Design method of steady-state anti-disturbance controller for aero-engine

Abstract

The present invention discloses a method for designing a steady-state anti-disturbance controller for an aero-engine, comprising the following steps: Step 1, for a steady-state operating point of an aero-engine for which a steady-state anti-disturbance controller needs to be designed, a linear model of the steady-state point neighborhood band interference influence of the steady-state operating point of the aero-engine is established; Step 2, the linear model is transformed into the frequency domain, and the frequency response function of the control quantity u after the controller acts in the frequency domain is obtained; Step 3, with the minimum performance optimization index as the optimization target, a multi-objective optimization model with the frequency response function of the controller as the quantity to be optimized is established; Step 4, the established multi-objective optimization model is solved to obtain an optimized steady-state anti-disturbance controller. Compared with the prior art, the present invention can design an anti-disturbance controller at any frequency point, and intuitively obtain the existence, optimality, and even the anti-disturbance performance limit of the anti-disturbance controller under limited conditions during the design process.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engine control, and in particular to a design method for a steady-state anti-disturbance controller for an aero-engine. Background Art

[0002] Interference factors are widespread throughout aircraft engines. System interference can be categorized as external or internal, depending on its source. External interference includes atmospheric turbulence, electromagnetic interference, rain and snow, and engine power extraction. Internal interference can be categorized as environmental interference affecting components like fuel pumps and sensors, and degradation of turbine or compressor health parameters.

[0003] The energy of various external interferences that aircraft engines may encounter during operation is generally concentrated within a certain or limited frequency range. If the limited frequency domain characteristics of the interference signal are ignored when designing an anti-interference controller, the designed controller will often be quite conservative. Therefore, an ideal aircraft engine anti-interference controller design method should have the following characteristics:

[0004] (1) Allows the definition of disturbance rejection control performance indicators at any specific frequency;

[0005] (2) Allowing for improvements to the disturbance rejection performance of current controllers;

[0006] (3) Allows intuitive quantitative optimization of global anti-interference performance for different output performance energies when the number of sensors or actuators is limited;

[0007] However, in the current field of control theory, there is no control theory that can possess all these characteristics at the same time. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide a method for designing a steady-state anti-disturbance controller for an aircraft engine. The anti-disturbance controller can be designed at any frequency point, and the existence, optimality and even the anti-disturbance performance limit of the anti-disturbance controller under restricted conditions can be intuitively obtained during the design process.

[0009] The present invention specifically adopts the following technical solutions to solve the above technical problems:

[0010] A method for designing a steady-state anti-disturbance controller for an aircraft engine comprises the following steps:

[0011] Step 1: For the steady-state operating point of the aircraft engine for which a steady-state anti-disturbance controller is to be designed, a linear model of the influence of disturbances on the steady-state point neighborhood of the steady-state operating point of the aircraft engine is established as follows:

[0012]

[0013] Among them, u is the control quantity of the aircraft engine, d is the interference quantity, y is the output feedback energy, z is the controllable output energy, G 00 is the open-loop transfer function from u to y, G 01 is the open-loop transfer function from d to y, G 10 is the open-loop transfer function from u to z, G 11 is the open-loop transfer function from d to z;

[0014] Step 2: transform the linear model into the frequency domain to obtain the frequency response function U(jω) of the control variable u after the controller acts in the frequency domain:

[0015] U(jω)=K(jω)Y(jω)

[0016] Where ω is the frequency, Y(jω) is the frequency response function of the output performance y; K(jω) is the frequency response function of the controller;

[0017] Step 3: Optimize the performance index η yd and η zd Minimum is the optimization goal, As the constraint condition, a multi-objective optimization model is established with the controller's frequency response function K(jω) as the quantity to be optimized; where δ1 and δ2 are the anti-disturbance performance requirements of the output feedback energy and the controllable output performance, respectively; γ min and γ max are the minimum and maximum values ​​of the control quantity respectively; G 01 (jω) and G 11 (jω) respectively represent G 01 and G 11 Frequency response function of T yd_c (jω) and T yd_c (jω) represent the closed-loop frequency response functions of the disturbance d to the output feedback energy y and the controllable energy z under the action of the controller K(jω), and their expressions are:

[0018] T yd_c (jω)=(1-G 00 (jω)K(jω)) -1 G 01 (jω)

[0019]

[0020] Step 4: Solve the established multi-objective optimization model to obtain the optimized steady-state anti-disturbance controller.

[0021] Furthermore, the established multi-objective optimization model is solved using an optimization method based on complex plane geometric analysis, as follows:

[0022] Define α(jω) and β(jω) as the frequency domain response functions of feedback sensitivity and disturbance sensitivity, respectively, expressed as:

[0023]

[0024]

[0025] G 00 (jω) and G 10 (jω) respectively represent G 00 and G 10 The frequency response function of the controller can be transformed into the following structure:

[0026] |α(jω)+1|≤δ1

[0027] |α(jω)+G(jω)|≤δ2|G(jω)|

[0028] r γ_min ≤|α(jω)|≤r γ_max

[0029] Among them, r γ_max and r γ_min Respectively represent the upper and lower bounds of the modulus of α(jω); each inequality can correspond to a different circular area on the complex plane, and the intersection of all areas is represented as the selectable area of ​​the controller that meets all constraints;

[0030] The performance circle and control quantity limit area are defined as follows:

[0031] The performance circles are α-circle and β-circle: α-circle can be expressed in the complex plane as a circle with (-1, 0) as the center and δ1 as the radius; β-circle can be expressed in the complex plane as a circle with (-Re(G(jω)),-Im(G(jω))) as the center and δ2|G(jω)| as the radius;

[0032] The control amount limit area is the γ ring: the γ ring can be expressed in the complex plane as a circle with (0, 0) as the center, r γ_max and r γ_min A ring formed by two circles with a radius of

[0033] If the α circle, β circle and γ circle have an intersection, the controller design point selected in the intersection area is recorded as α d (jω), the expression of the designed controller K(jω) is as follows:

[0034] K(jω)=α d(jω)[(1+α d (jω))G 00 (jω)] -1 ;

[0035] If there is no intersection area on the complex plane, there is no controller that meets the anti-disturbance performance requirements. In this case, δ1 and δ2 are redesigned until there is a selectable controller area on the complex plane.

[0036] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0037] Compared to traditional anti-disturbance controller design methods, this invention defines an anti-disturbance control index that can accurately measure the anti-disturbance performance of the controller at different frequencies. Based on the defined anti-disturbance control index, a multi-objective optimization model is constructed. This allows the design of an anti-disturbance controller at any frequency point, fully meeting the characteristics of an ideal engine anti-disturbance controller design method mentioned in the background art.

[0038] The present invention further adopts parameter transformation and substitution to express the complex mathematical problem of optimal design of a controller with constraints as a geometric diagram problem of whether different circles intersect in a complex plane coordinate system, which is more intuitive and clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a diagram showing the frequency characteristics of interference in the embodiment;

[0040] Figure 2 Schematic diagram of α, β and γ circles in the embodiment. DETAILED DESCRIPTION

[0041] In response to the shortcomings of the existing technology, the solution of the present invention is to define an anti-disturbance control index that can accurately measure the anti-disturbance performance of the controller at different frequencies, and construct a multi-objective optimization model based on the defined anti-disturbance control index, so that the anti-disturbance controller can be designed at any frequency point. Then, by analyzing the frequency characteristics of the interference source, an aircraft engine steady-state anti-disturbance controller with excellent anti-disturbance performance can be obtained at the frequency point where the interference energy is concentrated.

[0042] The method for designing an aero-engine steady-state anti-disturbance controller proposed in the present invention comprises the following steps:

[0043] Step 1: For the steady-state operating point of the aircraft engine for which a steady-state anti-disturbance controller is to be designed, a linear model of the influence of disturbances on the steady-state point neighborhood of the steady-state operating point of the aircraft engine is established as follows:

[0044]

[0045] Among them, u is the control quantity of the aircraft engine, d is the interference quantity, y is the output feedback energy, z is the controllable output energy, G 00 is the open-loop transfer function from u to y, G 01 is the open-loop transfer function from d to y, G 10 is the open-loop transfer function from u to z, G 11 is the open-loop transfer function from d to z;

[0046] Step 2: transform the linear model into the frequency domain to obtain the frequency response function U(jω) of the control variable u after the controller acts in the frequency domain:

[0047] U(jω)=K(jω)Y(jω)

[0048] Where ω is the frequency, Y(jω) is the frequency response function of the output performance y; K(jω) is the frequency response function of the controller;

[0049] Step 3: Optimize the performance index η yd and η zd Minimum is the optimization goal, As the constraint condition, a multi-objective optimization model is established with the controller's frequency response function K(jω) as the quantity to be optimized; where δ1 and δ2 are the anti-disturbance performance requirements of the output feedback energy and the controllable output performance, respectively; γ min and γ max are the minimum and maximum values ​​of the control quantity respectively; G 01 (jω) and G 11 (jω) respectively represent G 01 and G 11 Frequency response function of T yd_c (jω) and T yd_c (jω) represent the closed-loop frequency response functions of the disturbance d to the output feedback energy y and the controllable energy z under the action of the controller K(jω), and their expressions are:

[0050] T yd_c (jω)=(1-G 00 (jω)K(jω)) -1 G 01 (jω)

[0051]

[0052] Step 4: Solve the established multi-objective optimization model to obtain the optimized steady-state anti-disturbance controller.

[0053] The above objective optimization model can be solved using various existing algorithms, such as the multi-objective ant colony algorithm and the multi-objective simulated annealing algorithm. Considering that the existing methods for solving the above optimization problems are generally complex and not intuitive, the present invention further proposes an optimization method based on complex plane geometric analysis, and uses this method to solve the established multi-objective optimization model, as follows:

[0054] Define α(jω) and β(jω) as the frequency domain response functions of feedback sensitivity and disturbance sensitivity, respectively, expressed as:

[0055]

[0056]

[0057] G 00 (jω) and G 10 (jω) respectively represent G 00 and G 10 The frequency response function of the controller can be transformed into the following structure:

[0058] |α(jω)+1|≤δ1

[0059] |α(jω)+G(jω)|≤δ2|G(jω)|

[0060] r γ_min ≤|α(jω)|≤r γ_max

[0061] Among them, r γ_max and r γ_min Respectively represent the upper and lower bounds of the modulus of α(jω); each inequality can correspond to a different circular area on the complex plane, and the intersection of all areas is represented as the selectable area of ​​the controller that meets all constraints;

[0062] The performance circle and control quantity limit area are defined as follows:

[0063] The performance circles are α-circle and β-circle: α-circle can be expressed in the complex plane as a circle with (-1, 0) as the center and δ1 as the radius; β-circle can be expressed in the complex plane as a circle with (-Re(G(jω)),-Im(G(jω))) as the center and δ2|G(jω)| as the radius;

[0064] The control amount limit area is the γ ring: the γ ring can be expressed in the complex plane as a circle with (0, 0) as the center, r γ_max and r γ_min A ring formed by two circles with a radius of

[0065] If the α circle, β circle and γ circle have an intersection, the controller design point selected in the intersection area is recorded as αd (jω), the expression of the designed controller K(jω) is as follows:

[0066] K(jω)=α d (jω)[(1+α d (jω))G 00 (jω)] -1 ;

[0067] If there is no intersection area on the complex plane, there is no controller that meets the anti-disturbance performance requirements. In this case, δ1 and δ2 are redesigned until there is a selectable controller area on the complex plane.

[0068] To facilitate public understanding, the technical solution of the present invention is described in detail below through an embodiment with reference to the accompanying drawings:

[0069] This embodiment is aimed at a certain type of aviation turbofan engine to develop a steady-state anti-disturbance controller. The specific design process is as follows:

[0070] Determine in advance the steady-state operating point of the aircraft engine for which the anti-disturbance controller needs to be designed, select the interference quantity that needs to be paid attention to and the performance variables for which the anti-disturbance performance optimization design needs to be carried out; this embodiment selects the steady-state operating condition of the engine cruise phase for research, considers the Mach number interference caused by atmospheric turbulence, and pays attention to the fan reduced speed N fc And the two output performances of thrust F can be used to carry out anti-interference performance optimization design.

[0071] A linear model of the influence of disturbances in the neighborhood of the steady-state point is established, and the frequency characteristics of the disturbance are analyzed to select the frequency ω that needs to be focused on when designing the anti-disturbance controller. In this embodiment, a linear model of the influence of disturbances in the neighborhood of the engine cruise steady-state point is established using the system identification method as follows:

[0072]

[0073] Where: W f is the fuel flow rate of the aircraft engine, Ma is the Mach number interference, N fc G is the fan speed equivalent to the output feedback energy, and F is the controllable output energy thrust. 00 is the open-loop transfer function from fuel flow to fan reduced speed, G 01 is the open-loop transfer function from Mach number interference to fan reduced speed, G 10 is the open-loop transfer function from fuel flow to thrust, G 11 is the open-loop transfer function from Mach number disturbance to thrust.

[0074] After system identification, G 00 , G 01 , G 10 and G11 The expression is as follows:

[0075]

[0076]

[0077] The frequency characteristics of the Mach number interference are as follows: Figure 1 As shown, in this embodiment, the frequencies that require special attention are 3 rad / s, 8 rad / s, and 15 rad / s.

[0078] The established linear model is transformed into the frequency domain, and the controller is designed using the geometric design frequency domain analysis method based on the anti-disturbance performance requirements. The specific process is as follows:

[0079] To measure the anti-interference performance of the controller at different frequencies, the present invention defines a performance optimization index η, which is characterized by the ratio of the modulus of the closed-loop frequency response function from the control variable to the output variable to the modulus of the open-loop frequency response function:

[0080]

[0081]

[0082] Among them, η yd and η zd are the performance optimization indicators of output feedback energy and controllable output energy respectively; G 01 (jω) and G 11 (jω) respectively represent G 01 and G 11 Frequency response function of T yd_c (jω) and T yd_c (jω) represents the closed-loop frequency response function from the disturbance d to the output feedback energy y and the controllable energy z under the action of the controller K(jω); T yd_c (jω) and T yd_c The expression of (jω) is:

[0083] T yd_c (jω)=(1-G 00 (jω)K(jω)) -1 G 01 (jω)

[0084]

[0085] The basic constraints of the controller optimization problem are:

[0086] η yd ≤δ1

[0087] η yd≤δ2

[0088] γ min ≤|U(jω)|≤γ max

[0089] δ1 and δ2 are the anti-interference performance requirements of output feedback energy and controllable output energy, respectively. min and γ max are the minimum and maximum values ​​of the control quantity, respectively, which represent the limitation of the control quantity itself. In this example, they are defined as δ1=1, δ2=1, γ min =0,γ max =0.04;

[0090] In this way, the design problem of the steady-state anti-disturbance controller of an aircraft engine is transformed into: finding a suitable K(jω) to optimize the performance index η under the conditions of satisfying the basic constraints and the frequencies ω = 3 rad / s, 8 rad / s and 15 rad / s. yd and η zd Achieve the minimum possible multi-objective optimization problem.

[0091] To solve the above controller optimization problem, this embodiment adopts a controller K(jω) optimization method based on complex plane geometric analysis, which is as follows:

[0092] Define α(jω) and β(jω) as the frequency domain response functions of feedback sensitivity and disturbance sensitivity, respectively, expressed as:

[0093]

[0094]

[0095] G 00 (jω) and G 10 (jω) respectively represent G 00 and G 10 The frequency response function of the controller can be transformed into the following structure:

[0096] |α(jω)+1|≤1

[0097] |α(jω)+G(jω)|≤|G(jω)|

[0098] r γ_min ≤|α(jω)|≤r γ_max

[0099] In the constrained inequality, r γ_max and r γ_minRespectively represent the upper and lower bounds of the α(jω) modulus value; each inequality can correspond to a different circular area on the complex plane, and the intersection of all areas represents the selectable area of ​​the controller that meets all constraints. The performance circle and control quantity limit circle drawn on the complex plane of this embodiment are as follows Figure 2 As shown, it can be seen that there is an intersection area, that is, there is a controller that can meet the anti-disturbance performance requirements.

[0100] At the intersection of all circles, the design point α d (jω) can be calculated by K(jω) = α d (jω)[(1+α d (jω))G 00 (jω)] -1 To obtain the controller that meets the anti-disturbance performance requirements, take the design point α d (jω)=-1.15-0.02j, then the controllers designed at each selected frequency point of interest are:

[0101] ω=3rad / s:K(jω)=29.43+46.9j;

[0102] ω=8rad / s:K(jω)=23.48+148.2j;

[0103] ω=15rad / s:K(jω)=27.5+304.7j.

Claims

1. A method for designing a steady-state anti-disturbance controller for an aircraft engine, characterized in that: The following steps are involved: Step 1: For the steady-state operating point of the aircraft engine for which a steady-state anti-disturbance controller needs to be designed, a linear model of the steady-state point neighborhood with disturbance influence of the steady-state operating point of the aircraft engine is established as follows: Among them, u is the control quantity of the aircraft engine, d is the disturbance quantity, y is the output feedback energy, z is the controllable output energy, G 00 is the open-loop transfer function from u to y, G 01 is the open-loop transfer function from d to y, G 10 is the open-loop transfer function from u to z, G 11 is the open-loop transfer function from d to z; Step 2: transform the linear model to the frequency domain to obtain the frequency response function U(jω) of the control quantity u after the controller acts in the frequency domain: U(jω)=K(jω)Y(jω) Where ω is the frequency, Y(jω) is the frequency response function of the output performance y; K(jω) is the frequency response function of the controller; Step 3: Optimize the performance index η yd and η zd Minimum is the optimization goal, As the constraint condition, a multi-objective optimization model is established with the frequency response function K(jω) of the controller as the quantity to be optimized; where δ1 and δ2 are the anti-disturbance performance requirements of the output feedback energy and the controllable output performance quantity respectively; γ min and γ max are the minimum and maximum values ​​of the control quantity respectively; G 01 (jω) and G 11 (jω) respectively represent G 01 and G 11 The frequency response function of T yd_c (jω) and T yd_c (jω) respectively represent the closed-loop frequency response function of the disturbance d to the output feedback energy y and the controllable energy z under the action of the controller K(jω), and the expressions of the two are: T yd_c (jω)=(1-G 00 (jω)K(jω)) -1 G 01 (jω) Step 4: Solve the established multi-objective optimization model to obtain an optimized steady-state anti-disturbance controller.

2. The method for designing a steady-state anti-disturbance controller for an aircraft engine as claimed in claim 1, characterized in that: The established multi-objective optimization model is solved using an optimization method based on complex plane geometric analysis, as follows: Define α(jω) and β(jω) as the frequency domain response functions of feedback sensitivity and disturbance sensitivity, respectively, expressed as: G 00 (jω) and G 10 (jω) respectively represent G 00 and G 10 The frequency response function of the controller can be transformed into the following structure: |α(jω)+1|≤δ1 |α(jω)+G(jω)|≤δ2|G(jω)| r γ_min ≤|α(jω)|≤r γ_max Among them, r γ_max and r γ_min They represent the upper and lower bounds of the modulus of α(jω) respectively; each inequality can correspond to a different circular area on the complex plane, and the intersection of all areas is represented as the selectable area of ​​the controller that satisfies all constraints; The performance circle and control volume limit area are defined as follows: The performance circles are α circle and β circle: α circle can be expressed in the complex plane as a circle with (-1, 0) as the center and δ1 as the radius; β circle can be expressed in the complex plane as a circle with (-Re(G(jω)),-Im(G(jω))) as the center and δ2|G(jω)| as the radius; The control volume restriction area is the γ ring: The γ ring can be expressed in the complex plane as a circle with (0, 0) as the center and r γ_max and r γ_min A ring formed by two circles with a radius of If the α circle, β circle and γ circle have an intersection, the controller design point selected in the intersection area is recorded as α d (jω), then the expression of the designed controller K(jω) is as follows: K(jω)=α d (jω)[(1+α d (jω))G 00 (jω)] -1 ; If there is no intersection area on the complex plane, there is no controller that meets the anti-disturbance performance requirements, and δ1 and δ2 are redesigned until there is a selectable area for the controller on the complex plane.

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