Adaptive robust control method and device with inertia compensation

Abstract

The present disclosure provides an adaptive robust control method with inertia compensation, applicable to an electro-hydraulic flight simulation turntable, the electro-hydraulic flight simulation turntable comprising an outer frame, an outer frame hydraulic motor connected to the outer frame, and a middle frame connected to the outer frame; the method comprising: establishing a nonlinear model of a valve-controlled hydraulic motor servo system, the nonlinear model being capable of characterizing how the inertia of the outer frame changes with the rotation angle of the middle frame; wherein the valve-controlled hydraulic motor servo system comprises an outer frame and an outer frame hydraulic motor connected to the outer frame; and establishing control equations for the valve-controlled hydraulic motor servo system based on the nonlinear model. The present disclosure provides an adaptive robust control method and device with inertia compensation, capable of improving the tracking accuracy of the outer frame of the electro-hydraulic flight simulation turntable.

Description

Technical Field

[0001] The present disclosure relates to the technical field of electro-hydraulic flight turntables, and in particular to an adaptive robust control method and device with inertia compensation. Background Art

[0002] The electro-hydraulic flight simulation turntable is used to simulate missile attitude. It has large dynamics and high acceleration and is a key device for testing and calibrating inertial devices.

[0003] A significant characteristic of flight simulation turntable outer frame control is its large inertia. Furthermore, when the middle frame is in motion, the outer frame's inertia changes significantly in real time. This large and variable inertia creates significant challenges for precise position control of the outer frame. Especially when the middle frame is in high-speed motion, changes in inertia create a significant parameter uncertainty disturbance for the outer frame. As missiles and aircraft become increasingly maneuverable during development, the demand for turntable control precision is becoming increasingly stringent. Summary of the Invention

[0004] The present disclosure provides an adaptive robust control method and device with inertia compensation to improve the tracking accuracy of an electro-hydraulic flight simulation turntable frame.

[0005] In one aspect, an adaptive robust control method with inertia compensation is provided, which is applicable to an electro-hydraulic flight simulation turntable, wherein the electro-hydraulic flight simulation turntable includes an outer frame, an outer frame hydraulic motor connected to the outer frame, and a middle frame connected to the outer frame; the method includes:

[0006] Establishing a nonlinear model of a valve-controlled hydraulic motor servo system, wherein the nonlinear model can characterize how the inertia of the outer frame changes with the rotation angle of the middle frame; wherein the valve-controlled hydraulic motor servo system includes an outer frame and an outer frame hydraulic motor connected to the outer frame;

[0007] Based on the nonlinear model, a control equation of the valve-controlled hydraulic motor servo system is established.

[0008] In some embodiments, the nonlinear model is

[0009]

[0010]

[0011]

[0012] Where J is the sum of the inertia of the outer frame, middle frame, inner frame and load;

[0013] D is the effective volume of the hydraulic motor, m 3 ;

[0014] θ m is the angular displacement of the outer frame;

[0015] is the angular velocity of the outer frame;

[0016] is the angular acceleration of the outer frame;

[0017] B is the total viscous load factor, N·m / (rad / s);

[0018] A f is the modelable Coulomb friction amplitude;

[0019] S f is a continuous approximate Coulomb friction shape function;

[0020] f e Represents external disturbances and unmodeled dynamics of the system;

[0021] P1 is the pressure of the first chamber of the hydraulic motor, Pa;

[0022] P2 is the pressure of the second chamber of the hydraulic motor, Pa;

[0023] is the derivative of the pressure in the first chamber of the hydraulic motor;

[0024] is the derivative of the pressure in the second chamber of the hydraulic motor;

[0025] q1(t) and q2(t) are unmodeled errors;

[0026] Q1 is the flow rate from the valve port into the first chamber of the hydraulic motor, m 3 / s;

[0027] Q2 is the flow rate from the second chamber of the hydraulic motor to the valve port, m 3 / s;

[0028] β e1 , β e2 The bulk modulus of the hydraulic oil in the first and second cavities of the hydraulic motor, respectively, includes the effect of elastic deformation of the cavity wall and the tube wall, N / m 2 ;

[0029] V1 is the volume of the closed chamber connected to the first chamber of the hydraulic motor, m 3 ,

[0030] V2 is the volume of the closed chamber connected to the second chamber of the hydraulic motor, m 3 ,

[0031] V 01The initial volume of the sealed chamber connected to the first chamber of the hydraulic motor;

[0032] V 02 The initial volume of the sealed chamber connected to the second chamber of the hydraulic motor;

[0033] V1=V 01 +D m θ m , V2=V 02 -D m θ m ;

[0034] C t is the internal leakage coefficient of the hydraulic motor, m 3 / (s·Pa);

[0035] P l =P1-P2, which is the load pressure.

[0036] In some embodiments, establishing the control equation of the valve-controlled hydraulic motor servo system based on the nonlinear model includes:

[0037] Define the system state variables as:

[0038]

[0039] The system state equation is:

[0040]

[0041]

[0042] in, is the derivative of the outer frame's angular displacement, i.e., the angular velocity of rotation;

[0043] is the derivative of the outer frame's angular velocity, i.e., the angular acceleration;

[0044] is the derivative of the load pressure;

[0045] q(t) is the unmodeled error;

[0046] |fe(t)|≤δ1, |q(t)|≤δ2, where δ1 and δ2 are known positive constants;

[0047]

[0048]

[0049]

[0050] Ps is the set pressure of the safety valve, which is a constant value;

[0051] P r is the system return oil pressure;

[0052] Define the uncertain parameter set:

[0053] θ=[θ1,θ2,θ 3， θ4, θ5] T

[0054] θ1=B,θ2=A f ,θ3=β e k t ,θ4=β e D, θ5=β e C t

[0055] in, is the estimator of θ;

[0056] is the estimation error of the unknown parameter θ,

[0057] k t is the total flow gain;

[0058] The defined parameter set satisfies

[0059]

[0060] Among them, θ min =[θ 1min ,θ 2min ,...,θ 5min ] T ;

[0061] θ max =[θ 1max ,θ 2max ,...,θ 5max ] T and is known;

[0062] Definition error:

[0063] z1=x1-x 1d

[0064]

[0065] z3=x3-α2

[0066] The error dynamics is:

[0067]

[0068]

[0069] Based on the backstepping design process, the virtual control law α2 and the nonlinear adaptive robust controller u are designed as follows:

[0070]

[0071]

[0072] α 2s =α 2s1 +α 2s2

[0073] α 2s1 =-k2z2

[0074]

[0075]

[0076]

[0077] u s =u s1 +u s2

[0078] u s1 =-k3z3

[0079]

[0080] ψ2 and ψ3 are smooth functions and satisfy the following conditions

[0081]

[0082] Among them, θ M =θ max -θ min ;

[0083] Substitute the virtual control law α2 and the actual control input u into the error dynamics equation to obtain

[0084]

[0085] in,

[0086]

[0087] x 1d is the desired motion trajectory;

[0088] z1 is the output tracking error;

[0089] k1 is the positive feedback gain;

[0090] k2 and k3 are positive nonlinear gains;

[0091] ε2, ε3 are positive constants;

[0092] α1 is the virtual control law of state x2;

[0093] z2 is the difference between the actual state x2 and the virtual control α1;

[0094] α2 is the virtual control law of state x3;

[0095] z3 is the difference between the actual state x3 and the virtual control α2;

[0096] is the derivative of z1;

[0097] is the derivative of z2;

[0098] is the derivative of z3;

[0099] is the derivative of α1;

[0100] is the derivative of α2;

[0101] u is the control input;

[0102] k s2 and k s3 is the positive nonlinear gain.

[0103] In some embodiments, after establishing the control equation of the valve-controlled hydraulic motor servo system, the method further includes performing a stability analysis on the control equation of the valve-controlled hydraulic motor servo system:

[0104] Define a positive Lyapunov function

[0105]

[0106] Its time derivative is:

[0107]

[0108]

[0109]

[0110] Similarly,

[0111]

[0112] therefore,

[0113]

[0114] This proves that the control equation of the valve-controlled hydraulic motor servo system is stable.

[0115] On the other hand, an adaptive robust control device with inertia compensation is provided, the device comprising a processor and a memory, the memory storing computer program instructions suitable for execution by the processor, and the computer program instructions, when executed by the processor, executing the steps of the adaptive robust control method with inertia compensation as described in any of the above embodiments.

[0116] On the other hand, a computer-readable storage medium is provided, wherein the storage medium stores computer program instructions. When the computer program instructions are executed by a processor of a user device, the user device executes the adaptive robust control method with inertia compensation described in any of the above embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] The accompanying drawings illustrate exemplary embodiments of the present disclosure and together with the description serve to explain the principles of the present disclosure. These drawings are included to provide a further understanding of the present disclosure and are incorporated in and constitute a part of this specification.

[0118] Figure 1 This is a block diagram model of the flight simulation turntable;

[0119] Figure 2 Schematic diagram of a valve-controlled hydraulic motor servo system with an adaptive robust control method with inertia compensation according to some embodiments;

[0120] Figure 3 is a control diagram of an adaptive robust control method with inertia compensation according to some embodiments;

[0121] Figure 4 is the ARC error curve at 10Hz;

[0122] Figure 5 This is the ICARC error curve at 10Hz;

[0123] Figure 6 is the ARC error curve at 8Hz;

[0124] Figure 7 This is the ICARC error curve at 8Hz. DETAILED DESCRIPTION

[0125] The present disclosure will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to explain the relevant content and are not intended to limit the present disclosure. It should also be noted that, for ease of description, only the portions relevant to the present disclosure are shown in the accompanying drawings.

[0126] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in the present disclosure may be combined with each other. The present disclosure will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0127] The method provided in this embodiment can be executed by a related processor, and the following description uses the processor as an example of the execution subject. The execution subject can be adjusted according to the specific case, such as a server, electronic device, computer, etc.

[0128] In related technologies, model uncertainty is widely present in electro-hydraulic servo systems and is often divided into two categories: parameter uncertainty and uncertain nonlinearity. Parameter uncertainty refers to the situation where the structure of the uncertainty is known, but the values ​​of the relevant parameters are unknown, but they are constant or slowly changing and can be considered constant. Uncertain nonlinearity refers to uncertainty that cannot be accurately modeled, and the nonlinear functions that can describe these quantities are also unknown. Adaptive robust control methods are robust to both parameter uncertainty and unknown uncertain nonlinearity. Adaptive robust control methods treat the outer frame inertia in a conservative manner, using the nominal value of the inertia and aggregating the inertia deviation effects into generalized fluctuations. However, in reality, the outer frame inertia changes in real time, and the nonlinear adaptive robust control method is not rigorous and accurate enough to handle such situations.

[0129] Figure 1 Shown is a block diagram model of a flight simulation turntable. A notable feature of the outer frame control of a flight simulation turntable is its large inertia problem, and when the middle frame is in motion, the inertia of the outer frame will also change in real time, and the magnitude of the change is quite large. This characteristic of large inertia and variable inertia creates great difficulties for the precise position control of the outer frame. In particular, when the middle frame is moving at high speed, the change in inertia value is a strong parameter uncertainty disturbance for the outer frame. Therefore, the inertia value cannot be regarded as a constant, it is a function of the middle frame's rotation angle, and is a variable quantity. The present disclosure provides a turntable adaptive robust control method and device with inertia compensation, which takes into account the change in the inertia of the outer frame and compensates for the inertia change, thereby improving the tracking accuracy of the outer frame of the electro-hydraulic flight simulation turntable.

[0130] Some embodiments of the present disclosure provide an adaptive robust control method with inertia compensation, referred to as ICARC. ICARC is applicable to an electro-hydraulic flight simulation turntable, which includes an outer frame, an outer frame hydraulic motor connected to the outer frame, and a middle frame connected to the outer frame. ICARC includes:

[0131] Establishing a nonlinear model of a valve-controlled hydraulic motor servo system, wherein the nonlinear model can characterize how the inertia of the outer frame changes with the rotation angle of the middle frame; wherein the valve-controlled hydraulic motor servo system includes an outer frame and an outer frame hydraulic motor connected to the outer frame;

[0132] Based on the nonlinear model, a control equation of the valve-controlled hydraulic motor servo system is established.

[0133] like Figure 1 The flight simulation turntable shown includes two external frame hydraulic motors. In actual application, in order to reduce the difficulty of control, the two external frame hydraulic motors are usually not used at the same time, but are used alternately. Therefore, the valve-controlled hydraulic motor servo system actually works with one external frame hydraulic motor. The schematic diagram of the valve-controlled hydraulic motor servo system is shown in FIG. Figure 2 shown.

[0134] according to Figure 2 , the nonlinear model is

[0135]

[0136]

[0137]

[0138] Where J is the sum of the inertia of the outer frame, middle frame, inner frame and load;

[0139] D is the effective volume of the hydraulic motor, m 3 ;

[0140] θ m is the angular displacement of the outer frame;

[0141] is the angular velocity of the outer frame;

[0142] is the angular acceleration of the outer frame;

[0143] B is the total viscous load factor, N·m / (rad / s);

[0144] A f is the modelable Coulomb friction amplitude;

[0145] S f is a continuous approximate Coulomb friction shape function;

[0146] f e Represents external disturbances and unmodeled dynamics of the system, such as unmodeled nonlinear friction;

[0147] P1 is the pressure of the first chamber of the hydraulic motor, Pa;

[0148] P2 is the pressure of the second chamber of the hydraulic motor, Pa;

[0149] is the derivative of the pressure in the first chamber of the hydraulic motor;

[0150] is the derivative of the pressure in the second chamber of the hydraulic motor;

[0151] q1(t) and q2(t) are unmodeled errors;

[0152] Q1 is the flow rate from the valve port into the first chamber of the hydraulic motor, m 3 / s; the first chamber of the hydraulic motor corresponds to Figure 2 The left side of the hydraulic motor (the side marked with pressure P1) in the chamber;

[0153] Q2 is the flow rate from the second chamber of the hydraulic motor to the valve port, m 3 / s; the second chamber of the hydraulic motor corresponds to Figure 2 The chamber on the right side of the hydraulic motor (the side marked with pressure P2);

[0154] β e1 , β e2 The bulk modulus of the hydraulic oil in the first and second cavities of the hydraulic motor, respectively, includes the effect of elastic deformation of the cavity wall and the tube wall, N / m 2 ;

[0155] V1 is the volume of the closed chamber connected to the first chamber of the hydraulic motor, m 3 ,

[0156] V2 is the volume of the closed chamber connected to the second chamber of the hydraulic motor, m 3 ,

[0157] V 01 The initial volume of the sealed chamber connected to the first chamber of the hydraulic motor;

[0158] V 02 The initial volume of the sealed chamber connected to the second chamber of the hydraulic motor;

[0159] V1=V 01 +D m θ m , V2=V 02 -D m θ m ;

[0160] C t is the internal leakage coefficient of the hydraulic motor, m 3 / (s·Pa);

[0161] P L =P1-P2, which is the load pressure.

[0162] The following combination Figure 3 The design process of the controller is introduced.

[0163] Figure 3 in, u a is an adaptive control item that makes the parameter estimation closer to the true value; u s1 Used to ensure system stability; u s2 For robust control terms, approximate processing methods are used to solve model uncertainties with bounded range. Figure 3 u input to Figure 2 In the middle.

[0164] The control equation of the valve-controlled hydraulic motor servo system is established based on the nonlinear model, including:

[0165] Define the system state variables as:

[0166]

[0167] The system state equation is:

[0168]

[0169]

[0170] |f e (t)|≤δ1, |q(t)|≤δ2

[0171] in, is the derivative of the outer frame's angular displacement, i.e., the angular velocity of rotation;

[0172] is the derivative of the outer frame's angular velocity, i.e., the angular acceleration;

[0173] is the derivative of the load pressure;

[0174] q(t) is the unmodeled error;

[0175] |fe(t)|≤δ1, |q(t)|≤δ2, where δ1 and δ2 are known positive constants;

[0176]

[0177]

[0178]

[0179] P s is the set pressure of the safety valve, which is a constant value;

[0180] P r The system return oil pressure.

[0181] Define the uncertain parameter set:

[0182] θ=[θ1, θ2, θ3, θ4, θ5] T

[0183] θ1=B,θ2=A f ,θ3=β e k t ,θ4=β e D, θ5=β e C t

[0184] in, is the estimator of θ;

[0185] is the estimation error of the unknown parameter θ,

[0186] k t is the total flow gain.

[0187] The defined parameter set satisfies

[0188]

[0189] Among them, θ min =[θ 1min ,θ 2min ,...,θ 5min ] T ,

[0190] θ max =[θ 1max ,θ 2max ,...,θ 5max ] T And known.

[0191] Definition error:

[0192] z1=x1-x 1d

[0193]

[0194] z3=x3-α2

[0195] The error dynamics is then:

[0196]

[0197]

[0198] Based on the backstepping design process, the virtual control law α2 and the nonlinear adaptive robust controller u can be designed as:

[0199]

[0200]

[0201] α 2s =α 2s1 +α 2s2

[0202] α 2s1 =-k2z2

[0203]

[0204]

[0205]

[0206] u s =u s1 +u s2

[0207] u s1 =-k323

[0208]

[0209] Among them, ψ2 and ψ3 are smooth functions that satisfy the following conditions

[0210]

[0211] Among them, θ M =θ max -θ min .

[0212] Substituting the virtual control law α2 and the actual control input u into the error dynamics equation, we can get

[0213]

[0214] in,

[0215]

[0216] x 1d is the desired motion trajectory;

[0217] z1 is the output tracking error;

[0218] k1 is the positive feedback gain;

[0219] k2 and k3 are positive nonlinear gains;

[0220] ε2, ε3 are positive constants;

[0221] α1 is the virtual control law of state x2;

[0222] z2 is the difference between the actual state x2 and the virtual control α1;

[0223] α2 is the virtual control law of state x3;

[0224] z3 is the difference between the actual state x3 and the virtual control α2;

[0225] is the derivative of z1;

[0226] is the derivative of z2;

[0227] is the derivative of z3;

[0228] is the derivative of α1;

[0229] is the derivative of α2;

[0230] u is the control input;

[0231] k s2 and k s3 is the positive nonlinear gain.

[0232] For the general case, define the positive Lyapunov function

[0233]

[0234] Its time derivative can be written as:

[0235]

[0236]

[0237]

[0238] Similarly,

[0239]

[0240] therefore,

[0241]

[0242] This proves that the control equation of the valve-controlled hydraulic motor servo system is stable.

[0243] Simulink is used for simulation. When the instruction frequency is 10Hz, the input instruction is a sine function with an amplitude of 0.01rad and a frequency of 10Hz, that is, the instruction x 1d =0.01sin(20Πt)[1-exp(-5t)]. The simulation results of ARC and ICARC are as follows Figure 4 、 5 At a command frequency of 10 Hz, ICARC achieves a 21.93% improvement in maximum tracking error, a 31.33% improvement in average tracking error, and a 22.52% improvement in standard deviation compared to ARC. Table 1 shows the control accuracy comparison between ICARC and ARC at 10 Hz.

[0244] Table 1

[0245] Maximum error (°) Average error (°) Error standard deviation (°) ARC control 0.0202888 0.0086056 0.0055565 ICARC Control 0.0158401 0.0059094 0.0043051 Increase percentage 21.9269％ 31.3307％ 22.5215％

[0246] When the command frequency is 8 Hz, the input command is a sine function with an amplitude of 0.01 rad and a frequency of 8 Hz, that is, the command x 1d =0.01sin(16Πt)[1-exp(-5t)]. The simulation results of ARC and ICARC are as follows Figure 6 、 7 Compared to ARC, ICARC achieves an 11.33% improvement in maximum tracking error, a 13.52% improvement in average tracking error, and a 10.31% improvement in standard deviation. Table 2 shows the control accuracy comparison between ICARC and ARC at 8 Hz.

[0247] Table 2

[0248] Maximum error (°) Average error (°) Error standard deviation (°) ARC control 0.019008 0.0077803 0.0051371 ICARC Control 0.016855 0.006728 0.0046073 Increase percentage 11.3264％ 13.5248％ 10.3127％

[0249] The adaptive robust control method with inertia compensation provided by the present disclosure takes into account the change of outer frame inertia with the rotation angle of the middle frame. In the design of the controller, the function expression of the outer frame inertia is substituted to perform inertia compensation, which effectively reduces the impact of inertia change on control accuracy and improves tracking accuracy.

[0250] The present disclosure also provides an adaptive robust control device with inertia compensation, comprising a processor and a memory. The memory stores computer program instructions suitable for execution by the processor. When the processor executes the computer program instructions, the processor executes the adaptive robust control method with inertia compensation provided in any of the above-described embodiments.

[0251] An embodiment of the present disclosure further provides a computer-readable storage medium, in which computer program instructions are stored. When the computer program instructions are executed by a processor of a user device, the user device executes the method disclosed in any of the above embodiments.

[0252] The computer-readable storage media provided by any embodiment of the present disclosure include permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, modules of programs or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, tape disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0253] An embodiment of the present disclosure further provides an electronic device, including a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, and the computer program instructions are executed by the processor to execute the method disclosed in any of the above embodiments when executed.

[0254] The electronic device provided in any embodiment of the present disclosure may be a mobile phone, a computer, a tablet computer, a server, a network device, etc., or may also be a USB flash drive, a mobile hard disk, a read-only memory (ROM), a magnetic disk, or an optical disk, etc.

[0255] For example, the electronic device may include: a processor, a memory, an input / output interface, a communication interface, and a bus, wherein the processor, the memory, the input / output interface, and the communication interface are communicatively connected to each other within the device via the bus.

[0256] The processor can be implemented as a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0257] The memory can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage devices, dynamic storage devices, etc. The memory can store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory and called and executed by the processor.

[0258] Input / output interfaces connect to input / output modules to enable information input and output. Input / output modules can be built into the device as components or externally connected to provide corresponding functionality. Input devices may include keyboards, mice, touch screens, microphones, and various sensors. Output devices may include displays, speakers, vibrators, and indicator lights.

[0259] The communication interface is used to connect the communication module to enable communication between the device and other devices. The communication module can achieve communication through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WiFi, Bluetooth, etc.).

[0260] The bus comprises a pathway that transmits information between various components of a device, such as a processor, memory, input / output interfaces, and communication interfaces.

[0261] It should be noted that although the above device only shows a processor, memory, input / output interface, communication interface, and bus, in a specific implementation, the device may also include other components necessary for normal operation. In addition, it will be understood by those skilled in the art that the above device may only include the components necessary to implement the embodiments of this specification, and does not necessarily include all of the components described.

[0262] Through the description of the above implementation methods, it can be known that those skilled in the art can clearly understand that the embodiments of this specification can be implemented by means of software plus a necessary general hardware platform. Based on this understanding, the technical solutions of the embodiments of this specification, or the part that contributes to the prior art, can be embodied in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments of this specification.

[0263] In the description of this specification, the description with reference to the terms "one embodiment / method", "some embodiments / methods", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment / method or example are included in at least one embodiment / method or example of the present application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment / method or example. Moreover, the specific features, structures, materials or characteristics described may be combined in an appropriate manner in any one or more embodiments / methods or examples. In addition, those skilled in the art may combine and combine different embodiments / methods or examples described in this specification and the features of different embodiments / methods or examples, unless they are contradictory.

[0264] In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present disclosure, the meaning of "multiple" is at least two, such as two, three, etc., unless otherwise clearly defined. At the same time, in the description of the present disclosure, unless otherwise clearly defined and defined, the terms "connected" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present disclosure can be understood according to the specific circumstances.

[0265] Those skilled in the art will appreciate that the above embodiments are merely intended to clearly illustrate the present disclosure and are not intended to limit the scope of the present disclosure. Other changes or modifications may be made based on the above disclosure, and such changes or modifications are still within the scope of the present disclosure.

Claims

1. An adaptive robust control method with inertia compensation, characterized in that: Applicable to an electro-hydraulic flight simulation turntable, the electro-hydraulic flight simulation turntable includes an outer frame, an outer frame hydraulic motor connected to the outer frame, and a middle frame connected to the outer frame; the method includes: Establishing a nonlinear model of a valve-controlled hydraulic motor servo system, wherein the nonlinear model can characterize how the inertia of the outer frame changes with the rotation angle of the middle frame; wherein the valve-controlled hydraulic motor servo system includes an outer frame and an outer frame hydraulic motor connected to the outer frame; Based on the nonlinear model, establishing a control equation of the valve-controlled hydraulic motor servo system; The nonlinear model is Where J is the sum of the inertia of the outer frame, middle frame, inner frame and load; D is the effective volume of the hydraulic motor, m 3 ; θ m is the angular displacement of the outer frame; is the angular velocity of the outer frame; is the angular acceleration of the outer frame; B is the total viscous load factor, N·m / (rad / s); A f is the modelable Coulomb friction amplitude; S f is a continuous approximate Coulomb friction shape function; f e Represents external disturbances and unmodeled dynamics of the system; P1 is the pressure of the first chamber of the hydraulic motor, Pa; P2 is the pressure of the second chamber of the hydraulic motor, Pa; is the derivative of the pressure in the first chamber of the hydraulic motor; is the derivative of the pressure in the second chamber of the hydraulic motor; q1(t) and q2(t) are unmodeled errors; Q1 is the flow rate from the valve port into the first chamber of the hydraulic motor, m 3 / s; Q2 is the flow rate from the second chamber of the hydraulic motor to the valve port, m 3 / s; β e1 , β e2 The bulk modulus of the hydraulic oil in the first and second cavities of the hydraulic motor, respectively, includes the effect of elastic deformation of the cavity wall and the tube wall, N / m 2 ; V1 is the volume of the closed chamber connected to the first chamber of the hydraulic motor, m 3 , V2 is the volume of the closed chamber connected to the second chamber of the hydraulic motor, m 3 , V 01 The initial volume of the sealed chamber connected to the first chamber of the hydraulic motor; V 02 The initial volume of the sealed chamber connected to the second chamber of the hydraulic motor; V1=V 01 +D m θ m ,V2=V 02 -D m θ m ; C t is the internal leakage coefficient of the hydraulic motor, m 3 / (s·Pa); P L =P1-P2, is the load pressure; The control equation of the valve-controlled hydraulic motor servo system is established based on the nonlinear model, including: Define the system state variables as: The system state equation is: in, is the derivative of the outer frame's angular displacement, i.e., the angular velocity of rotation; is the derivative of the outer frame's angular velocity, i.e., the angular acceleration; is the derivative of the load pressure; q(t) is the unmodeled error; |fe(t)|≤δ1, |q(t)|≤δ2, where δ1 and δ2 are known positive constants; P s is the set pressure of the safety valve, which is a constant value; P r is the system return oil pressure; Define the uncertain parameter set: θ=[θ1,θ2,θ3,θ4,θ5] T θ1=B,θ2=A f ,θ3=β e k t ,θ4=β e D,θ5=β e C t in, is the estimator of θ; is the estimation error of the unknown parameter θ, k t is the total flow gain; The defined parameter set satisfies among them,i min =[θ 1min ,i 2min ,…,θ 5m ] T ; θ max =[θ 1max ,θ 2max ,…,θ 5max ] T and is known; Definition error: z1=x1-x 1d z3=x3-α2 The error dynamics is: Based on the backstepping design process, the virtual control law α2 and the nonlinear adaptive robust controller u are designed α 2s ＝α 2s1 +α 2s2 a 2s1 =-k2z2 in s =in s1 +in s2 <h2 style=";text-align:left;direction:ltr">u<h2 style=";text-align:left;direction:ltr"> s1 <h2 style=";text-align:left;direction:ltr"> =-k3z3 ψ2 and ψ3 are smooth functions and satisfy the following conditions among them,i M =θ max -θ min ; Substitute the virtual control law α2 and the actual control input u into the error dynamics equation to obtain in, x 1d is the desired motion trajectory; z1 is the output tracking error; k1 is the positive feedback gain; k2 and k3 are positive nonlinear gains; ε2, ε3 are positive constants; α1 is the virtual control law of state x2; z2 is the difference between the actual state x2 and the virtual control α1; α2 is the virtual control law of state x3; z3 is the difference between the actual state x3 and the virtual control α2; is the derivative of z1; is the derivative of z2; is the derivative of z3; is the derivative of α1; is the derivative of α2; u is the control input; k s2 and k s3 is the positive nonlinear gain.

2. The adaptive robust control method with inertia compensation according to claim 1, characterized in that: After establishing the control equation of the valve-controlled hydraulic motor servo system, the method further includes performing a stability analysis on the control equation of the valve-controlled hydraulic motor servo system: Define a positive Lyapunov function Its time derivative is: Similarly therefore, This proves that the control equation of the valve-controlled hydraulic motor servo system is stable.

3. An adaptive robust control device with inertia compensation, characterized in that: The device includes a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, and when the computer program instructions are executed by the processor, the steps of the adaptive robust control method with inertia compensation according to any one of claims 1 to 2 are executed.

4. A computer-readable storage medium, characterized in that The storage medium stores computer program instructions, and when the computer program instructions are executed by a processor of a user device, the user device executes the adaptive robust control method with inertia compensation according to any one of claims 1 to 2.

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