A design method for a fuel and lubricating oil thermal management system for an aircraft engine gear pump based on MPC-NLPIDsech

Abstract

The present invention discloses a design method of an aircraft engine gear pump fuel and lubricating oil thermal management system of MPC-NLPIDsech, including: determining each module of the aircraft engine gear pump fuel and lubricating oil thermal management system, which includes: a fuel tank, an external gear pump, a DC motor, an MPC-NLPIDsech controller, a shell and tube fuel and lubricating oil heat exchanger, and a lubricating oil tank; modeling the external gear pump, the DC motor, and the shell and tube fuel and lubricating oil heat exchanger respectively; designing an MPC-NLPIDsech controller according to the models of the external gear pump, the DC motor, and the shell and tube fuel and lubricating oil heat exchanger. In order to improve the control performance, the present invention adopts the MPC-NLPIDsech control algorithm to replace the traditional PID algorithm, reduces the overshoot, speeds up the response speed, and achieves a good control effect.

Description

Technical Field

[0001] The invention relates to the field of thermal management of aircraft engine fuel and lubricating oil, and in particular to a design method of an aircraft engine gear pump fuel and lubricating oil thermal management system of MPC-NLPIDsech. Background Art

[0002] The thermal management system is an important factor in ensuring the normal operation of aircraft engine accessories. With the continuous development of aircraft engines, its status is becoming more and more important. The function of aircraft engine lubricating oil is to reduce friction and remove excess heat from engine components, so that aircraft engine components do not overheat and ensure the normal operation of the engine. At the same time, lubricating oil has an optimal operating temperature. If the lubricating oil temperature is too high, it will lead to a decrease in lubrication effect and poor effect in removing excess heat from the engine, affecting the normal operation of the engine. Therefore, it is necessary to keep the lubricating oil temperature within a certain range, which requires the use of relevant heat exchangers to remove the heat in the lubricating oil.

[0003] In the aircraft engine fuel and lubricating oil thermal management system, the heat exchanger can be divided into air cooling and fuel cooling according to different cooling media. Fuel cooling has a larger specific heat capacity than air, which can take away more heat. It can also heat the fuel, so that the heat in the lubricating oil can be more fully utilized, improve the overall efficiency of the engine, and make the engine cleaner and more environmentally friendly. In the aircraft engine thermal management system, this type of heat exchanger is often called a fuel and lubricating oil heat exchanger. As the place for heat exchange in the thermal management system, it is very critical. Shell and tube fuel and lubricating oil heat exchangers are very common in aircraft engines, and have the characteristics and advantages of simple and reliable structure. This type of heat exchanger is structurally divided into tube side and shell side. One heat exchange fluid runs through the tube side, and the other runs through the shell side. Heat is exchanged through the wall of the heat exchange tube.

[0004] A gear pump is a positive displacement pump that relies on the change in working volume between the pump body and the meshing gears to pressurize and transport the fluid. There are two types of gear pumps: external meshing and internal meshing. External gear pumps are more common than internal gear pumps. When a DC motor drives a gear pump, the flow rate of cooling fuel delivered by the gear pump can be controlled by controlling the speed of the DC motor, thereby affecting the heat exchange effect of the fuel and lubricating oil, so that the lubricating oil at the outlet of the heat exchanger is maintained at the optimal working temperature. In this way, the lubricating oil has been fully cooled before returning to the lubricating oil tank, and when it is transported from the lubricating oil tank to the engine again, it can achieve the purpose of sufficient lubrication and take away excess heat.

[0005] The conventional linear PID control method controls the system by feeding back the error signal and reasonably setting the proportional and integral coefficients. Both the proportional coefficient and the integral coefficient need to be within a reasonable range, and the two need to cooperate with each other. If they are too large or too small, they cannot achieve the desired effect. When the dynamic characteristics of the system are required to be high, the conventional linear PID method is difficult to achieve the purpose of better suppressing overshoot and making the system dynamic response faster. Therefore, it is necessary to introduce a nonlinear PID method to improve and supplement the original PID method. The nonlinear PID method based on hyperbolic sine can modify the proportional coefficient and the integral coefficient in real time during the control process to achieve fast and accurate control effects.

[0006] Model Predictive Control (MPC) was introduced in the 1970s. It is a modern control method based on models. Its principles can be summarized as: model prediction, rolling optimization, and feedback correction. After decades of development, model predictive control has developed a variety of typical methods suitable for different industries and objects, such as generalized predictive control widely used in process industries and finite set predictive control used in power electronics. Although predictive control has been studied and applied in a wide range of fields, its control depends on the model. When the model is inaccurate, the control effect may not be good. Therefore, it is necessary to combine model predictive control with nonlinear PID methods, which can obtain better control effects and reduce the degree of dependence on model accuracy. Summary of the invention

[0007] In view of this, the purpose of the present invention is to provide a design method for an aircraft engine gear pump fuel and lubricating oil thermal management system of MPC-NLPIDsech to solve the technical problems mentioned in the background technology.

[0008] In order to achieve the above object, the present invention adopts the following technical solution:

[0009] A design method for an aircraft engine gear pump fuel and lubricating oil thermal management system of MPC-NLPIDsech, the design method comprising the following steps:

[0010] Step S1, determining the various modules of the aircraft engine gear pump fuel and lubricating oil thermal management system, which includes: a fuel tank, an external gear pump, a DC motor, an MPC-NLPIDsech controller, a shell and tube fuel and lubricating oil heat exchanger, and a lubricating oil tank;

[0011] Step S2, modeling the external gear pump, the DC motor and the shell and tube fuel and lubricating oil heat exchanger respectively;

[0012] Step S3: designing the MPC-NLPIDsech controller according to the models of the external gear pump, the DC motor and the shell and tube fuel oil heat exchanger obtained in step S2.

[0013] Furthermore, in the step S2, modeling is performed for the external gear pump, specifically including:

[0014] First, for an external gear pump consisting of two gears with exactly the same involute parameters and geometric dimensions, its theoretical output flow is:

[0015]

[0016] In formula (1), ω is the motor speed, rad / s, B=15mm is the gear thickness, R a =19.25mm is the radius of the tooth tip circle, R c =15.75mm is the gear pitch radius,

[0017] Then the external gear pump is provided with side grooves and symmetrical ideal unloading grooves, specifically: The base length is defined as:

[0018]

[0019] In formula (2), R b =13.78mm is the base length; z=8 is the number of gear teeth.

[0020] Furthermore, in step S2, modeling is performed for the DC motor, specifically including:

[0021] The transfer function of the DC motor is set to:

[0022]

[0023] In formula (3), S is a function about time, which is used to transform the time domain into the complex domain through Lagrange transformation.

[0024] Furthermore, in the step S2, modeling is performed for the shell and tube fuel oil heat exchanger, specifically including:

[0025] First, the shell and tube type fuel and lubricating oil heat exchanger is set to cool the lubricating oil and heat the fuel oil, and the lubricating oil flows through the shell side and the fuel oil flows through the tube side;

[0026] Then, the shell side parameters and tube side parameters are set, wherein the shell side parameters are set, specifically including:

[0027] Set the fuel volume flow adjustable range to:

[0028]

[0029] In formula (4), L represents volume in liters, and H represents time in hours;

[0030] Set the fuel mass flow range to:

[0031] m f =Q fv ×ρ f (5)

[0032] In formula (5), ρ f =726.4kg / m 3 is the fuel density;

[0033] The dynamic viscosity of the fluid at the qualitative temperature is set to:

[0034] μ f =v f ×ρ f (6)

[0035] In formula (6), v f is the kinematic viscosity of the fuel, specifically v f =0.7mm 2 / s;

[0036] Set the lubricating oil mass flow rate to:

[0037] m h =ρ h ×U s ×S m (7)

[0038] In formula (7), ρ h Expressed as oil density, U s Expressed as shell-side cross-flow velocity, S m Represents the shell side cross flow area.

[0039] Furthermore, the fuel temperature is set to 90°C, the lubricating oil temperature is set to 125°C, and the shell cross flow velocity U s =0.839m / s, shell side cross flow area S m =993.75mm 2 , the density of lubricating oil is: ρ h =0.9729-0.000035T, where T is the lubricating oil temperature.

[0040] Furthermore, the pipe parameters are set, including:

[0041] Set the characteristic pipe diameter size:

[0042]

[0043] In formula (8), d0 represents the outer diameter of the heat dissipation pipe, and the outer diameter of the heat dissipation pipe do =2mm, P t Expressed as tube center distance, 1.25d o ;

[0044] Set the total number of heat exchange tubes:

[0045] N n =N×n (9)

[0046] In formula (9), N represents the number of tubes in each tube pass, and n represents the number of tube passes;

[0047] Set the fluid area in the tube:

[0048]

[0049] In formula (10), d i Expressed as the inner diameter of the heat pipe;

[0050] The average temperature difference between the lubricating oil and the fuel is assumed to be:

[0051]

[0052] In formula (11), the temperature difference correction coefficient F t =1, Δt1 represents the lubricating oil outlet temperature minus the fuel inlet temperature, Δt2 represents the lubricating oil inlet temperature minus the fuel outlet temperature, T f,o Expressed as fuel outlet temperature, T f,i Expressed as fuel inlet temperature, T h,o Expressed as the lubricating oil outlet temperature, T h,i Expressed as lubricating oil inlet temperature;

[0053] The heat transfer capacity in the heat exchanger is:

[0054] Q=KAΔt m (12)

[0055] In formula (12), K is the heat transfer coefficient, and A is the total heat transfer area;

[0056] The expression for the total heat transfer area is:

[0057] A=N×π×d1×L (13)

[0058] In formula (13), the median diameter of the heat exchange tube d1 = 1.8 mm, and the length of the heat exchange tube L = 200 mm;

[0059] According to the steady-state heat transfer principle of convection heat transfer and heat conduction, the heat transfer coefficient K based on the outer area of ​​the tube is calculated as follows:

[0060]

[0061] In formula (14), α o is the shell side heat transfer coefficient, α i is the tube heat transfer coefficient, r o is the heat resistance of the dirt on the outer wall of the tube, r i is the thermal resistance of the dirt on the inner wall of the tube, w =50.211m 2 k / w;

[0062] Calculation of shell-side heat transfer coefficient α using Kern method o , the expression is:

[0063]

[0064] In formula (15), Re h is the lubricating oil Reynolds number, Pr h is the oil Prandtl number, take Among them, the lubricating oil Reynolds number Re h for Prandtl number Pr h for Specific heat capacity at constant pressure C p,h =1.76+0.0031T;

[0065] Tube heat transfer coefficient α i for:

[0066]

[0067] Based on the heat exchange energy balance, we get:

[0068] Q=m f C p,f (T f,o -T f,i ) = η c m h C p,h (T h,i -T h,o ) (17)

[0069] In the formula, take η c =0.97;

[0070] The fuel flow rate Q is obtained from formula (17): fv The fuel and lubricating oil temperatures at the heat exchanger outlet are expressed as:

[0071]

[0072] According to formula (18), the oil and fuel temperatures at the heat exchanger outlet at different fuel flow rates are simulated by changing the pumped fuel flow rate.

[0073] Furthermore, the step S3 specifically includes:

[0074] Step S301, selecting the lubricating oil temperature at the heat exchanger outlet as a feedback signal, comparing it with the set lubricating oil temperature, thereby forming a negative feedback structure, and obtaining the deviation e between the set value and the actual value. The deviation e at a certain moment is correspondingly recorded as e(k);

[0075] Step S302: According to the hyperbolic sine function, the proportional coefficient and integral coefficient of the nonlinear PID controller are set as follows:

[0076]

[0077] In formula (19), k p is the proportional coefficient of the nonlinear PI controller, a p 、b p and c p is an adjustable parameter when designing the proportional coefficient, where a p Controls the basic value of the proportional coefficient, b p Control the change degree of the proportional coefficient, c p Controls how fast the proportional coefficient changes with the deviation rate e; k i is the integral coefficient of the nonlinear PI controller, a i and c i is an adjustable parameter when designing the integral coefficient, where a i Control the degree of change of the integral coefficient, c i Control how fast the integral coefficient changes with the deviation rate e;

[0078] Step S303, designing the parameters of the nonlinear PI based on the hyperbolic sine according to the expressions of the proportional coefficient and the integral coefficient determined in step S302;

[0079] Step S304: constructing a linear model used in MPC, specifically including:

[0080] Step S3041: According to the fuel flow Q fv The expression of the fuel and lubricating oil temperature at the outlet of the heat exchanger is used to identify the relationship between the heat exchanger flow rate and the outlet lubricating oil temperature, and its transfer function is obtained as follows:

[0081]

[0082] Step S3042: Combining formula (1) and formula (20), we obtain:

[0083]

[0084] In formula (21), G(s) pumpRepresents the transfer function relationship between the motor speed, ω(s) and the gear pump delivery flow rate;

[0085] Step S3043: According to formula (3), formula (20) and formula (21), the linearization parameters for MPC linear model design are derived and converted into state space form, which is:

[0086]

[0087] In the formula, y=T h,ref -T h,o is the difference between the set lubricating oil outlet temperature and the actual outlet temperature, D = 0, A, B, C are the corresponding dynamic matrices;

[0088] Formula (22) can be simplified to the form expressed in time as follows:

[0089]

[0090] Step S3044: According to formula (23), predict the output and control amount at the future time, the expression is:

[0091]

[0092] In formula (24), p represents the prediction time domain length, N c represents the length of the control time domain, Y represents the output matrix of the predicted future time, k represents the kth time, and U is the control matrix of the future time;

[0093] Step S3045: According to formula (24), the prediction model is derived and expressed as:

[0094]

[0095] In formula (25),

[0096] Step S3046, set the target output signal as follows:

[0097] R k =[y(k+1)...y(k+p)] (26)

[0098] Step S3047: Select the optimization objective function as follows:

[0099] J=(R k -Y) T Q(R k -Y)+U T WU (27)

[0100] In formula (27), Q and W are the output error and control quantity increment weight matrices respectively;

[0101] Step S3048: Obtain a control quantity sequence by solving formula (27), and apply the first term of the sequence to the system;

[0102] Step S305: pass the control value u(k) at this moment obtained by formula (28) to e(k) in formula (19), and the expression is:

[0103] u(k)=e(k) (28)

[0104] The beneficial effects of the present invention are:

[0105] 1. The present invention is aimed at the shell and tube fuel and lubricating oil heat exchanger used. Starting from the perspective of energy conservation during heat transfer, combined with relevant theoretical formulas of heat exchangers, based on actual data of a certain type of heat exchanger, the relationship between the flow rate of the cooling medium fuel and the fuel and lubricating oil temperatures at the final heat exchanger outlet is derived, and the working conditions of the core components of the thermal management system are quantified;

[0106] 2. The present invention aims at solving the problem that the proportional coefficient and the integral coefficient in the traditional PID control method are fixed and cannot be adjusted and cannot be changed as the controlled system changes. By introducing a nonlinear control method and a model predictive control method, the proportional coefficient and the integral coefficient in the PID control can be changed as the controlled system changes, thereby improving the system response speed and reducing the overshoot.

[0107] 3. The present invention reasonably sets the predictive control parameters and the nonlinear PID controller parameters based on the hyperbolic sine, so that when the tracking error is large, the proportional coefficient is large and the integral coefficient is small, and when the tracking error is small, the proportional coefficient is small and the integral coefficient is large, thereby accelerating the response speed, reducing the overshoot, achieving a good control effect, and achieving the purpose of thermal management of aircraft engines;

[0108] 4. In order to verify the effectiveness of the proposed solution, the present invention carried out simulation verification in Matlab / Simulink, which provided a strong basis for the application of relevant theories in the thermal management of aircraft engine fuel and lubricating oil systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 This is a structural block diagram of an MPC-NLPIDsech aircraft engine gear pump fuel and lubricating oil thermal management system provided in Example 1;

[0110] Figure 2 It is a structural block diagram of the MPC-NLPIDsech controller provided in Example 1;

[0111] Figure 3A schematic diagram of the change in the delivery flow rate of the external gear pump provided in Example 1;

[0112] Figure 4 For Follow Figure 3 Schematic diagram of the change in fuel and lubricating oil temperature at the outlet of the heat exchanger when the delivery flow of the Chinese and foreign meshing gear pumps changes. Figure 3 and Figure 4 It reflects the nonlinear relationship between the heat exchanger outlet fluid temperature and the fuel flow rate, and reflects the working characteristics of the heat exchanger;

[0113] Figure 5 The hyperbolic sine function image provided in Example 1;

[0114] Figure 6 A schematic diagram of comparison of the reference oil output temperature, the actual oil output temperature when using conventional PID control and the actual oil output temperature when using MPC-NLPIDsech control as provided in Example 1, when changing with time;

[0115] Figure 7 A comparison of the actual speed of the DC motor when using conventional PID control and MPC-NLPIDsech control as provided in Example 1, when changing over time;

[0116] Figure 8 A comparison of the actual fuel flow rate delivered by the external gear pump when using conventional PID control and MPC-NLPIDsech control as provided in Example 1 over time;

[0117] Fig. 9 Provided in Example 1, the actual fuel output temperature is compared when using traditional PID control and MPC-NLPIDsech control as it changes over time. DETAILED DESCRIPTION

[0118] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0119] Example 1

[0120] See also Figure 1-Figure 9 This embodiment provides a design method for an aircraft engine gear pump fuel and lubricating oil thermal management system of MPC-NLPIDsech, comprising the following steps:

[0121] Step S1: The aircraft engine fuel oil thermal management system, such as Figure 1 As shown in the figure, it consists of the following parts: fuel tank, external gear pump, DC motor, MPC-NLPIDsech controller, shell and tube fuel and lubricating oil heat exchanger, lubricating oil tank, etc.

[0122] Among them, the lubricating oil tank and the fuel tank increase the lubricating oil and fuel required by the thermal management system, the fuel cooling lubricating oil is delivered by the meshing gear pump, the DC motor drives the external meshing gear pump, and the MPC-NLPIDsech controller controls the speed of the DC motor. The MPC-NLPIDsech structure used in this embodiment is as follows Figure 2 shown.

[0123] Step S2, respectively carry out and complete the modeling of the external gear pump, the DC motor, and the fuel and lubricating oil heat exchanger.

[0124] Specifically, in this embodiment, step S2 is as follows:

[0125] Step S201: Modeling an external gear pump.

[0126] Select an external gear pump consisting of two gears with exactly the same involute parameters and geometric dimensions. Its theoretical output flow is:

[0127]

[0128] Where, ω is the motor speed, rad / s; B = 15mm is the gear thickness; R a =19.25mm is the radius of the tooth tip circle; R c =15.75mm is the gear pitch radius;

[0129] The gear pump has side grooves and symmetrical ideal unloading grooves, so there are:

[0130]

[0131] The base length is:

[0132]

[0133] Among them, R b =13.78mm is the base length; z=8 is the number of gear teeth.

[0134] Step S202: Modeling the DC motor used in the thermal management system.

[0135] The DC motor used is an armature-controlled one, and its transfer function is:

[0136]

[0137] Among them, U a is the input armature voltage and N is the motor output speed.

[0138] After experimental determination, the transfer function is:

[0139]

[0140] Step S203: Modeling the shell and tube fuel and lubricating oil heat exchanger.

[0141] The main function of the shell and tube fuel and lubricating oil heat exchanger in the aircraft engine thermal management system is to cool the lubricating oil and heat the fuel. Therefore, the present invention uses the shell and tube fuel and lubricating oil heat exchanger model to cool the lubricating oil and heat the fuel. The lubricating oil flows through the shell and the fuel flows through the tube.

[0142] The qualitative temperature of fuel is 90℃ and that of lubricating oil is 125℃.

[0143] The adjustable range of fuel volume flow is:

[0144]

[0145] The fuel mass flow range is:

[0146] m f =Q fv ×ρ f (8)

[0147] The kinematic viscosity of fuel is:

[0148] v f =0.7mm 2 / s (9)

[0149] The dynamic viscosity of the fluid at the qualitative temperature is:

[0150] μ f =v f ×ρ f (10)

[0151] Among them, ρ f =726.4kg / m 3 is the fuel density.

[0152] The mass flow rate of lubricating oil is:

[0153] m h =ρ h ×U s ×S m (11)

[0154] Among them, the shell side cross flow velocity U s =0.839m / s, shell cross flow area S m=993.75mm 2 .

[0155] The density of lubricating oil is:

[0156] ρ h =0.9729-0.000035T (12)

[0157] Where T is the lubricating oil temperature.

[0158] The fuel oil flows through the pipe, so we also need to know the relevant parameters of the pipe. As follows:

[0159] The characteristic pipe diameter dimensions are as follows:

[0160]

[0161] Among them, the outer diameter of the heat dissipation pipe is d o =2mm.

[0162] The tube center distance is:

[0163] P t =1.25d o (14)

[0164] The total number of heat exchange tubes is:

[0165] N n =N×n (15)

[0166] Among them, the number of tubes in each tube pass is N=915, and the number of tube passes is n=5.

[0167] The area of ​​the fluid in the tube is:

[0168]

[0169] Among them, the inner diameter of the heat dissipation pipe is d i =1.6mm.

[0170] The average flow rate of the shell passage is:

[0171] u0=0.839m / s (17)

[0172] The average temperature difference between the two fluids in heat exchange is:

[0173]

[0174] Among them, the temperature difference correction coefficient F t =1, Δt1: smaller inlet and outlet temperature difference = lubricating oil outlet temperature - fuel inlet temperature, Δt2: larger inlet and outlet temperature difference = lubricating oil inlet temperature - fuel outlet temperature, T f,o : Fuel outlet temperature, T f,i : Fuel inlet temperature, Th,o : Lubricating oil outlet temperature, T h,i : Lubricating oil inlet temperature.

[0175] The heat transfer capacity in the heat exchanger is calculated using the following formula:

[0176] Q=KAΔt m (19)

[0177] Among them, K is the heat transfer coefficient and A is the total heat transfer area.

[0178] The total heat exchange area is:

[0179] A=N×π×d1×L (20)

[0180] Among them, the middle diameter of the heat exchange tube d1 = 1.8 mm, and the length of the heat exchange tube L = 200 mm.

[0181] According to the steady-state heat transfer formula of convection heat transfer and heat conduction, the heat transfer coefficient K based on the outer area of ​​the tube can be calculated:

[0182]

[0183] Among them, α o is the shell side heat transfer coefficient, α i is the tube heat transfer coefficient, r o is the heat resistance of the dirt on the outer wall of the tube, r i is the thermal resistance of the dirt on the inner wall of the tube, w =50.211m 2 ·k / w.

[0184] Calculation of shell-side heat transfer coefficient α using Kern method o :

[0185]

[0186] Among them, Re h is the lubricating oil Reynolds number, Pr h is the oil Prandtl number, take

[0187] Thermal conductivity of lubricating oil λ h for:

[0188]

[0189] Lubricating oil Reynolds number Re h for:

[0190]

[0191] Prandtl number Pr h for:

[0192]

[0193] Among them, the constant pressure specific heat capacity C p,h =1.76+0.0031T.

[0194] Calculate the tube heat transfer coefficient α i for:

[0195]

[0196] Based on the heat exchange energy balance, we can get:

[0197] Q=m f C p,f (T f,o -T f,i ) = η c m h C p,h (T h,i -T h,o ) (27)

[0198] Among them, take η c =0.97.

[0199] The fuel flow rate Q can be derived from the above formula: fv The fuel and lubricating oil temperatures at the heat exchanger outlet are as follows:

[0200]

[0201] According to the corresponding relationship derived from this formula, the oil and fuel temperatures at the heat exchanger outlet under different fuel flow rates are simulated by changing the pumped fuel flow rate. Figure 3 As shown, the corresponding lubricating oil and fuel temperature changes at the heat exchanger outlet are as follows Figure 4 As shown. In the period from 0 to 20 seconds, the pumped fuel flow rate takes the minimum value, which is 0.278×10 -3 m 3 / s; from 20 to 70 seconds, the pumped fuel flow rate increases linearly, and finally reaches a maximum of 1.94×10 -3 m 3 / s. As the pumping flow rate increases, the temperature of the lubricating oil and fuel at the heat exchanger outlet decreases. The outlet fuel temperature drops from the initial 135.4°C to 113.8°C, and the outlet lubricating oil temperature drops from 128.0°C to 98.5°C. At the same time, this phenomenon is also consistent with the general situation that the cooling effect is better and the outlet temperature is lower as the cooling fluid flow rate increases.

[0202] Step S3: Design a nonlinear PI controller based on hyperbolic sine for each part of the model completed in step S2. The details are as follows:

[0203] Step S301: Select the lubricating oil temperature at the heat exchanger outlet as a feedback signal and compare it with the set lubricating oil temperature.

[0204] Step S302: According to the hyperbolic sine function, the proportional coefficient and integral coefficient of the nonlinear PID controller are set as follows:

[0205]

[0206] The hyperbolic sine function is Figure 5 shown.

[0207] Step S303: According to Formula 29, design the parameters of the nonlinear PI based on the hyperbolic sine.

[0208] In this embodiment, the parameters of the nonlinear PI based on the hyperbolic sine are calculated by:

[0209] Step S3031, select and determine a rough a p , and then determine b according to the situation of the controlled object p and c p the approximate scope of

[0210] Step S3032: Comprehensive adjustment a p 、b p and c p , determine the more accurate values ​​of the three;

[0211] Step S3033: Based on step S3032, add a i and c i Design and adjustment to obtain the final a p 、b p 、c p 、b p and c p ;

[0212] Step S3034: using the obtained p 、b p 、c p 、b p and c p , the proportionality coefficient k is determined by the relationship described in formula (29) p And the integration coefficient k i .

[0213] Step S304: derive a linear model used in MPC (Model Predictive Control).

[0214] First, the relationship between the heat exchanger flow rate and the outlet lubricating oil temperature in equation 28 is identified, and its transfer function is obtained as follows:

[0215]

[0216] Transform equation 1 to get:

[0217]

[0218] Combining Equation 6, Equation 30, and Equation 31, the linearization parameters used for MPC design are derived and converted into state space form:

[0219]

[0220] in, y=T h,ref -T h,o The difference between the set lubricating oil outlet temperature and the actual outlet temperature, D=0.

[0221] Equation 32 can be simplified into a general form expressed in time as follows:

[0222]

[0223] After obtaining the linearized model represented by equation 32, the MPC can be derived and designed accordingly. The output and control quantity predicted at the future moment are as follows:

[0224]

[0225] Among them, p represents the prediction time domain length, N c Indicates the control time domain length.

[0226] Equation 33 can be derived to obtain the prediction equation, such as Equation 35:

[0227]

[0228] in,

[0229] Let the target output signal be as follows:

[0230] R k =[y(k+1)...y(k+p)] (36)

[0231] The optimization objective function is selected as follows:

[0232] J=(R k -Y) T Q(R k -Y)+U T WU (37)

[0233] Among them, Q and W are the output error and control quantity increment weight matrices respectively.

[0234] Specifically, in this embodiment, the weight matrix values ​​are determined based on the degree of emphasis on different factors;

[0235] Therefore, by solving the objective function described in equation 37, a control quantity sequence can be obtained, and the first term of the sequence can be applied to the system.

[0236] Step S305: pass the control value u(k) obtained by equation 38 to e(k) in equation 29, that is,

[0237] u(k)=e(k) (38)

[0238] In this way, the design of MPC-NLPIDsech controller is completed, and its structure is as follows: Figure 2 shown.

[0239] Step S4, according to the aircraft engine fuel and lubricating oil thermal management system established in step S2 and the MPC-NLPIDsech controller designed in step S3, the lubricating oil outlet temperature is set, the heat exchanger fluid outlet temperature is obtained by measurement, the DC motor speed is controlled, and thus the flow rate of the external gear pump is controlled to ensure that the lubricating oil outlet temperature is consistent with the set temperature and to perform thermal management on the aircraft engine.

[0240] In order to fully verify the effectiveness of the control scheme proposed in this embodiment, simulation experiments were carried out on the Matlab / Simulink platform.

[0241] First, the total simulation time is set to 1 second, the reference oil output temperature is set to 110°C in 0-0.5 seconds, and the reference temperature is changed to 105°C at 0.5 seconds. The tracking effect of the two methods on the reference temperature is compared. Figure 6 shown.

[0242] Second, the control effect comparison Figure 6-9 As shown in the figure, it can be seen that MPC-NLPIDsech has better effect than traditional PID, with faster response and smaller overshoot oscillation. Figure 6 It can be seen that MPC-NLPIDsech has a faster tracking speed than traditional PID and reduces overshoot by 0.9%. It can also track the changing reference oil outlet temperature. Figure 7 It can be seen that the use of MPC-NLPIDsech can obtain a more stable DC motor speed than the traditional PID. Figure 6 It can be seen that the speed at stability changes with the reference temperature. Figure 8 Combination Figure 6 It can be seen that as the reference oil outlet temperature decreases, the pumping flow rate increases from 1.14×10 -3 m 3 / s increased to 1.45×10 -3 m 3 / s. By Fig. 9 Combination Figure 6 It can be seen that the output fuel temperature decreases as the output lubricating oil reference temperature decreases, satisfying Figure 3 and Figure 4 Reaction trend.

[0243] Thirdly, the solution of the present invention meets the requirement of tracking the lubricating oil output temperature and achieves the purpose of thermal management of the aircraft engine.

[0244] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0245] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A design method for a fuel and lubricating oil thermal management system for an aircraft engine gear pump based on MPC-NLPIDsech, characterized in that: The design method comprises the following steps: Step S1, determining the various modules of the aircraft engine gear pump fuel and lubricating oil thermal management system, which includes: a fuel tank, an external gear pump, a DC motor, an MPC-NLPIDsech controller, a shell and tube fuel and lubricating oil heat exchanger, and a lubricating oil tank; Step S2, modeling the external gear pump, the DC motor and the shell and tube fuel and lubricating oil heat exchanger respectively; Step S3, designing the MPC-NLPIDsech controller according to the models of the external gear pump, the DC motor and the shell and tube fuel and lubricating oil heat exchanger obtained in step S2; In the step S2, modeling is performed for the external gear pump, specifically including: First, for an external gear pump consisting of two gears with exactly the same involute parameters and geometric dimensions, its theoretical output flow is: In formula (1), ω is the motor speed, rad / s, B=15mm is the gear thickness, R a =19.25mm is the radius of the tooth tip circle, R c =15.75mm is the gear pitch radius, Then the external gear pump is provided with side grooves and symmetrical ideal unloading grooves, specifically: The base length is defined as: In formula (2), R b =13.78mm is the base length; z=8 is the number of gear teeth; In the step S2, modeling is performed for the DC motor, specifically including: The transfer function of the DC motor is set to: In formula (3), S is a function about time, which is used to transform the time domain into the complex domain through Latent transformation; In the step S2, modeling is performed for the shell and tube fuel oil heat exchanger, specifically including: First, the shell and tube type fuel and lubricating oil heat exchanger is set to cool the lubricating oil and heat the fuel oil, and the lubricating oil flows through the shell side and the fuel oil flows through the tube side; Then, the shell side parameters and tube side parameters are set, wherein the shell side parameters are set, specifically including: Set the fuel volume flow adjustable range to: Q fv =(1-7)×10 3 L / H (4) =(0.278-1.94)×10 -3 m 3 / s In formula (4), L represents volume in liters, and H represents time in hours; Set the fuel mass flow range to: m f =Q fv ×ρ f (5) In formula (5), ρ f =726.4kg / m 3 is the fuel density; The dynamic viscosity of the fluid at the qualitative temperature is set to: m f =v f ×r f (6) In formula (6), v f is the kinematic viscosity of the fuel, specifically v f =0.7mm 2 / s; Set the lubricating oil mass flow rate to: m h =ρ h ×U s ×S m (7) In formula (7), ρ h Expressed as oil density, U s Expressed as shell-side cross-flow velocity, S m It represents the cross-flow area of ​​the shell side; The fuel temperature is set to 90℃, the lubricating oil temperature is set to 125℃; the shell cross flow velocity is U s =0.839m / s, shell side cross flow area S m =993.75mm 2 , the density of lubricating oil is: ρ h =0.9729-0.000035T, where T is the lubricating oil temperature; Set the pipe parameters, including: Set the characteristic pipe diameter size: In formula (8), d0 represents the outer diameter of the heat dissipation pipe, and the outer diameter of the heat dissipation pipe d o =2mm, P t Expressed as tube center distance, 1.25d o ; Set the total number of heat exchange tubes: N n =N×n (9) In formula (9), N represents the number of tubes in each tube pass, and n represents the number of tube passes; Set the fluid area in the tube: In formula (10), d i Expressed as the inner diameter of the heat pipe; The average temperature difference between the lubricating oil and the fuel is assumed to be: In formula (11), the temperature difference correction coefficient F t =1, Δt1 represents the lubricating oil outlet temperature minus the fuel inlet temperature, Δt2 represents the lubricating oil inlet temperature minus the fuel outlet temperature, T f,o Expressed as fuel outlet temperature, T f,i Expressed as fuel inlet temperature, T h,o Expressed as the lubricating oil outlet temperature, T h,i Expressed as lubricating oil inlet temperature; The heat transfer capacity in the heat exchanger is: Q=KAΔt m (12) In formula (12), K is the heat transfer coefficient, and A is the total heat transfer area; The expression for the total heat transfer area is: A=N×π×d1×L (13) In formula (13), the median diameter of the heat exchange tube d1 = 1.8 mm, and the length of the heat exchange tube L = 200 mm; According to the steady-state heat transfer principle of convection heat transfer and heat conduction, the heat transfer coefficient K based on the outer area of ​​the tube is calculated as follows: In formula (14), α o is the shell side heat transfer coefficient, α i is the tube heat transfer coefficient, r o is the heat resistance of the dirt on the outer wall of the tube, r i is the thermal resistance of the dirt on the inner wall of the tube, w =50.211m 2 k / w; Calculation of shell-side heat transfer coefficient α using Kern method o , the expression is: In formula (15), Re h is the lubricating oil Reynolds number, Pr h is the oil Prandtl number, take Among them, the lubricating oil Reynolds number Re h for Prandtl number Pr h for Specific heat capacity at constant pressure C p,h =1.76+0.0031T, u0 is the average velocity in the shell, λ h is the thermal conductivity of lubricating oil; Tube heat transfer coefficient α i for: Based on the heat exchange energy balance, we get: Q=m f C p,f (T f,o -T f,i )=η c m h C p,h (T h,i -T h,o ) (17) In the formula, take η c =0.97; The fuel flow rate Q is obtained from formula (17): fv The fuel and lubricating oil temperatures at the heat exchanger outlet are expressed as: According to formula (18), the oil and fuel temperatures at the heat exchanger outlet are simulated at different fuel flow rates by changing the fuel flow rate of the pump; The step S3 specifically includes: Step S301, selecting the lubricating oil temperature at the heat exchanger outlet as a feedback signal, comparing it with the set lubricating oil temperature, thereby forming a negative feedback structure, and obtaining the deviation e between the set value and the actual value. The deviation e at a certain moment is correspondingly recorded as e(k); Step S302: According to the hyperbolic sine function, the proportional coefficient and integral coefficient of the nonlinear PID controller are set as follows: In formula (19), k p is the proportional coefficient of the nonlinear PI controller, a p 、b p and c p is an adjustable parameter when designing the proportional coefficient, where a p Controls the basic value of the proportional coefficient, b p Control the change degree of the proportional coefficient, c p Controls how fast the proportional coefficient changes with the deviation rate e; k i is the integral coefficient of the nonlinear PI controller, a i and c i is an adjustable parameter when designing the integral coefficient, where a i Control the degree of change of the integral coefficient, c i Control how fast the integral coefficient changes with the deviation rate e; Step S303, designing the parameters of the nonlinear PI based on the hyperbolic sine according to the expressions of the proportional coefficient and the integral coefficient determined in step S302; Step S304: constructing a linear model used in MPC, specifically including: Step S3041: According to the fuel flow Q fv The expression of the fuel and lubricating oil temperature at the outlet of the heat exchanger is used to identify the relationship between the heat exchanger flow rate and the outlet lubricating oil temperature, and its transfer function is obtained as follows: Step S3042: Combining formula (1) and formula (20), we obtain: In formula (21), G(s) pump Represents the transfer function relationship between the motor speed, ω(s) and the gear pump delivery flow rate; Step S3043: According to formula (3), formula (20) and formula (21), the linearization parameters for MPC linear model design are derived and converted into state space form, which is: In the formula, y=T h,ref -T h,o is the difference between the set lubricating oil outlet temperature and the actual outlet temperature, D = 0, A, B, C are the corresponding dynamic matrices; Formula (22) can be simplified to the form expressed in time as follows: Step S3044: According to formula (23), predict the output and control amount at the future time, the expression is: In formula (24), p represents the prediction time domain length, N c represents the length of the control time domain, Y represents the output matrix of the predicted future time, k represents the kth time, and U is the control matrix of the future time; Step S3045: According to formula (24), the prediction model is derived and expressed as: Formula (25) Step S3046, set the target output signal as follows: R k =[y(k+1)...y(k+p)] (26) Step S3047: Select the optimization objective function as follows: J=(R k -AND) T Q(R k -Y)+U T WU (27) In formula (27), Q and W are the output error and control quantity increment weight matrices respectively; Step S3048: Obtain a control quantity sequence by solving formula (27), and apply the first term of the sequence to the system; Step S305: pass the control value u(k) at this moment obtained by formula (27) to e(k) in formula (19), and the expression is: u(k)=e(k) (28).

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