 2: dividing the formula (2) into two parts according to the correlation degree of the pneumatic parameters and the control surface, wherein one part is generated by the state of the aircraft and is recorded as The other part is generated by the control surface and is marked asThe unfolding is as follows:
Wherein δ a、δe and δ r represent ailerons, elevators, and rudders, which are inputs to the flight control system; c l' (beta, p, r), And C n' (β, p, r) represents the aerodynamic derivative associated with the flight state; And Representing steering derivatives associated with the steering surface, respectively; alpha and beta respectively represent an attack angle and a sideslip angle;
Step 3: the aircraft angular velocity motion equation (1) is abbreviated as:
Wherein,
Step 4: by adopting a Taylor series method, an aircraft angular velocity motion equation (4) is developed:
Wherein omega 0 and u 0 respectively represent the angular velocity and the control surface input quantity at the previous moment, Representing the moment generated by the flight condition,Representing a control efficacy matrix;
neglecting the influence of the angular velocity change and the higher order term on the angular acceleration in consideration of the dominant factor, converting the equation (4) into:
The specific development is as follows:
Wherein p 0、q0、r0 represents roll, pitch and yaw angular velocities, respectively, at a previous time, delta a,0、δe,0、δr,0 represents aileron, elevator and rudder deflection, respectively, at a previous time;
Step 5: combining aerodynamic parameters with an adaptive law estimated angular acceleration signal based on a projection operator, and specifically comprises the following steps:
step 5-1: estimating the angular acceleration at the previous moment according to the existing state and aerodynamic parameters of the aircraft in combination with (4) The method comprises the following steps:
Step 5-2: from modeling errors Δf (ω) and Δg (ω) existing in the pneumatic data, the formula (9) becomes:
wherein Δf (ω) and Δg (ω) represent disturbances related to state, input, respectively;
Step 5-3: under the condition of meeting the requirement of Lyapunov stability, the adaptive law based on a projection operator is adopted to estimate modeling error disturbance influence, and the adaptive law based on the projection operator is designed as follows:
Where e (t) =ω ref (t) - ω (t) is the error of the angular velocity ω (t) and the command signal ω ref (t); Γ 1 and Γ 2 are adaptive gains, Γ 1 and Γ 2 are inversely proportional to the error e (t); And The estimated values of modeling errors Δf (ω) and Δg (ω), respectively, proj represent the projection operator, specifically defined as follows:
wherein θ represents the boundary of the set, f (θ) represents the convex function, and y represents the output of the function; the meaning of the projection operator symbol is as follows: when theta epsilon R n |f (theta) is less than or equal to 0, the projection operator Proj (theta, y) does not change y; when θ εR n |0 is less than or equal to f (θ) is less than or equal to 1, if Projection operator Proj (θ, y) does not change y as well; conversely, ifIf so, the projection operator Proj (θ, y) will subtract one perpendicular to the boundaryTo obtain a smooth transition from the original vector field to a vector y that is inward or tangential with respect to the vector field omega 1;
Thus, the final estimation of the angular acceleration takes the form of:
step 6: adopting an incremental feedback inverse method to design an angular speed flight control law;
The taylor series method is adopted to obtain an angular velocity motion equation in an increment form, so that the increment feedback inverse angular velocity flight control law is formed as follows:
where the virtual control quantity v represents the desired angular acceleration dynamics, typically designed by a linear controller, with the following consequences:
Where p ref、qref、rref represents command signals for roll, pitch and yaw angular velocities, respectively, and ω p、ωq、ωr represents bandwidths for roll, pitch and yaw angular velocities.
The beneficial effects of the invention are as follows:
(1) The method has the advantages of simple structure and few parameters, and can realize the expected dynamic angular velocity without complex parameter adjustment process. Compared with the traditional PID control, the incremental feedback inverse angular speed control based on the angular acceleration estimation has good universality, and different controllers are not required to be designed at a plurality of leveling points, so that the control law development cost is greatly reduced, and the development time is shortened.
(2) The angular velocity control of the increment feedback inverse based on the angular acceleration estimation solves the problem of angular acceleration signal acquisition in the traditional angular velocity control of the increment feedback inverse, and accurately estimates the angular acceleration signal with high reliability and good real-time performance from the algorithm level, so the method provided by the invention is more beneficial to practical application, and the influence of noise on a system is obviously reduced. Under the same condition, the control precision of the angular velocity controller designed based on the method is more accurate;
(3) The invention abandons the form of obtaining angular acceleration by the traditional differential method, so that the residual noise in the angular velocity is not amplified, and the interference of time delay caused by the angular acceleration of the filter is compensated to a certain extent due to the existence of the self-adaptive law of the projection operator.
(4) The method can improve the robustness of the angular velocity flight control system and weaken the adverse effect of interference on the aircraft.
(5) Compared with the traditional incremental feedback inverse control method, the method can accommodate larger transmission delay from the perspective of delay tolerance of the system.
Drawings
Fig. 1 is a diagram of the angular velocity control law structure of the incremental feedback inversion based on angular acceleration estimation according to the present invention.
FIG. 2 is a block diagram of the structure of the angular acceleration estimation based on projection operator adaptation of the present invention.
FIG. 3 is a graph showing roll angle velocity response at different perturbations in an embodiment of the present invention.
FIG. 4 is a graph of pitch rate response at different perturbations of an embodiment of the present invention.
FIG. 5 is a graph of yaw rate response at different disturbances according to an embodiment of the present invention.
FIG. 6 is a graph showing pitch rate response versus noise interference for an embodiment of the present invention.
FIG. 7 is a graph comparing pitch acceleration under noise interference according to an embodiment of the present invention.
FIG. 8 is a graph showing the rolling angle velocity response under noise interference according to an embodiment of the present invention.
FIG. 9 is a graph showing the comparison of roll angle acceleration under noise interference according to an embodiment of the present invention.
FIG. 10 is a graph showing yaw rate response versus time under noise interference in accordance with an embodiment of the present invention.
FIG. 11 is a graph showing yaw acceleration versus yaw acceleration under noise interference in accordance with an embodiment of the present invention.
FIG. 12 is a noise variance comparison chart of an embodiment of the present invention.
FIG. 13 is a graph showing the pitch rate response versus delay for an embodiment of the present invention.
FIG. 14 is a graph showing the roll angle velocity response versus delay in accordance with an embodiment of the present invention.
FIG. 15 is a graph showing yaw rate response versus delay for an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
Since conventional incremental dynamic inverse aircraft control methods rely on angular acceleration signals, such signals are often difficult to obtain. The invention provides a flight control law design method based on incremental feedback inversion of angular acceleration estimation. In the method, the obtained aerodynamic parameters are combined with the adaptive basis of the projection operator to estimate the angular acceleration signal, and then an angular velocity flight control law based on incremental feedback inversion is designed according to the estimated angular acceleration signal. Compared with the traditional differential acquisition mode, the estimated angular acceleration signal is more accurate and has lower delay, so that the angular velocity control law performance based on the incremental feedback inverse of the angular acceleration estimation is more outstanding.
The angular velocity control law based on the incremental feedback inverse of the angular acceleration estimation mainly includes the following:
(1) Establishing an advanced aircraft dynamics model;
(2) Modifying an aircraft angular velocity motion equation by adopting a Taylor series expansion method;
(3) The obtained aerodynamic parameters and the projection operator self-adaptive law are combined, and the angular acceleration signal is estimated on the premise of meeting the Lyapunov stability significance;
(4) According to the idea of feedback linearization, an angular velocity control law based on the incremental feedback inverse of the angular acceleration estimation is designed.
As shown in fig. 1, an incremental feedback inverse angular velocity control law design method based on angular acceleration estimation includes the following steps:
Step 1: according to aerodynamic parameters obtained by wind tunnel experiments or calculation software, an aircraft angular velocity motion equation is established:
Wherein J represents a moment of inertia matrix, and p, q and r represent roll, pitch and yaw angular velocities respectively; l, M and N represent roll, pitch and yaw moments, respectively, and the correspondence between L, M and N and the respective corresponding moment coefficients C l、Cm and C n is as follows:
wherein Q is dynamic pressure, S is airfoil area, b and Respectively representing the extended length and average aerodynamic chord length of the aircraft;
step 2: dividing the formula (2) into two parts according to the correlation degree of the pneumatic parameters and the control surface, wherein one part is generated by the state of the aircraft and is recorded as The other part is generated by the control surface and is marked asThe unfolding is as follows:
Wherein δ a、δe and δ r represent ailerons, elevators, and rudders, which are inputs to the flight control system; c l' (beta, p, r), And C n' (β, p, r) represents the aerodynamic derivative associated with the flight state; And Representing steering derivatives associated with the steering surface, respectively; alpha and beta respectively represent an attack angle and a sideslip angle;
Step 3: the aircraft angular velocity motion equation (1) is abbreviated as:
Wherein,
Step 4: by adopting a Taylor series method, an aircraft angular velocity motion equation (4) is developed:
Wherein omega 0 and u 0 respectively represent the angular velocity and the control surface input quantity at the previous moment, Representing the moment generated by the flight condition,Representing a control efficacy matrix;
neglecting the influence of the angular velocity change and the higher order term on the angular acceleration in consideration of the dominant factor, converting the equation (4) into:
The specific development is as follows:
Wherein p 0、q0、r0 represents roll, pitch and yaw angular velocities, respectively, at a previous time, delta a,0、δe,0、δr,0 represents aileron, elevator and rudder deflection, respectively, at a previous time;
Step 5: combining aerodynamic parameters with adaptive law estimated angular acceleration signals based on a projection operator, as shown in fig. 2, the specific steps are as follows:
step 5-1: estimating the angular acceleration at the previous moment according to the existing state and aerodynamic parameters of the aircraft in combination with (4) The method comprises the following steps:
Step 5-2: from modeling errors Δf (ω) and Δg (ω) existing in the pneumatic data, the formula (9) becomes:
wherein Δf (ω) and Δg (ω) represent disturbances related to state, input, respectively;
Step 5-3: under the condition of meeting the requirement of Lyapunov stability, the adaptive law based on a projection operator is adopted to estimate modeling error disturbance influence, and the adaptive law based on the projection operator is designed as follows:
Where e (t) =ω ref (t) - ω (t) is the error of the angular velocity ω (t) and the command signal ω ref (t); Γ 1 and Γ 2 are adaptive gains, Γ 1 and Γ 2 are inversely proportional to the error e (t); And The estimated values of modeling errors Δf (ω) and Δg (ω), respectively, proj represent the projection operator, specifically defined as follows:
wherein θ represents the boundary of the set, f (θ) represents the convex function, and y represents the output of the function; the meaning of the projection operator symbol is as follows: when theta epsilon R n |f (theta) is less than or equal to 0, the projection operator Proj (theta, y) does not change y; when θ εR n |0 is less than or equal to f (θ) is less than or equal to 1, if Projection operator Proj (θ, y) does not change y as well; conversely, ifIf so, the projection operator Proj (θ, y) will subtract one perpendicular to the boundaryTo obtain a smooth transition from the original vector field to a vector y that is inward or tangential with respect to the vector field omega 1;
Thus, the final estimation of the angular acceleration takes the form of:
step 6: adopting an incremental feedback inverse method to design an angular speed flight control law;
The taylor series method is adopted to obtain an angular velocity motion equation in an increment form, so that the increment feedback inverse angular velocity flight control law is formed as follows:
where the virtual control quantity v represents the desired angular acceleration dynamics, typically designed by a linear controller, with the following consequences:
Specific examples:
(1) Under the influence of interference, the robustness of the angular velocity control law based on the incremental feedback inversion of the angular acceleration estimation is verified.
Assuming that the aircraft had a sudden change in center of gravity at 1s, the degree of sudden change in center of gravity and the moment of inertia were as shown in Table 1:
TABLE 1 aircraft parameter Change Table under center of gravity abrupt disturbance
Under the action of the angular velocity control law based on the estimated incremental feedback inverse, the angular velocity response under the sudden change of the center of gravity disturbance is shown in fig. 3 to 5. From simulation results, after the aircraft is subjected to gravity center abrupt change disturbance, the angular speed instantaneously changes, but the aircraft quickly returns to a balanced state under the action of a designed controller, and the follow-up process can still quickly track an upper instruction signal, and no steady-state error exists in the response process. Overall, the angular velocity dynamic response meets the expected requirement, which indicates that the angular velocity controller designed based on the method provided by the invention has strong robustness and can overcome the influence caused by gravity center change. Simulation results demonstrate the effectiveness of the angular velocity control method based on the estimated incremental feedback inverse.
(2) Under the influence of sensor noise, the noise immunity of the angular velocity control law based on the incremental feedback inversion of the angular acceleration estimation provided by the invention is verified.
The sensor noise is simulated by using Gaussian white noise, and the noise variance is sigma 2＝1×10-4. Under the same conditions, the anti-noise capability of the traditional incremental feedback inverse controller and the incremental feedback inverse controller based on the angular acceleration estimation are compared, the comparison results of the angular velocity response and the angular acceleration response are shown in fig. 6-11, and the variances of the triaxial angular velocity and the angular acceleration are counted in fig. 12.
The angular acceleration estimation method provided by the invention abandons a differential mode, so that noise is prevented from being further amplified. From simulation results, the angular velocity and the noise variance in the angular acceleration response under the incremental feedback inverse controller of the angular acceleration estimation are far smaller than those of the traditional incremental feedback inverse controller, and the noise immunity of the method provided by the invention is proved to be stronger than that of the traditional incremental feedback inverse control method.
(3) Under the influence of delay interference, the angular velocity control law of the incremental feedback inverse based on the angular acceleration estimation provided by the invention is used for verifying the delay tolerance.
It is assumed that there is a 30ms delay in angular velocity during transmission. Under the same conditions, the delay resistance of the traditional incremental feedback inverse controller and the incremental feedback inverse controller of the angular acceleration estimation are compared, and the comparison results are shown in fig. 13-15.
From the comparison result, the performance of the traditional incremental feedback inverse controller is reduced after the angular velocity signal is delayed due to the accuracy and real-time property of the angular acceleration signal, and the angular velocity also generates undesirable oscillation. In contrast, the angular acceleration estimation method provided by the invention comprises an adaptive structure, so that the influence caused by delay can be compensated to a certain extent, and the angular velocity response can still meet the expected dynamic performance under 30ms delay disturbance.
By combining the simulation results, the angular velocity control law design method of the incremental feedback inverse based on the angular acceleration estimation has robustness, can overcome the influence of disturbance on the aircraft, and solves the problem that the angular acceleration is difficult to obtain in the traditional incremental feedback inverse control. In addition, the noise immunity and the delay tolerance of the method provided by the invention are both stronger than those of the traditional incremental feedback inverse control method.
The invention innovatively solves the problem of acquiring the angular acceleration signal from the algorithm level, and further provides a flight control law design method based on incremental feedback inversion of angular acceleration estimation. In addition, a certain advanced aircraft model is built through Matlab/Simulink software, and the effectiveness and the robustness of the angular velocity control law based on the angular acceleration estimation increment feedback inversion provided by the invention are designed and simulated and verified. Because the algorithm of the method has a simple structure, the method does not need additional hardware support to achieve the aim, and does not cause additional burden on a processor, thereby being convenient for application in the design of an actual flight controller.
Claims (1)
1. The incremental feedback inverse angular velocity control law design method based on angular acceleration estimation is characterized by comprising the following steps of:
Step 1: according to aerodynamic parameters obtained by wind tunnel experiments or calculation software, an aircraft angular velocity motion equation is established:
Wherein J represents a moment of inertia matrix, and p, p and r represent roll, pitch and yaw angular velocities respectively; l, M and N represent roll, pitch and yaw moments, respectively, and the correspondence between L, M and N and the respective corresponding moment coefficients C l、Cm and C n is as follows:
wherein Q is dynamic pressure, S is airfoil area, b and Respectively representing the extended length and average aerodynamic chord length of the aircraft;
step 2: dividing the formula (2) into two parts according to the correlation degree of the pneumatic parameters and the control surface, wherein one part is generated by the state of the aircraft and is recorded as The other part is generated by the control surface and is marked asThe unfolding is as follows:
Wherein δ a、δe and δ r represent ailerons, elevators, and rudders, which are inputs to the flight control system; c l' (beta, p, r), And C n' (β, p, r) represents the aerodynamic derivative associated with the flight state; And Representing steering derivatives associated with the steering surface, respectively; alpha and beta respectively represent an attack angle and a sideslip angle;
Step 3: the aircraft angular velocity motion equation (1) is abbreviated as:
Wherein,
Step 4: by adopting a Taylor series method, an aircraft angular velocity motion equation (4) is developed:
Wherein omega 0 and u 0 respectively represent the angular velocity and the control surface input quantity at the previous moment, Representing the moment generated by the flight condition,Representing a control efficacy matrix;
neglecting the influence of the angular velocity change and the higher order term on the angular acceleration in consideration of the dominant factor, converting the equation (4) into:
The specific development is as follows:
wherein p 0、q0、r0 represents roll, pitch and yaw angular velocities, respectively, at a previous time, delta a,0、δe,0、δr,0 represents aileron, elevator and rudder deflection, respectively, at a previous time;
Step 5: combining aerodynamic parameters with an adaptive law estimated angular acceleration signal based on a projection operator, and specifically comprises the following steps:
step 5-1: estimating the angular acceleration at the previous moment according to the existing state and aerodynamic parameters of the aircraft in combination with (4) The method comprises the following steps:
Step 5-2: from modeling errors Δf (ω) and Δg (ω) existing in the pneumatic data, the formula (9) becomes:
wherein Δf (ω) and Δg (ω) represent disturbances related to state, input, respectively;
Step 5-3: under the condition of meeting the requirement of Lyapunov stability, the adaptive law based on a projection operator is adopted to estimate modeling error disturbance influence, and the adaptive law based on the projection operator is designed as follows:
Where e (t) =ω ref (t) - ω (t) is the error of the angular velocity ω (t) and the command signal ω ref (t); Γ 1 and Γ 2 are adaptive gains, Γ 1 and Γ 2 are inversely proportional to the error e (t); And The estimated values of modeling errors Δf (ω) and Δg (ω), respectively, proj represent the projection operator operators, which are defined specifically as follows:
Wherein θ represents the boundary of the set, f (θ) represents the convex function, and y represents the output of the function; the meaning of the projection operator symbol is as follows: when theta epsilon R n |f (theta) is less than or equal to 0, the projection operator Proj (theta, y) does not change y; when θ εR n |0 is less than or equal to f (θ) is less than or equal to 1, if Projection operator Proj (θ, y) does not change y as well; conversely, ifIf so, the projection operator Proj (θ, y) will subtract one perpendicular to the boundaryTo obtain a smooth transition from the original vector field to a vector y that is inward or tangential with respect to the vector field omega 1;
Thus, the final estimation of the angular acceleration takes the form of:
step 6: adopting an incremental feedback inverse method to design an angular speed flight control law;
The taylor series method is adopted to obtain an angular velocity motion equation in an increment form, so that the increment feedback inverse angular velocity flight control law is formed as follows:
Where the virtual control amount y represents the desired angular acceleration dynamics, typically designed by a linear controller, with the following results:
Where p ref、qref、rref represents command signals for roll, pitch and yaw angular velocities, respectively, and ω p、ωq、ωr represents bandwidths for roll, pitch and yaw angular velocities.
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| CN102736631A (en) * | 2012-06-11 | 2012-10-17 | 北京航空航天大学 | Closed-loop control distribution method of multi-control surface unmanned aerial vehicle based on angular acceleration sensor |
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| CN109032171B (en) * | 2018-06-26 | 2019-07-16 | 中国空气动力研究与发展中心低速空气动力研究所 | A kind of control method of the aircraft wind tunnel free-flight based on Nonlinear control law |
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| CA2828444A1 (en) * | 2011-03-14 | 2012-09-20 | Mitsubishi Heavy Industries, Ltd. | Aircraft control system, aircraft, aircraft control program, and method for controlling aircraft |
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