Optimization method for minimum fuel consumption mode of aero-engine based on PSM matrix

Abstract

The invention discloses an aero-engine minimum fuel consumption mode optimization method based on a PSM matrix. Compared with a component-level steady-state model, the PSM matrix does not involve complex aerodynamic thermodynamics and rotor dynamics iterative computation, so that the solving real-time performance is greatly improved. Meanwhile, due to the linear characteristic of the PSM matrix, various constraint conditions in the minimum fuel consumption optimization process can be conveniently processed. Meanwhile, the direct switching method inevitably causes the problem of overshoot of the controlled quantity, the actual controlled quantity possibly exceeds the safe operation boundary of the engine in the changing process, and in order to meet the switching requirement of the engine performance optimization control mode, a multivariable steady-state controller is designed based on MPC. Compared with the traditional Min-Max control, the MPC can improve the control quality and reduce the complexity of the control system under the condition of meeting the constraint conditions.

Description

1. Technical Field

[0001] The invention relates to the field of aircraft engine control, and in particular to a method for optimizing an aircraft engine minimum fuel consumption mode based on a PSM matrix. 2. Background technology

[0002] With the development of full authority digital electronic control systems and the increasing maturity of multivariable control, performance seeking control (PSC) was listed as one of the advanced control technologies for aircraft engines by NASA in the 1980s, with the purpose of improving / optimizing the quasi-steady-state performance of aircraft and propulsion systems. Performance seeking control requires different control modes to be used in different flight mission segments. When the aircraft is climbing or accelerating, the maximum thrust mode is used to provide the aircraft with the maximum effective thrust to achieve the fastest climb or acceleration; the minimum fuel consumption mode is used in the cruising state to reduce fuel consumption and increase the range while ensuring the thrust remains unchanged; the minimum turbine pre-temperature mode is used to protect the turbine blades and increase the engine life while ensuring the engine performance. In the performance seeking process of the steady-state point, although the starting point and the end point of the optimization must be able to meet the constraints set at the beginning, the various control quantities may still have problems such as overshoot during the optimization process, resulting in overheating and overspeeding of the engine, resulting in a decrease in the life of the turbine blades, affecting the safe and stable operation of the aircraft engine.

[0003] Although the traditional constraint management architecture based on PI controller can ensure that the controlled variable does not exceed the given limit value, its design is relatively conservative and increases the response time of the engine. This is inconsistent with the design concept of performance optimization control to maximize the potential of the engine. In addition, traditional PI control can no longer meet the needs of multivariable control. Therefore, it is necessary to consider the transition state control algorithm separately so that the engine controlled variable can meet the requirements of not exceeding the limit and responding quickly during the optimization process.

[0004] The propulsion system matrix (PSM) is a small-scale linearized model of the component-level model near the steady-state point. Compared with the component-level steady-state model, the PSM matrix does not involve complex aerodynamic thermodynamics and rotor dynamics iterative calculations, so it has greatly improved the real-time performance of the solution. At the same time, due to the linear characteristics of the PSM matrix, it can easily handle various constrained linear optimization problems, such as engine maximum thrust optimization, minimum fuel consumption optimization, and minimum infrared radiation optimization.

[0005] Model Predictive Control is a model-based control algorithm that can handle multi-input and multi-output problems. Its essence is an optimization algorithm, that is, solving the optimal control sequence that satisfies the future period at each moment, so that the performance indicators of the controlled quantity are optimal. There are many types of performance indicators, such as response time indicators, steady-state error indicators, etc. In addition, model predictive control can explicitly handle various constraints, that is, the upper and lower limits of the control quantity can be added to the solution of the optimization problem, which greatly reduces the complexity of the control structure. 3. Summary of the invention

[0006] When dealing with the problem of optimizing the minimum fuel consumption of aircraft engines, the PSM matrix is ​​used to linearize the aircraft engine component-level model in a small range near the steady-state point, which greatly reduces the amount of solution calculations.

[0007] The PSM matrix has the following general form:

[0008] ΔY=PΔX (3.1)

[0009] In the formula, ΔY represents the output change of the system, ΔX represents the input change of the system, and P is the PSM matrix of the system. The PSM matrix of the engine studied in this paper near the steady-state point can be expressed as follows:

[0010]

[0011] p is an element of the PSM matrix, and its size represents the influence of the control variable on the controlled variable, which can be calculated by the following formula:

[0012]

[0013] Where X i0 Represents the initial input value, Y i0 represents the initial steady-state point value, X i represents the input value after a small disturbance, Y i Represents the steady-state point value obtained after a small disturbance occurs.

[0014] Based on the PSM matrix, the optimization objectives and constraints of the linear optimization algorithm can be extracted. The optimization objective is the minimum fuel consumption, and the constraints include the control quantity feasible area restriction, the engine safe operation limit value, the controller power, and the control actuator displacement restriction. While the engine meets the minimum fuel consumption requirements, it is also necessary to ensure that the engine does not overheat, overspeed, surge, and the thrust remains basically unchanged. At the same time, the input ΔX also needs to meet certain restrictions. The problem of optimizing the minimum fuel consumption of aircraft engines can be described as follows:

[0015]

[0016] The linear optimization algorithm can be used to obtain the steady-state point with the minimum fuel consumption rate under the constraints. Although equation (3.4) restricts the surge margin, turbine pre-temperature, etc. of the optimized point, the direct switching method inevitably brings about the problem of overshoot of the controlled variable. The actual controlled variable may still exceed the safe operating boundary of the engine during the change process. Moreover, the performance optimization control itself is based on sacrificing the engine surge margin, and its operating boundary is closer to the surge line. Therefore, the restriction protection problem in the transition state cannot be ignored in the performance optimization control process. In order to meet the needs of switching the engine performance optimization control mode, a multivariable steady-state controller is designed based on MPC.

[0017] Model predictive control (MPC) is a control algorithm that can directly incorporate the constraints of the control quantity, controlled quantity, and state quantity into the algorithm solution process. Compared with traditional Min-Max control, it can improve the control quality and reduce the complexity of the control system while satisfying the constraints. Its basic principles are as follows: Figure 1 shown.

[0018] MPC estimates the future state of the system and calculates the control sequence based on the estimated results. Here, the necessary deductions are made for the tracking problem of MPC.

[0019] Assume that the system has a discrete state-space equation of the following form:

[0020] x(k+1)=Ax(k)+Bu(k) (3.5)

[0021] The system will be N In the time domain, the cost function J needs to be minimized:

[0022]

[0023] Among them, Q, R, and F are all diagonal matrices, Q represents the weight coefficient of the state quantity in the prediction time domain, R represents the weight coefficient of the control quantity in the prediction time domain, and F represents the weight coefficient of the terminal performance index. ref represents the set value of the state quantity, x(k+i|k) represents the system's estimate of the state quantity at time k+i at time k, and u(k+i|k) represents the system's estimate of the control quantity at time k+i at time k. Through recursive calculation, we can get:

[0024]

[0025] Further simplify formula (3.7):

[0026] X k =[x(k|k),x(k+1|k),...,x(k+N|k)] T(3.8)

[0027] U k =[u(k|k),u(k+1|k),...,u(k+N-1|k)] T (3.9)

[0028] M=[I,A,A 2 , ....A N ] T (3.10)

[0029]

[0030] Then (3.8) becomes:

[0031] X k =Mx(k)+CU k (3.12)

[0032] Further simplifying formula (3.6), we can get:

[0033]

[0034] in:

[0035]

[0036] Combining (3.12) and (3.13) we can get

[0037]

[0038] In formula (3.17), since x k Only the initial state of the system determines, so when solving minJ, only x is included k The constant term can be eliminated, and equation (3.17) becomes the following form:

[0039]

[0040] Also because They are all diagonal matrices, and formula (3.13) can be further simplified:

[0041]

[0042] Formula (3.19) is about U k The quadratic programming problem can be solved by calling the quadprog function in Matlab. 4. Description of the drawings

[0043] Figure 1 It is the principle of model predictive control.

[0044] Figure 2 It is the dynamic accuracy verification result of the composite model compared with the component-level model.

[0045] Figure 3 It is the optimization result of super cruise state.

[0046] Figure 4 yes The influence of matrix elements on MPC control results.

[0047] Figure 5 It is the verification of MPC control effect in super cruise state. 5. Specific implementation methods

[0048] In order to enable those skilled in the art to better understand the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0049] Since the model after PSM matrix transformation is a small-scale linearization, its accuracy will affect the optimization results, so it is necessary to verify the model accuracy.

[0050] Taking the supercruise state as an example, when Ma = 2.35, H = 20000m, the fuel flow rate of the multifunctional combustion chamber is continuously stepped, and the simulation results of the component-level model and the composite model are as follows: Figure 2 As shown:

[0051] It can be seen from the figure that the modeling error between the composite model and the component-level model can be basically ignored, indicating that the composite model can meet the accuracy requirements of dynamic simulation.

[0052] The problem described by formula (3.4) is a typical linear programming problem. The objective function and the constraints are both linear functions. Many mature methods have been developed to solve linear programming problems, including interior point method, exterior point method, etc. The above linear programming problem can also be easily solved using the linprog function of matlab. Taking the super cruise state as an example, when Ma = 2.35, H = 20000m, the change of the input ΔX is limited to within ±2%, and the simulation results are as follows Figure 3 shown.

[0053] As can be seen from the figure above, the fuel consumption rate can be reduced by 2.6% in the minimum fuel consumption mode, meeting the expected requirements, but the thrust fluctuation, turbine front temperature, speed and other overshoots are large. The actual controlled quantity may still exceed the safe operation boundary of the engine during the change process. Therefore, this paper designs a multivariable steady-state controller based on MPC to meet the needs of engine performance optimization control mode switching.

[0054] The solution of MPC is related to the prediction time domain N, control time domain M, and weight matrix The value of is directly related to The value of the element q on the diagonal of the matrix is ​​used to solve the problem of overshoot of the controlled quantity caused by the step of the controlled quantity. The following example illustrates this point.

[0055] like Figure 4 As shown in the figure, the larger the q value is, the greater the proportion of the controlled quantity in the optimization problem J is, and the better the final control effect is. As the q value increases, the overshoot and fluctuation of the controlled quantity gradually disappear. In the super cruise state of Ma = 2.35, H = 20000m, the control effect of the MPC controller is verified:

[0056] like Figure 5 As shown in the figure, the simulation results of the supercruise state show that MPC can effectively suppress the thrust fluctuation phenomenon generated in the optimization process, and at the same time significantly suppress the overshoot problem of the surge margin, and can achieve a smooth transition of the engine steady-state point switching.

Claims

1. Solve the minimum fuel consumption optimization problem of aircraft engines based on the PSM matrix. Use the PSM matrix to linearize the aircraft engine component-level model in a small range near the steady-state point to meet the accuracy requirements of dynamic simulation.

2. In order to meet the needs of engine optimization control mode switching, a multivariable steady-state controller is designed based on MPC. MPC is a control algorithm that can directly incorporate the constraints of control quantity, controlled quantity, and state quantity into the algorithm solution process. Compared with traditional Min-Max control, it can improve control quality and reduce the complexity of the control system while meeting the constraints.

Images