Aero-engine sliding mode output adjustment control method based on switching affine model

Abstract

The invention discloses an aero-engine sliding mode output adjustment control method based on a switching affine model. The method comprises the steps that S1, the aero-engine switching affine model is established; s2, establishing an augmented dynamical model, and designing an aero-engine error model based on the augmented dynamical model; s3, designing a sliding-mode robust output regulation controller, and designing a nonlinear part of the sliding-mode robust output regulation controller by adopting an integral sliding-mode control method; and S4, determining a safety set, verifying the stability of the sliding-mode robust output adjustment controller, and carrying out sliding-mode output adjustment control on the aero-engine system based on the sliding-mode robust output adjustment controller passing verification. The sliding mode output adjustment control method provided by the invention ensures that the system output gradually converges to zero under the conditions of state constraint, input saturation and external disturbance influence of the switching affine model of the aero-engine, so that equipment damage or system failure caused by the fact that the system runs beyond the boundary is avoided, and the safety is ensured.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft engine control, and in particular to an aircraft engine sliding mode output regulation control method based on a switching affine model which is state-constrained and affected by disturbances. Background Art

[0002] The aircraft engine system is a kind of equipment with high requirements for safety and reliability. In the study of control theory and dynamic systems, the aircraft engine system can be divided into nonlinear systems and linear systems. The analysis and control of nonlinear systems are very challenging. A switching system is a dynamic system composed of multiple subsystems switching according to certain rules. Traditional switching systems often assume that the subsystems are linear, but in reality, many aircraft engine systems often exhibit nonlinear dynamic characteristics. Therefore, in practice, the research perspective is extended to the switching affine model to analyze the nonlinear dynamic characteristics of the aircraft engine. In the prior art, although a lot of research has been done on the switching affine model of aircraft engines, there is still a lack of research on the attenuation of bounded disturbances in the switching affine model and the state constraint problem in the switching affine model, so that the existing aircraft engines are not accurate in adjusting the thrust under the influence of disturbances, which may cause the performance of the aircraft engine to decline, the fuel efficiency to decrease, etc. Summary of the invention

[0003] The present invention provides an aircraft engine sliding mode output regulation control method based on a switching affine model, so as to overcome the technical problem that the thrust regulation of the existing aircraft engine is not accurate under the influence of disturbance, which may cause the performance of the aircraft engine to decline and the fuel efficiency to decrease.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] A method for adjusting and controlling the sliding mode output of an aircraft engine based on a switching affine model, the specific steps of which include:

[0006] S1: Considering the situation where the aircraft engine system is affected by disturbances, an aircraft engine switching affine model is established based on the aircraft engine system;

[0007] S2: establishing an augmented dynamics model based on the aircraft engine switching affine model, and designing an aircraft engine error model based on the augmented dynamics model, wherein the aircraft engine error model is used to characterize the error between the adjustment output of the engine system and a given reference output;

[0008] S3: Design a sliding mode robust output regulation controller based on the aircraft engine error model. The nonlinear part of the sliding mode robust output regulation controller is designed using the integral sliding mode control method and used to compensate for the bounded disturbances inside the aircraft engine system. The linear part of the sliding mode robust output regulation controller is designed under state constraints and input saturation conditions.

[0009] S4: Considering the situation where the state of the aircraft engine system is restricted, a safety set is determined based on the aircraft engine error model, the stability of the sliding mode robust output regulation controller is verified based on the safety set, and the aircraft engine system is subjected to sliding mode output regulation control based on the verified sliding mode robust output regulation controller.

[0010] Furthermore, in S1, the established aircraft engine switching affine model is:

[0011]

[0012] e(t)=C κ(t) x(t),

[0013] in, represents the rate of change of the state of the aircraft engine switching affine model, x(t) represents the state of the aircraft engine switching affine model, u(t) represents the control input, that is, the sliding mode robust output regulation controller to be designed, u(t)∈[-U max ,U max ],U max represents the maximum value of u(t), and U max > 0; ω(t) represents the bounded disturbance inside the aircraft engine system, e(t) represents the regulation output, b κ(t) represents the affine term of the aircraft engine switching affine model, A κ(t) The system matrix representing the aircraft engine switching affine model, B κ(t) represents the input matrix of the aircraft engine switching affine model, C κ(t) represents the output matrix of the aircraft engine switching affine model, κ(t) represents the switching indicator, and κ(t)∈S, S represents the set of switching signals, S={1,2,…,N κ ,N κ ∈N +}.

[0014] Furthermore, in S2, the process of establishing an augmented dynamics model based on the aircraft engine switching affine model and designing an aircraft engine error model based on the augmented dynamics model is as follows:

[0015] S21: An augmented dynamics model is established based on the aircraft engine switching affine model, which is expressed as:

[0016]

[0017]

[0018] in,

[0019]

[0020]

[0021]

[0022]

[0023] e y (t) = re(t),

[0024] in, represents the rate of change of the state of the augmented dynamics model, represents the state of the augmented dynamics model, represents the system matrix of the augmented dynamics model, represents the input matrix of the augmented dynamics model, C represents the reference matrix of the augmented dynamics model, represents the affine matrix of the augmented dynamics model, represents the output matrix of the augmented dynamics model; r is the reference signal; A i represents the system matrix of the i-th sub-model of the aircraft engine switching affine model; B i represents the input matrix of the ith sub-model of the aircraft engine switching affine model; C i represents the output matrix of the i-th sub-model of the aircraft engine switching affine model, i∈S;

[0025] S22: Based on the augmented dynamics model, the error model of the aeroengine is designed, which can be expressed as:

[0026]

[0027]

[0028] in, The rate of change of the error variable of the augmented dynamics model, represents the error variable of the augmented dynamics model, and represents the affine term, and represents the regulated output that transforms the system to the origin, and x * Represents a given reference output.

[0029] Furthermore, in S3, the process of designing a sliding mode robust output regulation controller based on the aircraft engine error model is:

[0030] S31: The general form of the sliding mode robust output regulation controller is expressed as:

[0031] u(t)=σ(u0(t))+u I (t),

[0032] Among them, σ(u0(t)) and u I (t) represent the linear part and nonlinear part of the sliding mode robust output regulation controller considering system state constraints and input saturation, respectively;

[0033] S32: The integral sliding mode control method is used to design the integral sliding mode surface based on the general form of the aircraft engine error model and the sliding mode robust output regulation controller. The corresponding design process is as follows:

[0034] S321: Substitute the general form of the aircraft engine sliding mode robust output regulation controller model into the aircraft engine error model to obtain the first model:

[0035]

[0036]

[0037] S322: Design an integral sliding surface based on the first model, expressed as:

[0038]

[0039] in, represents the integral sliding surface, G i represents the matrix associated with the integral sliding surface, And G i Satisfy at the same time

[0040] S33: Derivative the time t in the integral sliding surface formula to obtain the sliding mode dynamics model, which is expressed as:

[0041]

[0042] S34: Design the nonlinear part of the final sliding mode robust output regulation controller as:

[0043]

[0044] Under the conditions of state constraints and input saturation, the linear part σ(u0(t)) in the final sliding mode robust output regulation controller is designed based on the sliding mode dynamics model and Lemma 3. The process is:

[0045] The third lemma is:

[0046] For a given constant uimax ,u imax >0, if Then the following exists:

[0047]

[0048] Based on Lemma 3, when the state of the aircraft engine switching affine model reaches the sliding mode state, that is,

[0049] When , it can converge to the origin in a finite time, that is, reach the sliding surface;

[0050] Therefore, the second model is obtained through the first model:

[0051]

[0052]

[0053] According to the second model, u0(t) is obtained, which is expressed as:

[0054]

[0055] Among them, K i represents the controller gain.

[0056] Furthermore, in S4, considering the situation where the aircraft engine system state is limited, the process of determining the safety set based on the aircraft engine error model is:

[0057] First assume is stable, that is, the system matrix There are no unstable characteristic roots;

[0058] Since the constraint set of the system state x(t) of the aircraft engine switching affine model is Then the solution of the aeroengine error model is constrained within the following set:

[0059]

[0060] in, d represents any vector, d p represents a vector representing the constraints of the system state; represents the number of safe sets, and k x Indicates the number of ellipsoids; represents the set of real numbers;

[0061] Using the ellipsoid set method, we can get the state constraint set P from z Find an approximate set of constraints within And R>0;

[0062] verify Is it satisfied? If satisfied, then This is the safe set.

[0063] Further, in S4, the process of verifying the stability of the sliding mode robust output regulation controller based on the safety set is:

[0064] According to Theorem 1, given the constant U 0max >0,δ>0,k>0 and r>0, the expected equilibrium point x * , convex combination λ∈S, if there exists a matrix R>0, the matrix G0 associated with the sliding surface, the symmetric matrix Q i , i∈S, so that the constraints satisfied by the sliding mode robust output regulation controller parameters are:

[0065]

[0066] Q(λ)<0,

[0067]

[0068]

[0069] r 2 P<R,

[0070] in, Requirements:

[0071] Under the action of the switching signal, there are:

[0072]

[0073] Therefore, when the system state reaches the sliding surface When the model trajectory can converge to the safe set without violating state constraints and input saturation This verifies the stability of the sliding mode robust output regulation controller.

[0074] Beneficial effects: The present invention takes into account the situation affected by disturbances, and establishes an aircraft engine switching affine model based on the aircraft engine system; when it is assumed that the disturbance of the system is bounded, an augmented dynamic model is obtained based on the switching affine model of the aircraft engine, thereby designing an aircraft engine error model; based on the aircraft engine error model, an aircraft engine sliding mode robust output regulation controller is designed, wherein the nonlinear part of the sliding mode robust output regulation controller is designed by an integral sliding mode control method, and is used to compensate for the bounded disturbances inside the aircraft engine system; the linear part of the sliding mode robust output regulation controller is designed under state constraints and input saturation conditions; at the same time, a safety set is proposed based on the aircraft engine error model, and the stability of the sliding mode robust output regulation controller is verified based on the safety set. The sliding mode output regulation control method proposed in the present invention ensures that the switching affine model of the aircraft engine converges to zero asymptotically under the conditions of state constraints, input saturation and external disturbances, thereby avoiding the system from operating beyond the boundary and causing equipment damage or system failure, thereby ensuring safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0076] Figure 1 It is a flow chart of a method for adjusting and controlling the sliding mode output of an aircraft engine based on a switching affine model in the present invention;

[0077] Figure 2 The proposed sliding mode robust output regulation control method and the H switching affine system are selected for numerical simulation verification in the embodiments of the present invention. ∞ Comparison diagram of the system state x1(t) of the anti-disturbance control method;

[0078] Figure 3 The proposed sliding mode robust output regulation control method and the H switching affine system are selected for numerical simulation verification in the embodiments of the present invention. ∞ Comparison diagram of system state x2(t) of anti-disturbance control method;

[0079] Figure 4 The proposed sliding mode robust output regulation control method and the H switching affine system are selected for numerical simulation verification in the embodiments of the present invention. ∞ Comparison diagram of system state x3(t) of anti-disturbance control method;

[0080] Figure 5The proposed sliding mode robust output regulation control method and the H switching affine system are selected for numerical simulation verification in the embodiments of the present invention. ∞ Comparison diagram of the regulation output e(t) of the anti-interference control method;

[0081] Figure 6 It is a trajectory diagram of the sliding surface s(t) verified by numerical simulation in an embodiment of the present invention;

[0082] Figure 7 The proposed sliding mode robust output regulation control method and the H switching affine system are selected for numerical simulation verification in the embodiments of the present invention. ∞ Comparison chart of switching rules for anti-interference control methods. DETAILED DESCRIPTION

[0083] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0084] This embodiment provides an aircraft engine sliding mode output regulation control method based on a switching affine model. Figure 1 As shown, the specific steps include:

[0085] S1: Considering the situation where the aircraft engine system is affected by disturbances, an aircraft engine switching affine model is established based on the aircraft engine system.

[0086] In a specific embodiment, in S1, the established aircraft engine switching affine model is:

[0087]

[0088] e(t)=C κ(t) x(t),

[0089] in, represents the rate of change of the state of the aircraft engine switching affine model, x(t) represents the state of the aircraft engine switching affine model, u(t) represents the control input, that is, the sliding mode robust output regulation controller to be designed, u(t)∈[-U max ,U max ],U max represents the maximum value of u(t), and U max > 0, ω(t) represents the bounded disturbance inside the aircraft engine system, e(t) represents the regulation output, b κ(t)represents the affine term of the aircraft engine switching affine model, A κ(t) The system matrix representing the aircraft engine switching affine model, B κ(t) represents the input matrix of the aircraft engine switching affine model, C κ(t) represents the output matrix of the aircraft engine switching affine model. Specifically, κ(t) represents the switching indicator, and κ(t)∈S; S is the set of switching indication signals, and S={1,2,…,N κ ,N κ ∈N +}; When the i-th sub-model of the aircraft engine switching affine model is running, that is, when κ(t) = i, i∈S, the i-th sub-model of the aircraft engine switching affine model is obtained, which is expressed as:

[0090]

[0091] e(t)=C i x(t),

[0092] Among them, A i represents the system matrix of the i-th submodel of the aircraft engine switching affine model, B i represents the input matrix of the ith sub-model of the aircraft engine switching affine model, and (A i ,B i ) is controllable; C i Represents the output matrix of the i-th sub-model of the aircraft engine switching affine model.

[0093] It is worth noting that the constraint of the controller u(t), that is, u(t)∈[-U max ,U max ] will inevitably impose restrictions on the system state x(t), so the constraint set for switching the affine model system state x(t) is set as follows:

[0094]

[0095] Among them, d p represents the vector representing the system state constraints, k x Indicates the number of ellipsoids; Represents the set of real numbers.

[0096] S2: establishing an augmented dynamics model based on the aircraft engine switching affine model, and designing an aircraft engine error model based on the augmented dynamics model, wherein the aircraft engine error model is used to characterize the error between the adjustment output of the engine system and a given reference output;

[0097] In a specific embodiment, in S2, the process of establishing an augmented dynamics model based on the aircraft engine switching affine model and designing an aircraft engine error model based on the augmented dynamics model is:

[0098] Assumption 1: The disturbance ω(t) of the system is bounded, that is

[0099] Based on the aircraft engine switching affine model, let Where r is the reference signal, and given Thus, the augmented dynamics model is established, which is expressed as:

[0100]

[0101]

[0102] in

[0103]

[0104]

[0105] in, represents the rate of change of the state of the augmented dynamics model, represents the state of the augmented dynamics model, represents the system matrix of the augmented dynamics model, represents the input matrix of the augmented dynamics model, represents the reference matrix of the augmented dynamics model, represents the affine matrix of the augmented dynamics model, represents the output matrix of the augmented dynamics model; r is the reference signal; A i represents the system matrix of the i-th sub-model of the aircraft engine switching affine model; B i represents the input matrix of the ith sub-model of the aircraft engine switching affine model; C i represents the output matrix of the i-th sub-model of the aircraft engine switching affine model, i∈S;

[0106] Specifically, due to the affine term b i , each subsystem in the switching affine model has its own equilibrium point. Generally speaking, the common equilibrium points of the augmented dynamics model belong to the set

[0107]

[0108] in

[0109]

[0110] λ∈P={λ=[λ1λ2…λs ]∈R N+},

[0111]

[0112] Therefore, in order to move the equilibrium point of the augmented dynamics model to the origin, the error variable is defined Thus, the error model of the aeroengine is designed and expressed as:

[0113]

[0114]

[0115] in, The rate of change of the error variable of the augmented dynamics model, represents the error variable of the augmented dynamics model, and represents the affine term, and represents the regulated output that transforms the system to the origin, and x * Represents a given reference output.

[0116] S3: Design a sliding mode robust output regulation controller based on the aircraft engine error model. The nonlinear part of the sliding mode robust output regulation controller is designed using the integral sliding mode control method and used to compensate for the bounded disturbances inside the aircraft engine system. The linear part of the sliding mode robust output regulation controller is designed under state constraints and input saturation conditions.

[0117] In a specific embodiment, in S3, the process of designing a sliding mode robust output regulation controller based on the aircraft engine error model is:

[0118] S31: The general form of the sliding mode robust output regulation controller is expressed as:

[0119] u(t)=σ(u0(t))+u I (t),

[0120] Among them, σ(u0(t)) and u I (t) represent the linear part and nonlinear part of the sliding mode robust output regulation controller considering system state constraints and input saturation respectively; u I (t) is used to suppress the influence of bounded disturbance ω in the aero-engine error model.

[0121] S32: The integral sliding mode control method is used to design the integral sliding mode surface based on the aircraft engine error model and the general form of the sliding mode robust output regulation controller to compensate for the bounded disturbance inside the system. The corresponding design process is:

[0122] S321: Substitute the general form of the aircraft engine sliding mode robust output regulation controller model into the aircraft engine error model to obtain the first model:

[0123]

[0124]

[0125] S322: Design an integral sliding surface based on the first model, expressed as:

[0126]

[0127] in, represents the integral sliding surface, G i represents the matrix associated with the integral sliding surface, And G i Satisfy at the same time To minimize the impact of disturbances on the sliding surface,

[0128]

[0129] S33: Derivative the time t in the integral sliding surface formula to obtain the sliding mode dynamics model, which is expressed as:

[0130]

[0131] S34: Design the nonlinear part of the final sliding mode robust output regulation controller to ensure the existence of sliding mode under the conditions of system state constraints and input saturation, expressed as:

[0132]

[0133] Under the conditions of state constraints and input saturation, the linear part σ(u0(t)) in the final sliding mode robust output regulation controller is designed based on the sliding mode dynamics model and Lemma 3, so that the system state and regulation output converge to zero, while suppressing the influence of bounded disturbance ω(t). The process is:

[0134] The third lemma is:

[0135] For a given constant u imax ,u imax >0, if Then the following exists:

[0136]

[0137] Based on Lemma 3, when the state of the aircraft engine switching affine model reaches the sliding mode state, that is, When , it can converge to the origin in a finite time;

[0138] Therefore, the second model can be obtained through the first model:

[0139]

[0140]

[0141] According to the second model, u0(t) is obtained, which is expressed as:

[0142]

[0143] Among them, K i represents the controller gain.

[0144] In a specific embodiment, in S4, the process of determining the safety set based on the aircraft engine error model is:

[0145] Hypothesis 2: Hypothesis is stable, that is, the system matrix There are no unstable characteristic roots.

[0146] Since the constraint set of the system state x(t) of the aircraft engine switching affine model is Then the solution of the aeroengine error model is constrained within the following set:

[0147]

[0148] in, d represents an arbitrary vector. Since the reference output r is given and is not subject to any constraints, d can take any value. p represents a vector representing the constraints of the system state; represents the number of safe sets, and k x Indicates the number of ellipsoids; Represents the set of real numbers.

[0149] Using the ellipsoid set method, we can get the state constraint set P from z Find an approximate set of constraints within And R>0;

[0150] verify Is it satisfied? If satisfied, then That is, it is a safe set that neither violates the state constraints nor the input saturation.

[0151] S4: Considering the situation where the state of the aircraft engine system is restricted, a safety set is determined based on the aircraft engine error model to ensure that the system trajectory satisfies both the state constraints and the input saturation; the stability of the sliding mode robust output regulation controller is verified based on the safety set, and the aircraft engine system is subjected to sliding mode output regulation control based on the verified sliding mode robust output regulation controller.

[0152] In a specific embodiment, in S4, the process of verifying the stability of the sliding mode robust output regulation controller based on the safety set is:

[0153] According to Theorem 1, sufficient conditions are provided for the convergence of system state and regulation output, which can be expressed as: Given a constant U 0max >0,δ>0,k>0 and r>0, the expected equilibrium point x * , convex combination λ∈S, if there exists a matrix R>0, the matrix G0 associated with the sliding surface, the symmetric matrix Q i , i∈S, so that the parameters of the sliding mode robust output regulation controller meet the following constraints:

[0154]

[0155] Q(λ)<0,

[0156]

[0157]

[0158] r 2 P<R,

[0159] in, Requirements:

[0160] Under the action of the switching signal, there are:

[0161]

[0162] Therefore, through analysis, it can be seen that when the system state reaches the sliding surface When the model trajectory can converge to the safe set without violating state constraints and input saturation This verifies the stability of the sliding mode robust output regulation controller.

[0163] In this embodiment, a barrier Lyapunov function considering state constraints is also designed, and the barrier Lyapunov function is used to verify whether the designed sliding mode robust output regulation controller is effective. If not, the gain of the sliding mode robust output regulation controller is adjusted until the aircraft engine switches to an affine model and runs smoothly, thereby obtaining a verified sliding mode robust output regulation controller.

[0164] Specifically, the process of designing the barrier Lyapunov function considering the state constraints is:

[0165] Let φ(u0(t)) = σ(u0(t)) - u0(t), and add it together with u0(t) = K i When the system state reaches the sliding mode state The model when is the second model, and the third model can be derived as follows:

[0166]

[0167]

[0168] The barrier Lyapunov function V(t) is designed based on the third model and is expressed as:

[0169]

[0170] Taking the derivative of the time t in the above formula, we get:

[0171]

[0172] set up Then the above formula can be written as:

[0173]

[0174] according to get:

[0175]

[0176] Because S z >0, combining the above two formulas yields:

[0177]

[0178] in,

[0179]

[0180]

[0181]

[0182] Then, add or subtract S from the right side of the above equation. z δr 2 and S z δz T (t)Pz(t), we get:

[0183]

[0184] in,

[0185]

[0186] In this embodiment, Lemma 1 is given, which is expressed as:

[0187] Given belong The function φ(α) satisfies the condition for all k>0

[0188] Lemma 2 is expressed as:

[0189] For a matrix R and a positive definite matrix P, -PRP ≤ R -1 -2P always holds true.

[0190] According to Lemma 1 and Lemma 2, considering that the controller exists ‖u(t)‖≤U max , then each part of the controller u(t) has an upper bound and ‖σ(u0(t))‖≤U 0max , ‖u I (t)‖≤U Imax and U 0max +U Imax ≤U max All of them hold, and U 0max ,U Imax ,U max are all greater than 0; where the range of σ(u0(t)) is expressed as:

[0191]

[0192] In the formula, is a constant, and

[0193] According to Lemma 1 and set up It turns out that:

[0194]

[0195] Derived from the above two formulas:

[0196]

[0197] in,

[0198]

[0199]

[0200]

[0201] Depend on And Q(λ)<0, we know:

[0202]

[0203] For all All of them hold true, that is, all The reinitialized state is kept in the collection and gradually converges to the set therefore It is also established by It can be seen that when the aircraft engine switches the affine model considering state constraints and output saturation, the safety set is When r 2 P<R can be deduced This not only ensures that the trajectory of the aircraft engine switching affine model satisfies the state constraints and input saturation at the same time, but also verifies the effectiveness of the designed sliding mode robust output regulation controller.

[0204] Specifically, in this embodiment, the sliding mode robust output regulation controller gain K is designed i The process is:

[0205] According to Theorem 2, that is:

[0206] Given a constant U 0max >0,δ>0,k>0 and r>0, the expected equilibrium point x * , convex combination λ∈S, if the matrix R>0, the matrix G0 associated with the sliding surface, the symmetric matrix Q i , i∈S, so that the constraints:

[0207]

[0208] Q(λ)<0,

[0209]

[0210]

[0211]

[0212] in, Then the sliding mode robust output regulation controller model u(t)=σ(u0(t))+u I (t) can make the state of the third model converge to the safe set Right now

[0213]

[0214] for Multiply both sides by {R-1 ,I}, we get:

[0215]

[0216] in,

[0217] make Using Schur's complement to supplement Lemma 1 and Lemma 2, we can conclude that

[0218] for Multiply both sides by R -1 ,get Established;

[0219] Similarly, if and r 2 P<R can be deduced and If the system state converges, the domain is completely contained in the safety set. Otherwise, the gain of the sliding mode robust output regulation controller is readjusted until the aircraft engine switches to the affine model and runs smoothly, and the verified sliding mode robust output regulation controller is obtained, that is, the asymptotic stability and input regulation performance of the sliding mode robust output regulation controller are guaranteed.

[0220] Specifically, in order to verify the effect of the sliding mode output regulation control scheme proposed in this embodiment, a certain type of aircraft engine is used as an example for simulation verification. It is assumed that the aircraft engine switching affine model consists of two subsystems, which are expressed as:

[0221]

[0222]

[0223] in, Δπ(t) and ΔU w (t) represent the core engine speed, fan speed and relative fuel flow rate at the equilibrium point of the aircraft engine switching affine model, The affine term representing the performance degradation parameter of the aircraft engine, ΔT 48 represents the turbine outlet temperature of an aircraft engine, and r is the reference value of the turbine outlet temperature.

[0224] The parameters of the given aero-engine switching affine model are as follows:

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231] Given the following constants and other matrices:

[0232] G0=[1 1 0],k=1.1,δ=1,r=0.5,U 0max =20.

[0233] By solving the linear matrix inequality in Theorem 2, we obtain:

[0234] K1=[-0.4963 -0.6657 0.0097],

[0235] K2=[-0.5217 -0.7022 0.0163],

[0236]

[0237]

[0238]

[0239]

[0240] In order to verify the superiority of the proposed sliding mode robust output regulation control scheme, the experiments are divided into two groups according to the control method: (i) the sliding mode robust output regulation control method proposed in this embodiment; (ii) the H switching affine system ∞ Anti-interference control method. Through numerical simulation verification, the results are as follows Figures 2 to 7 As shown, from Figure 2 and Figure 3 It can be seen that the system states x1(t) and x2(t) in control method (i) converge faster and have smaller overshoot than the system states x1(t) and x2(t) in control method (ii), while still satisfying the state constraints. Figure 4 It can be seen from the figure that the system state x3(t) has a smaller fluctuation convergence in the case of control method (i) and better satisfies the state constraints. Figure 5 It can be seen that in control method (i), the regulation output The regulated output in the ratio control method (ii) The convergence speed is faster. Figure 6 It can be seen that the sliding surface s(t) is stable. Figure 7It can be seen from the comparison of switching rules under the two control methods that the sliding mode robust output regulation control method proposed in this embodiment is effective.

[0241] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for adjusting the output of an aircraft engine by sliding mode based on a switching affine model, characterized in that: The specific steps include: S1: Considering the situation where the aircraft engine system is affected by disturbances, an aircraft engine switching affine model is established based on the aircraft engine system; S2: establishing an augmented dynamics model based on the aircraft engine switching affine model, and designing an aircraft engine error model based on the augmented dynamics model, wherein the aircraft engine error model is used to characterize the error between the adjustment output of the engine system and a given reference output; S3: Design a sliding mode robust output regulation controller based on the aircraft engine error model. The nonlinear part of the sliding mode robust output regulation controller is designed using the integral sliding mode control method and used to compensate for the bounded disturbances inside the aircraft engine system. The linear part of the sliding mode robust output regulation controller is designed under state constraints and input saturation conditions. S4: Considering the situation where the state of the aircraft engine system is restricted, a safety set is determined based on the aircraft engine error model, the stability of the sliding mode robust output regulation controller is verified based on the safety set, and the aircraft engine system is subjected to sliding mode output regulation control based on the verified sliding mode robust output regulation controller.

2. The method for adjusting the output of an aircraft engine by sliding mode based on a switching affine model according to claim 1, characterized in that: In S1, the established aero-engine switching affine model is: e(t)=C κ(t) x(t), in, represents the rate of change of the state of the aircraft engine switching affine model, x(t) represents the state of the aircraft engine switching affine model, u(t) represents the control input, that is, the sliding mode robust output regulation controller to be designed, u(t)∈[-U max ,U max ],U max represents the maximum value of u(t), and U max > 0; ω(t) represents the bounded disturbance inside the aircraft engine system, e(t) represents the regulation output, b κ(t) represents the affine term of the aircraft engine switching affine model, A κ(t) The system matrix representing the aircraft engine switching affine model, B κ(t) represents the input matrix of the aircraft engine switching affine model, C κ(t) represents the output matrix of the aircraft engine switching affine model, κ(t) represents the switching indicator, and κ(t)∈S, S represents the set of switching signals, S={1,2,…,N κ ,N κ ∈N + }.

3. The aircraft engine sliding mode output regulation control method based on switching affine model according to claim 2 is characterized in that: In S2, the process of establishing an augmented dynamics model based on the aircraft engine switching affine model and designing the aircraft engine error model based on the augmented dynamics model is as follows: S21: An augmented dynamics model is established based on the aircraft engine switching affine model, which is expressed as: in, e y (t)=r-e(t), in, represents the rate of change of the state of the augmented dynamics model, represents the state of the augmented dynamics model, represents the system matrix of the augmented dynamics model, represents the input matrix of the augmented dynamics model, represents the reference matrix of the augmented dynamics model, represents the affine matrix of the augmented dynamics model, represents the output matrix of the augmented dynamics model; r is the reference signal; A i represents the system matrix of the i-th submodel of the aircraft engine switching affine model; B i represents the input matrix of the ith sub-model of the aircraft engine switching affine model; C i represents the output matrix of the i-th sub-model of the aircraft engine switching affine model, i∈S; S22: Based on the augmented dynamics model, the error model of the aeroengine is designed, which can be expressed as: in, The rate of change of the error variable of the augmented dynamics model, represents the error variable of the augmented dynamics model, and represents the affine term, and represents the regulated output that transforms the system to the origin, and x * Represents a given reference output.

4. The aircraft engine sliding mode output regulation control method based on the switching affine model according to claim 3 is characterized in that: In S3, the process of designing a sliding mode robust output regulation controller based on the aircraft engine error model is: S31: The general form of the sliding mode robust output regulation controller is expressed as: u(t)=σ(u0(t))+u I (t), Among them, σ(u0(t)) and u I (t) represent the linear part and nonlinear part of the sliding mode robust output regulation controller considering system state constraints and input saturation, respectively; S32: The integral sliding mode control method is used to design the integral sliding mode surface based on the general form of the aircraft engine error model and the sliding mode robust output regulation controller. The corresponding design process is as follows: S321: Substitute the general form of the aircraft engine sliding mode robust output regulation controller model into the aircraft engine error model to obtain the first model: S322: Design an integral sliding surface based on the first model, expressed as: in, represents the integral sliding surface, G i represents the matrix associated with the integral sliding surface, And G i Satisfy at the same time S33: Derivative the time t in the integral sliding surface formula to obtain the sliding mode dynamics model, which is expressed as: S34: Design the nonlinear part of the final sliding mode robust output regulation controller as: Under the conditions of state constraints and input saturation, the linear part σ(u0(t)) in the final sliding mode robust output regulation controller is designed based on the sliding mode dynamics model and Lemma 3. The process is: The third lemma is: For a given constant u imax ,u imax >0, if Then the following exists: Based on Lemma 3, when the state of the aircraft engine switching affine model reaches the sliding mode state, that is, When , it can converge to the origin in a finite time, that is, reach the sliding surface; Therefore, the second model is obtained through the first model: According to the second model, u0(t) is obtained, which is expressed as: Among them, K i represents the controller gain.

5. The method for adjusting the output of an aircraft engine by sliding mode based on a switching affine model according to claim 4, characterized in that: In S4, considering the situation where the aircraft engine system state is limited, the process of determining the safety set based on the aircraft engine error model is: First assume is stable, that is, the system matrix There are no unstable characteristic roots; Since the constraint set of the system state x(t) of the aircraft engine switching affine model is Then the solution of the aeroengine error model is constrained within the following set: in, d represents any vector, d p represents a vector representing the constraints of the system state; represents the number of safe sets, and k x Indicates the number of ellipsoids; represents the set of real numbers; Using the ellipsoid set method, we can get the state constraint set P from z Find an approximate set of constraints within And R>0; verify Is it satisfied? If satisfied, then This is the safe set.

6. The method for adjusting the output of an aircraft engine by sliding mode based on a switching affine model according to claim 5, characterized in that: In S4, the process of verifying the stability of the sliding mode robust output regulation controller based on the safety set is: According to Theorem 1, given the constant U 0max >0,δ>0,k>0 and r>0, the expected equilibrium point x * , convex combination λ∈S, if there exists a matrix R>0, the matrix G0 associated with the sliding surface, the symmetric matrix Q i , i∈S, so that the constraints satisfied by the sliding mode robust output regulation controller parameters are: Q(λ)<0, r 2 P<R, in, Requirements: Under the action of the switching signal, there are: Therefore, when the system state reaches the sliding surface When the model trajectory can converge to the safe set without violating state constraints and input saturation This verifies the stability of the sliding mode robust output regulation controller.

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