Adaptive PID aircraft electro-hydraulic servo system control method based on fuzzy logic

Abstract

The invention discloses an adaptive PID aircraft electro-hydraulic servo system control method based on fuzzy logic, and belongs to the technical field of aircraft electro-hydraulic servo system control. The control optimization design based on the PID algorithm is developed according to the established airplane electro-hydraulic servo system mathematical model, then the fuzzy logic is introduced, and the intelligent control performance of the system is improved by utilizing the self-adaptive PID control of the fuzzy logic. Compared with a traditional control method, the method provided by the invention considers the problems of complex environment faced by the aircraft electro-hydraulic servo system and high precision and high feedback requirements, such as the related problems of nonlinearity, uncertainty and time-varying characteristics of an input signal. The system parameters are adaptively adjusted by means of the adaptive PID of the fuzzy logic, the adaptability to the uncertainty of the model is improved, a solution is provided for improving the control capability of agile control response of the system, the precision and robustness of the electro-hydraulic servo system are effectively improved, and the method has long-term application prospects.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft electro-hydraulic servo system control, and relates to a fuzzy logic-based adaptive PID aircraft electro-hydraulic servo system control method. Background Art

[0002] Electro-hydraulic servo systems are an indispensable part of modern aircraft control systems, and they directly affect the flight safety and performance of aircraft. Electro-hydraulic servo systems combine the advantages of both electrical and hydraulic systems, and have the characteristics of high control accuracy and fast response speed. They are essential for precise control of aircraft in flight environments that require fast response and high-precision operation. Electro-hydraulic servo control systems play a vital role in the field of aircraft control, not only improving the control accuracy and response speed of aircraft, but also enhancing the reliability and safety of the system, and reducing maintenance costs and system complexity.

[0003] In existing research, the aircraft electro-hydraulic servo control system has uncertainty in the output displacement signal due to its structural nonlinearity and time-varying characteristics of parameters, making parameter setting difficult and affecting control performance. At present, researchers have proposed a variety of nonlinear control methods, such as backstepping control algorithm, NDOB (nonlinear disturbance observer) combined control strategy, and controller based on Lyapunov theory, but some strong interference factors are not fully considered, such as the pressure flow characteristics of the servo valve, the friction between the piston and the hydraulic cylinder, and the non-matching interference in the system; the control strategy of the electro-hydraulic servo is also relatively complex and dependent. The control strategy currently used in the electro-hydraulic servo control system has the disadvantages of strong dependence on accurate models, complex structure, and difficulty in practical application. For example, the nonlinear robust adaptive control strategy based on the Lyapunov stabilization method has the characteristics of simple structure and strong robustness, but its design method is relatively complex.

[0004] In response to the problems existing in the system, the control method can be improved so that the system can respond more accurately to changes in the external environment and fluctuations in the internal state, thereby effectively reducing errors, improving stability, enhancing robustness, and significantly improving the system's adaptability and efficiency. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes an adaptive PID aircraft electro-hydraulic servo system control method based on fuzzy logic, which uses the PID algorithm to perform a closed-loop control on the system, effectively enhancing the stability and reliability of the system and ensuring stable operation under various working conditions. At the same time, on this basis, by introducing fuzzy logic, the system can more quickly identify and respond to changes in input signals, improve the dynamic response speed of the system, and use the adaptive PID algorithm of fuzzy logic to optimize and improve the control system and setting parameters, so that the system can adjust the PID parameters according to the real-time state and changes in the external environment, improve the adaptability and robustness of the system, and in addition, the method more accurately describes the nonlinear characteristics and uncertainty of the system, thereby achieving higher precision control to solve the inaccuracy and nonlinear problems existing in the system. Finally, accurate position control is achieved, and a given voltage signal can be fed back in a timely and rapid manner, and the displacement motion output of the servo is achieved through the transmission of each structure in the system.

[0007] The technical solution of the present invention:

[0008] The control method of the adaptive PID aircraft electro-hydraulic servo system based on fuzzy logic includes establishing a mathematical model of the aircraft electro-hydraulic servo control system, designing a control method based on a PID algorithm, and designing an adaptive PID control method based on fuzzy logic. The system is optimized and designed using the PID algorithm and the adaptive PID algorithm based on fuzzy logic on the basis of the mathematical model of the electro-hydraulic servo control system. The specific steps are as follows:

[0009] Step (1) Establish a mathematical model of the aircraft electro-hydraulic servo control system

[0010] By comprehensively considering the physical characteristics, dynamic characteristics and control logic of the system, a mathematical model of the system's electro-hydraulic servo valve, valve-controlled hydraulic cylinder, spring buffer component, sensor and the entire system is constructed to more accurately describe the dynamic behavior and response characteristics of the system.

[0011] (1.1) Mathematical model of electro-hydraulic servo valve

[0012] The electro-hydraulic servo valve consists of an electronically controlled amplifier, a pre-valve, a three-stage slide valve and a displacement sensor. The voltage signal is amplified by the electronically controlled amplifier and then sent to the pre-valve and the three-stage differential slide valve group of the primary transfer function to complete the conversion of voltage to valve core displacement. The role of the displacement sensor is to feed back the displacement information to the input, thereby realizing closed-loop control.

[0013] The electronic control amplifier and the displacement sensor form a proportional connection. The electronic control amplifier (servo amplifier) ​​converts the voltage signal into current. By adjusting the current, the position of the electromagnet in the valve changes, thereby achieving flow control. The amplified electrical signal passes through the pre-valve and the three-stage slide valve in turn, and is converted into the actual displacement of the valve core. The displacement sensor monitors and feeds back the displacement information in real time to ensure the closed-loop control of the system. The servo amplifier gain of the servo control system is , which can be expressed as:

[0014] ( )

[0015] in, represents the output current of the servo amplifier, Indicates the servo amplifier voltage of the control system.

[0016] When constructing the dynamic equation of the servo valve, the natural frequency of the power mechanism is usually used as the transfer function of the servo valve in order to more accurately simulate the response characteristics of the servo valve. It is expressed as:

[0017] ( )

[0018] In the formula, is the servo valve damping ratio; is the servo valve amplification factor (m 3 / s•A); is the natural frequency of the servo valve (rad), is a complex variable.

[0019] When the natural frequency of the electro-hydraulic servo valve is low, especially below 50 Hz, the dynamic response characteristics of the servo valve in the working range can be simplified as a first-order inertia link. The first-order inertia link is usually used to simulate linear systems with inertia or damping. The transfer function of the servo valve is expressed as It is expressed as:

[0020] ( )

[0021] Where: is the amplification factor of the servo valve; is the time constant of the servo valve.

[0022] The slide valve is considered as an integral element, and the transfer function of the slide valve is expressed as It is expressed as:

[0023] ( )

[0024] Where: is the amplification factor of the slide valve; is the time constant of the slide valve.

[0025] (1.2) Mathematical model of valve-controlled hydraulic cylinder

[0026] In the aircraft electro-hydraulic servo actuation system, a valve-controlled asymmetric hydraulic cylinder structure is used, and its flow characteristics are affected by the structure of the valve and the pressure difference between the front and rear. Considering that the two chambers of the asymmetric cylinder have unequal effective areas, the flow equation is related to the direction of piston movement. For the convenience of research, the nonlinear system is linearized to obtain three key equations: the electro-hydraulic servo valve flow conversion equation, the flow continuity equation, and the mechanical balance equation.

[0027] Before building the asymmetric hydraulic cylinder model, the following assumptions are made:

[0028] The servo valve is a zero-opening four-side slide valve to ensure uniform flow distribution;

[0029] The hydraulic energy system supplies oil stably, and the pressure on the return oil side is close to zero;

[0030] The servo valve responds quickly, and the flow change is synchronized with the valve core movement;

[0031] The oil temperature and density are constant, simplifying fluid dynamics analysis.

[0032] (1.2.1) Flow equation of electro-hydraulic servo valve

[0033] Considering only the movement of the piston rod extending outward, the flow equations of the rodless chamber and the rod chamber of the hydraulic cylinder can be calculated based on the oil inlet flow rate of the valve-controlled hydraulic cylinder. and oil outlet flow :

[0034] ( )

[0035] Where: , It is the flow rate of the rodless chamber and the rod chamber of the hydraulic cylinder; , It is the pressure of the rodless chamber and the rod chamber of the hydraulic cylinder; is the flow coefficient of the servo valve port; is the servo valve port area gradient; is the displacement of the servo valve core; is the rated oil supply pressure, assumed to be a constant value; is the oil density.

[0036] The relationship between the flow rate and the piston rod movement speed of the hydraulic cylinder with rod control and rodless control is:

[0037] ( )

[0038] Where: is the piston area of ​​the rodless chamber and the rod chamber of the hydraulic cylinder; is the movement speed of the hydraulic cylinder piston rod.

[0039] The flow ratio of the two chambers of the hydraulic cylinder can be obtained from equations (5) and (6): for:

[0040] ( )

[0041] Define the load pressure as , as shown in (8):

[0042] ( )

[0043] Combining (7) and (8) we can get:

[0044] ( )

[0045] Therefore, the flow equation of the servo valve main valve of the valve-controlled hydraulic cylinder can be written as:

[0046] ( )

[0047] Define the servo valve load flow as , expressed as:

[0048] ( )

[0049] By linearizing equation (11), we can get equation (12):

[0050] ( )

[0051] Where: is the increment of the servo valve load flow, is the increment of load pressure, is the increment of the servo valve spool displacement.

[0052] Only the outward extension of the hydraulic cylinder is considered, that is When , simplifying formula (12) we get the flow linearization equation:

[0053] ( )

[0054] Where: is the servo valve flow gain; is the servo valve flow-pressure coefficient.

[0055] (1.2.2) Hydraulic cylinder flow continuity equation

[0056] In an ideal situation, ignoring pipeline pressure loss and dynamic effects, assuming that the hydraulic cylinder and its pipeline are symmetrical, short and thick, and that the pressure distribution inside the hydraulic cylinder is uniform, and the oil temperature and bulk elastic modulus are constant. Considering oil leakage and compression, the flow continuity equation of the rodless and rod chambers of the hydraulic cylinder can be established, as shown in the following equation (14).

[0057] ( )

[0058] In the formula, is the internal leakage coefficient, is the external leakage coefficient, , is the volume of the rodless chamber and the rod chamber of the hydraulic cylinder, is the elastic modulus of the oil, is the displacement of the hydraulic cylinder piston rod.

[0059] Combining (10) and (14), the load flow equation of the hydraulic cylinder can be obtained as follows:

[0060] ( )

[0061] In the formula, is the total leakage coefficient, .

[0062] Taking the incremental form of formula (15), we can get:

[0063] Δ q L = C t Δ ( P 1 − P 2 ) + 1 2 β e Δ ( V 1 dP 1 dt − V 2 dP 2 dt ) + Δ [( A 1 + A 2 2 ) dx dt ] ( )

[0064] In the formula, is the pressure difference change between the rodless chamber and the rod chamber of the hydraulic cylinder, is the energy conversion rate change between the rodless chamber and the rod chamber of the hydraulic cylinder, Δ [( A 1 + A 2 2 ) dx dt ] It is the flow change between the rodless chamber and the rod chamber of the hydraulic cylinder.

[0065] Assume that the maximum effective stroke of the hydraulic cylinder is L, and V is the maximum volume of the cylinder, then:

[0066] ( )

[0067] When x > 0, the hydraulic cylinder extends forward, and formula (17) yields:

[0068] ( )

[0069] Combining (16) and (18), the servo valve load flow can be derived Translates to:

[0070] ( )

[0071] Where: is the equivalent leakage coefficient, ; is the equivalent piston action area of ​​the hydraulic cylinder, ; is the equivalent volume of the hydraulic cylinder, V e = 2 V [ V 1 ( 1 − η 3 ) / V + η 3 ] 1 + η 3 , is the rate of change of load pressure, is the flow rate of the hydraulic cylinder piston rod displacement.

[0072] Equivalent volume As the piston moves, when the piston is at the left end Minimum , when the rightmost Minimum . Servo valve load flow After Laplace transformation of formula (19), we get:

[0073] ( )

[0074] (1.2.3) Hydraulic cylinder force balance equation

[0075] Ignoring factors such as friction, viscosity, and elastic load, the force analysis of the piston rod and the load as a whole is performed, and the force balance equation (21) is obtained based on Newton's second law:

[0076] ( )

[0077] In the formula, is the total output force of the hydraulic cylinder; is the equivalent total mass; is the viscous damping coefficient; is the load spring stiffness; is the external load force; is the equivalent piston action area of ​​the hydraulic cylinder.

[0078] By performing Laplace transformation on equation (21), we can obtain:

[0079] ( )

[0080] In the formula, Represents the output displacement of the system hydraulic cylinder piston rod.

[0081] Combining equations (13), (20), and (22), we can obtain the output displacement of the piston rod of the hydraulic cylinder of the system. for:

[0082] ( )

[0083] In the formula, is the equivalent pressure-flow coefficient, ; is the viscous damping coefficient.

[0084] The general system has no springs. , and the system generally does not add a damping cylinder, that is, is also very small, then , then formula (23) is simplified to:

[0085] ( )

[0086] In the formula, is the natural frequency of the hydraulic cylinder, ;

[0087] is the hydraulic cylinder damping, .

[0088] Equation (24) describes the dynamic behavior of the hydraulic cylinder, which is divided into two parts. One part is the direct influence of the valve core displacement signal on the output displacement of the hydraulic cylinder (no load); the other part is the influence of the external load on the output displacement.

[0089] First, = 0, get the displacement of the hydraulic cylinder Valve core displacement The transfer function is:

[0090] ( )

[0091] Second order , and the displacement of the hydraulic cylinder is obtained External load force The transfer function is

[0092] ( )

[0093] (1.3) Mathematical model of spring buffer components

[0094] In the structural design of the electro-hydraulic servo system, in order to enhance the stability of the system and reduce the impact force, a rubber metal buffer spring is integrated into the connection between the piston of the valve-controlled hydraulic cylinder and the system as a spring buffer component. The rubber metal buffer spring structure can not only resist the external interference of the system to a certain extent, but also significantly enhance the buffering and shock absorption capacity of the system. The buffer spring follows Hooke's law, and the mechanical characteristics can be described by the formula of this law.

[0095] ( )

[0096] In the formula, is the spring stiffness coefficient (T / mm); is the servo displacement (mm).

[0097] (1.4) Sensor mathematical model

[0098] When the displacement sensor is working, there is a direct proportional relationship between the output signal and the measured displacement, that is, the transfer function has a linear proportional characteristic.

[0099] ( )

[0100] Where U p is the voltage signal output by the displacement sensor (V); K p is the amplification factor of the displacement sensor.

[0101] By combining the above-mentioned derivation of the mathematical model of the electro-hydraulic servo valve, valve-controlled hydraulic cylinder, spring buffer component and sensor in the aircraft electro-hydraulic servo control system, the overall mathematical model of the aircraft electro-hydraulic system can be constructed.

[0102] Step (2) Design of control method based on PID algorithm

[0103] Overall idea: Based on the in-depth analysis of the working principle of the aircraft electro-hydraulic servo system and the establishment of an accurate mathematical model, the high control accuracy and stability of the PID algorithm are utilized to clearly control the displacement feedback of the servo in the object system, combine the PID algorithm with the system, and adjust the PID coefficient to achieve the ideal effect, that is, the system can quickly respond to changes in the input signal, maintain high accuracy and stability, and avoid unnecessary oscillation and overshoot.

[0104] The specific steps are as follows:

[0105] (2.1) Preparation and initialization of the aircraft electro-hydraulic servo system: Ensure the system is stable, delete the differential and integral links in the PID controller, retain only the proportional link in the PID controller, and set the proportional coefficient to an acceptable small value.

[0106] (2.2) Finding critical oscillation:

[0107] Reapply a small step signal to the aircraft electro-hydraulic servo system to cause a deviation between the controlled quantity and the initial value, and then gradually increase the proportional coefficient of the PID controller until the closed-loop response curve of the system changes from an attenuated amplitude response to an equal amplitude response. If the closed-loop response curve of the system changes to an amplification response when the proportional coefficient is adjusted again, adjust the proportional coefficient in the opposite direction until the closed-loop response curve changes to an equal amplitude response.

[0108] (2.3) Setting PID parameters: Proportional coefficient when the closed-loop response curve is equal amplitude response and oscillation period , then use the setting formula shown in (29) based on and Set the calculation of the PID controller , and Three parameters.

[0109] ( )

[0110] (2.4) Implementation and verification: Apply the adjusted PID controller to the control of the aircraft electro-hydraulic servo control system in step (1) and observe the latest control effect. If the tuning effect is ideal, it remains stable in the absence of external interference, the steady-state error is small and it can reach the desired output value in a short time, then the corresponding parameters can be used as the final PID controller parameters. If the tuning effect is not ideal, repeat steps (2.1) to (2.4) to further fine-tune the PID parameters.

[0111] The core of this method is to find the critical stability point of the system by gradually adjusting the proportional coefficient, and determine the optimal parameters of the PID controller based on this point. Through this method, the PID controller parameters that adapt to the system characteristics can be easily adjusted, thereby improving the control performance of the system.

[0112] Step (3) Adaptive PID control optimization design based on fuzzy logic

[0113] Overall idea: The fuzzy logic adaptive PID algorithm combines the stability of the traditional PID control algorithm and the flexibility of its own fuzzy logic. It has excellent robustness and adaptability, improves the ability to cope with the nonlinearity, uncertainty, time-varying properties of the servo system, and realizes online adaptive adjustment and improvement of PID parameters.

[0114] The working principle of the fuzzy adaptive controller is to first convert the input continuous variable into the form of a fuzzy set, that is, fuzzification processing. Then, according to the pre-set membership function and fuzzy rules, the fuzzy set is logically inferred, that is, fuzzy reasoning. Finally, the result of fuzzy reasoning is converted into a specific control quantity, that is, defuzzification processing, so as to obtain an output value that can be applied to the actual system. In the aircraft electro-hydraulic servo system, a two-dimensional fuzzy controller can be used to adjust and optimize the PID parameters of the system obtained in step (2). The state error and its differential are used as input to output the increment of the PID controller parameters. , and , and update the PID parameters according to formula (30).

[0115] ( )

[0116] In the formula, , and They respectively refer to the proportional, integral, and differential parameters of the updated PID of the state controller; , and They are the proportional, integral and differential parameters of the initial PID of the state controller respectively.

[0117] Among them, the specific steps of the fuzzy logic adaptive PID improved control method are as follows:

[0118] 1) Design of fuzzy set domain and membership function

[0119] The purpose of setting the fuzzy set domain is to effectively describe and process the fuzziness of the input variables. The fuzzy set domain is a mathematical space composed of a series of fuzzy word set domains, which is used to represent the fuzzy characteristics of the input variables. By setting the fuzzy set domain, the uncertainty and fuzziness of the input variables can be more accurately captured and expressed, so as to make reasoning and decision in the fuzzy control system. Differentiate with the PID error term and the proportional parameters of the initial PID of the state controller , integration parameters , differential parameters The ratio of the output state controller to the updated PID , integration parameters , differential parameters A set of fuzzy sets is used to describe fuzziness. The fuzzy set contains seven fuzzy subsets: NB, NM, NS, ZO, PS, PM, and PB, which represent negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively. The expression of is shown in formula (31).

[0120] ( )

[0121] Establishing membership function is an important task to realize input fuzzification processing. By mapping the fuzziness of input quantity to fuzzy subsets, the similarity and membership degree between input quantity and fuzzy subset domain can be described in detail. Common membership functions include triangular membership function, trapezoidal membership function, Gaussian membership function, etc.

[0122] The present invention adopts a triangular membership function, whose mathematical form is shown in formula (32), where a, b, and c are the minimum value of the membership function interval, the interval value corresponding to when the membership function is 1, and the maximum value of the membership function interval, respectively. represents a fuzzy set, The degree of membership to the fuzzy set λ, express For fuzzy sets The membership function of .

[0123] ( )

[0124] 2) Fuzzy rule design

[0125] Designing fuzzy rules is the key to the excellent performance of fuzzy controller. The design of fuzzy rules mainly follows the following parameter adjustment principles: When the error When the proportional gain is large, increase To speed up the adjustment, but to prevent stability degradation and integral saturation, the integral should be reduced. and differential gain .

[0126] When the error Differentiate the error For medium size, reduce the proportional gain To reduce overshoot, select the appropriate differential gain To maintain responsiveness.

[0127] error hours, increase the integral gain and differential gain To improve control performance. Especially when the error differential When the change is fast, increase the differential gain To improve the anti-interference ability; when the error differential When the change is slow, reduce the integral gain .

[0128] 3) Fuzzy reasoning and defuzzification

[0129] Based on the established fuzzy rules, fuzzy reasoning of the fuzzy controller can be performed. The description of fuzzy reasoning usually adopts If-then statements. The fuzzy rule table constructed by the present invention can construct 7 fuzzy subsets of e and ec as shown in formula (31) through the fuzzy set domain. Then , , The fuzzy rules are composed of 7 fuzzy subsets of the input quantities e and ec, totaling 49 (7*7). Each rule can be described by an If-then statement, such as: if (E is NB) and (EC isNB) then ( is PB)( is NB)( is PS). The mathematical expression of the fuzzy reasoning relationship is shown in formula (40), where: and are the fuzzy results of error e and error differential ec, represents the error after fuzzification, represents the error differential after fuzzification, Indicates The proportional gain after the fuzzification of the parameters is Indicates The integral gain after the fuzzification of the parameters is Indicates The differential gain after the fuzzification of the parameters, a total of 49 fuzzy rules From 1 to 49, represents the proportional gain after fuzzification, represents the integral gain after fuzzification, Represents the differential gain after fuzzification .

[0130] ( )

[0131] According to the fuzzy reasoning relationship, the fuzzy set of output quantity can be calculated. The gain set is expressed as The mathematical expression is shown in formula (34).

[0132] ( )

[0133] Furthermore, the fuzzy quantity needs to be defuzzified. Common defuzzification methods include the centroid method, the area average method, the maximum membership method, etc. The present invention adopts the centroid method for defuzzification.

[0134] The present invention combines the adaptive PID control of fuzzy logic with the aircraft electro-hydraulic servo system to adapt to the changes of electrical signals and improve the robustness and adaptive performance of the electro-hydraulic servo system. The adaptive adjustment of PID parameters can cope with the nonlinearity, uncertainty and time-varying problems of the input signal, thereby improving the control performance of the aircraft electro-hydraulic servo system.

[0135] Beneficial effects of the present invention:

[0136] The present invention takes into account the complex environment faced by the aircraft electro-hydraulic servo system and the problem of requiring high precision and high feedback, adopts the PID algorithm to perform control optimization design on the servo system, and considers the related problems of nonlinearity, uncertainty and time-varying of the input signal at the same time, introduces fuzzy logic, and uses the adaptive PID of fuzzy logic to realize adaptive adjustment of system parameters, improves the adaptability to model uncertainty, and provides a solution for improving the control ability of the system to quickly adjust and make feedback, effectively improves the control accuracy and robustness of the electro-hydraulic servo system, has good intelligent control performance, and has long-term application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0138] Figure 1 It is the overall control flow chart of the aircraft electro-hydraulic servo system;

[0139] Figure 2 It is a control flow chart combining the adaptive PID of fuzzy logic with the system;

[0140] Figure 3 It is the simulation result of PID control system signal monitoring;

[0141] Figure 4 It is the simulation curve of PID control system;

[0142] Figure 5 It is the fuzzy reasoning output proportional coefficient output surface simulation result;

[0143] Figure 6 It is the fuzzy reasoning output integral coefficient output surface simulation result;

[0144] Figure 7 It is the fuzzy reasoning output differential coefficient output surface simulation result;

[0145] Figure 8It is the comparison result of the adaptive PID optimization of fuzzy logic and the simulation curve of PID control system;

[0146] Fig. 9 It is the simulation result of introducing interference factors to verify the anti-disturbance ability of the system;

[0147] Fig.10 It is the anti-disturbance simulation curve of the fuzzy logic adaptive PID optimization system. DETAILED DESCRIPTION

[0149] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0150] The overall control process of the aircraft electro-hydraulic servo system is as follows: Figure 1 As shown in the figure, the control process of the fuzzy logic adaptive PID combined with the system is as follows Figure 2 shown.

[0151] (1) Input the initial state and give the target state

[0152] First, it is necessary to set the initial states of key components in the aircraft electro-hydraulic servo system, such as electro-hydraulic servo valves, valve-controlled hydraulic cylinders and other structures, to ensure that the simulation process can accurately simulate the initial states of actual working conditions. Table 1 shows the state data of key components in the electro-hydraulic servo system.

[0153] Table 1 Simulation parameters

[0154]

[0155] (2) Establishing the mathematical model of the electro-hydraulic servo system

[0156] In order to accurately describe the simulation process and working state of the electro-hydraulic servo system, it is necessary to further build and improve the mathematical model of the system based on the working principle of the system, and build the mathematical model of the system electro-hydraulic servo valve, valve-controlled hydraulic cylinder, spring buffer component, sensor and the whole system by comprehensively considering the physical characteristics, dynamic characteristics and control logic of the system, so as to more accurately describe the dynamic behavior and response characteristics of the system. The construction of the mathematical model of the simulation is detailed in the invention content section.

[0157] (3) Optimization of PID algorithm and adaptive PID control method based on fuzzy logic

[0158] (3.1) Simulation based on the combination of PID algorithm and system model

[0159] First, a step response signal with an amplitude of 50T is input, and the parameters are adjusted through the specific steps of the PID algorithm in the invention content section. cm and T cm Calculate Kp , K i and K d , the calculated PID parameters are applied to the electro-hydraulic servo system, and the PID parameters are further fine-tuned to obtain the following Figure 3 The simulation result curve is shown.

[0160] Table 2 PID algorithm parameter setting formula table

[0161]

[0162] from Figure 3 It can be seen that, under the conventional PID control, after the rise time of 2.82s, the system peak time is 8.493s, and the overshoot is small. However, in order to make the output signal better reflect the tracking command signal, a step signal with a smaller input amplitude is input for simulation observation. The step response signal with an input amplitude of 1T can be obtained after adjusting the parameters. Figure 4 The simulation curve is shown.

[0163] Depend on Figure 4 The analysis shows that the performance of conventional PID control in the steering gear electro-hydraulic servo system is insufficient, with a rise time of 87.2ms, a peak time of 108.4ms, and an overshoot of 3.36%, and the step response speed needs to be improved. Considering the strong interference and randomness of the aircraft steering gear displacement, the conventional PID controller requires tedious tuning before each experiment, which is inefficient. Therefore, in order to improve the control effect and achieve accurate tracking of the command signal, it is necessary to improve the PID controller. Fuzzy control algorithm, as an advanced control strategy, will be introduced to optimize the simulation effect.

[0164] (3.2) Simulation of improved optimization method based on adaptive PID and system model based on fuzzy logic

[0165] According to the specific steps of the fuzzy logic adaptive PID in the content of the invention, a fuzzy controller is designed. Before the fuzzy controller is designed, the parameter information of the fuzzy adaptive PID controller needs to be set as shown in Table 3.

[0166] Table 3 Parameter data table of electro-hydraulic servo valve

[0167]

[0168] And through the design of fuzzy set domain and membership function, the fuzzy rules are determined, the expression is updated according to the parameters, and the selection , , The fuzzy rule table is shown in Table 3-5. Electro-hydraulic servo system state PID controller , , The fuzzy domains are [ − 10 , 10 ] ,error Differentiate the error The fuzzy domains are [ − 6 , 6 ] , the fuzzy domain and the actual domain need to be converted according to the corresponding proportional relationship.

[0169] Table 4 Fuzzy rules

[0170]

[0171] Table 5 Fuzzy rules

[0172]

[0173] Table 6 Fuzzy rules

[0174]

[0175] Then start designing the fuzzy controller, open the fuzzy logic toolbox, set the error e and the error change rate ec as input variables and define the output variable as the adjustment amount ∆K of the PID parameter p , ∆K i , ∆K d Then, set the system input and output with the determined fuzzy domain and triangular membership function. Enter the rules in Table 4, Table 5, and Table 6 into the fuzzy rule editor in the form of "If...Then..." to build a fuzzy rule table to easily set and adjust the fuzzy controller. After the design and simulation verification of the fuzzy controller, the system can generate ∆K p , ∆K i , ∆K d The fuzzy reasoning output surface diagram is as follows: Figure 5-Figure 7 These surface plots intuitively show the relationship between the PID parameter adjustment amount and the input variable. For easier query and application, these surface plots can be converted to "Rules" mode to quickly obtain the corresponding PID parameter adjustment value under any input value. This conversion process simplifies parameter query and improves the ease of use and efficiency of the system.

[0176] Use simulink to build a simulation model for the fuzzy controller PID, design the controller and input relevant parameters, and finally output image comparison from Figure 8In the figure, it can be seen that the rise time is 115 ms when fuzzy PID control is used. The peak time of the system is 134.2 ms, and the overshoot is 0.28%. Compared with the conventional PID, it can be seen that the steady-state time of the fuzzy adaptive PID controller is 0.12 s, which is shorter than the conventional PID in reaching steady-state time, with smaller overshoot, faster response and better control effect. When this algorithm is applied to the aircraft electro-hydraulic servo actuator control system, it can learn and adapt autonomously, and the overshoot is basically negligible. The control performance and robustness are much better than the conventional PID controller, which has obvious advantages.

[0177] (4) Verification of system output regulation feedback with disturbance wave equation

[0178] The interference waveform analysis of aircraft electro-hydraulic servo systems involves multiple aspects, including coupled oscillations of the system, non-command oscillation signals, and electromagnetic interference. There may be coupled oscillation problems between the hydraulic servo actuation system of large aircraft and the aircraft structure, which involves the mutual interference between multiple degrees of freedom within the system and the inconsistency of dynamic characteristics. Similarly, non-command oscillation signals in the electromechanical actuation system, especially oscillations in the frequency range of 0.2~3 Hz and 8~10 Hz, will cause unacceptable fluctuations in the electromagnetic torque and rudder deflection angle, thereby reducing the speed of the system tracking instructions. In order to improve system performance, it is necessary to deeply analyze the generation mechanism, source, and manifestation of these oscillation signals in order to adopt targeted fault diagnosis and control strategies. In addition, the aircraft electromechanical system is very sensitive to the surrounding electromagnetic interference when working, and it will also send electromagnetic interference signals to the surrounding area, affecting other electronic equipment or systems.

[0179] Based on the analysis of the interference factors described above, it is necessary to introduce interference to verify the system's anti-interference ability and the robustness of the system, such as Fig. 9 As shown, the interference waveform of the interference simulation output can be introduced by two reverse rectangular waves.

[0180] By building a simulation mathematical model for introducing interference factors, the observer is used to observe the feedback and control effect of the fuzzy logic adaptive PID controller in the aircraft electro-hydraulic servo system after interference, as shown below Fig.10 As shown. Fig.10 It can be seen that between 0.6s and 0.8s, when the system is subject to external disturbances, the fuzzy logic adaptive PID control gives feedback after 20ms and can quickly adjust to restore the stable state, can better adapt to these changes, and its output fluctuation is small, showing higher robustness and stability, can reduce the error caused by interference in the system, and improve the overall performance and output accuracy of the system, thereby ensuring that the aircraft can operate safely and reliably in a complex and changing environment.

Claims

1. The adaptive PID aircraft electro-hydraulic servo system control method based on fuzzy logic is characterized by: The specific steps are as follows: Step (1) Establish a mathematical model of the aircraft electro-hydraulic servo control system (1.1) Mathematical model of electro-hydraulic servo valve The electro-hydraulic servo valve is composed of an electronically controlled amplifier, a pre-valve, a three-stage slide valve and a displacement sensor; The servo amplifier gain of the servo control system is , expressed as: ( ) in, represents the output current of the servo amplifier, Indicates the servo amplifier voltage of the control system; When constructing the dynamic equation of the servo valve, the second-order oscillation link is used as the transfer function of the servo valve. It is expressed as: ( ) In the formula, is the servo valve damping ratio; is the servo valve amplification factor; is the natural frequency of the servo valve, is a complex variable; When the natural frequency of the electro-hydraulic servo valve is below 50 Hz, the dynamic response characteristics of the servo valve in the working range are simplified and described as a first-order inertia link; the first-order inertia link is used to simulate a linear system with inertia or damping; the transfer function of the servo valve is expressed as It is expressed as: ( ) Where: is the amplification factor of the servo valve; is the time constant of the servo valve; The slide valve is considered as an integral element, and the transfer function of the slide valve is expressed as It is expressed as: ( ) Where: is the amplification factor of the slide valve; is the time constant of the slide valve; (1.2) Mathematical model of valve-controlled hydraulic cylinder In the aircraft electro-hydraulic servo actuation system, a valve-controlled asymmetric hydraulic cylinder structure is used, and its flow characteristics are affected by the valve structure and the front-rear pressure difference. Considering that the two chambers of the asymmetric cylinder have unequal effective areas, the flow equation is related to the piston movement direction. The nonlinear system is linearized to obtain three key equations: the electro-hydraulic servo valve flow conversion equation, the flow continuity equation and the mechanical balance equation. Before building the asymmetric hydraulic cylinder model, the following assumptions are made: The servo valve is a zero-opening four-side slide valve to ensure uniform flow distribution; The hydraulic energy system supplies oil stably, and the pressure on the return oil side is close to zero; The servo valve responds quickly, and the flow change is synchronized with the valve core movement; The oil temperature and density are constant, simplifying fluid mechanics analysis; (1.2.1) Flow equation of electro-hydraulic servo valve Considering only the movement of the piston rod extending outward, the flow equations of the rodless chamber and the rod chamber of the hydraulic cylinder are based on the oil inlet flow of the valve-controlled hydraulic cylinder. and oil outlet flow : ( ) Where: , It is the flow rate of the rodless chamber and the rod chamber of the hydraulic cylinder; , It is the pressure of the rodless chamber and the rod chamber of the hydraulic cylinder; is the flow coefficient of the servo valve port; is the servo valve port area gradient; is the displacement of the servo valve core; is the rated oil supply pressure, assumed to be a constant value; is the oil density; The relationship between the flow rate and the piston rod movement speed of the hydraulic cylinder with rod control and rodless control is: ( ) Where: is the piston area of ​​the rodless chamber and the rod chamber of the hydraulic cylinder; is the movement speed of the hydraulic cylinder piston rod; The flow ratio of the two chambers of the hydraulic cylinder is obtained by equations (5) and (6): for: ( ) Define the load pressure as , as shown in (8): ( ) Combining (7) and (8) we get: ( ) Therefore, the flow equation of the servo valve main valve of the valve-controlled hydraulic cylinder is written as: ( ) Define the servo valve load flow as , expressed as: ( ) Linearize equation (11) to get equation (12): ( ) Where: is the increment of the servo valve load flow, is the increment of load pressure, is the increment of the servo valve core displacement; Only the outward extension of the hydraulic cylinder is considered, that is When , simplifying formula (12) we get the flow linearization equation: ( ) Where: is the servo valve flow gain; is the servo valve flow-pressure coefficient; (1.2.2) Hydraulic cylinder flow continuity equation Under ideal conditions, ignoring pipeline pressure loss and dynamic effects, assuming that the hydraulic cylinder and its pipeline are symmetrical, short and thick, and that the pressure distribution inside the hydraulic cylinder is uniform, and that the oil temperature and bulk elastic modulus are constant; considering oil leakage and compression, the flow continuity equations of the rodless and rod chambers of the hydraulic cylinder are established, as shown in the following equation (14); ( ) In the formula, is the internal leakage coefficient, is the external leakage coefficient, , is the volume of the rodless chamber and the rod chamber of the hydraulic cylinder, is the elastic modulus of the oil, is the displacement of the hydraulic cylinder piston rod; Combining (10) and (14), we get the load flow equation of the hydraulic cylinder: ( ) In the formula, is the total leakage coefficient, ; Taking the incremental form of formula (15), we get: ( ) In the formula, is the pressure difference change between the rodless chamber and the rod chamber of the hydraulic cylinder, is the energy conversion rate change between the rodless chamber and the rod chamber of the hydraulic cylinder, is the flow change between the rodless chamber and the rod chamber of the hydraulic cylinder; Assume that the maximum effective stroke of the hydraulic cylinder is L, and V is the maximum volume of the cylinder, then: ( ) When x > 0, the hydraulic cylinder extends forward, and formula (17) gives: ( ) Combining (16) and (18), we can deduce the servo valve load flow Translates to: ( ) Where: is the equivalent leakage coefficient, ; is the equivalent piston action area of ​​the hydraulic cylinder, ; is the equivalent volume of the hydraulic cylinder, , is the rate of change of load pressure, is the flow rate of the hydraulic cylinder piston rod displacement; Equivalent volume As the piston moves, when the piston is at the left end Minimum , when the rightmost Minimum ; Servo valve load flow After Laplace transformation of formula (19), we get: ( ) (1.2.3) Hydraulic cylinder force balance equation Ignoring friction, viscosity, and elastic load factors, the force analysis of the piston rod and the load as a whole is performed, and the force balance equation (21) is obtained according to Newton's second law: ( ) In the formula, is the total output force of the hydraulic cylinder; is the equivalent total mass; is the viscous damping coefficient; is the load spring stiffness; is the external load force; is the equivalent piston action area of ​​the hydraulic cylinder; By Laplace transforming equation (21), we can obtain: ( ) In the formula, Indicates the output displacement of the piston rod of the system hydraulic cylinder; Combining equations (13), (20), and (22), we can obtain the output displacement of the piston rod of the hydraulic cylinder of the system. for: ( ) In the formula, is the equivalent pressure-flow coefficient, ; is the viscous damping coefficient; The system has no springs, ,and , then formula (23) is simplified to: ( ) In the formula, is the natural frequency of the hydraulic cylinder, ; is the hydraulic cylinder damping, ; Equation (24) describes the dynamic behavior of the hydraulic cylinder, which is divided into two parts: one part is the direct influence of the valve core displacement signal on the output displacement of the hydraulic cylinder without load; the other part is the influence of the external load on the output displacement; First, = 0, and the displacement of the hydraulic cylinder is obtained Valve core displacement The transfer function is: ( ) Second order , and the displacement of the hydraulic cylinder is obtained External load force The transfer function is ( ) (1.3) Mathematical model of spring buffer components In the structural design of the electro-hydraulic servo system, a rubber metal buffer spring is integrated into the connection between the piston of the valve-controlled hydraulic cylinder and the system as a spring buffer component; the buffer spring follows Hooke's law, and the mechanical characteristics are described by the formula of this law; ( ) In the formula, is the spring stiffness coefficient; is the displacement of the servo; (1.4) Sensor mathematical model When the displacement sensor is working, there is a direct proportional relationship between the output signal and the measured displacement, that is, the transfer function has a linear proportional characteristic; ( ) Where U p is the voltage signal output by the displacement sensor; K p is the amplification factor of the displacement sensor; Combining the above mathematical model derivation of the electro-hydraulic servo valve, valve-controlled hydraulic cylinder, spring buffer component and sensor in the aircraft electro-hydraulic servo control system, the overall mathematical model of the aircraft electro-hydraulic system can be constructed; Step (2) Design of control method based on PID algorithm (2.1) Preparation and initialization of the aircraft electro-hydraulic servo system: Ensure the system is stable, delete the differential and integral links in the PID controller, retain only the proportional link in the PID controller, and set the proportional coefficient; (2.2) Finding critical oscillation: Reapply a step signal to the aircraft electro-hydraulic servo system to cause a deviation between the controlled quantity and the initial value, and then gradually increase the proportional coefficient of the PID controller until the closed-loop response curve of the system changes from an attenuated amplitude response to an equal amplitude response; if the closed-loop response curve of the system changes to an amplification response when the proportional coefficient is adjusted again, adjust the proportional coefficient in the opposite direction until the closed-loop response curve changes to an equal amplitude response; (2.3) Set PID parameters: Obtain the proportional coefficient when the closed-loop response curve is an equal amplitude response and oscillation period , and then use the setting formula shown in (29) based on and Set the calculation of the PID controller , and Three parameters; ( ) (2.4) Implementation and verification: Apply the adjusted PID controller to the control of the aircraft electro-hydraulic servo control system in step (1) and observe the latest control effect. If the adjustment effect is ideal, it remains stable without external interference, the steady-state error is small and the expected output value can be achieved in a short time, then the corresponding parameters are used as the final PID controller parameters. If the adjustment effect is not ideal, repeat steps (2.1) to (2.4) to further fine-tune the adjusted PID parameters. Step (3) Adaptive PID control optimization design based on fuzzy logic In the aircraft electro-hydraulic servo system, a two-dimensional fuzzy controller is used to tune and optimize the PID parameters of the system obtained in step (2). The state error and its differential are used as input to output the increment of the PID controller parameters. , and , and update the PID parameters according to formula (30); ( ) In the formula, , and They respectively refer to the proportional, integral, and differential parameters of the updated PID of the state controller; , and They respectively refer to the proportional, integral, and differential parameters of the initial PID of the state controller; The specific steps of the adaptive PID control method based on fuzzy logic are as follows: 1) Design of fuzzy set domain and membership function The input PID error term of the present invention Differentiate with the PID error term and the proportional parameters of the initial PID of the state controller , integration parameters , differential parameters The ratio of the output state controller to the updated PID , integration parameters , differential parameters A set of fuzzy sets is used to describe the fuzziness. The fuzzy set contains seven fuzzy subsets: NB, NM, NS, ZO, PS, PM, and PB, which represent negative large, negative medium, negative small, zero, positive small, positive medium, and positive large respectively. The expression of is shown in formula (31); ( ) The membership function is established by mapping the fuzziness of the input quantity to the fuzzy subset to specifically describe the similarity and membership degree between the input quantity and the fuzzy subset domain; The triangular membership function is used, and its mathematical form is shown in formula (32). In this formula, a, b, and c are the minimum value of the membership function interval, the interval value corresponding to the membership function being 1, and the maximum value of the membership function interval, respectively. In this formula, represents a fuzzy set, The degree of membership to the fuzzy set λ, express For fuzzy sets The membership function of ( ) 2) Fuzzy rule design The fuzzy rule design follows the following parameter adjustment principles: When the error When the proportional gain is large, increase To speed up the adjustment, but to prevent stability degradation and integral saturation, reduce the integral and differential gain ; When the error Differentiate the error For medium size, reduce the proportional gain To reduce overshoot, select the appropriate differential gain To maintain responsiveness; error hours, increase the integral gain and differential gain To improve control performance; especially when the error differential When the change is fast, increase the differential gain To improve the anti-interference ability; when the error differential When the change is slow, reduce the integral gain ; 3) Fuzzy reasoning and defuzzification Based on the constructed fuzzy rules, through the fuzzy set domain, we can construct 7 fuzzy subsets of e and ec as shown in formula (31), then , , The fuzzy rules of are composed of 7 fuzzy subsets of input quantity e and ec, totaling 49. Each rule is described by If-then statement. The mathematical expression of fuzzy reasoning relationship is shown in formula (40), where: and are the fuzzy results of error e and error differential ec, represents the error after fuzzification, represents the error differential after fuzzification, Indicates The proportional gain after the fuzzification of the parameters is Indicates The integral gain after the fuzzification of the parameters is: Indicates The differential gain after the fuzzification of the parameters, a total of 49 fuzzy rules From 1 to 49, represents the proportional gain after fuzzification, represents the integral gain after fuzzification, Represents the differential gain after fuzzification ; ( ) Based on the fuzzy reasoning relationship, the fuzzy set of output quantity is calculated. The gain set is expressed as The mathematical expression is shown in formula (34); ( )。

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