WO2021027093A1 - 一种涡扇发动机控制系统主动容错控制方法 - Google Patents
一种涡扇发动机控制系统主动容错控制方法 Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
- F02C—GAS-TURBINE PLANTS; AIR INTAKES FOR JET-PROPULSION PLANTS; CONTROLLING FUEL SUPPLY IN AIR-BREATHING JET-PROPULSION PLANTS
- F02C9/00—Controlling gas-turbine plants; Controlling fuel supply in air- breathing jet-propulsion plants
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
- G05B23/0254—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model based on a quantitative model, e.g. mathematical relationships between inputs and outputs; functions: observer, Kalman filter, residual calculation, Neural Networks
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2220/00—Application
- F05D2220/30—Application in turbines
- F05D2220/32—Application in turbines in gas turbines
- F05D2220/323—Application in turbines in gas turbines for aircraft propulsion, e.g. jet engines
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2260/00—Function
- F05D2260/80—Diagnostics
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2260/00—Function
- F05D2260/81—Modelling or simulation
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2260/00—Function
- F05D2260/82—Forecasts
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2270/00—Control
- F05D2270/30—Control parameters, e.g. input parameters
- F05D2270/305—Tolerances
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2270/00—Control
- F05D2270/40—Type of control system
- F05D2270/46—Type of control system redundant, i.e. failsafe operation
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2270/00—Control
- F05D2270/70—Type of control algorithm
- F05D2270/701—Type of control algorithm proportional
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2270/00—Control
- F05D2270/70—Type of control algorithm
- F05D2270/71—Type of control algorithm synthesized, i.e. parameter computed by a mathematical model
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2270/00—Control
- F05D2270/80—Devices generating input signals, e.g. transducers, sensors, cameras or strain gauges
- F05D2270/803—Sampling thereof
Definitions
- the present invention relates to an active fault-tolerant control method for a turbofan engine control system, which belongs to the technical field of aviation control. Specifically, it refers to the concurrent failure of an actuator and a sensor in a turbofan engine control system, and there is external disturbance. Next, the method of fault estimation and active fault tolerance control.
- Turbofan engines are widely used in civil and military aircraft, and their safety and reliability are closely related to flight safety.
- the control system ensures the safety and performance of the turbofan engine in the full flight envelope.
- the function realization of the control system needs to rely on a large number of sensors and actuators. If some of the components fail, it will be difficult to achieve the desired control effect and even affect flight safety. Therefore, it is of great significance to monitor the performance of the turbofan engine control system, estimate and warn the fault status in real time, and take corresponding fault-tolerant control measures.
- the literature shows that the existing turbofan engine control system uses fault diagnosis and passive fault-tolerant control for the fault handling of sensors and actuators, that is, the control algorithm adopts a control method that combines PID and Min/Max switching.
- the turbofan engine The operating conditions and the output speed, temperature, pressure and other measurable parameters based on the Kalman filter are used to judge whether the sensors and actuators of the control system are faulty. When a fault occurs, further use based on hardware redundancy and control Passive fault-tolerant control of loop switching.
- the existing methods can ensure the safe operation of turbofan engines, they are somewhat conservative, which are mainly reflected in the following points:
- the PID+Min/Max control method will affect the control bandwidth, amplitude/phase margin of the aeroengine As well as the introduction of undesirable characteristics in terms of response speed, it is difficult to obtain fast dynamic response characteristics.
- the fault is only detected, that is, as soon as a fault occurs, a conservative passive fault-tolerant control method such as hardware redundancy or control loop switching is used for processing.
- the use of hardware redundancy will inevitably lead to a waste of hardware resources; based on controller switching
- the fault-tolerant control is at the expense of some performance indicators to ensure the safe operation of aero engines.
- the traditional passive fault-tolerant control has great limitations, that is, it is necessary to consider all possible fault conditions in advance, resulting in the controller having a certain Conservativeness. It is worth mentioning that the turbofan control system is often interfered by noise signals. The existing method has no ideal solution for fault-tolerant control of the sensor and actuator faults of the turbofan engine control system under the interference signal.
- the present invention provides an active fault-tolerant control method for the turbofan engine control system.
- LUV linear variable parameter
- the adaptive estimation of the fault amplitude of the sensor and the actuator is realized, and the fault signal is accurately reconstructed.
- an active fault-tolerant control strategy based on virtual actuators is designed. Without the need to redesign the controller, through the designed active fault-tolerant control strategy, under the premise of ensuring the stability of the control system, The control effect is similar to the non-fault state of the control system.
- An active fault-tolerant control method for a turbofan engine control system includes the following steps:
- Step 1 Based on the turbofan engine test data, establish a turbofan engine LPV model:
- x ⁇ R n is the state variable
- u c ⁇ R m is the control input of the turbofan engine
- d ⁇ R q is the disturbance signal
- the scheduling parameter ⁇ is the normalized turbofan Engine high pressure turbine relative converted speed
- ⁇ min ⁇ max , ⁇ min and ⁇ max are the minimum and maximum values of scheduling parameters, respectively, the system matrix A( ⁇ ) ⁇ R n ⁇ n , B( ⁇ ) ⁇ R n ⁇ m , C ⁇ R p ⁇ n , E ⁇ R n ⁇ q , G ⁇ R p ⁇ q
- R ( ⁇ ) represents a ( ⁇ )-dimensional real number column vector
- R a ⁇ b represents a ⁇ b-dimensional real number matrix
- Step 2 Design a robust tracking controller for LPV gain scheduling for the turbofan engine LPV model with disturbances
- Step 2.1 Introduce a new state variable x e , defined as
- Step 2.2 For equation (3), construct and solve the following linear matrix inequality LMIs:
- Step 2.3 Calculate the output of the robust tracking controller for LPV gain scheduling:
- Step 3 For the turbofan engine LPV model with disturbances and sensor and actuator faults, based on the robust H ⁇ optimization method, establish an adaptive fault estimator for the turbofan engine to realize the fault estimation of the sensor and actuator;
- Step 3.1 Consider that there are actuator and sensor failures in the turbofan engine control system.
- the failure system is represented by equation (6):
- x f ⁇ R n is the fault system state variable
- u ⁇ R m is the fault system control input
- y f ⁇ R p is the fault system measurement output
- f [f a T f s T ]
- ⁇ R l is the fault signal
- B f ( ⁇ ) ⁇ R n ⁇ m is the fault system matrix
- F f ( ⁇ ) ⁇ R n ⁇ l and H f ( ⁇ ) ⁇ R p ⁇ l are the fault matrices of the actuator and the sensor respectively;
- Step 3.2 Separate the time-varying part from the time-invariant part in formula (6) and rewrite it as follows
- x e ⁇ R k , u e [u T y f T ] T ⁇ R (p+m) and Respectively represent the state variable, control input and fault estimation output of the fault estimator, z e ⁇ ⁇ R r and w e ⁇ ⁇ R r respectively represent the input and output of the time-varying part of the fault estimator,
- a e ⁇ R k ⁇ k , B e1 ⁇ R k ⁇ (m+p) , B e2 ⁇ R k ⁇ r , C e1 ⁇ R l ⁇ k , C e2 ⁇ R r ⁇ k , De11 ⁇ R l ⁇ (p+m) , De12 ⁇ R l ⁇ r , De21 ⁇ R r ⁇ (p+m) and De22 ⁇ R r ⁇ r are the coefficient matrix of the fault estimator to be designed;
- Step 3.3 Construct a state space joint representation of the turbofan engine fault system equation (7) and fault estimator equation (8):
- ⁇ is the estimation matrix of the fault estimator
- L, V, and Y respectively represent the sub-matrix block of X
- J, W, and Z respectively represent the sub-matrix block of X -1 ;
- Q 1 , Q 2 , and Q 3 represent the sub-matrix blocks of Q respectively
- S 1 , S 2 , S 3 , and S 4 represent the sub-matrix blocks of S respectively
- R 1 , R 2 , and R 3 represent the sub-matrix blocks of R respectively.
- N L and N J are [C 3 D 31 D 32 ] and Basis of nuclear space;
- Step 3.5 Further, according to the solution result of step 3.4, solve X in (17):
- Step 3.6 Solve the following LMIs to obtain the estimated matrix ⁇ of the fault estimator
- Step 4 According to the fault estimation result, design the turbofan engine active fault-tolerant controller based on the virtual actuator, so that the control system is stable without redesigning the controller, and the control effect is similar to that of the trouble-free system;
- Step 4.1 Consider the turbofan engine failure system. When there are sensor and actuator failures, design a virtual actuator based on the reconstruction principle.
- the state space model of the reconstruction system is expressed as follows:
- x ⁇ is the state variable of the virtual actuator
- C ⁇ ( ⁇ ) M( ⁇ )
- D ⁇ ( ⁇ ) N( ⁇ )
- z re is the controlled output of the reconstructed system
- M( ⁇ ) and N( ⁇ ) are the waiting matrices in the active fault-tolerant control law
- i 1, 2
- ⁇ is the minimum attenuation rate of the LMI region
- r is the radius of the LMI region
- q is the center of the circle
- ⁇ is the angle between the closed loop pole in the LMI region and the horizontal axis
- Step 4.3 Calculation among them, Means Pseudo-inverse
- Step 4.4 Calculate the system matrix:
- the active fault-tolerant controller of the turbofan engine control system designed by the method of the present invention is aimed at when the actuator and sensor failures of the turbofan engine control system occur simultaneously, without the need to redesign the controller.
- the designed reconfiguration controller makes the control system stable and obtains a speed tracking effect similar to that of a trouble-free system.
- Figure 1 is the design flow chart of the active fault-tolerant controller for the sensor and actuator of the turbofan aeroengine control system
- Figure 2 is a block diagram of a robust tracking controller for turbofan engine LPV gain scheduling
- Figure 3(a) is the simulation result of the robust tracking control of the turbofan engine LPV gain scheduling when the relative converted speed of the high-pressure rotor is 88%;
- Figure 3(b) is the simulation result of the robust tracking control of the turbofan engine LPV gain scheduling when the relative conversion speed of the high-pressure rotor is 94%;
- Figure 4 is a block diagram of a turbofan engine fault estimator
- Figure 5(a) is the result of sensor fault estimation for turbofan engine
- Figure 5(b) is the result of the turbofan engine's fault estimation result for the actuator
- Figure 6 is a block diagram of an active fault-tolerant controller for sensors and actuators of turbofan aeroengine control system
- Figure 7(a) is the output of the faulty system when the relative converted speed of the high-pressure rotor is 90%;
- Figure 7(b) shows the output of the faulty system when the relative converted speed of the high-pressure rotor is 94%
- Figure 8(a) is the normal output result of the turbofan engine control system when the relative conversion speed of the high-pressure rotor is 90%;
- Figure 8(b) is the result of active fault-tolerant control of the turbofan engine control system when the relative converted speed of the high-pressure rotor is 90%;
- Figure 9(a) is the normal output result of the turbofan engine control system when the relative converted speed of the high-pressure rotor is 94%;
- Figure 9(b) shows the result of active fault-tolerant control of the turbofan engine control system when the relative converted speed of the high-pressure rotor is 94%.
- the research object of the present invention is a turbofan engine after the failure of the control system sensor and the actuator.
- the design method is shown in the flowchart in Figure 1, and the detailed design steps are as follows.
- Step 1 Based on the turbofan engine test data, establish a turbofan engine LPV model:
- the scheduling parameter ⁇ is the normalized relative conversion speed of the turbofan engine high-pressure turbine, and -1 ⁇ 1, so the time-varying parameter ⁇ forms a parameter polyhedron with -1 and 1 as the vertices, and the disturbance d takes the standard deviation Gaussian white noise of 0.0001.
- Step 2 As shown in Figure 2, for the turbofan engine LPV model with disturbances, design the LPV gain scheduling robust tracking controller.
- V 1 [5589 -3460 -946]
- V 2 [5894 -1975 -2096]
- the gain of the speed tracking controller can change with the change of the time-varying parameter ⁇ , and has scheduling characteristics.
- the turbofan engine LPV Gain scheduling robust tracking control simulation results it can be seen from the simulation results that the designed LPV speed tracking controller can ensure that the output responds quickly and tracks the reference command, whether it is for the vertex or non-vertex parameters. Therefore, the controller is within the range of the full-time varying parameters. Both have good control performance, can realize tracking stably and quickly, and have good robustness and stability.
- Step 3 Establish an adaptive fault estimator for turbofan engine, as shown in Figure 4, to realize fault estimation of sensors and actuators.
- the turbofan engine control system has actuator and sensor failures, as shown in (28)
- the time-varying parameter ⁇ is measurable in real time and it is assumed to change as follows
- x e ⁇ R k , u e [u T y f T ] T ⁇ R (p+m) and Respectively represent the state variable, control input and fault estimation output of the fault estimator, z e ⁇ ⁇ R r and w e ⁇ ⁇ R r respectively represent the input and output of the time-varying part of the fault estimator,
- a e ⁇ R k ⁇ k , B e1 ⁇ R k ⁇ (m+p) , B e2 ⁇ R k ⁇ r , C e1 ⁇ R l ⁇ k , C e2 ⁇ R r ⁇ k , De11 ⁇ R l ⁇ (p+m) , De12 ⁇ R l ⁇ r , De21 ⁇ R r ⁇ (p+m) and De22 ⁇ R r ⁇ r are the coefficient matrices of the fault estimator to be designed.
- ⁇ is the estimation matrix of the fault estimator.
- L, V, and Y respectively represent the sub-matrix block of X
- J, W, and Z respectively represent the sub-matrix block of X -1 .
- Q 1 , Q 2 , and Q 3 represent the sub-matrix blocks of Q respectively
- S 1 , S 2 , S 3 , and S 4 represent the sub-matrix blocks of S respectively
- R 1 , R 2 , and R 3 represent the sub-matrix blocks of R respectively.
- Matrix block Respectively represent the sub-matrix blocks of P ⁇ , Respectively Submatrix block, Respectively Submatrix block, Respectively The sub-matrix block.
- N L and N J are [C 3 D 31 D 32 ] and The basis of nuclear space.
- Figure 5 shows the estimation results of the proposed fault estimator when a sudden fault occurs in the sensor and actuator of the control system. It can be seen from the simulation results that the proposed LPV fault estimator can adaptively adjust parameters, adapt to the current system dynamics, quickly detect faults, and accurately reconstruct fault signals.
- Step 4 According to the fault estimation result, design the turbofan engine active fault-tolerant controller based on the virtual actuator, as shown in Figure 6.
- Figure 7 shows the output of the fault system when the relative converted speed of the high-pressure rotor is 90% and 94%, respectively. It can be seen that in the fault state, the system output is quite different from the fault-free state.
- the simultaneous LMIs of (22)-(24) solve the positive definite matrix X v , Y 1 and Y 2 .
- Figures 8 and 9 are the results of the normal output of the control system and the faulty system after active fault-tolerant control when the relative converted speed of the high-pressure rotor is 90% and 94%, respectively. Compared. It can be seen from the simulation results that after the introduction of the active fault-tolerant controller, the control performance of the reconstructed system is similar to that of the fault-free system, the fault is hidden, and the active fault tolerance is realized. In addition, due to the use of virtual actuators for reconstruction, the redesign of the original speed tracking controller is avoided, and the complexity of system maintenance is reduced, which is of great significance to engineering applications.
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Abstract
一种涡扇发动机控制系统主动容错控制方法,设计一个具有良好动态性能的线性变参数增益调度鲁棒跟踪控制器。根据涡扇发动机运行状态的变化,实现传感器与执行机构故障幅值的自适应估计,准确地重构故障信号。根据故障估计结果,设计基于虚拟执行器的主动容错控制策略,在无需重新设计控制器的情况下,通过所设计的主动容错控制策略,在保证控制系统稳定性的前提下,获得和控制系统无故障状态相似的控制效果。通过该方法设计的涡扇发动机控制系统主动容错控制器,针对涡扇发动机控制系统同时发生执行机构与传感器故障时,在无需重新设计控制器的情况下,通过所设计的重构控制器,使得控制系统稳定,并获得和无故障系统相近的转速跟踪效果。
Description
本发明涉及一种涡扇发动机控制系统主动容错控制方法,属于航空控制技术领域,具体来说,是指针对涡扇发动机控制系统中,执行机构与传感器的并发性故障,且存在外部扰动的情况下,进行故障估计与主动容错控制的方法。
涡扇发动机广泛应用于民机及军机,其安全性与可靠性与飞行安全密切相关。控制系统作为涡扇发动机的“大脑”,确保涡扇发动机在全飞行包线内的安全与性能。控制系统的功能实现需要依靠大量的传感器和执行机构,若其中某些器件发生故障,则很难实现期望的控制效果,甚至影响飞行安全。因此,对涡扇发动机控制系统的性能进行监测,对故障状态实时估计、告警,并采取相应的容错控制措施,具有重要的意义。
文献表明,现有的涡扇发动机控制系统针对传感器和执行机构的故障处理方式采用的是故障诊断和被动容错控制,即控制算法采用PID和Min/Max切换相结合的控制方式,根据涡扇发动机的运行工况及输出的转速、温度、压力等可测参数基于卡尔曼滤波器对控制系统的传感器及执行机构是否发生故障给出判断,当有故障发生时,进一步采用基于硬件余度和控制回路切换的被动容错控制。尽管现有方法可以保证涡扇发动机的安全运行,但存在一定的保守性,主要体现在以下几点:首先,PID+Min/Max控制方式会在航空发动机的控制带宽、幅值/相位裕度以及响应速度等方面引入不理想的特性,难以获得较快的动态响应特性。其次,对故障只进行检测,即判断一有故障发生,就采用如硬件余度或控制回路切换等较为保守的被动容错控制方式进行处理,采用硬件余度难免造成硬件资源浪费;基于控制器切换的容错控制则是以牺牲部分性能指标为代价来确保航空发动机的安全运行。最后,随着涡扇发动机控制系统复杂性增加,故障种类及数量也会增加,因此传统的被动容错控制存在很大的局限性,即需要提前考虑全部可能发生的故障情况,导致控制器具有一定的保守性。值得提出的是,涡扇控制系统常受到噪声信号干扰,现有方法在处理干扰信号下,针对涡扇发动机控制系统传感器及执行器故障的容错控制,尚无理想的解决方法。
发明内容
针对现有涡扇发动机控制系统传感器与执行机构故障诊断与容错控制方法的保守性及难以保证扰动环境下的控制系统鲁棒性问题,本发明提供一种涡扇发动机控制系统主动容错控制方法。首先,设计一个具有良好动态性能的线性变参数(LPV)增益调度鲁棒跟踪控制器。进一步,根据涡扇发动机运行状态的变化,实现传感器与执行机构故障幅值的自适应估计,准确地重构故障信号。然后,根据故障估计结果,设计一种基于虚拟执行器的主动容错控制 策略,在无需重新设计控制器的情况下,通过所设计的主动容错控制策略,在保证控制系统稳定性的前提下,获得和控制系统无故障状态相似的控制效果。
为实现上述目的,本发明采用的技术方案步骤如下:
一种涡扇发动机控制系统主动容错控制方法,包括以下步骤:
步骤1:基于涡扇发动机试车数据,建立涡扇发动机LPV模型:
其中,x∈R
n为状态变量,u
c∈R
m为涡扇发动机的控制输入,d∈R
q为扰动信号,输出y∈R
p,调度参数λ取值为归一化后的涡扇发动机高压涡轮相对换算转速,且λ
min≤λ≤λ
max,λ
min和λ
max分别为调度参数的最小和最大值,系统矩阵A(λ)∈R
n×n,B(λ)∈R
n×m,C∈R
p×n,E∈R
n×q,G∈R
p×q,R
(·)表示(·)维实数列向量,R
a×b表示a×b维实数矩阵;
步骤2:针对带有扰动的涡扇发动机LPV模型,设计LPV增益调度鲁棒跟踪控制器;
步骤2.1:引入新的状态变量x
e,定义为
其中,e(·)为跟踪误差,y
r(·)为期望的跟踪信号;将式(1)改写为广义形式式(3)
步骤2.2:对于式(3),构建并求解如下线性矩阵不等式LMIs:
步骤2.3:计算LPV增益调度鲁棒跟踪控制器输出:
步骤3:针对带有扰动,且存在传感器与执行机构故障的涡扇发动机LPV模型,基于鲁棒H
∞优化方法,建立涡扇发动机自适应故障估计器,实现传感器及执行机构的故障估计;
步骤3.1:考虑涡扇发动机控制系统存在执行机构和传感器故障,故障系统表示如式(6)所示:
其中,x
f∈R
n为故障系统状态变量,u∈R
m为故障系统控制输入,y
f∈R
p为故障系统测量输出,f=[f
a
T f
s
T]
T∈R
l为故障信号,
为执行机构故障,
为传感器故障,B
f(λ)∈R
n×m为故障系统矩阵,F
f(λ)∈R
n×l和H
f(λ)∈R
p×l分别为执行机构和传感器的故障矩阵;
步骤3.2:将式(6)中时变部分和时不变部分分离,改写为如下形式
其中,外部输入w=[u
T d
T f
T]
T,z
λ,w
λ∈R
r分别为式(6)中r维时变子系统Λ=λI的输入和输出变量,B
f1∈R
n×r、B
f2∈R
n×(m+q+l)、C
f1∈R
r×n、C
f2∈R
p×n、D
f11∈R
r×r、D
f12∈R
r×(m+q+l)、D
f21∈R
p×r和D
f22∈R
p×(m+q+l)为系统状态空间矩阵;
基于式(7),构建故障估计器状态空间表达式如下:
其中,x
e∈R
k,u
e=[u
T y
f
T]
T∈R
(p+m)和
分别表示故障估计器的状态变量、控制输入和故障估计输出,z
eλ∈R
r和w
eλ∈R
r分别表示故障估计器时变部分的输入和输出,A
e∈R
k×k、B
e1∈R
k×(m+p)、B
e2∈R
k×r、C
e1∈R
l×k、C
e2∈R
r×k、D
e11∈R
l×(p+m)、D
e12∈R
l×r、D
e21∈R
r×(p+m)和D
e22∈R
r×r为待设计的故障估计器系数矩阵;
步骤3.3:构建涡扇发动机故障系统式(7)和故障估计器式(8)的状态空间联合表示:
步骤3.4:令
其中,L、V、Y分别表示X的子矩阵块,J、W、Z分别表示X
-1的子矩阵块;
其中,Q
1、Q
2、Q
3分别表示Q的子矩阵块,S
1、S
2、S
3、S
4分别表示S的子矩阵块,R
1、R
2、R
3分别表示R的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块;
R>0,Q=-R,S+S
T=0 (18)
步骤3.5:进一步,根据步骤3.4的求解结果,求解(17)中的X:
步骤3.6:求解下列LMIs,得到故障估计器的估计矩阵Γ;
其中,
进一步,计算故障估计器的系数矩阵:
步骤4:根据故障估计结果,设计基于虚拟执行器的涡扇发动机主动容错控制器,在无需重新设计控制器的情况下,使得控制系统稳定,并获得和无故障系统相近的控制效果;
步骤4.1:考虑涡扇发动机故障系统,当存在传感器与执行机构故障时,设计基于重构原理的虚拟执行器,重构系统的状态空间模型表示如下:
根据(22)-(24)联立的LMIs,求解正定矩阵X
v、Y
1和Y
2;
其中,i=1,2,ρ为LMI区域的最小衰减率,r为LMI区域的半径,q为圆心,θ为LMI区域中闭环极点与横轴的夹角;
步骤4.2:根据Y
i=M
iX
v,得到矩阵M
i;
步骤4.4:计算系统矩阵:
C
△(λ)=M(λ),D
△(λ)=N(λ)
构造主动容错控制器状态空间方程及控制律:
本发明的有益效果:通过本发明的方法设计的涡扇发动机控制系统主动容错控制器,针对涡扇发动机控制系统同时发生执行机构与传感器故障时,在无需重新设计控制器的情况下,通过所设计的重构控制器,使得控制系统稳定,并获得和无故障系统相近的转速跟踪效果。
图1是涡扇航空发动机控制系统传感器与执行机构主动容错控制器设计流程图;
图2是涡扇发动机LPV增益调度鲁棒跟踪控制器框图;
图3(a)是高压转子相对换算转速为88%时,涡扇发动机LPV增益调度鲁棒跟踪控制仿真结果;
图3(b)是高压转子相对换算转速为94%时,涡扇发动机LPV增益调度鲁棒跟踪控制仿真结果;
图4是涡扇发动机故障估计器框图;
图5(a)是涡扇发动机为传感器故障估计结果;
图5(b)是涡扇发动机为执行机构故障估计结果;
图6是涡扇航空发动机控制系统传感器与执行机构主动容错控制器框图;
图7(a)是高压转子相对换算转速为90%时,故障系统输出;
图7(b)是高压转子相对换算转速为94%时,故障系统输出;
图8(a)是高压转子相对换算转速为90%时,涡扇发动机控制系统正常输出结果;
图8(b)是高压转子相对换算转速为90%时,涡扇发动机控制系统主动容错控制结果;
图9(a)是高压转子相对换算转速为94%时,涡扇发动机控制系统正常输出结果;
图9(b)是高压转子相对换算转速为94%时,涡扇发动机控制系统主动容错控制结果。
下面结合附图对本发明作进一步说明,本发明的研究对象为控制系统传感器与执行机构故障后涡扇发动机,其设计方法如图1流程图所示,详细设计步骤如下。
步骤1:基于涡扇发动机试车数据,建立涡扇发动机LPV模型:
其中
调度参数λ为归一化后的涡扇发动机高压涡轮相对换算转速,且-1≤λ≤1,所以时变参数λ组成了一个以-1和1为顶点的参数多面体,扰动d取标准差为0.0001的高斯白噪声。
步骤2:如图2所示,针对带有扰动的涡扇发动机LPV模型,设计LPV增益调度鲁棒跟踪控制器。
给定γ=2,求解LMI(4),可得如下相应的矩阵解X和V
i(i=1,2)。
V
1=[5589 -3460 -946]
V
2=[5894 -1975 -2096]
结合式(5)可得转速跟踪控制器的增益K(λ),且有
由此,转速跟踪控制器的增益可以随着时变参数λ的变化而变化,具有调度特性,如图3所示,分别为高压转子相对换算转速为90%和94%时,涡扇发动机LPV增益调度鲁棒跟踪控制仿真结果。从仿真结果可以看出,无论是针对顶点处参数还是非顶点处参数,设计的LPV转速跟踪控制器都能保证输出较快地响应并跟踪参考指令,因此该控制器在全时变参数范围内都具有良好的控制性能,能够稳定、较快地实现跟踪,并有着较好的鲁棒性和稳定性。
步骤3:建立涡扇发动机自适应故障估计器,如图4所示,实现传感器及执行机构的故障估计。考虑涡扇发动机控制系统存在执行机构和传感器故障,如(28)所示
其中,f
1(λ)=0.1+0.01λ,-1≤λ≤1,h(λ)=0.5+0.02λ,-1≤λ≤1,扰动取标准差为0.0001的高斯白噪声。时变参数λ是实时可测的且假设其变化如下
乘性执行机构故障表示为
将(28)中时变部分和时不变部分分离,改写为如下形式
其中,外部输入w=[u
T d
T f
T]
T,z
λ,w
λ∈R
r分别为(6)中r维时变子系统Λ=λI的输入和输出变量,B
f1∈R
n×r、B
f2∈R
n×(m+q+l)、C
f1∈R
r×n、C
f2∈R
p×n、D
f11∈R
r×r、D
f12∈R
r×(m+q+l)、D
f21∈R
p×r和D
f22∈R
p×(m+q+l)为系统状态空间矩阵。
构建故障估计器状态空间表达式如下
其中,x
e∈R
k,u
e=[u
T y
f
T]
T∈R
(p+m)和
分别表示故障估计器的状态变量、控制输入和故障估计输出,z
eλ∈R
r和w
eλ∈R
r分别表示故障估计器时变部分的输入和输出, A
e∈R
k×k、B
e1∈R
k×(m+p)、B
e2∈R
k×r、C
e1∈R
l×k、C
e2∈R
r×k、D
e11∈R
l×(p+m)、D
e12∈R
l×r、D
e21∈R
r×(p+m)和D
e22∈R
r×r为待设计的故障估计器系数矩阵。
构建涡扇发动机故障系统和故障估计器的状态空间联合表示
令
其中,L、V、Y分别表示X的子矩阵块,J、W、Z分别表示X
-1的子矩阵块。
其中,Q
1、Q
2、Q
3分别表示Q的子矩阵块,S
1、S
2、S
3、S
4分别表示S的子矩阵块,R
1、R
2、R
3分别表示R的子矩阵块,
分别表示P~的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块。
进一步,求解X
求解下列LMIs,得到故障估计器的估计矩阵Γ
其中,
进一步,计算故障估计器的系数矩阵。
图5分别为控制系统传感器和执行机构发生突变故障时,所提故障估计器的估计结果。由仿真结果可以看出,所提的LPV故障估计器能够自适应地调整参数,适应当前系统动态,快速地检测到故障,并准确地重构故障信号。
步骤4:根据故障估计结果,设计基于虚拟执行器的涡扇发动机主动容错控制器,如图6所示。考虑涡扇发动机故障系统(28),图7是高压转子相对换算转速分别为90%和94%时,故障系统输出。可以看出,故障状态下,系统输出较无故障状态具有较大区别。根据(22)-(24)联立的LMIs,求解正定矩阵X
v,Y
1和Y
2。
其中,i=1,2,ρ=10,r=-4.5,q=15,θ=π/6。
根据Y
i=M
iX
v得到矩阵M
i(i=1,2)。
计算系统矩阵
C
△(λ)=M(λ),D
△(λ)=N(λ)
构造主动容错控制器状态空间方程及控制律
利用综上设计出的虚拟执行器对故障系统进行重构,图8和图9分别是高压转子相对换算转速为90%和94%时,控制系统正常输出和故障系统经主动容错控制后的结果对比。仿真结果可以看出,引入主动容错控制器后,重构系统的控制性能和无故障系统的相近,对故障进行了隐藏,进而实现了主动容错。此外,由于采用虚拟执行器进行重构,避免了对原转速跟踪控制器的重新设计,降低了系统维护的复杂性,对工程应用具有重大意义。
Claims (1)
- 一种涡扇发动机控制系统主动容错控制方法,其特征在于,包括以下步骤:步骤1:基于涡扇发动机试车数据,建立涡扇发动机LPV模型:其中,x∈R n为状态变量,u c∈R m为涡扇发动机的控制输入,d∈R q为扰动信号,输出y∈R p,调度参数λ取值为归一化后的涡扇发动机高压涡轮相对换算转速,且λ min≤λ≤λ max,λ min和λ max分别为调度参数的最小和最大值,系统矩阵A(λ)∈R n×n,B(λ)∈R n×m,C∈R p×n,E∈R n×q,G∈R p×q,R(·)表示(·)维实数列向量,R a×b表示a×b维实数矩阵;步骤2:针对带有扰动的涡扇发动机LPV模型,设计LPV增益调度鲁棒跟踪控制器;步骤2.1:引入新的状态变量x e,定义为其中,e(·)为跟踪误差,y r(·)为期望的跟踪信号;将式(1)改写为广义形式式(3)步骤2.2:对于式(3),构建并求解如下线性矩阵不等式LMIs:步骤2.3:计算LPV增益调度鲁棒跟踪控制器输出:步骤3:针对带有扰动,且存在传感器与执行机构故障的涡扇发动机LPV模型,基于鲁棒H ∞优化方法,建立涡扇发动机自适应故障估计器,实现传感器及执行机构的故障估计;步骤3.1:考虑涡扇发动机控制系统存在执行机构和传感器故障,故障系统表示如式(6)所示:其中,x f∈R n为故障系统状态变量,u∈R m为故障系统控制输入,y f∈R p为故障系统测量输出,f=[f a T f s T] T∈R l为故障信号, 为执行机构故障, 为传感器故障,B f(λ)∈R n×m为故障系统矩阵,F f(λ)∈R n×l和H f(λ)∈R p×l分别为执行机构和传感器的故障矩阵;步骤3.2:将式(6)中时变部分和时不变部分分离,改写为如下形式其中,外部输入w=[u T d T f T] T,z λ,w λ∈R r分别为式(6)中r维时变子系统Λ=λI的输入和输出变量,B f1∈R n×r、B f2∈R n×(m+q+l)、C f1∈R r×n、C f2∈R p×n、D f11∈R r×r、D f12∈R r×(m+q+l)、D f21∈R p×r和D f22∈R p×(m+q+l)为系统状态空间矩阵;基于式(7),构建故障估计器状态空间表达式如下:其中,x e∈R k,u e=[u T y f T] T∈R (p+m)和 分别表示故障估计器的状态变量、控制输入和故障估计输出,z eλ∈R r和w eλ∈R r分别表示故障估计器时变部分的输入和输出,A e∈R k×k、B e1∈R k×(m+p)、B e2∈R k×r、C e1∈R l×k、C e2∈R r×k、D e11∈R l×(p+m)、D e12∈R l×r、 D e21∈R r×(p+m)和D e22∈R r×r为待设计的故障估计器系数矩阵;步骤3.3:构建涡扇发动机故障系统式(7)和故障估计器式(8)的状态空间联合表示:步骤3.4:令其中,L、V、Y分别表示X的子矩阵块,J、W、Z分别表示X -1的子矩阵块;其中,Q 1、Q 2、Q 3分别表示Q的子矩阵块,S 1、S 2、S 3、S 4分别表示S的子矩阵块,R 1、R 2、R 3分别表示R的子矩阵块, 分别表示 的子矩阵块, 分别表示 的子矩阵块, 分别表示 的子矩阵块, 分别表示 的子矩阵块;R>0,Q=-R,S+S T=0 (18)步骤3.5:进一步,根据步骤3.4的求解结果,求解(17)中的X:步骤3.6:求解下列LMIs,得到故障估计器的估计矩阵Γ;其中,进一步,计算故障估计器的系数矩阵:步骤4:根据故障估计结果,设计基于虚拟执行器的涡扇发动机主动容错控制器,在无需重新设计控制器的情况下,使得控制系统稳定,并获得和无故障系统相近的控制效果;步骤4.1:考虑涡扇发动机故障系统,当存在传感器与执行机构故障时,设计基于重构原理的虚拟执行器,重构系统的状态空间模型表示如下:根据(22)-(24)联立的LMIs,求解正定矩阵X v、Y 1和Y 2;其中,i=1,2,ρ为LMI区域的最小衰减率,r为LMI区域的半径,q为圆心,θ为LMI区域中闭环极点与横轴的夹角;步骤4.2:根据Y i=M iX v,得到矩阵M i;步骤4.4:计算系统矩阵:C △(λ)=M(λ),D △(λ)=N(λ)构造主动容错控制器状态空间方程及控制律:
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