Aircraft active side stick force feedback control method based on feedback linearization

Abstract

The invention discloses an aircraft active side lever force feedback control method based on feedback linearization. The method is suitable for pitch axial force feedback control and roll axial force feedback control of an aircraft active side lever. The method comprises the following steps: establishing a kinetic equation of a mechanical transmission system and a pitch axis motor or a roll axis motor, and establishing a state-space equation of an active side lever system according to the equation; designing a linear expansion observer, and estimating the thrust applied to the active side lever by the driver based on the linear expansion observer; and designing a feedback linearization control method, deducing a control law according to a state-space equation of the active side lever system, and introducing the estimated thrust applied to the active side lever by the driver into the control law to realize real-time compensation of external interference. Under the condition that the thrust of the driver cannot be measured, the thrust of the driver is obtained through the linear expansion observer, the thrust of the driver is compensated by designing the control law, and therefore the dynamic performance and the steady-state performance of the servo system are improved.

Description

Technical Field

[0001] The invention relates to an aircraft active sidestick force feedback control method based on feedback linearization, and belongs to the technical field of aircraft active sidestick electromechanical servo control. Background Art

[0002] As the operating component of an aircraft's fly-by-wire system, active sidesticks have gradually replaced traditional mechanical joysticks due to their simple structure and high safety. Compared to mechanical joysticks with fixed spring-damping characteristics, active sidesticks can change the stick's force-displacement characteristic curve based on the aircraft's flight state and autopilot configuration, providing dynamic force feedback and a better driving experience for the pilot.

[0003] However, in actual active sidestick mechanical designs, there's often insufficient space to install a force sensor to measure the driver's thrust on the sidestick, preventing the controller from accurately determining the driver's thrust. Furthermore, the driver's thrust and the system's control input are not routed through the same channel, making it difficult to address this through traditional control law design. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an aircraft active sidestick force feedback control method based on feedback linearization, so that the system can obtain the pilot's thrust through a linear expansion observer in the absence of a force sensor, and compensate for the pilot's thrust by designing a control law, thereby improving the dynamic performance and steady-state performance of the servo system.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A method for force feedback control of an aircraft active sidestick based on feedback linearization is disclosed. The method is applicable to the pitch axis force feedback control and roll axis force feedback control of the aircraft active sidestick. The aircraft active sidestick system includes a pitch axis motor, a roll axis motor, and a mechanical transmission system. The mechanical transmission system includes an active sidestick and a reducer. The method comprises the following steps:

[0007] Step 1: Establish the dynamic equations of the mechanical transmission system and the pitch axis motor or the roll axis motor, and establish the state space equations of the active sidestick system based on the above equations;

[0008] Step 2: Design a linear expansion observer and estimate the thrust applied by the driver to the active side stick based on the linear expansion observer;

[0009] In step 3, a feedback linearization control method is designed to derive the control law based on the state-space equation of the active sidestick system. The thrust applied by the driver to the active sidestick estimated in step 2 is introduced into the control law to achieve real-time compensation of external disturbances.

[0010] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0011] This paper first analyzes the dynamic characteristics of the active sidestick servo system and establishes a mathematical model of the system. Based on this, and considering the system's inability to obtain the driver's actual thrust, a linear expansion observer is used to estimate the driver's thrust on the sidestick in real time. Furthermore, in the design of the force outer-loop controller, the system's disturbance term is matched to the same channel as the control input based on the principle of feedback linearization. This allows for compensation of disturbances through the design of the control law and the observer's estimation of the disturbance term, thereby achieving force feedback control and improving the system's dynamic and steady-state performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a structural block diagram of the aircraft active sidestick force feedback control method based on feedback linearization of the present invention;

[0013] Figure 2 This is the active side rod structure diagram;

[0014] Figure 3 is the observer's estimation diagram of the ramp interference signal;

[0015] Figure 4 is the active sidestick force feedback diagram corresponding to the feedback linearization algorithm under ramp thrust;

[0016] Figure 5 This is the active sidestick force feedback diagram corresponding to the traditional PI algorithm under ramp thrust;

[0017] Figure 6 is the observer's estimation diagram of the sinusoidal interference signal;

[0018] Figure 7 is the active sidestick force feedback diagram corresponding to the feedback linearization algorithm under sinusoidal thrust;

[0019] Figure 8 This is the active sidestick force feedback diagram corresponding to the traditional PI algorithm under sinusoidal thrust;

[0020] Figure 9 It is the rod force characteristic curve under the feedback linearization algorithm and PI algorithm. DETAILED DESCRIPTION

[0021] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be interpreted as limiting the present invention.

[0022] The present invention proposes an active side stick force feedback control method based on feedback linearization algorithm. The active side stick is mainly composed of a pitch axis motor, a roll axis motor and a corresponding mechanical transmission system, including a stick head, a stick, a reducer and a gear box, etc. Figure 2 As shown. The mechanical structure incorporates a pitch-axis and roll-axis linkage bracket, allowing for decoupling of the motion of each axis. For simplicity, this invention focuses solely on pitch-axis force feedback control; a similar approach can be used for roll-axis force feedback control.

[0023] like Figure 1 As shown, the method proposed by the present invention comprises the following steps:

[0024] (1) Establish the dynamic model of the mechanical transmission system and the permanent magnet synchronous motor;

[0025] Ignoring the gravity of the rod, when the driver applies thrust to the rod, the dynamic model of the mechanical transmission system can be expressed as:

[0026]

[0027] Among them, T c =F c L, T p =F p L, represents the torque applied by the driver and the active side stick feedback torque. c represents the thrust applied by the driver, L represents the length of the rod, and F p Indicates the feedback force output by the active side stick, J p Indicates the moment of inertia and friction coefficient of the rod. In traditional mechanical systems, the permanent magnet synchronous motor (PMSM) increases the output torque and reduces the speed through the action of the reducer, satisfying the following relationship:

[0028] θ l =nθ p

[0029] T p =nT l

[0030] Among them, θ l 、T l Respectively represent the angle and torque at the reducer input end, θ p 、T p They represent the rotation angle and torque at the output end of the reducer respectively, and n represents the reduction ratio.

[0031] In an active sidestick system, the PMSM generates a feedback torque opposite to the driver's applied torque. When the applied torque is greater than the electromagnetic torque, the applied torque forces the PMSM to move. When the applied torque is less than the electromagnetic torque, the PMSM moves in the opposite direction. Therefore, based on the above analysis, the following formula is used to describe the relationship between the PMSM's rotation angle and torque:

[0032]

[0033] Among them, T l =K l (θ l -θ m ), T l represents the applied torque, T e represents the electromagnetic torque, w m is the mechanical angular velocity of the PMSM, θ m is the mechanical angular displacement of the PMSM, J m represents the moment of inertia, B m Represents the damping coefficient, K l Represents the stiffness coefficient of the connection between PMSM and reducer. Assuming that the current control instruction i d =0, the electromagnetic torque can be expressed as:

[0034] T e =K e i q

[0035] Among them, K e is the motor torque coefficient, i d and i q are the d-axis and q-axis currents respectively. According to the mechanical transmission equation and PMSM dynamic equation, the state space equation of the active side rod can be derived as follows:

[0036]

[0037] y=Cx

[0038] in,

[0039] The state variables, inputs, and outputs of the model are x = [x1, x2, x3, x4] T =[θ m ,w m ,θ p ,w p ] T , u=i q , y=[y1,y2] T =[F p ,θ p ] T, where ε = F c represents the thrust applied by the driver to the side stick. Due to its unmeasurable characteristics, it is regarded as an external disturbance here and treated as an unknown quantity in the design of the control algorithm.

[0040] (2) Design a linear expansion observer to estimate the driver's thrust based on the control variable and the angle output;

[0041] Taking ε as the expanded state variable of the active sidestick system model, the expanded state equation is obtained as follows:

[0042]

[0043] Among them, the expanded state variable With the coefficient matrix Respectively expressed as:

[0044]

[0045] Based on this, the expanded observer is designed as:

[0046]

[0047] in, is the expanded state variable The estimated value of , l is the gain coefficient matrix of the observer.

[0048] (3) Design a feedback linearization control method, derive the control law based on the system state equation, and introduce the estimated value of the driver's thrust into the control law for compensation;

[0049] A. Two PI controllers are used in the current inner loop of the control system to drive the current i q and i d Make it track the desired current i generated by the outer loop q * and 0.

[0050] B. Use feedback linearization algorithm in the outer loop of the control system to design the control law based on the angle, angular velocity and feedback force output by the PMSM and calculate the desired current i q * For motor drive.

[0051] In practice, because the sampling frequency of the inner current loop in the active sidearm system is much higher than that of the outer loop, both loops are controlled independently. In this paper, the current loop controller is considered to be able to stably track the desired current, so the design of the control law for the outer loop is focused.

[0052] In order to provide the pilot with appropriate feedback force through the active sidestick during flight, the expected feedback force is usually calculated based on the stick force-displacement curve. The relationship between the expected feedback force and the stick rotation displacement is as follows:

[0053]

[0054] in, represents the desired feedback force, and f(·) represents the rod force-displacement curve function, which is usually a nonlinear function and is positively correlated with y2.

[0055] According to the state space equation of the system, define the state variables The state transfer equation is obtained as:

[0056]

[0057] in, The expression of the control law is derived as:

[0058]

[0059] Among them, v is a dummy control variable, which is expressed as:

[0060]

[0061] Among them, k1 and k2 are gain coefficients, which are usually positive numbers.

[0062] According to Lyapunov's stability theorem and separation theorem, the asymptotic stability of the designed observer and control law are derived respectively, thereby verifying the stability of the system.

[0063] According to the linear expansion observer equation, the observability discriminant matrix is ​​obtained as:

[0064]

[0065] in,

[0066] That is, the observability discriminant matrix is ​​a full-rank matrix. Therefore, there exists a positive definite symmetric matrix P such that the following holds:

[0067]

[0068] Where Q is a positive definite matrix. Definition You can get:

[0069]

[0070] Take the Lyapunov function as Then its derivative is Available And if and only if hour, According to the Lyapunov stability principle, the estimated error system is asymptotically stable. Therefore, it can be concluded that the designed observer is stable and can accurately estimate the external disturbance of the active sidestick system.

[0071] The stability of the control law proposed in the present invention is further analyzed below. The state variables of the feedback force tracking error system are defined as:

[0072]

[0073] Substituting the control law designed in (3) into the state transfer equation, we can obtain:

[0074]

[0075] in, Since k1 and k2 are positive, the tracking error system is asymptotically stable.

[0076] From the above formula, we can see that the system has a relative degree r = 2 at point x0. Since r is smaller than the system dimension, we define functions φ1(x) and φ2(x) to realize the transformation from state vector x to e f Coordinate transformation, where:

[0077] e f =Φ(x)=[e T ,φ1(x),φ2(x)] T

[0078] Analyzing the zero dynamics of the system, let e1=e2=0, we can get:

[0079]

[0080] From the above formula, we can get the equilibrium point of the system as when When the desired feedback force and the actual feedback force are equal to the thrust provided by the pilot, the angular velocity of the rotating rod converges to x4 = 0, indicating that the rod stops moving. At this time, the displacement angle of the rod is When the pilot pushes or pulls the sidestick, increasing or decreasing x3, the desired feedback force f(x3) also changes. In this case, the pilot must increase or decrease the thrust ε to bring the system to a new equilibrium point.

[0081] In order to move the equilibrium point toward the origin, let According to Lagrange's mean value theorem, the above formula can be converted into the following form:

[0082]

[0083] in, ξ is the distance from x3 to The middle value. Since f(x3) is positively correlated with x3, Therefore, A η is a Hurwitz matrix, and the above equation is asymptotically stable. Therefore, it can be shown that the active sidestick system is a minimum phase system. For the functions φ1(x) and φ2(x), choose φ1(x) = x3-f -1 (ε), φ2(x)=x4, satisfying:

[0084]

[0085] It can make Φ(x) a differential homeomorphism. Therefore, there is a global coordinate transformation:

[0086]

[0087] According to the above analysis, since the formula and All of them are asymptotically stable, so it can be concluded that the active sidestick system is asymptotically stable when the proposed feedback linearization control algorithm is adopted.

[0088] According to Lyapunov's separation theorem, since the designed control algorithm and extended observer are both asymptotically stable, the active sidestick system is asymptotically stable under this control strategy.

[0089] Example

[0090] The force feedback control simulation experiment of the active side stick system was carried out using Matlab / Simulink simulation tools. The parameter settings in the simulation experiment are shown in Table 1:

[0091] Table 1 Active side stick system parameters

[0092] parameter value unit <![CDATA[J p ]]> <![CDATA[0.5×0.3 2 ]]> <![CDATA[kg·m 2 ]]> <![CDATA[B p ]]> <![CDATA[0.1×0.3 2 ]]> N·s / rad n 15 L 0.3 m <![CDATA[J m ]]> <![CDATA[4.25×10 -5 ]]> <![CDATA[kg·m 2 ]]> <![CDATA[B m ]]> 0.01 N·s / rad <![CDATA[K l ]]> <![CDATA[1×10 3 ]]> N / m <![CDATA[K e ]]> 18.83 N·m / A

[0093] Set the rod force-displacement curve to:

[0094]

[0095] The gain coefficient of the linear expansion observer is set to l = [-4.1656 × 10 5 ,5.5055×10 7 ,8.7645×10 3 ,3.9066×10 6 ,2.2950×10 8 ], the gain of the feedback linearization control algorithm is set to k1 = 4 × 10 7 , k2=2×103 .

[0096] like Figure 3-Figure 4 The figure shows the estimation of the disturbance by the designed observer and the force feedback output by the system when the method proposed in the present invention is used when the sidebar is subjected to a ramp thrust with a slope of 40N / t. Figure 5 Figure 2 shows the force feedback output of the system using a traditional PI controller. It can be seen that the designed linear expansion observer can accurately estimate the disturbance with an estimation error within 0.09 N. Furthermore, the designed algorithm has a smaller steady-state error and shorter settling time than the PI algorithm.

[0097] like Figure 6-Figure 7 The figure shows the estimation of the disturbance by the designed observer and the force feedback output by the system when the method proposed in the present invention is used, when a sinusoidal thrust with an amplitude of 10N and a frequency of 2π is applied to the sidebar. Figure 8 Figure 2 shows the force feedback output of the system using a traditional PI controller under these conditions. It can be seen that the designed linear expansion observer accurately estimates the disturbance with an error within 1.8 N. Furthermore, under sinusoidal thrust, the designed algorithm still achieves smaller steady-state error and shorter settling time than the PI algorithm.

[0098] like Figure 9 The figure shows a comparison of the active sidestick force curves using the proposed method and the PI algorithm. It can be seen that compared with the PI algorithm, the active sidestick force feedback control system using the feedback linearization algorithm is closer to the desired force curve, indicating that the proposed method has more accurate force feedback control performance.

[0099] Based on the same inventive concept, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the aforementioned feedback linearization-based aircraft active sidestick force feedback control method are implemented.

[0100] Based on the same inventive concept, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the aforementioned aircraft active sidestick force feedback control method based on feedback linearization.

[0101] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0102] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0103] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0104] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0105] The above embodiments are only for illustrating the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for aircraft active sidestick force feedback control based on feedback linearization, applicable to pitch axis force feedback control and roll axis force feedback control of an aircraft active sidestick, wherein the aircraft active sidestick system includes a pitch axis motor, a roll axis motor, and a mechanical transmission system, wherein the mechanical transmission system includes an active sidestick and a reducer; characterized in that: The method comprises the following steps: Step 1: Establish the dynamic equations of the mechanical transmission system and the pitch axis motor or the roll axis motor, and establish the state space equations of the active sidestick system based on the above equations; Step 2: Design a linear expansion observer and estimate the thrust applied by the driver to the active side stick based on the linear expansion observer; In step 3, a feedback linearization control method is designed to derive the control law based on the state-space equation of the active sidestick system. The thrust applied by the driver to the active sidestick estimated in step 2 is introduced into the control law to achieve real-time compensation of external disturbances.

2. The aircraft active sidestick force feedback control method based on feedback linearization according to claim 1, characterized in that: The specific process of step 1 is as follows: Step 1.1: Ignore the gravity factor of the active side stick. When the driver applies thrust to the active side stick, the dynamic equation of the mechanical transmission system is expressed as: Among them, T c 、T p are the driver's torque and the active side stick feedback torque, T c =F c L, T p =F p L, F c represents the thrust applied by the driver, L represents the length of the rod, and F p Indicates the feedback force output by the active side stick, J p represents the moment of inertia of the rod, w p represents the angular velocity of the rod, B p represents the friction coefficient of the rod; Step 1.2: The dynamic equation of the pitch axis motor or roll axis motor is expressed as: Among them, T l Indicates the torque applied by the pitch axis motor or the roll axis motor, T l =K l (θ l -θ m ), K l Indicates the stiffness coefficient of the connection between the pitch axis motor or roll axis motor and the reducer, θ l Indicates the rotation angle of the reducer input end, θ l =nθ p , n represents the reduction ratio, θ p Indicates the angle of rotation at the output end of the reducer, θ m Indicates the mechanical angular displacement of the pitch axis motor or roll axis motor, T e Represents electromagnetic torque, J m represents the moment of inertia, w m Indicates the mechanical angular velocity of the pitch axis motor or roll axis motor, B m represents the damping coefficient; When the current control instruction i d =0, the electromagnetic torque is expressed as: T e =K e i q Among them, K e is the motor torque coefficient, i q is the q-axis current; Step 1.3: Based on the dynamic equations of the mechanical transmission system and the pitch axis motor or roll axis motor, derive the state space equation of the active side stick as follows: y=Cx in, x, u, and y represent the state variables, inputs, and outputs of the active sidestick system model, respectively. x = [x1, x2, x3, x4] T =[θ m ,w m ,θ p ,w p ] T , u=i q , y=[y1,y2] T =[F p ,θ p ] T ,ε=F c , ε is an unknown quantity.

3. The aircraft active sidestick force feedback control method based on feedback linearization according to claim 2, characterized in that: The specific process of step 2 is as follows: Taking ε as the expanded state variable of the active sidestick system model, the expanded state equation is obtained as follows: in, represents the expanded state variable, are coefficient matrices, The linear extended observer is designed according to the extended state equation as follows: in, is the estimated value of the expanded state variable x, l is the gain coefficient matrix of the observer, y2=θ p .

4. The aircraft active sidestick force feedback control method based on feedback linearization according to claim 3, characterized in that: The specific process of step 3 is as follows: The feedback force provided to the pilot by the active sidestick during flight is calculated based on the stick force-displacement curve. The relationship between the expected feedback force and the stick rotational displacement is as follows: in, represents the desired feedback force, f(·) represents the rod force-displacement curve function; According to the state space equation of the active sidestick system, the state variables are defined as The state transfer equation is obtained as: in, The expression of the control law is derived as: Among them, v is a dummy control variable, and its expression is: Among them, k1 and k2 are gain coefficients.

5. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: When the processor executes the computer program, the steps of the aircraft active sidestick force feedback control method based on feedback linearization are implemented as described in any one of claims 1 to 4.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the aircraft active sidestick force feedback control method based on feedback linearization according to any one of claims 1 to 4 are implemented.

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