A model predictive control method for variable cycle engines

Abstract

The invention relates to the field of variable cycle engine control, and specifically discloses a variable cycle engine model predictive control method, which compares a state estimation value calculated by a state observer with an input reference signal, outputs an optimal control quantity to an engine model according to a control law, linearizes a nonlinear engine variable specific heat model, extracts its state space description, and discretizes the state space description, and transforms a state observer parameter design problem into a state matrix eigenvalue optimal problem for solving the observer's dynamic characteristics; the invention uses a linear model as the output of model prediction, optimizes a cost function, balances the relationship between a final steady-state error and a controller output, has a relatively small calculation cost, and can complete the part with a large calculation cost offline, has good real-time performance, and realizes the engine working at an optimal operating point.

Description

Technical Field

[0001] The invention relates to the field of variable cycle engine control, and in particular to a variable cycle engine model predictive control method. Background Art

[0002] The variable cycle engine is a new type of variable bypass aircraft engine. Compared with ordinary turbofan engines, variable cycle engines have higher unit thrust, and compared with ordinary turbojet engines, variable cycle engines have a larger bypass ratio and can achieve lower fuel consumption. However, the variable cycle engine has more adjustable components than ordinary aircraft engines, and traditional control methods such as improved multivariable PID cannot well achieve the engine working at the optimal operating point.

[0003] In the existing patents of variable cycle engine control, for example, patent application number CN202211307109.0 discloses a modeling method for designing a steady-state control law model for a variable cycle engine. The important control parameters are determined by sensitivity analysis, so that the model pays more attention to the parameters that have a greater impact on the system performance, which helps to optimize the control effect and improve the operating efficiency of the engine. However, in terms of data dependence, the performance of the model depends to a large extent on the quality and integrity of the input data. If there is noise in the data or the data is not collected completely in practical applications, the accuracy and reliability of the model may be affected; patent application number CN202310893665.9 discloses a computer-based optimal control method for the acceleration process of a variable cycle engine. Through a highly mathematical method, the C-Bézier curve is used to represent the open-loop control plan of the adjustable geometric mechanism in the variable cycle engine. By minimizing the mode switching time and thrust fluctuation as the optimization goal, the engine operation is also set as a constraint not to exceed the safety boundary. This method uses a multi-objective optimization approach, taking into account both the shortest mode switching time and the smallest thrust fluctuation, ensuring the comprehensive performance of the optimization results. However, the formulation and optimization of the C-Bézier curve requires high computing resources and mathematical modeling skills, which increases the complexity and cost of the implementation process.

[0004] To this end, the present application proposes a variable cycle engine model predictive control method to solve the above technical problems. Summary of the invention

[0005] In view of the existing problems, the present invention provides a variable cycle engine model predictive control method, which uses a linear model as the output of model prediction, and optimizes the cost function by taking the output increment of the controller, the error between the current output and the specified output, and the accumulated error as the cost function, thereby well balancing the relationship between the final steady-state error and the controller output. At the same time, the state quantity of the engine is used as the hard constraint of the system, and the entire problem is converted into a constrained dynamic programming problem to solve the optimal control increment. The computational cost is relatively small, and the part with a larger computational cost can be completed offline, which has good real-time performance and can effectively solve the problems raised in the background technology.

[0006] To solve the above problems, the present invention adopts the following technical solutions:

[0007] A variable cycle engine model predictive control method comprises the following steps:

[0008] 1) In the controller part, the model predictive control algorithm based on output increment control is used as the control law. The state estimation value calculated by the state observer is compared with the input reference signal. According to the control law, the optimal control quantity is output to the engine model;

[0009] 2) In the engine model part, the nonlinear engine variable specific heat model is linearized, its state space description is extracted, and the state space description is discretized to adapt to the simulation operation and reduce the computational cost required for the simulation;

[0010] 3) In the state observer part, the Lumberg full-dimensional state observer is used, and the state observer parameter design problem is transformed into solving the optimal problem of the state matrix eigenvalue of the observer's dynamic characteristics to ensure that the estimated state converges to the real state as quickly as possible.

[0011] As a further solution of the present invention: in step 1), the output increment of the controller, the error between the current output and the specified output, and the accumulated error are used as a cost function, and the cost function is: (1)

[0012] in, is the value of the cost function, Representative The augmented state of the step includes the current state, the reference state and the control amount of the previous step; is the control quantity input in the current state, R is the control quantity penalty coefficient matrix, , is the transformed augmented weight matrix.

[0013] As a further solution of the present invention: the cost function in step 1) is subjected to matrix operation and transformation, the quadratic sum is split into a compact matrix form, and each state quantity on the predicted time series is expanded to represent the system matrix And the control amount The product form of , hard constraints are imposed on the cost function, and the cost function is converted into the form of quadratic programming. The final cost function is converted into: (2)

[0014] in, , is the value of the cost function, It can be expressed as a column vector composed of the control quantities of the first k steps, It can be expressed as the coefficient matrix in the cost function The diagonal matrix composed of is the coefficient matrix of the linear system state equation, To predict the number of steps, is the current system status;

[0015] Add hard constraints and convert the upper and lower limits of the system state and state quantity into the standard form of quadratic programming problem. The constraints of state and control quantity are written as: (3)

[0016] Expand the system state and control quantity, write them into a compact matrix form, and perform linear transformation to convert them into the following form:

[0017] (4)

[0018] in,

[0019] Substitute the initial state of the system and the discrete control sequence into the state quantity at each time point, write it in a compact format, and perform matrix transformation according to the standard form of hard constraints in quadratic programming, we have:

[0020] (5)

[0021] in,

[0022]

[0023] As a further solution of the present invention: in step 2), the engine model system is linearized using the forward method, and the linear model is expressed in the form of a state space description: (6)

[0024] in, is the state quantity of the system, is the control quantity of the system, is the state quantity of the system.

[0025] As a further solution of the present invention: in step 2), the state space description model is converted into a generalized state space model, and the generalized state space description is discretized. After the transformation, the generalized state space model is expressed as: (7)

[0026] in, .

[0027] As a further solution of the present invention: the estimated state expression of the Lumberg full-dimensional state observer in step 3) is: (8)

[0028] in, represents the estimated state at the next moment, represents the estimated state at this moment, Output for the current system, is the current control input, are the four coefficient matrices describing the system state space, is the observer gain matrix; ensure Negative determination, the observer parameter L is designed to ensure The maximum eigenvalue of is as small as possible, so that the estimated state is as close to the true state as possible.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention uses a linear model as the output of model prediction, and optimizes the cost function by taking the output increment of the controller, the error between the current output and the specified output, and the accumulated error as the cost function, thereby balancing the relationship between the final steady-state error and the controller output. At the same time, the state quantity of the engine is taken as a hard constraint of the system, and the entire problem is converted into a constrained dynamic programming problem to solve the optimal control increment. The computational cost is relatively small, and the part with a larger computational cost can be completed offline, with good real-time performance, so that the engine can operate at the optimal operating point. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a block diagram of the variable cycle engine model predictive control system of the present invention;

[0031] Figure 2 This is a large closed-loop control principle diagram of a variable cycle engine in the present invention;

[0032] Figure 3 FIG1 is a simulation diagram of the control effect of the control system in MATLAB according to the present invention;

[0033] Figure 4FIG2 is a simulation diagram of the control effect of the control system in MATLAB according to the present invention;

[0034] Figure 5 A comparison diagram of the high-pressure rotor speed under the conditions of constraint and unconstraint in the present invention;

[0035] Figure 6 It is a comparison diagram of the temperature before the turbine under the conditions of constraint and no constraint in the present invention;

[0036] Figure 7 It is a comparison diagram of the low-pressure rotor speed under constrained and unconstrained conditions in the present invention. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0038] This embodiment provides a variable cycle engine model predictive control method, such as Figure 1 As shown in the figure, A and B are the system matrices of the linearized system, Q, R, and S are the three gain matrices of optimal control, which can be adjusted according to needs. This figure illustrates the basic principles of the variable cycle engine model predictive control system.

[0039] In the controller part, the model predictive control algorithm based on output increment control is adopted as the control law. The state estimation value calculated by the state observer is compared with the input reference signal. According to the control law, the optimal control quantity is output to the engine model.

[0040] In the engine model part, the nonlinear engine variable specific heat model is linearized, its state space description is extracted, and the state space description is discretized to adapt to the simulation operation and reduce the computational cost required for the simulation.

[0041] In the state observer part, the Lumberg full-dimensional state observer is used, and the state observer parameter design problem is transformed into solving the optimal problem of the state matrix eigenvalue of the observer dynamic characteristics to ensure that the estimated state converges to the real state as quickly as possible.

[0042] Specific:

[0043] The controller is designed by adopting a model predictive controller design scheme based on output increment control, and at the same time considers the constraints of various state quantities of the engine, such as the high and low pressure rotor speeds not over-speeding, the turbine inlet temperature not exceeding the limit, etc. Ultimately, the cost function is minimized based on the prediction of the linear model, and the first step control quantity is output.

[0044] The controller's output increment, the error between the current output and the specified output, and the accumulated error are used as the cost function, which is: (1)

[0045] in, is the value of the cost function, Representative The augmented state of the step includes the current state, the reference state and the control amount of the previous step; is the control quantity input in the current state, R is the control quantity penalty coefficient matrix, , is the transformed augmented weight matrix. The purpose of introducing these augmented matrices is to make the steady-state error of the system as small as possible. The problem is regarded as a trajectory tracking problem, and the system tracks the reference input command by minimizing the error between the actual state and the reference state. Formula (1) is the standard cost function form. However, it is difficult to add constraints to the cost function in this form. Therefore, it is necessary to convert it into a quadratic programming form. After a series of matrix operations and transformations, the quadratic sum is decomposed into a compact matrix form. At the same time, the state quantities on the predicted time series are expanded and represented as the system matrix And the control amount The final cost function is transformed into the product form of: (2)

[0046] in, , is the value of the cost function, It can be expressed as a column vector composed of the control quantities of the first k steps, It can be expressed as the coefficient matrix in the cost function The diagonal matrix composed of is the coefficient matrix of the linear system state equation, To predict the number of steps, is the current system status;

[0047] In the part of adding hard constraints, the upper and lower limits of the system state and state quantity need to be converted into the standard form of the quadratic programming problem. The constraints of the state and control quantity are: (3)

[0048] The system expands the state quantity and control quantity into a compact matrix form and performs linear transformation to convert them into the following form: (4)

[0049] in, .

[0050] However, this form is still different from the standard form of constraints in quadratic programming, and the state quantity needs to be eliminated. Therefore, the initial state and discrete control sequence need to be substituted into the state quantity at each time point and written in a compact format. The matrix transformation is performed according to the standard form of hard constraints in quadratic programming, and the result is: (5)

[0051] in,

[0052]

[0053] At this point, the constraints have been converted into the standard optimization form of quadratic programming, the constraints on the system state and control quantity have been successfully added to the quadratic programming problem, and the solution to the system's optimal control input has been successfully converted into a quadratic programming problem for solution.

[0054] System model design:

[0055] The variable cycle engine is a system with strong nonlinear characteristics. The method of designing controllers for nonlinear systems is not yet fully mature. Therefore, this paper linearizes the engine model at the design point using the forward method and expresses the linear model in the form of state space description: (6)

[0056] in, is the state quantity of the system, is the control quantity of the system, It is the state quantity of the system. It should be pointed out that here the system is treated as a three-input and three-output system with three control quantities. The existence of the inverse can be guaranteed when the system is inverted in the later stage. There is no need to process the generalized inverse, which is more concise in mathematics.

[0057] In order to facilitate instruction tracing, the classic state space description model needs to be transformed into a generalized state space model. In order to facilitate computer simulation, the generalized state space description also needs to be discretized. After the transformation, the generalized state space model can be expressed as: (7)

[0058] in, .

[0059] State Observer Design:

[0060] Since the system state is not easy to measure in actual process, but the accurate state value is very important for the model predictive control process, it is necessary to design a state observer with the fastest convergence speed to meet the needs of the control system.

[0061] Here, the framework of the Lumberg full-dimensional state observer is used for state observer design. The estimated state expression of the Lumberg observer can be written as: (8)

[0062] in, represents the estimated state at the next moment, represents the estimated state at this moment (solved at the previous moment), Output for the current system, is the current control input, are the four coefficient matrices describing the system state space, is the observer gain matrix. To make the estimated state as close to the real state as possible, it is necessary to ensure Negative definite, so this rule is used to calculate the observer parameters To design, we only need to transform this problem into an optimization problem, ensuring The maximum eigenvalue of can be as small as possible.

[0063] In this embodiment, a control algorithm based on model predictive control is used for the control of a variable cycle engine. A traditional linear model is used as the output of model prediction. The cost function is optimized by taking the output increment of the controller, the error between the current output and the specified output, and the accumulated error as the cost function. This balances the relationship between the final steady-state error and the controller output. At the same time, the state quantities of the engine, such as the speed of the high and low pressure turbines and the temperature before the turbine, are taken as hard constraints of the system. The entire problem is converted into a constrained dynamic programming problem to solve the optimal control increment. The computational cost is relatively small, and the part with a larger computational cost can be completed offline. Therefore, in the case of actual engine control, it has good real-time performance.

[0064] Control system verification

[0065] 1) Simulation verification

[0066] Run simulation on the control effect of the control system in MATLAB and impose a 3% step expectation of low-pressure speed on the system, such as Figure 3-4 As shown in the simulation results, it can be seen that the overshoot of the system is controlled within 0.3%, which effectively avoids the speed of the low-pressure rotor Over limit, at the same time the turbine inlet temperature There is not much fluctuation, which prevents the turbine from overheating. From the perspective of adjustment time, the system is stabilized within 100 time steps, which corresponds to a simulation time of 1s. Therefore, the system adjustment time is less than 1s, which can also meet the design requirements.

[0067] 2) Verify the impact of state constraints on system performance

[0068] The constrained model predictive control algorithm is compared with the unconstrained quadratic optimal control algorithm. The results are as follows: Figure 5-7 As shown, it can be seen that compared with the uncontrolled quadratic optimal control, the overshoot of the engine turbine pre-temperature is reduced by 70% after adding constraints, which effectively avoids the influence of turbine overheating on engine performance. At the same time, by observing the adjustment time, it can be seen that even if the constraints are added, the adjustment time of the low-pressure rotor does not change much, and can still be controlled within 100 time steps, that is, within 1s. The addition of constraints will not significantly increase the adjustment time of the system, which fully reflects the superiority of the control algorithm.

[0069] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus.

[0070] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A variable cycle engine model predictive control method, characterized in that: The steps include: 1) In the controller part, the model predictive control algorithm based on output increment control is used as the control law. The state estimation value calculated by the state observer is compared with the input reference signal. According to the control law, the optimal control quantity is output to the engine model; 2) In the engine model part, the nonlinear engine variable specific heat model is linearized, its state space description is extracted, and the state space description is discretized to adapt to the simulation operation and reduce the computational cost required for the simulation; 3) In the state observer part, the Lumberg full-dimensional state observer is used, and the state observer parameter design problem is transformed into solving the optimal problem of the state matrix eigenvalue of the observer dynamic characteristics to ensure that the estimated state converges to the real state as soon as possible; In step 1), the output increment of the controller, the error between the current output and the specified output, and the accumulated error are used as the cost function, and the cost function is: Among them, J is the value of the cost function, x a[k] =[x [k] x d[k] u [k-1] ] T The augmented state of the k-1th step includes the current state, the reference state and the control amount of the previous step; u [k] is the control quantity input in the current state, R is the control quantity penalty coefficient matrix, S a =[I-I0] T S[I-I0],Q a =[I-I0] T Q[I-I0] is the transformed augmented weight matrix; The cost function in step 1) is subjected to matrix operations and transformations, the quadratic sum is split into a compact matrix form, and each state quantity on the predicted time series is expanded and expressed as the product of the system matrix AB and the control quantity u, and hard constraints are imposed on the cost function, and the cost function is converted into a quadratic programming form. Finally, the cost function is converted into: J=U T [k] (τ T Ωτ+ψ)U [k] +U T [k] (τ T Ωφ)x [k|k] (2) Among them, J is the value of the cost function, U [k] It can be expressed as a column vector composed of the first k steps of control quantities, Ω can be expressed as a diagonal matrix composed of the coefficient matrices Q and R in the cost function, A and B are the coefficient matrices of the linear system state equation, N p is the number of predicted steps, x [k|k] is the current system status; Add hard constraints and convert the upper and lower limits of the system state and state quantity into the standard form of quadratic programming problem. The constraints of state and control quantity are written as: Expand the system state and control quantity, write them into a compact matrix form, and perform linear transformation to convert them into the following form: in, Substitute the initial state of the system and the discrete control sequence into the state quantity at each time point, write it in a compact format, and perform matrix transformation according to the standard form of hard constraints in quadratic programming, we have: in, In the step 2), the engine model system is linearized using the sequential method, and the linear model is expressed in the form of a state space description: Where x = [n L n H T t4 ] T is the state quantity of the system, u=[W f A8A 163 ] T is the control quantity of the system, y=[F N lepreprs] T is the state quantity of the system; In the step 2), the state space description model is transformed into a generalized state space model, and the generalized state space description is discretized. After the transformation, the generalized state space model is expressed as: in, The estimated state expression of the Lumberg full-dimensional state observer in step 3) is: in, represents the estimated state at the next moment, represents the estimated state at this moment, y [k] Output for the current system, u [k] is the current control input, ABCD are the four coefficient matrices describing the system state space, and L is the observer gain matrix; to ensure that A-LC is negative definite, the observer parameter L is designed to ensure that the maximum eigenvalue of A-LC is as small as possible, so that the estimated state is as close to the real state as possible.

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