Aero-engine active limit protection control method under time-varying output constraint

Abstract

The application belongs to the technical field of aero-engine control, and proposes an active limiting protection control method of aero-engine under time-varying output constraint. On the basis of unchanged ordinary limiting quantity setting, the output limitation is expanded to support real-time limitation of multiple outputs by designing a nonlinear model predictive controller; in the establishment of the aero-engine model, the LPV model which belongs to the nonlinear model in essence is selected, the application has universality, and the limited output value can be integrated into the target function regardless of the dimension. At the same time, the active limiting protection control method strategy has the characteristics of real-time rolling optimization, so it supports real-time variables of actual constraint values. According to the actual demand of the turbofan engine, the active limiting protection control of multiple output time-varying constraints can be carried out by using the double-mode nonlinear optimization algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aero-engine control technology, and particularly relates to an aero-engine active limiting protection control method under time-varying output constraints. BACKGROUND

[0002] An aero-engine is a highly complex nonlinear controlled object, and its working process is an extremely complex aerodynamic thermodynamic process. The engine characteristics vary greatly with changes in environmental conditions and working conditions, so the control system needs not only to track instructions quickly and with high precision, but also to make correct responses to the restrictions of various constraints in the working process.

[0003] Traditional aero-engine control systems usually use linear regulators with maximum-minimum selection structure to achieve output constraint management. Many research results in recent years, such as the paper "Reducing Conservatism in Aircraft Engine Response Using Conditionally Active Min-Max Limit Regulators" by NASA, show that the control structure using linear regulators has various problems in aero-engine output constraint management. On the one hand, when the limit is still far from the limit line, the corresponding limiter is activated, making it difficult for the engine to obtain better dynamic response, and having a certain conservatism. On the other hand, when the distance between normal control and safety control is too small, due to the existence of disturbances, switching oscillation is easily sent. The more critical problem is that this limit management system can only guarantee that the variable does not exceed the limit at steady state, and cannot guarantee the limiting protection effect at transient state.

[0004] It can be concluded that the modern engine control system not only ensures that the engine works within the limit range, but also ensures good dynamic quality, such as fast response, small overshoot, less oscillation, and smooth and reliable. With the widespread use of engine FADEC control system, relying on advanced control algorithm to coordinate power management and limit management has become the key to the research of aero-engine control, in order to exert the best performance of aero-engine under the limit protection. Professor Shi Yugen mentioned in 'Predictive Control' that model predictive control (MPC) is an advanced control algorithm based on model, which can avoid the key thermodynamic variables from exceeding the given limit range while maintaining the dynamic response speed of aero-engine, and the output limit value can be more flexible by innovating the algorithm. Reberga L studied the linear parameter varying (LPV) system as a high-precision nonlinear model with linear expression in 'LPV modeling of a turbofan engine', which provides an important guarantee for the design of engine advanced control algorithm system, meets the requirements of fast and reliable tracking under wide range of engine command changes, and widens the application range of aero-engine multivariable variable constraint controller. SUMMARY

[0005] In order to solve the problems in the aero-engine control system, such as the conservatism of the traditional limit management system, the easy generation of switching oscillation, and the inability to guarantee the limit protection in the transition state, an active limit protection control method of aero-engine under time-varying output constraint is proposed. For various mechanical structure limits and safe operation limits in the aero-engine control system, based on the advantages of LPV system model and predictive control, an improved time-varying constraint management method of aero-engine control system is proposed, and is extended to multiple outputs. On the basis of unchanged ordinary limit quantity setting, by designing a nonlinear model predictive controller, the output limit is expanded to support real-time limit of multiple outputs, and the calculation burden is reduced in the model prediction stage and the optimization algorithm stage; in the establishment of the aero-engine model, the LPV model which belongs to the nonlinear model in essence is selected, so that it can reflect the dynamic response characteristics of the aero-engine at different steady states, and therefore the controller designed based on the LPV model can guarantee the stability and robustness of the aero-engine in a wide range.

[0006] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0007] An active limit protection control method of aero-engine under time-varying output constraint, comprising the following steps:

[0008] Step 1: Based on the test data of the turbofan engine, n steady-state nominal points are segmented, and a LPV linear parameter-varying model of the turbofan engine is fitted in each sub-interval;

[0009]

[0010] wherein x p ∈R n is a state variable, u p ∈R m is a control input of the turbofan engine, y p ∈R p is an output, y q ∈R q is a constraint variable, i is a sub-interval number, and the scheduling parameter λ takes a value of a physical quantity reflecting the dynamic performance of the turbofan engine, λ (i,min) ≤λ≤λ (i,max) , λ (i,min) and λ (i,max) are respectively a minimum value and a maximum value of the scheduling parameter in the i-th LPV linear parameter-varying model, the system matrix A i (λ)∈R n×n , the system matrix B i (λ)∈R n×m , the system matrix C i (λ)∈R q×n , and the system matrix D i (λ)∈R q ×m , R (·) represents a (·) -dimensional real number column vector, and R a×b represents an a×b-dimensional real number matrix; C p is a matrix corresponding to the output of the turbofan engine;

[0011] Step 2: A state feedback controller and an augmented model are designed for the LPV linear parameter-varying model of the turbofan engine;

[0012] Step 2.1: The control instruction of the constraint variable y p is r, the output deviation e = r-y p , and the integral of the deviation is x e = ∫edt, the integral of the deviation is augmented as a state variable to eliminate the steady-state error of the output deviation system; the state equation of the generalized controlled object in the augmented system is:

[0013]

[0014] In the formula:

[0015] Step 2.2: Adding state feedback controller to the augmented system; the state feedback controller K(λ) = W(λ)X -1 (λ) is designed according to the LPV linear parameter varying model shown in equation (2) to ensure the tracking performance of the augmented system. Then the state equation of the closed loop system of turbofan engine is:

[0016]

[0017] Step 2.3: Designing the switching controller based on H ∞ algorithm;

[0018] It is very difficult to solve the LMI optimization problem containing polynomials for the formula (3) of the closed loop system of turbofan engine. The SOS programming is used to solve the LMI optimization problem containing polynomials; the state feedback H ∞ controller K(λ) = W(λ)X -1 (λ) is designed, where X(λ) is a real symmetric matrix, W(λ) is a real matrix; the H ∞ performance index {γ ∞,i > 0} i∈(1,α) is given. When there exists a real symmetric matrix X(λ), a real matrix W(λ) and a SOS matrix {M i (λ)} i∈(1,α) , the following polynomial matrix is obtained, otherwise it cannot be switched to the state feedback controller

[0019]

[0020] For any i∈(1, α), it satisfies the SOS matrix, then the closed loop system of turbofan engine is asymptotically stable and satisfies the H ∞ performance index γ ∞ = max{γ ∞,i} i∈(1,α) ; where g i (λ) = (λ i - λ i,min )(λ i,max - λ i ).

[0021] Step 3: Designing the discrete prediction model according to equation (3);

[0022] Step 3.1: Considering the calculation burden of online optimization iteration, a discrete prediction model containing the main dynamic characteristics of turbofan engine is proposed to replace the component-level mathematical model which can accurately describe the dynamic characteristics of aero-engine but is relatively complex in calculation and operation. The discrete piecewise linear model is established through the existing continuous model, and G and H are the discrete state matrices of A(λ) and B respectively.

[0023]

[0024] Step 3.2: The discrete prediction model includes the main dynamic characteristics of the turbofan engine, which is expressed as a steady-state nonlinear and dynamic linear. The output state after kT (the sampling time) is predicted by iteration (k+1) times, and T is the sampling time;

[0025] The output matrix C parameter value is determined by the scheduling quantity λ at the current state. When the current operating point is between two steady-state points, the system matrix and the output matrix are the interpolation of the matrices at the two steady-state nominal points. The state vector at the current stable operating state is also the interpolation of the corresponding vectors at the steady-state nominal points. The output equation z(k) of equation (5) is the prediction output equation.

[0026] Step 4: Design a dual-mode nonlinear optimization algorithm to realize the multi-output time-varying constraint protection management. The limitation processing capacity can be saved under the premise of more accurate, which can save the traditional limiter and selection logic, thereby reducing the complexity and conservatism of the original controller. At the same time, in order to further reduce the calculation burden of online optimization iteration, the state in the control process is divided, and the corresponding nonlinear optimization algorithm is also divided into dual-mode.

[0027] Step 4.1: The switching signal of the dual-mode prediction controller is designed as:

[0028]

[0029] N is the prediction time domain, y p (k+i) = C p x p (k+i) represents the predicted value of y p at the future i step from the current time; Due to the actual problem of an aero-engine, as the control quantity u p increases, the constrained output has jumped out of the limit area before the control output reaches the command value.

[0030] Given the deviation value ε, when δ<ε, it is determined that the system is located in the non-limiting area at this time, and the control system switches to the non-limiting mode for work. The switching controller is a state feedback controller for calculation; otherwise, it is determined that the system is in the limiting area, and the control system switches to the limiting mode. The switching controller is a limiting mode prediction controller based on a nonlinear optimization algorithm for calculation.

[0031] Step 4.2: Design of the limiting mode prediction controller based on the nonlinear optimization algorithm.

[0032] In the limiting mode, considering the limiting operation of the constrained output y q , the controller obtained by the rolling optimization calculation directly affects the control quantity up The whole closed loop system is in a transition state, and the constraint output is considered to satisfy the non-limiting while y p Try to achieve r; the following quadratic objective function is proposed:

[0033]

[0034]

[0035] y p (k+i)=C p x p (k+i)

[0036]

[0037]

[0038] In the formula, a, b, c are weight coefficients; r is the expected value of y p ; N is the prediction time domain; y q (k+i) represents the predicted output value of y q at the future i step from the current time, which is obtained by iteration from formula (5); y q,max is the maximum constraint limit value of y q , which is set according to the dimension of y q ; It should be noted that in the actual dynamic process in the aero-engine, the constraint value is not the fixed value usually adopted in the traditional limiting protection method, but can be customized according to the specific requirements to achieve the time-varying output constraint.

[0039] For the quadratic objective function optimization problem with constraints, the SQP method is used to solve it, and the online optimization module obtains the parameters of the optimal state feedback controller K of the future N steps at each sampling time and outputs, and then obtains the optimal control amount At the same time, the first component is taken as the initial value of the next time optimization calculation, and the rolling optimization control is realized.

[0040] The beneficial effects of the present application are: the aero-engine active limiting protection control method under time-varying output constraints proposed in the present application has universality, and the limiting output value can be integrated into the objective function regardless of the dimension. At the same time, the active limiting protection control method strategy has the characteristics of real-time rolling optimization, so it supports real-time variable of the actual constraint value. According to the actual demand of the turbofan engine, the double-mode nonlinear optimization algorithm can be used for active limiting protection control of multi-output time-varying constraints. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is a flow chart of the aero-engine active limiting protection control method under time-varying output constraints;

[0042] Figure 2 is the control principle diagram of the active limit protection control method of the aero-engine under time-varying output constraints;

[0043] Fig. 3(a) is a high-pressure rotor speed comparison diagram of the step response of the LPV model and the nonlinear model when wfm=1500 kg / h, the input step Δwfm=500, and the scheduling parameter λ changes from 0.21 to 0.34;

[0044] Fig. 3(b) is a high-pressure rotor speed comparison diagram of the step response of the LPV model and the nonlinear model when wfm=3500 kg / h, the input step Δwfm=500, and the scheduling parameter λ changes from 0.70 to 0.81;

[0045] Figure 4 is a large-range variation tracking result diagram of the high-pressure rotor speed of the LPV model based on the state feedback controller;

[0046] Figure 5 is a high-pressure rotor speed tracking comparison diagram based on the control of the dual-mode nonlinear optimization algorithm;

[0047] Fig. 6(a) is a comparison diagram of the turbine inlet temperature under time-varying constraints based on the control of the dual-mode nonlinear optimization algorithm and the ordinary state feedback control;

[0048] Fig. 6(b) is a partial enlargement of the limited part of Fig. 6(a);

[0049] Fig. 7(a) is a comparison diagram of the turbine drop pressure ratio under time-varying constraints based on the control of the dual-mode nonlinear optimization algorithm and the ordinary state feedback control;

[0050] Fig. 7(b) is a partial enlargement of the limited part of Fig. 7(a). DETAILED DESCRIPTION

[0051] The present application will be further described below in combination with the drawings. The research object of the present application is an aero-engine control system under various mechanical structure limits and safe operation limits, and the design method thereof is as shown in the flowchart, and the detailed design steps are as follows. Figure 1

[0052] Step 1: based on the aero-engine test data, an aero-engine LPV linear variable parameter model is established;

[0053] Since the dynamic characteristics of the aero-engine change continuously with the high-pressure rotor speed, the high-pressure rotor speed n H is selected as the scheduling parameter, which is represented as λ, and is normalized:

[0054]

[0055] ​To ensure the accuracy of the LPV linear parameter varying model, 81 steady-state nominal points are divided into three sub-intervals according to the relationship between the matrix elements and λ: [0, 0.34], [0.34, 0.71] and [0.71, 1]. The linear parameter varying (LPV) model of the aero-engine is fitted and established in each sub-interval:

[0056]

[0057] x p =[Δn L Δn H ] T are the increments of the low-pressure rotor speed (r / min) and the high-pressure rotor, respectively, p =Δw f is the increment of the engine fuel flow (kg / h), y p =Δn H is the increment of the engine high-pressure rotor speed, y q =[ΔT 41 ΔPi t ] T are the turbine inlet temperature (℃) and the turbine pressure ratio, respectively. It can be seen from the simulation comparison between the LPV linear parameter varying model and the nonlinear model that the step response of the LPV linear parameter varying model at different speeds can well fit the step response of the nonlinear model, and the steady-state error is less than 1%, which indicates that the designed LPV model has high matching degree with the nonlinear model in the scheduling parameter range, and can accurately reflect the dynamic response change rule of the nonlinear model in the scheduling parameter range.

[0058] Step 2: Design an augmented model and a state feedback controller for the aero-engine LPV linear parameter varying model;

[0059] Step 2.1: For the constraint variable y p , the control command is r, and the output error is e = r - y p , the integral of the error is x e = ∫e dt, and the integral of the error is augmented as a state variable to eliminate the steady-state error of the error system. The state equation of the generalized controlled object in the augmented system is:

[0060]

[0061] In the formula,

[0062] Step 2.2: Adding state feedback controller to the augmented system. The state feedback controller designed according to the LPV linear parameter varying model shown in equation (2) can easily guarantee the tracking performance of the augmented system, and the control rate is Then the state space equation of the aeroengine closed loop system is

[0063]

[0064] Where K = [K1K2];

[0065] Step 2.3: Designing the switching controller based on H ∞ algorithm;

[0066] It is very difficult to solve the parameterized LMI optimization problem for the aeroengine closed loop system (3), and it is much easier to convert it into SOS programming in operation: design the state feedback H ∞ controller K (λ) = W (λ) X -1 (λ), given H ∞ performance index {γ ∞,i > 0} i∈(1,α) If there exists a real symmetric matrix X (λ), a real matrix W (λ) and a SOS polynomial matrix {M i (λ)} i∈(1,α) , the following polynomial matrix is obtained, otherwise it cannot be switched to the state feedback controller;

[0067]

[0068] SOS for any i ∈ (1, α) is satisfied, then the aeroengine closed loop system is asymptotically stable, and satisfies H ∞ performance index γ ∞ = max{γ ∞,i} i∈(1,α) . Where g i (λ) = (λ i - λ i,min )(λ i,max - λ i ). The state feedback controller is K (λ) = [K1 (λ) K2 (λ)] = W (λ) X -1 (λ).

[0069] According to the above theory, the corresponding switching controller of the aeroengine is designed. Select γ ∞ = 2, and put it into the augmented model data, and solve it through SOSTOOLS to get K1 (λ) = [-2.21 λ 2 + 0.16 λ + 2.1, -27.72 λ 2 - 2.61 λ - 52.01], K2 (λ) = [-132.56 λ 2-26.08λ + 832.77].

[0070] The simulation is performed according to the following process:

[0071] Phase a: In the process of 0-1 s, the engine is in the first sub-region. The high-pressure rotor speed command is kept at 1.162 x 10 4 (θ = 0) in 0-0.5 s, and then the high-pressure rotor speed command is raised to 0.834 (θ = 0.259) at 0.5 s, and then kept;

[0072] Phase b: In the process of 1-1.5 s, the engine is in the second sub-region. The high-pressure rotor speed command is raised to 1.323 x 10 4 (θ = 0.480) at 1 s, and crosses the switching surface for the first time;

[0073] Phase c: In the process of 1.5-2.5 s, the engine is in the third sub-region. The high-pressure rotor speed command is raised to 1.492 x 10 4 (θ = 0.925) at 1.5 s, and crosses the switching surface for the second time;

[0074] Phase d: In the process of 2.5-3 s, the engine is in the first sub-region. The high-pressure rotor speed command is lowered to 1.180 x 10 4 (θ = 0.054) at 2.5 s, and crosses the switching surface for the third time.

[0075] According to the simulation results, it can be seen that the following effect of the LPV model output is good with the change of the control command r, the response time is within 0.25 s, and the steady-state error is less than 0.5%, which meets the control requirements. At the same time, in the switching of different sub-regions, the stability of the switching can be ensured, and the change is smooth when crossing the switching surface.

[0076] Step 3: Design a prediction model according to formula (3);

[0077] Step 3.1: Considering the calculation burden of online optimization iteration, a discrete prediction model containing the main dynamic characteristics of an aero-engine is proposed to replace the component-level mathematical model which can accurately describe the dynamic characteristics of an aero-engine but is relatively complex in calculation and operation. A discrete piecewise linear model is established through a continuous model, and G and H are the discrete state matrices of A(λ) and B, respectively;

[0078]

[0079] Step 3.2: The discrete prediction model contains the main dynamic characteristics of an aero-engine, which is in the form of a steady-state nonlinear and dynamic linear as a prediction model, and the output state after kT (T is the sampling time) is predicted through iteration (k+1) times;

[0080] The output matrix C specific parameter value is determined by the scheduling matrix λ in the current state, if the current operating point is between two steady state points, the system matrix, output matrix is the interpolation of the matrix at two steady state nominal points. Similarly, the state vector in the current stable working state is also the interpolation of the corresponding vector at the steady state nominal point, in addition, the output equation z(k) of formula (5) is also called the prediction output equation;

[0081] Step 4: design a dual-mode nonlinear optimization algorithm to realize the multi-output time-varying constraint protection management, which can save the traditional limiter and selection logic under the premise of more accurate limit processing capability, thereby reducing the complexity and conservatism of the original controller, and at the same time, in order to further reduce the calculation burden of online optimization iteration, the state in the control process is divided, and the corresponding nonlinear optimization algorithm is also divided into dual-mode accordingly;

[0082] Step 4.1: the switching signal of the dual-mode predictive controller is designed as:

[0083]

[0084] N is the prediction time domain, y p (k+i)=C p x p (k+i) represents the predicted value of y p at the future i step from the current time. Due to the actual problem of aero-engine, with the continuous increase of the control variable u p , the constrained output has jumped out of the limit area before the control output reaches the command value.

[0085] Given the deviation value ε, when δ<ε, it is determined that the system is located in the non-limiting region at this time, and the control system switches to the non-limiting mode for work, and the switching controller is a state feedback controller for calculation; otherwise, it is determined that the system is in the limiting region, and the control system switches to the limiting mode, and the switching controller is a limiting mode predictive controller based on nonlinear optimization algorithm for calculation.

[0086] Step 4.2: design of limiting mode predictive controller based on nonlinear optimization algorithm;

[0087] In the limiting mode, considering the limiting operation of the constrained output y q , the controller obtained by the rolling optimization calculation directly affects the value of u p , and the whole closed-loop system is in a transition state, only needs to consider that the constrained output does not exceed the limit at the same time y p reaches r as much as possible, in the actual problem, y p can reach r only in the non-limiting state, and the system stability does not need to be considered. Therefore, the following quadratic objective function is proposed:

[0088]

[0089]

[0090] y p (k+i) = C p x p (k+i)

[0091]

[0092]

[0093] where a, b, c are weight coefficients; r is the desired value of y p ; N is the length of time domain; y q (k+i) represents the predicted output value of y q at the i-th step in the future from the current time, which is obtained by iteration according to formula (4), y q,max is the maximum constraint limit value of y q , which is set according to the dimension of y q . It should be noted that in the actual dynamic process in an aero-engine, the constraint value is not a fixed value as usually adopted in the traditional limit protection method, but can be customized according to specific requirements to achieve time-varying output constraint.

[0094] For this constrained quadratic optimization problem, the SQP method is adopted to solve it, and the online optimization module obtains the parameters of the optimal controller K of the future N steps at each sampling time and outputs, thereby obtaining the optimal control amount At the same time, the first component is taken as the initial value of the optimization calculation at the next time, realizing the rolling optimization control.

[0095] In order to further illustrate the superiority of the active limit protection control strategy of the aero-engine under the time-varying output constraint, a simulation comparison is made with the H ∞ switching controller without adding the limit algorithm.

[0096] The simulation gives the control instruction speed as 1.396x10 4 ~1.433x10 4 , and the given time-varying constraint value

[0097]

[0098]

[0099] It can be seen that under the action of the controller designed by the protection control strategy, although the control output n HThe response speed of the proposed method is about 0.7s slower than that of the unrestricted protection strategy, but the control instruction value is still accurately reached, and the constrained output T 41 and Pi t The accurate limit is under the time-varying constraint, and the dynamic response effect of the aero-engine is maximally ensured, so that the high-pressure rotor speed reaches the instruction as fast as possible under the limit, greatly reducing the conservatism of the traditional limiting method.

Claims

1. An active limit protection control method for an aeroengine under time-varying output constraints, characterized in that, The method comprises the following steps: Step 1: based on the turbofan engine test data, segmenting n steady-state nominal points, fitting a turbofan engine LPV linear variable parameter model in each sub-interval; where x p ∈R n is the state variable, u p ∈R m is the control input of the turbofan engine, y p ∈R p is the output quantity, y q ∈R q is the constraint variable, i is the sub-interval serial number, the scheduling parameter λ takes a value of a physical quantity reflecting the dynamic performance of the turbofan engine, λ (i,min) ≤λ≤λ (i,max) , λ (i,min) and λ (i,max) are respectively the minimum value and the maximum value of the scheduling parameter in the i-th LPV linear variable parameter model, the system matrix A i (λ)∈R n×n , the system matrix B i (λ)∈R n×m , the system matrix C i (λ)∈R q×n , the system matrix D i (λ)∈R q×m , R (·) represents a (·) -dimensional real number column vector, R a×t represents a a×b-dimensional real number matrix; C p is the output quantity corresponding matrix of the turbofan engine; Step 2: designing an augmented model and a state feedback controller for the turbofan engine LPV linear variable parameter model; Step 2.1: For the output quantity y p , the control instruction is r, the output deviation e = r - y p , the integral of the deviation is x e = ∫e dt, the integral of the deviation is augmented to the state quantity, and the augmented system is obtained to eliminate the steady-state error of the output deviation system; the state equation of the generalized controlled object in the augmented system is: In the formulae: Step 2.2: Adding state feedback controller to the augmented system; the state feedback controller K(λ) = W(λ)X -1 (λ) designed according to the LPV linear parameter varying model shown in equation (2) ensures the tracking performance of the augmented system, and the control rate is Then the state equation of the closed loop system of turbofan engine is: Step 2.3: H-based ∞ Switching controller design for algorithms; For the closed-loop system formula (3) of turbofan engine, the LMI optimization problem containing polynomial is solved by SOS programming; the state feedback H ∞ controller K(λ) = W(λ)X -1 (λ), X(λ) is a real symmetric matrix, and W(λ) is a real matrix; given H ∞ performance index {γ ∞,i > 0} i∈(1,α) When there is a real symmetric matrix X(λ), a real matrix W(λ) and a SOS matrix {M i (λ)} i∈(1,α) , the following polynomial matrix is obtained, otherwise it cannot be switched to a state feedback controller For any i∈(1,α), it satisfies the SOS matrix, then the closed loop system of turbofan engine is asymptotically stable, and satisfies H ∞ Performance index γ ∞ = max{γ ∞,i} i∈(1,α) ; wherein g i (λ) = (λ i - λ i,min )(λ i,max - λ i ); Step 3: designing a discrete prediction model according to formula (3); Step 3.1: proposing a discrete prediction model containing the main dynamic characteristics of the turbofan engine, establishing a discrete segmented linear model through an existing continuous model, and G and H are discrete state matrices of A(λ) and B respectively; Step 3.2: the discrete prediction model includes the main dynamic characteristics of the turbofan engine, which is a steady-state nonlinear and dynamic linear as a form of the discrete prediction model, and the output state after kT (the sampling time) is predicted through iteration (k+1) times, and T is the sampling time; The output matrix C parameter value is determined by the scheduling quantity λ in the current state. When the current working point is between two steady state points, the system matrix and the output matrix are interpolations of the matrices at the two steady state nominal points. The state vector x(k) in the current stable working state is an interpolation of the corresponding vectors at the steady state nominal points. The output equation z(k) of equation (5) is a predicted output equation. Step 4: designing a double-mode nonlinear optimization algorithm for realizing multi-output time-varying constraint protection management, Step 4.1: the switching signal of the double-mode prediction controller is designed as follows: N is the prediction horizon, y p (k+i) = C p x p (k+i) denotes the predicted value of y p at the future step i from the current time instant. Given the deviation value ε, when δ<ε, it is determined that the system is located in the non-limiting area at this time, the control system is switched to the non-limiting mode for work, and the switching controller is the state feedback controller for calculation; otherwise, it is determined that the system is in the limiting area, the control system is switched to the limiting mode, and the switching controller is the limiting mode prediction controller based on the nonlinear optimization algorithm for calculation; Step 4.2: designing the limiting mode prediction controller based on the nonlinear optimization algorithm; In the constrained mode, considering the constraint of the output y q , the control variable u p is directly affected by the controller calculated by the rolling optimization, and the whole closed-loop system is in a transient state, considering that the output y p tends to r while satisfying the constraint, the following quadratic objective function is proposed: y p (k+i) = X p x p (k+i) where a, b, c are weight coefficients; r is the expected value of y p ; N is the prediction horizon; y q (k+i) represents the predicted output value of y q at the i-th step in the future from the current time, which is obtained iteratively by equation (5); y q,max is the maximum constraint limit value of y q , which is set according to the dimension of y q ; for this constrained quadratic form objective function optimization problem, the SQP method is used to solve it, and the online optimization module obtains the parameters of the optimal state feedback controller K of the future N steps at each sampling time and outputs, and then obtains the optimal control amount At the same time, the first component is taken as the initial value of the next time optimization calculation, and the rolling optimization control is realized.

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