A boundary layer discrete-time optimal sliding mode control method for disturbed air propulsion intake pressure system

Abstract

The present application relates to a kind of boundary layer discrete-time optimal sliding mode control method of disturbed aero-propulsion intake pressure system. Including: based on the system characteristics of aero-propulsion intake pressure system, by deriving gas state equation, pipeline flow continuity equation, internal energy storage equation and thermodynamic energy change equation, the intake pressure system model is obtained and further rewritten as second-order integral series type state equation;According to optimal control theory, the switching curve equation of bang-bang control is used as nonlinear sliding surface, and the time optimal sliding mode control law is designed;A boundary layer and boundary curve are introduced to overcome the high-frequency chattering problem of discrete-time optimal sliding mode control;From the angle of practical control engineering, consider the measurement noise problem in engineering application, introduce tracking differentiator as the measurement noise suppression link, filter the measurement noise contained in output signal.The present application can be used for the high-quality pressure control of aero-propulsion intake pressure system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of air propulsion device intake pressure system control, and particularly relates to a boundary layer discrete-time optimal sliding mode control method for a disturbed air propulsion device intake pressure system. BACKGROUND

[0002] An aircraft engine flight environment simulation test device (referred to as an "air propulsion device") is a large device that simulates the flight environment of an engine at high altitudes on the ground, and its main purpose is to test the high-altitude performance of an aircraft engine, which is a key link of a high-performance advanced aircraft engine. As a key link of the high-altitude cabin, the intake pressure control system adjusts the gas supplied by the gas source according to the flight environment requirements of the aircraft engine at different Mach numbers and altitudes, and establishes a stable total intake pressure. Therefore, the control performance of the intake pressure system will directly affect the effectiveness of the evaluation of the function and performance of the aircraft engine.

[0003] In the high-altitude test process of an aircraft engine, there are transient tests and steady-state tests. In the state transient test, mainly includes: engine high-altitude starting test, turbine, turbofan engine thrust transient test, turboshaft engine power transient test, etc. During the transient test process, the aircraft engine usually causes a great increase or decrease in the engine intake flow in a short time due to the rapid and drastic changes in the working state. This flow change is equivalent to a large amplitude step disturbance, which greatly affects the control quality of the intake pressure system. In addition, the intake pressure system also contains strong nonlinearity, unmodeled dynamics and strong measurement noise, so that a satisfactory intake pressure control performance (including low valve swing, strong anti-disturbance ability and fast response) cannot be guaranteed.

[0004] In the traditional control of aircraft propulsion inlet pressure system, the proportional-integral-derivative control technology (i.e. PID control) is the most widely used control method due to its simple control structure, independence on system model, and clear physical meaning of controller parameters. However, the traditional PID control cannot achieve high-precision control of the high-altitude chamber inlet pressure system in the presence of large amplitude step air flow disturbances and external strong measurement noise in the process of aero-engine transient test. Active disturbance rejection control (ADRC) is a practical active anti-disturbance control method proposed by Professor Han Jingqing for the first time, which has strong anti-disturbance ability and does not depend on system mathematical model, and is widely used in various industrial scenarios. Among them, the extended state observer (ESO) is the key link of ADRC technology, which attributes the external disturbance and internal disturbance in the system to a lumped disturbance and expands it into a new state variable, and then performs real-time observation and feedforward compensation, combined with a feedback controller to complete system control. However, the original ADRC method (i.e. PD control based on ESO) still has room for improvement in terms of disturbance rejection and speed, and introducing mature and advanced feedback control technology to enhance its anti-disturbance ability and speed is an effective way. Sliding mode control (SMC) has attracted special attention from the theoretical and industrial communities due to its advantages in disturbance rejection, robustness, and speed.

[0005] In recent years, many effective sliding mode control techniques have been proposed by researchers at home and abroad to deal with various practical disturbed systems as the feedback controller of active disturbance rejection control. For example: integral sliding mode control (ISMC), high-order sliding mode control (HSMC), terminal sliding mode control (TSMC), etc. However, in actual control systems, the digital controller is in discrete form, and the sliding mode control method designed in continuous time is limited by the switching frequency, which usually leads to the problem of chattering. To solve this problem, through analysis, it is found that the discrete method in the literature (Wang Z, Li SH, Li Q. Discrete-time fast terminal sliding mode control design for DC-DC buck converters with mismatched disturbances [J]. IEEE Transactions on Industrial Informatics, 2019, 16(2): 1204-1213.) uses Euler method and the discrete method in the literature (Zhao Ximei, Zhao Jiwei. Complementary sliding mode variable structure control of permanent magnet linear synchronous motor [J]. Proceedings of the Chinese Society of Electrical Engineering, 2015, 35(10): 2552-2557.) introduces saturation function, which can slow down the high-frequency oscillation of discrete-time sliding mode control to a certain extent, but the high-frequency oscillation at steady state is still not eliminated. Therefore, how to design a discrete sliding mode control method with the characteristics of fast tracking, stability and no chattering, and combine it with the extended state observer to effectively deal with the large amplitude step air flow disturbance of the inlet pressure system of the aircraft propulsion device and the external strong measurement noise, is the key to improve the control performance of the system.

[0006] Problems in the prior art:

[0007] (1) The inlet pressure system of the aircraft propulsion device is a complex system with nonlinearity, strong disturbance and measurement noise. In the transient test of the aero-engine, the rapid and drastic state change leads to the large amplitude and instantaneous change of the engine inlet flow rate, which requires a control method with strong anti-interference ability and fast dynamic response to obtain accurate pressure control of the inlet pressure system and ensure the reliability and accuracy of the aero-engine test.

[0008] (2) The designed continuous sliding mode control is reasonably discretized to effectively suppress the high-frequency oscillation at steady state in the discrete sliding mode control, and successfully combines the sliding mode control technology with the extended state observer to form an efficient anti-interference control method.

[0009] (3) Because of the whole frequency band random noise intensity caused by the test of the aero-engine can reach 20dB, the pressure output signal in the inlet pressure system of the aero-propulsion device contains very strong measurement noise, and the measurement noise in the output signal is effectively processed to obtain a relatively clean filtered signal to ensure the engineering implementation of the control method. SUMMARY

[0010] The present application aims at the nonlinearity, strong disturbance and measurement noise of the inlet pressure system of the aero-propulsion device and the high-frequency oscillation problem in the discrete sliding mode control, and provides a boundary layer discrete time optimal sliding mode control method for the disturbed inlet pressure system of the aero-propulsion device.

[0011] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows: a boundary layer discrete time optimal sliding mode control method for the disturbed inlet pressure system of the aero-propulsion device, comprising:

[0012] Step 1, based on the system characteristics of the inlet pressure system of the aero-propulsion device, the inlet pressure system model is obtained by deducing the gas state equation, the pipeline flow continuity equation, the internal energy storage equation and the thermodynamic energy change equation, and is further rewritten as a second-order integral series type state equation;

[0013] Step 2, according to the optimal control theory, the time optimal control (the fastest control) of the system is bang-bang control, so the switching curve equation of the bang-bang control is used as the nonlinear sliding surface to design the time optimal sliding mode control law. The variable structure feedback control law with the switching curve as the nonlinear sliding surface not only satisfies the "reaching condition" on the entire sliding surface, but also makes the trajectory switch at most once along the sliding surface to reach the origin in a limited time.

[0014] Step 3, discrete time optimal sliding mode control, in order to overcome the high-frequency chattering problem of the discrete time optimal sliding mode control, a boundary layer and a boundary curve are introduced, the boundary layer is used as a "buffer area" to realize the linear change of the control quantity in the bounded interval and avoid the direct extreme value switching change; at the same time, the parameters of the boundary curve are adjusted to adjust the shape and thickness of each boundary curve equation and the boundary area according to the actual situation of the system, so as to coordinate and improve the comprehensive performance of the controller;

[0015] Step 4, from the perspective of actual control engineering, considering the measurement noise problem in engineering application, a tracking differentiator is introduced as a measurement noise suppression link to filter out the measurement noise contained in the output signal.

[0016] In an embodiment of the present application, step 1 is specifically implemented as follows:

[0017]

[0018] Where, T is the temperature in the chamber, p is the pressure in the chamber, V is the volume of the chamber, W in is the air mass flow of the intake regulating valve, W eng is the air mass flow of the engine, h in is the enthalpy of the intake air, h out is the enthalpy of the exhaust air, c p is the specific heat capacity of the gas at constant pressure, C in is the average flow speed of the intake air, C out is the average flow speed of the exhaust air, is the heat exchanged between the chamber and the metal pipe wall per unit time, R is the gas constant; wherein, the air mass flow of the intake regulating valve W in is expressed as:

[0019]

[0020] Where, p1 is the pressure before the regulating valve, p1 is the gas density before the regulating valve, K0 is the angle-area conversion coefficient of the regulating valve, F is the angle of the regulating valve, is the flow coefficient of the regulating valve; the air mass flow of the engine W eng is approximately expressed as:

[0021]

[0022] Where, W ahs is the air flow of the engine, n c1 is the fan speed of the engine, p is the intake air pressure of the engine, T in is the intake air temperature of the engine, H is the flight altitude, Ma is the flight Mach number, n is the fan speed of the engine; combining equations (1)-(3) to obtain equation (4):

[0023]

[0024] Let equation (5) is obtained:

[0025]

[0026] Considering that there is a first-order inertia link between the actual control input u F and the valve opening F, that is:

[0027]

[0028] Where, K θ is the proportional coefficient, T θ is the inertia time constant;

[0029] Combining equations (5) and (6) gives:

[0030]

[0031] wherein, the total disturbance and the control gain

[0032]

[0033] In an embodiment of the present application, step 2 is implemented as follows:

[0034] According to the optimal control theory, the time optimal control of the system is bang-bang control, and the time optimal control synthesis function with the origin of the phase plane as the terminal point is:

[0035]

[0036] wherein, x1, x2 are the intake pressure and the differential of the intake pressure respectively; sign is a switching function, and r is the control quantity extreme value. For the second-order integral series system shown in equation (7), equation (8) is obtained by being brought into equation (7):

[0037]

[0038] wherein, The optimal control synthesis function (8) is regarded as a variable structure control with a switching curve as a sliding surface:

[0039]

[0040] The controller switching gain of the optimal control synthesis function (8) is replaced by r1 instead of the control quantity extreme value r, and equation (9) is obtained:

[0041]

[0042] Considering the total disturbance w, equation (11) is substituted into the controlled object (7), and the sliding mode variable structure control system is obtained as:

[0043]

[0044] In order to meet the "reaching condition" of the sliding mode variable structure control system reaching the sliding surface s=0, equation (12) is obtained: r2 is introduced and 0

[0045]

[0046] For equation (13), the fastest feedback variable structure feedback control law is:

[0047]

[0048] In an embodiment of the present application, in step 3, the discretization time optimal sliding mode control is implemented as follows:

[0049] The discrete sliding mode variable structure feedback system (14) is discretized directly using the Euler polygon method to obtain a discrete fastest feedback sliding mode variable structure closed-loop control system as follows:

[0050]

[0051] wherein k is a constant and k = 0, 1, 2, 3…; h is the sampling step of the system; v0(t) is a command input signal.

[0052] Since the state quantity on both sides of the nonlinear sliding mode surface s is switched between the extreme values ±r of the control quantity, the discrete control system represented by equation (15) has very obvious high-frequency oscillation when entering a steady state.

[0053] In an embodiment of the present application, a saturation function sat(s, δ) is introduced to replace the switching function sign(s) to realize quasi-sliding mode control to eliminate high-frequency oscillation, and equation (15) is represented as:

[0054]

[0055] wherein

[0056] Although the introduction of the saturation function can slow down high-frequency oscillation, high-frequency oscillation at a steady state is still not eliminated.

[0057] In an embodiment of the present application, to completely avoid high-frequency oscillation caused by constant switching between extreme values of the control quantity, a "buffer zone" - i.e. a boundary layer, needs to be introduced. The existence of the boundary layer will make the control quantity change in a certain designed linear control law within a certain bounded region, instead of repeatedly jumping between two extreme values ±r. According to the optimal control theory, to make the system state return to the origin in the shortest time, in the discrete case, there must be two boundary curves near the switching curve. The control quantity changes linearly within the interval surrounded by the two boundary curves, from a positive number or a negative number to another negative number or positive number. Obviously, the two linearly changing intervals must be near the switching curve. Therefore, the boundary curves Γ + ,Γ - of the linear control region need to be determined. The curve equations of the two-step reachable regions outside Γ + ,Γ - ,Γ c are derived as follows:

[0058]

[0059] wherein y = x1 + hx2 and |y| ≥ h 2r; the linear region non-two-step reachable region Omega composed of four boundary line equations is:

[0060] Omega={(x1,x2):|y|≥h 2 r∩|a(x1,x2,r,h)|≤hr,y=x1+hx2} (18)

[0061] The optimal control law based on the linear region non-two-step reachable region Omega while taking into account the optimal control law of the nonlinear region is:

[0062] u=-rsat(a(x1,x2,r,h),hr),|y|≥h 2 r (19)

[0063] Two boundary layer correction coefficients alpha and beta are introduced, and the straight line equation y=x1+hx2 is modified as:

[0064] y=alpha x1+hbeta x2 (20)

[0065] Combining formula (19) and formula (20), and replacing the state variables x1 and x2 with the error e and the error differential respectively, the discrete-time optimal sliding mode feedback control law with a boundary layer is obtained as:

[0066]

[0067] Wherein, c is called a damping factor, r1 is called a controller switching gain, r is a control quantity extreme value, h1 is called a precision factor, d, a0, a, a1, a2 are intermediate variables, alpha and beta are called boundary layer correction coefficients.

[0068] In an embodiment of the present application, in step 4, the tracking differentiator adopts a tracking differentiator based on an enhanced discrete optimal control algorithm.

[0069] In an embodiment of the present application, the expression of the tracking differentiator based on the enhanced discrete optimal control algorithm is formula (22):

[0070]

[0071] Wherein,

[0072]

[0073] In the formula, v0 is the output signal of the tracking differentiator, v1 and v2 are the tracking signal and the differential signal thereof respectively, e0 is the tracking error, h is the sampling period, i.e., the integral step, r0 is the fast factor of the tracking differentiator, h0 is the filter factor of the tracking differentiator, t1 and t2 are the time of the initial point reaching the switching curve and the time of the initial point reaching the origin respectively.

[0074] The application further provides a boundary layer discrete time optimal sliding mode control system of a disturbed aviation propulsion device air inlet pressure system, comprising a memory, a processor and computer program instructions stored in the memory and capable of being executed by the processor, and when the processor executes the computer program instructions, the method steps described above can be realized.

[0075] The application further provides a computer readable storage medium, which stores computer program instructions capable of being executed by a processor, and when the processor executes the computer program instructions, the method steps described above can be realized.

[0076] Compared with the prior art, the application has the following beneficial effects:

[0077] (1) For the large step air flow disturbance caused by the rapid change of the state of the aviation engine in the transient test process, the time optimal sliding mode control with the switching curve as the nonlinear sliding surface not only has good dynamic quality and anti-disturbance ability, but also has high execution efficiency, meets the rapidity requirement of the actual altitude table air inlet pressure control, and enhances the robustness of the system to the large amplitude change air flow disturbance in the test.

[0078] (2) The introduction of the boundary layer makes the control quantity change in a certain specific bounded region according to the pre-designed linear control law, instead of repeatedly jumping between two extreme values, which is very helpful to overcome the high-frequency chattering problem inherent in the discrete time optimal sliding mode control system. In addition, by appropriately adjusting the boundary curve according to different aviation engine test conditions, the dynamic regulation quality of the air inlet pressure control is improved.

[0079] (3) The introduction of the tracking differentiator can extract the filtered output and the differential dynamic of the controlled pressure with high precision, smoothness and small phase under the measurement noise disturbance, and ensure the feasibility of the control scheme.

[0080] The application can be used for high-quality pressure control of the aviation propulsion device air inlet pressure system, ensures the accurate simulation of the aviation engine test environment, especially the transient test with complex working conditions. In addition, other similar systems with strong disturbance and measurement noise also have very broad application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0081] Figure 1 It is an aviation propulsion device air inlet pressure system control structure schematic diagram of an embodiment of the application;

[0082] Figure 2 It is a switching curve and state transition optimal trajectory line of an embodiment of the application;

[0083] Figure 3Reachable region and linear boundary region of one embodiment of the present application

[0084] Figure 4 DTOCSMC control block diagram of the air propulsion device inlet pressure system with boundary layer of one embodiment of the present application

[0085] Figure 5 Comparison of filtered output signals of one embodiment of the present application

[0086] Figure 6 Comparison of PID and DTOCSMC control effects of one embodiment of the present application

[0087] Figure 7 DTOCSMC control amount and regulating valve movement of one embodiment of the present application

[0088] Figure 8 Comparison of DTOCSMC and DTOCSMC-ESO control effects of one embodiment of the present application

[0089] Figure 9 DTOCSMC-ESO control amount and regulating valve movement of one embodiment of the present application

[0090] Figure 10 Flow chart of the DTOCSMC control of the disturbed air propulsion device inlet pressure system with boundary layer. DETAILED DESCRIPTION

[0091] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0092] The present application provides a DTOCSMC control method of the disturbed air propulsion device inlet pressure system with boundary layer, comprising:

[0093] Step 1, based on the system characteristics of the air propulsion device inlet pressure system, the inlet pressure system model is obtained by deriving the gas state equation, the pipeline flow continuity equation, the internal energy storage equation and the thermodynamic energy change equation, and is further rewritten as a second-order integral series state equation;

[0094] Step 2, according to the optimal control theory, the time optimal control (the fastest control) of the system is bang-bang control, so the switching curve equation of the bang-bang control is taken as a nonlinear sliding mode surface to design a time optimal sliding mode control law. The variable structure feedback control law with the switching curve as the nonlinear sliding mode surface can not only satisfy the "reaching condition" on the entire sliding mode surface, but also can make the trajectory switch at most once and reach the origin along the sliding mode surface in a finite time.

[0095] Step 3, discretization of the time optimal sliding mode control, in order to overcome the high frequency chattering problem of the discrete time optimal sliding mode control, a boundary layer and a boundary curve are introduced, the boundary layer is used as a "buffer area", the control quantity is changed in a linear manner in the bounded interval, and the direct extreme switching change is avoided; at the same time, the parameters of the boundary curve are adjusted to adjust the shape and thickness of each boundary curve equation and boundary area according to the actual situation of the system, so as to coordinate and improve the comprehensive performance of the controller;

[0096] Step 4, from the perspective of actual control engineering, considering the measurement noise problem in engineering application, a tracking differentiator is introduced as a measurement noise suppression link to filter out the measurement noise contained in the output signal.

[0097] The following is the specific implementation process of the application.

[0098] The application discloses a boundary layer discrete time optimal sliding mode control method for a disturbed air propulsion device air inlet pressure system. Figure 1 As shown in the air propulsion device air inlet pressure system control structure diagram, the basic principle is that the test aircraft engine is installed in the air propulsion device test cabin, when the engine is in the steady state / transition state test in the flight envelope of the high altitude platform, the control system is responsible for adjusting the regulating valve to meet the required air inlet pressure of the engine. The specific implementation process is as follows:

[0099] Step 1:

[0100] The theoretical modeling of the air inlet pressure is as shown in the following formula (1):

[0101]

[0102] Wherein, T is the temperature in the cavity, p is the pressure in the cavity, V is the volume of the cavity, W in is the air mass flow of the air inlet regulating valve, W eng is the air mass flow of the engine, h in is the enthalpy of the air inlet, h out is the enthalpy of the exhaust, c p is the specific heat capacity of the gas at constant pressure, C in is the average flow velocity of the air inlet, C out is the average flow velocity of the exhaust, Let R be the heat exchanged between the internal cavity and the metal tube wall per unit time, and R be the gas constant. The Win model for the airflow rate of the intake regulating valve can be expressed as:

[0103]

[0104] Where p1 is the pressure before the control valve, ρ1 is the gas density before the control valve, K0 is the angle-area conversion coefficient of the control valve, and F is the angle of the control valve. To regulate the valve flow coefficient. The airflow W of the tested engine. eng This can be approximated as:

[0105]

[0106] Among them, W ahs To calculate the airflow for the engine, n c1 This is the converted engine fan speed, p is the engine intake pressure, and T is the engine fan speed. in Let H be the engine intake air temperature, H be the flight altitude, Ma be the flight Mach number, and n be the engine fan speed. Combining equations (1)-(3), we can obtain equation (4):

[0107]

[0108] Among them, let Equation (5) can be obtained:

[0109]

[0110] Considering the actual control input u of the system F There exists a first-order inertial element between the valve opening degree F and the valve opening degree F, that is:

[0111]

[0112] Among them, K θ T is the proportionality coefficient. θ Let be the inertial time constant. Combining equations (5) and (6), we can obtain:

[0113]

[0114] Among them, the sum of disturbances With control gain

[0115]

[0116] Step 2:

[0117] According to optimal control theory, the time-optimal control (fastest control) of this system is a bang-bang control, and the time-optimal control synthesis function with the origin of the phase plane as the endpoint is:

[0118]

[0119] Wherein, x1, x2 are the intake pressure and the differential of the intake pressure respectively; sign is a switch function, and r is a control quantity extreme value. For the second-order integral series system shown in equation (7), equation (8) can be obtained by being brought into equation (8)

[0120]

[0121] Wherein, The switch curve and the optimal trajectory line of state transition are shown in Figure 2 The optimal control comprehensive function (8) can be regarded as a variable structure control with the switch curve as a sliding surface:

[0122]

[0123] The controller switching gain of the optimal control comprehensive function (8) is replaced by r1 instead of the control quantity extreme value r, and equation (8) is obtained:

[0124]

[0125] Considering the total disturbance w, equation (11) is substituted into the controlled object (7), and the sliding mode variable structure control system is obtained as:

[0126]

[0127] As shown in Figure 3 To meet the "reaching condition" of the sliding mode variable structure control system reaching the sliding surface s=0 is Introducing r2 and 0

[0128]

[0129] For equation (13), the fastest feedback variable structure feedback control law is:

[0130]

[0131] Step 3:

[0132] The sliding mode variable structure feedback system (14) is discretized, and the discrete fastest feedback sliding mode variable structure closed-loop control system is obtained by directly using the Euler polygon method for discretization:

[0133]

[0134] Wherein, k is a constant and k=0, 1, 2, 3…; h is the sampling step of the system; v0(t) is the command input signal.

[0135] Because of the state variable switching between the control variable extreme value ±r on both sides of the nonlinear sliding surface s, the discrete control system represented by equation (15) has very obvious high frequency oscillation when entering steady state. The introduction of saturation function sat(s, δ) instead of sign(s) to achieve quasi-sliding mode control to eliminate high frequency oscillation, then equation (15) is represented as:

[0136]

[0137] where, Test found that the introduction of saturation function can slow down the high frequency oscillation to a certain extent, but the high frequency oscillation at steady state is still not eliminated. In order to completely avoid the high frequency oscillation phenomenon caused by the control variable switching between the extreme value, it is necessary to introduce a "buffer zone" - the boundary layer. The existence of the boundary layer will make the control variable change in a certain designed linear control law within a certain bounded region, instead of repeatedly jumping between two extreme values ±r. According to the optimal control theory, in order to make the system state return to the origin in the shortest time, there must be two boundary curves near the switching curve in the discrete case. The control variable changes linearly in the interval surrounded by the two boundary curves, from a positive number (negative number) to another negative number (positive number). Obviously, the two linearly changing intervals must be near the switching curve. Therefore, it is necessary to determine the boundary curve Γ + ,Γ - of the linear control region. As shown in Fig. Figure 4 , the internal region surrounded by Γ + and Γ - is the linear control region. Figure 4 In the two-step reachable region, the curve equations of Γ + , Γ - and Γ c are respectively:

[0138]

[0139] where, y = x1 + hx2 and |y| ≥ h 2 r. The linear region non-two-step reachable region Ω composed of the four boundary line equations is:

[0140] Ω = {(x1, x2): |y| ≥ h 2 r∩|a(x1, x2, r, h)| ≤ hr, y = x1 + hx2} (18)

[0141] The optimal control law based on the linear region non-two-step reachable region Ω (also considering the nonlinear region) is:

[0142] u = -rsat(a(x1, x2, r, h), hr), |y| ≥ h2 r (19)

[0143] It is worth noting that the straight line equation y = x1+ hx2, if the introduction of alpha and beta two adjustment parameters and modify it to:

[0144] y = alpha x1+ h beta x2 (20)

[0145] Combined with the formula (19) and formula (20), and the error e and error differential Instead of state variables x1 and x2, respectively, the discrete time optimal sliding mode feedback control law with boundary layer can be obtained as:

[0146]

[0147] Where c is called the damping factor, r1 is called the controller switching gain, r is the control quantity extreme value, h1 is called the precision factor, d, a0, a, a1, a2 are intermediate variables, alpha and beta are called boundary layer correction coefficient.

[0148] Step 4:

[0149] The tracking differentiator expression based on the enhanced discrete optimal control algorithm is formula (22):

[0150]

[0151] Where,

[0152]

[0153] In the formula, v0 is the output signal of the tracking differentiator, v1, v2 are the tracking signal and its differential signal of v0 respectively, e0 is the tracking error, h is the sampling period, i.e. the integration step, r0 is the fast factor of the tracking differentiator, h0 is the filter factor of the tracking differentiator, t1, t2 are the time from the initial point to the switching curve and the time from the initial point to the origin respectively.

[0154] Combined with the above system model (7), the discrete time optimal sliding mode feedback control law with boundary layer (21) and the tracking differentiator based on the enhanced discrete optimal control algorithm (22), the block diagram of the inlet pressure system of the aero-propulsion device with boundary layer discrete time optimal sliding mode control is shown in Figure 4 .

[0155] In order to verify the effectiveness of the discrete time optimal sliding mode control method with boundary layer, the experimental results are shown in the following figures (5)-(9). Figure 5 As shown in the figure, the tracking differentiator based on the enhanced discrete optimal control algorithm can extract the filtered output and its differential dynamic of the controlled pressure with high precision, smoothness and small phase under the measurement noise disturbance. Figure 6As shown, in the target pressure tracking process with the set value changing, the DTOCSMC can make the controlled pressure quickly enter the steady state and almost has no overshoot phenomenon, and is obviously superior to the PID control method in response speed, tracking accuracy, regulation time and other indexes, and exhibits good target value tracking performance and stability. Figure 7 As shown, the control amount output by the DTOCSMC in the entire transition state simulation test has good performance of being fast, smooth and entering the steady state without chattering, and therefore the regulating valve also obtains excellent dynamic operation quality. Figure 8 As shown, the DTOCSMC+ESO obtains more excellent regulation quality and anti-disturbance ability relative to the single DTOCSMC control method, the maximum dynamic deviation of the controlled pressure is only 0.32kPa and can smoothly, without oscillation and overshoot, reach the steady state target value within 4.1s, and obtains very ideal dynamic control quality. Figure 9 As shown, the control amount can quickly converge to the steady state equilibrium point smoothly and without chattering, which fully shows that the discrete time optimal sliding mode controller DTOCSMC with a boundary layer can effectively avoid the inherent chattering problem of the conventional sliding mode controller. Therefore, by introducing the discrete time optimal sliding mode control method with a boundary layer, the chattering problem of the control amount can be effectively eliminated, and the high-performance control target of fast convergence and strong anti-disturbance can be realized. The algorithm flowchart of the scheme is as shown in Figure 10 As shown.

[0156] The above is the preferred embodiment of the present application, and any change made according to the technical solution of the present application, as long as the function effect generated does not exceed the range of the technical solution of the present application, belongs to the protection scope of the present application.

Claims

1. A discrete-time optimal sliding mode control method with boundary layer for the inlet pressure system of a disturbed aero-propulsion device, characterized in that, include: Step 1: Based on the system characteristics of the air intake pressure system of the aircraft propulsion device, the air intake pressure system model is obtained by deriving the gas state equation, pipeline flow continuity equation, internal energy storage equation and thermodynamic energy change equation, and further rewritten as a second-order integral series state equation. Step 2: Based on optimal control theory, using the switching curve equation of bang-bang control as the nonlinear sliding surface, design the time-optimal sliding mode control law; Step 3: Discrete-time optimal sliding mode control. To overcome the high-frequency chattering problem of discrete-time optimal sliding mode control, a boundary layer and boundary curves are introduced. The boundary layer is used as a "buffer region" to realize that the control quantity changes linearly in the bounded interval, avoiding direct extreme value switching. At the same time, the parameters of the boundary curves are adjusted so that the equations of each boundary curve, the shape and thickness of the boundary region are adjusted according to the actual situation of the system, so as to coordinate and improve the overall performance of the controller. Step 4: From the perspective of practical control engineering, considering the measurement noise problem in engineering applications, a tracking differentiator is introduced as a measurement noise suppression link to filter out the measurement noise contained in the output signal. Step 1 is implemented as follows: Where T is the temperature inside the cavity, p is the pressure inside the cavity, V is the volume of the cavity, and W is the temperature inside the cavity. in W represents the air mass flow rate of the intake regulating valve. eng For engine air mass flow rate, h in For the enthalpy of intake air, h out c is the enthalpy of the exhaust gas. p C is the specific heat capacity of a gas at constant pressure. in C represents the average velocity of the intake airflow. out The average velocity of the exhaust gas flow. R is the heat exchanged between the internal cavity and the metal tube wall per unit time, and R is the gas constant; where W is the air mass flow rate of the intake regulating valve. in Represented as: Where p1 is the pressure before the control valve, ρ1 is the gas density before the control valve, K0 is the angle-area conversion coefficient of the control valve, and F is the angle of the control valve. To adjust the valve flow coefficient, the engine's air mass flow rate W eng Approximate expression: where W ahs is the engine air flow, n c1 is the engine fan speed, p is the engine intake pressure, T in is the engine intake temperature, H is the flight altitude, Ma is the flight Mach number, and n is the engine fan speed; combining equations (1)-(3) gives equation (4): make Equation (5): Considering the actual control input u of the system F There exists a first-order inertial element between the valve opening degree F and the valve opening degree F, that is: Among them, K θ T is the proportionality coefficient. θ The inertial time constant; Combining equations (5) and (6), we get: Among them, the sum of disturbances With control gain Step 2 is implemented as follows: According to optimal control theory, the time-optimal control of the system is bang-bang control, and the time-optimal control synthesis function with the origin of the phase plane as the endpoint is: Where x1 and x2 are the intake pressure and its derivative, respectively; sign is the switching function, and r is the extreme value of the control quantity. For the second-order integral cascade system shown in equation (7), substituting into equation (8) yields... in, The optimal control synthesis function (8) is considered as a variable structure control with the switching curve as the sliding surface: And by changing the controller switching gain of the optimal control synthesis function (8) to r1 instead of the extreme value r of the control quantity, we get: Considering the total disturbance w, substituting (11) into the controlled object (7), we obtain the sliding mode variable structure control system as follows: To satisfy the "arrival condition" for the sliding mode variable structure control system to reach the sliding surface s=0, the following conditions must be met: Introducing r2 and 0 < r2 < r1, the sliding mode variable structure control system is further expressed as: For equation (13), the fastest feedback variable structure feedback control law is:

2. The discrete-time optimal sliding mode control method with boundary layer for the inlet pressure system of a disturbed aero-propulsion device according to claim 1, characterized in that, In step 3, the discretized time optimal sliding mode control method is as follows: Discretize the sliding mode variable structure feedback system (14) directly using the Euler piecewise linear method to obtain the discrete-type fastest feedback sliding mode variable structure closed-loop control system: Where k is a constant and k = 0, 1, 2, 3…; h is the sampling step size of the system; v0(t) is the command input signal; Since the state variables on both sides of the nonlinear sliding surface s constantly switch between the extreme values ​​of the control variable ±r, the discrete control system represented by Equation (15) has very obvious high-frequency oscillations when it enters the steady state.

3. The discrete-time optimal sliding mode control method with boundary layer for the inlet pressure system of a disturbed aero-propulsion device according to claim 2, characterized in that, The saturation function sat(s,δ) is introduced to replace the switching function sign(s) to achieve quasi-sliding mode control and eliminate high-frequency oscillations. Equation (15) is expressed as follows: in, Although the introduction of a saturation function can reduce high-frequency oscillations, the high-frequency oscillations in steady state are not eliminated.

4. The discrete-time optimal sliding mode control method with boundary layer for the inlet pressure system of a disturbed aero-propulsion device according to claim 3, characterized in that, To completely avoid the high-frequency oscillations caused by the constant switching between extreme values ​​of the control quantity, it is necessary to introduce a "buffer zone"—that is, a boundary layer. The existence of the boundary layer will cause the control quantity to change purposefully within a specific bounded region according to a pre-designed linear control law, rather than repeatedly jumping between two extreme values ​​±r. According to optimal control theory, in order for the system state to return to the origin in the shortest possible time, in the discrete case, there must be two boundary curves near the switching curve. The control quantity changes linearly within the interval enclosed by the two boundary curves, changing from one positive or negative number to another negative or positive number. Obviously, these two linear change intervals must be near the switching curve. Therefore, it is necessary to determine the boundary curve Γ of the linear control region. + ,Γ - ; Derive the two-step reachable region beyond Γ + ,Γ - ,Γ c The equations of the curves they represent are as follows: in, y = x1 + hx2 and |y| ≥ h 2 r; The linear region Ω formed by the equations of the four boundary lines is not reachable in two steps: Ω={(x1,x2):|y|≥h 2 r∩|a(x1,x2,r,h)|≤hr,y=x1+hx2} (18) The optimal control law, which considers both the linear region, the non-two-step reachable region Ω, and the nonlinear region, is as follows: u=-rsat(a(x1,x2,r,h),hr),|y|≥h 2 r (19) Introducing two boundary layer correction coefficients, α and β, and modifying the linear equation y = x1 + hx2 to: y=αx1+hβx2 (20) Combining equations (19) and (20), and considering the error e and the error differential... Substituting state variables x1 and x2 respectively, the discrete-time optimal sliding mode feedback control law with boundary layer is obtained as follows: Where c is called the damping factor, r1 is called the controller switching gain, r is the extreme value of the control quantity, h1 is called the accuracy factor, d, a0, a, a1, a2 are intermediate variables, and α and β are called boundary layer correction coefficients.

5. The discrete-time optimal sliding mode control method with boundary layer for the inlet pressure system of a disturbed aero-propulsion device according to claim 4, characterized in that, In step 4, the tracking differentiator adopts a tracking differentiator based on the enhanced discrete optimal control algorithm.

6. The discrete-time optimal sliding mode control method with boundary layer for the inlet pressure system of a disturbed aero-propulsion device according to claim 5, characterized in that, The expression for the tracking differentiator based on the enhanced discrete optimal control algorithm is given by equation (22): in, In the formula, v0 is the output signal of the tracking differentiator, v1 and v2 are the tracking signal and its derivative signal of v0, respectively, e0 is the tracking error, h is the sampling period, i.e. the integration step size, r0 is the fast factor of the tracking differentiator, h0 is the filtering factor of the tracking differentiator, and t1 and t2 are the time when the initial point reaches the switching curve and the time when the initial point reaches the origin, respectively.

7. A discrete-time optimal sliding mode control system with boundary layer for the inlet pressure system of a disturbed aero-propulsion device, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor, which, when executed by the processor, enable the implementation of the steps of the method as described in any one of claims 1-6.

8. A computer-readable storage medium having stored thereon computer program instructions executable by a processor, wherein when the processor executes the computer program instructions, it is able to implement the steps of the method as described in any one of claims 1-6.

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