A method for index allocation of control loops based on feasible region

Abstract

The application belongs to the technical field of electric signal processing, and particularly relates to a method for index allocation of a control loop based on a feasible region, which comprises the following steps: S1, establishing a general mathematical model of each servo loop of an aero-engine control system, wherein the general mathematical model comprises PID control parameters, an integral link, an inertia link, a delay link and loop feedback; S2, calculating a closed-loop transfer function based on the general mathematical model; S3, obtaining a plurality of performance indexes given by the servo loop, respectively calculating the value range of a time constant and loop gain under each performance index based on the closed-loop transfer function, adjusting the performance indexes until the intersection of the value range of the time constant and the loop gain is not an empty set when the intersection is an empty set, and taking the intersection as a feasible region; and S4, determining the performance indexes of the servo loop based on the feasible region, and allocating the performance indexes to actuators, feedback systems and controllers in the servo loop.

Description

Technical Field

[0001] This application belongs to the field of electrical signal processing technology, and specifically relates to a method for allocating indexes of control loops based on feasible regions. Background Technology

[0002] As a crucial component of aero-engines, the control system is key to ensuring engine function and performance. Servo loops involved in aero-engine control systems typically include main fuel metering valve control (Lm), afterburner fuel metering valve control (Lx), fan / compressor guide vane control (A1, A2), and nozzle throat area control (A8) loops. These control loops generally consist of a digital electronic controller, electro-hydraulic servo valves, metering devices / actuators, and sensors. The controller needs to perform input / output signal conversion and processing, filtering, and the implementation of control laws and algorithms. Under the influence of driving current, the electro-hydraulic servo valves output flow to the metering device or the rod / rodless chamber of the actuator, and output signals to feedback sensors, thus forming the control loop.

[0003] Existing technologies combine the architecture used in control systems of similar engines and use experimental methods to conduct feasibility assessments of newly developed control systems. However, they lack effective means to take into account multiple engine indicators and allocate positive indicators. Summary of the Invention

[0004] To address the aforementioned problems, this application provides a method for allocating control loop indices based on the feasible region, including:

[0005] Step S1: Establish a general mathematical model for each servo loop of the aero-engine control system. The general mathematical model includes: PID control parameters, integral element, inertial element, delay element, and loop feedback.

[0006] Step S2: Calculate the closed-loop transfer function based on the general mathematical model;

[0007] Step S3: Obtain multiple performance indicators given by the servo loop, and calculate the range of time constant and loop gain under each performance indicator based on the closed-loop transfer function. When the intersection of the range of time constant and loop gain is an empty set, adjust the performance indicators until the intersection is not an empty set, and take the intersection as the feasible region.

[0008] Step S4: Determine the performance index of the servo loop based on the feasible domain, and allocate the performance index to the actuator, feedback system and controller in the servo loop.

[0009] Preferably, the performance indicators include: overshoot, rise time, settling time, steady-state error, following error, phase margin, and gain margin.

[0010] Preferably, before establishing the closed-loop transfer function, the general mathematical model is simplified. The simplification includes: simplifying the delay element into an inertial element, treating multiple inertial elements into one inertial element based on bandwidth equivalence, and retaining only the proportional term of the PID control parameters.

[0011] Preferably, the servo circuit includes, but is not limited to, the main fuel metering valve control circuit, the fan / compressor guide vane control circuit, the nozzle throat area circuit, and the afterburner fuel metering valve control circuit. The actuator metering devices of the main fuel metering valve control circuit and the afterburner fuel metering valve control circuit are simplified into integral links. The actuator cylinder of the fan / compressor guide vane control circuit is simplified into an integral link. The fuel distribution valve and the nozzle actuator cylinder of the nozzle throat area circuit are both simplified into integral links. The fuel distribution valve becomes an inertial link after the loop is closed.

[0012] Preferably, the closed-loop transfer function CLTF is:

[0013]

[0014] In the formula, G(s) is the forward channel transfer function, H(s) is the feedback loop transfer function, and ω n For natural frequency, ξ is the damping ratio. T is the time constant of the inertial element after the equivalence in the loop, and K is the loop gain.

[0015] Preferably, step S4 is followed by:

[0016] Step S5: Establish a verification model for the servo loop, substitute the performance indicators of the servo loop determined based on the feasible domain into the verification model for verification, and verify the matching with the parameters and tolerances of each component of the servo loop.

[0017] If all verifications are successful, proceed to step 6; otherwise, redetermine the performance indicators of the servo loop in the feasible domain until all verifications are successful.

[0018] Step 6 involves sequentially performing desktop simulation verification of the servo loop, large closed-loop desktop simulation verification, hardware-in-the-loop simulation verification, semi-physical simulation verification, and engine simulation verification. If all verification results are satisfactory, the design is complete; otherwise, the servo loop specifications are modified, the time constant of the equivalent inertial element in the loop is optimized, or the overall specification requirements are iterated. Hardware-in-the-loop simulation verification, also known as hardware-in-the-loop, means that only the controller is a physical component. The process—desktop simulation → hardware-in-the-loop → semi-physical → complete engine—is a gradually realistic verification process, allowing for problem identification and iterative design iteration.

[0019] Preferably, the method for calculating the range of values ​​for the time constant and loop gain based on the overshoot σ% includes:

[0020] Obtain the upper limit value of overshoot σ max %, to obtain the lower limit ξ of the damping ratio. min :

[0021]

[0022] The lower limit of the damping ratio ξ min As an intermediate variable, combined with the formula get:

[0023]

[0024] Preferably, the rise time t r The inequalities relating to time constant and loop gain include:

[0025]

[0026] t r-max The given maximum adjustment time.

[0027] Preferably, the adjustment time t s The inequalities relating to time constant and loop gain include:

[0028]

[0029] Preferably, the inequalities between phase margin and time constant, and loop gain include:

[0030]

[0031] PM min This represents the minimum phase margin of the system.

[0032] The advantages of this application include: it can simultaneously consider multiple indicators when selecting control accessories in the early stages of scheme design, which has strong engineering practicality and can significantly improve the forward design capability of the control system. Attached Figure Description

[0033] Figure 1 It is a simplified mathematical model of the servo loop;

[0034] Figure 2 It is a general linear mathematical model for servo loops;

[0035] Figure 3 It is a graph showing the time constant and loop gain of the equivalent inertial element under overshoot constraint;

[0036] Figure 4 It is a graph showing the time constant and loop gain of the equivalent inertial element under rise time constraints;

[0037] Figure 5 It is a graph showing the time constant and loop gain of the equivalent inertial element under the following error constraint;

[0038] Figure 6 It is a graph showing the time constant and loop gain of the equivalent inertial element under frequency domain constraints;

[0039] Figure 7 This is a schematic diagram of the feasible region;

[0040] Figure 8 This is a flowchart of the quota allocation process for this application;

[0041] Figure 9 This is a schematic diagram of a servo control loop. Detailed Implementation

[0042] To make the technical solution and advantages of this application clearer, the technical solution of this application will be described in a clearer and more complete manner below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some embodiments of this application, and are only used to explain this application, not to limit this application. It should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings. Other related parts can be referred to the general design. In the absence of conflict, the embodiments and technical features in the embodiments of this application can be combined with each other to obtain new embodiments.

[0043] like Figure 8 As shown, the specific process of a method for allocating control loop indicators based on the feasible region is as follows:

[0044] I. Establishing a general simplified mathematical model for the servo loop

[0045] Modeling the servo loops (main fuel metering valve control Lm, fan / compressor guide vane control a1, a2, nozzle throat area A8, afterburner fuel metering valve control Lx), the actuator metering device in the Lm / Lx loop is simplified to an integral element, the actuator cylinder in a1 / a2 is simplified to an integral element, and both the fuel distribution valve and the nozzle actuator in the A8 control loop are simplified to integral elements. This results in an inertial element after the fuel distribution valve closes in. For multiple inertial elements, they can be simplified to a single inertial element based on bandwidth equivalence, resulting in a mathematical model with the same structure, such as... Figure 1 As shown. The parameters are defined as follows:

[0046] Parameter Definitions

[0047]

[0048] Further simplification of the model allows us to reduce the delay element to an inertial element, treat multiple inertial elements as a single inertial element based on bandwidth equivalence, and retain only the proportional term as the control parameter.

[0049] A general linear mathematical model for the servo loop can be obtained, such as Figure 2 As shown.

[0050] II. Establishing the Open-Loop Transfer Function of the Servo Loop

[0051] based on Figure 2 A general linear mathematical model for servo loops is used to calculate their open-loop transfer function.

[0052]

[0053] The simplified loop model is a typical second-order system, and its closed-loop transfer function is:

[0054]

[0055] In the formula, the natural frequency Damping ratio Where T is the time constant of the inertial element after the equivalence in the loop, and K is the loop gain.

[0056] III. Feasible Region Analysis

[0057] Each performance index has a mutually restrictive relationship with the K and T coefficients. Therefore, each index needs to be calculated separately, and their intersection taken to obtain the feasible region of K and T. In dual-loop control, the inner loop response speed must be fast; during calculation, ensure that the inner loop damping ratio ξ is less than 1. For example... Figures 3-6 As shown.

[0058] 1. Overshoot σ%

[0059] σ% is a relative value. Considering the step response performance index, the overshoot of the second-order system's step response is...

[0060]

[0061] If the overshoot is required to not exceed σ max %, to obtain the lower limit of the damping ratio:

[0062]

[0063] ξ min As an intermediate variable, because get

[0064]

[0065] It can be seen that the lower limit of the damping ratio can be solved from the overshoot index, and then the K and T constraint boundaries can be solved.

[0066] 2. Rise time t r

[0067] Considering the step response performance indicators, the rise time of the step response of a second-order system is...

[0068]

[0069] get

[0070]

[0071] If the rise time requirement is no greater than t r-max ,available

[0072]

[0073] It can be seen that the K and T constraint boundaries can be solved by the lower limit of the damping ratio and the rise time index.

[0074] 3. Adjusting time t s

[0075] Considering the step response performance indicators, the settling time of the second-order system's step response is:

[0076]

[0077] get

[0078]

[0079] If the adjustment time requirement is t s ≤t s-max , ξ≥ξ min We cannot obtain K and T constraints, but we can rely on t. r-max and ξ min , to obtain t s The range.

[0080]

[0081] It can be seen that the range of the settling time Ts can be obtained from the lower limit of the damping ratio and the rise time index.

[0082] 4. Steady-state error

[0083] The open-loop transfer function indicates that the system is a type I system with zero steady-state error. However, the actual system exhibits nonlinear characteristics, requiring experimental exploration to identify and incorporate integral components to reduce steady-state error.

[0084] 5. Following error ε%

[0085] ε% is a relative value. When proposing the follow-up error index, the rate of change of the ramp signal must be specified; otherwise, it cannot be evaluated.

[0086] If the full stroke of the main fuel metering valve is L, the rate of change of the ramp signal is R, and the loop gain is K, then

[0087]

[0088] It can be seen that, given R and L, ε% is only related to the loop gain. If the ε% index is not up to standard, it indicates that the loop gain K is small. The following error can be reduced by increasing the speed of the actuator or increasing the proportional coefficient of the controller.

[0089] Therefore, the K-boundary can be solved using the following error index.

[0090] 6. Phase margin

[0091] Let ω c Let P be the system's cutoff frequency, and PM be the system's phase margin. Then:

[0092] PM = 180° + ∠G(jω) c )

[0093]

[0094] It can be seen that the phase margin, damping ratio, and overshoot correspond one-to-one.

[0095] get

[0096]

[0097] It can be seen that the K and T constraint boundaries can be solved using the phase margin index.

[0098] 7. Gain Margin

[0099] Let ω x Let be the system's crossover frequency, and GM be the system's gain margin. Then:

[0100]

[0101] We can obtain ω x →infinity,

[0102] The ranges of K and T can be determined based on the relationship between each indicator and the constraints of K and T.

[0103] Finally, the intersection of the K and T ranges obtained from each indicator is defined as the feasible region of K and T.

[0104] IV. Indicator Allocation and Servo Loop Indicator Matching

[0105] Taking into account the constraints of various indicators, ensure Figure 7The feasible region is not empty. At the same time, it is necessary to evaluate the time constant of the inertial element of the control loop in combination with the actual situation of the control system software / hardware. If the evaluation result T is not within the feasible region, it is necessary to go back and modify the small closed-loop index or improve the time constant of the inertial element of the loop by improving the software / hardware, iteratively adjust, and finally determine the loop gain and small closed-loop index.

[0106] The feasible region analysis of the servo loop has been completed, and the loop gain range has been determined. The next step is to break it down into the actuator, feedback, and controller. The actuator's feasibility needs to be considered, and the controller parameters can be adjusted accordingly.

[0107] Indicator Allocation List

[0108]

[0109] The flowchart for indicator allocation is as follows: Figure 8 As shown, where:

[0110] Note 1: A: Modify servo loop specifications; B: Optimize the time constant of the loop's equivalent inertial element; C: Iterate on the overall specification requirements. The priority is A, then B, then C. The priority of A and B needs to be determined based on expert experience.

[0111] Note 2: After completing Node 2, it is necessary to evaluate the time constant of the equivalent inertial element of the loop (including the time constant of the delay element and the inertial element) based on relevant model development experience, and solve the loop gain range according to the initially allocated servo loop indicators. If the indicators cannot be found to intersect, the servo loop indicators should be modified or the time constant of the equivalent inertial element of the loop should be optimized.

[0112] Note 3: When simplifying the model at node 2, only the proportional term is retained for the control parameters. At node 7, nonlinear factors such as delay, zero drift, and dead zone need to be added, and then derivative or integral terms are introduced. Integral terms can overcome the influence of dead zone and eliminate steady-state error caused by zero drift. Derivative terms can improve system overshoot and oscillation caused by delay (friction, hysteresis). The tolerance range of each component can be determined by combining the control parameter bias and nonlinear factor bias simulation.

[0113] Note 4: When performing large closed-loop simulation verification at node 10, if there is already a specific control logic and engine nonlinear model, all performance indicators in the overall requirements can be simulated and verified and iterated. If not, the key indicators can be simulated and verified and iterated based on the engine transfer function model.

[0114] Note 5: When verifying nodes 9, 10, 11, and 12, if the index requirements are not met, the servo loop index (A) should be modified first, or the time constant of the equivalent inertial element of the loop should be optimized (B). If the overall index requirements are still not met, then proceed to C, that is, iterate on the overall index requirements.

[0115] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for allocating indexes to control loops based on feasible regions, characterized in that, include: Step S1: Establish a general mathematical model for each servo loop of the aero-engine control system. The general mathematical model includes: PID control parameters, integral element, inertial element, delay element, and loop feedback. Step S2: Calculate the closed-loop transfer function based on the general mathematical model; Step S3: Obtain multiple performance indicators given by the servo loop, and calculate the range of time constant and loop gain under each performance indicator based on the closed-loop transfer function. When the intersection of the range of time constant and loop gain is an empty set, adjust the performance indicators until the intersection is not an empty set, and take the intersection as the feasible region. Step S4: Determine the performance indicators of the servo loop based on the feasible domain, and allocate the performance indicators to the actuators, feedback systems, and controllers in the servo loop; Before establishing the closed-loop transfer function, the general mathematical model is simplified. The simplification includes: simplifying the delay element into an inertial element, treating multiple inertial elements into one inertial element based on bandwidth equivalence, and retaining only the proportional term in the PID control parameters. The servo circuit includes, but is not limited to, the main fuel metering valve control circuit, the fan / compressor guide vane control circuit, the nozzle throat area circuit, and the afterburner fuel metering valve control circuit. The actuator metering devices of the main fuel metering valve control circuit and the afterburner fuel metering valve control circuit are simplified into integral links. The actuator cylinder of the fan / compressor guide vane control circuit is simplified into an integral link. The fuel distribution valve and the nozzle actuator cylinder of the nozzle throat area circuit are both simplified into integral links. The fuel distribution valve becomes an inertial link after the loop is closed. The closed-loop transfer function for: ； In the formula, For the forward channel transfer function, For the feedback loop, the transfer function, For natural frequency, , For the damping ratio, T is the time constant of the inertial element after the loop is equivalent, and K is the loop gain; Step S4 is followed by: Step S5: Establish a verification model for the servo loop, substitute the performance indicators of the servo loop determined based on the feasible domain into the verification model for verification, and verify the matching with the parameters and tolerances of each component of the servo loop. If all verifications are successful, proceed to step 6; otherwise, redetermine the performance indicators of the servo loop in the feasible domain until all verifications are successful. Step 6 involves sequentially performing desktop simulation verification of the servo loop, desktop simulation verification of the large closed loop, hardware-in-the-loop simulation verification, semi-physical simulation verification, and engine simulation verification. If all verification results are satisfactory, the design is complete; otherwise, the servo loop specifications are modified, the time constant of the equivalent inertial element of the loop is optimized, or the overall specification requirements are iterated. Based on overshoot Methods for calculating the range of values ​​for the time constant and loop gain include: Get the upper limit of overshoot The lower limit of the damping ratio is obtained. : ； Lower limit of damping ratio As an intermediate variable, combined with the formula get: ； Ascent Time The inequalities relating to time constant and loop gain include: ； Given the maximum settling time; Adjusting time The inequalities relating to time constant and loop gain include: ； The inequalities between phase margin and time constant, and loop gain include: ； PM min This represents the minimum phase margin of the system. At the same time, it is necessary to evaluate the time constant of the inertial element of the control loop in combination with the actual situation of the control system software / hardware. If the evaluation result T is not within the feasible region, it is necessary to go back and modify the small closed-loop index or improve the time constant of the inertial element of the loop by improving the software / hardware, iteratively adjust, and finally determine the loop gain and small closed-loop index.

2. The method for allocating control loop indicators based on feasible region as described in claim 1, characterized in that, The performance indicators include: overshoot, rise time, settling time, steady-state error, following error, phase margin, and gain margin.

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