Transition state control method for aero-engine based on event-triggered model predictive control

Abstract

The application provides an aero-engine transition state control method based on an event-triggered model predictive control, and belongs to the field of aero-engine transition state optimization and control. A dynamic forced triggering mechanism is proposed for an aero-engine control system, a dynamic forced triggering interval is designed, and an event-triggered model predictive control algorithm (EMPC) is formed. The EMPC algorithm is used to control the aero-engine transition state process, so that the transition state control law design under the constraint condition is realized. The application can greatly reduce the number of solving optimization problems while basically guaranteeing the tracking effect of the control method, and saves the calculation resources.

Description

TECHNICAL FIELD

[0001] The application relates to a design method for optimizing a transition state control law of an aero-engine and belongs to the technical field of aero-engine transition state optimization and control. BACKGROUND

[0002] Generally, in engine control, mainly includes steady state control and transition state control. The steady state control is to ensure that the engine has small performance fluctuations when a certain steady state point is disturbed and can restore to a stable state, which is a small deviation control problem. In the transition state control of the engine, part or all of the performance of the engine changes over time, and the commonly said acceleration and deceleration performance is the main form of the transition state performance of the engine, and the transition state performance of the engine directly affects the take-off and acceleration performance of the airplane. In order to obtain good transition state performance, it is necessary to reasonably design the acceleration and deceleration control law of the engine, so that the engine can be ensured to have the shortest transition state time from one working state to another working state under the condition of meeting the constraint. For military aircraft, this can meet the combat demand of rapidity; similarly, for civil aircraft, from the perspective of safe flight, it is also necessary to ensure that the transition state time of the engine is short. Therefore, it is necessary to study the transition state control law of the engine.

[0003] The engine runs from the slow vehicle state to the take-off state to form a transition state acceleration curve. The engine needs to run from the slow vehicle state to the take-off state in the shortest time, and the acceleration curve needs to be as close to the safety boundary line as possible. If the acceleration curve of the engine is close to the safety boundary line but does not exceed the safety boundary line, then the performance variables of the engine run in the state close to the limit. In this way, the speed of the engine can quickly reach the maximum, and the transition to another stable state is realized with the maximum speed, which realizes the rapid acceleration transition process of the engine. Similarly, from the cruise state to the slow vehicle state, the closer the deceleration curve is to the lean-out boundary, the shorter the deceleration time is. When the engine works in the transition state, it must run in the corresponding limit boundary range, and these limit boundaries constitute the basis of the transition state control.

[0004] Model predictive control (MPC) is a new type of computer control algorithm generated in the process control field in the 1970s. With the great potential in dealing with the control problems of complex constraints and multivariable systems, model predictive control is favored in the industrial process control field.

[0005] Model predictive control itself is a method based on time rolling optimization, and long prediction time domain, system uncertainty and the like make the online optimization problem of model predictive control more complex. The rolling solution of the complex optimization control problem is frequently carried out by the system, so that the online calculation burden of the controller is heavy, which becomes the main difficulty hindering the practical application of the predictive control method. At present, reducing the online calculation amount and avoiding unnecessary resource waste have become the key research direction in the field of model predictive control theory research.

[0006] The control method based on the time trigger mechanism causes a large amount of system resource waste, and gradually cannot meet the increasing control demand. People have proposed a control strategy based on the event-driven mechanism.

[0007] The application adopts an event-triggered model predictive control method to optimize the design of the engine transient state control law, so that the engine can effectively improve the engine transient state performance without exceeding the constraint boundary condition. While basically guaranteeing the tracking effect of the control method, the frequency of solving the optimization problem is greatly reduced, and the calculation resources are saved. SUMMARY

[0008] In order to ensure that the engine transient state does not exceed the limit, while meeting the engine transient state time requirement, and aiming at the open-loop control problem of the engine in the acceleration and deceleration process, the application provides a design method for optimizing the control law of the engine transient state.

[0009] In order to achieve the above purpose, the technical scheme adopted by the application is:

[0010] An event-triggered model predictive control method for an aero-engine transient state control method, comprising the following steps:

[0011] Step 1, design the MPC control strategy of the aero-engine model

[0012] Consider the aero-engine model given in the following form:

[0013]

[0014] Wherein, x(t)∈R n represents the system state, u∈R m control input, y∈R k represents the output. A, B, C and D represent constant matrices with appropriate dimensions. The output includes the tracking output y t , such as the speed of the fan or the core machine, and the limited output y l , such as fan surge margin, turbine inlet temperature and the like. The control input can be composed of fuel flow, nozzle area and guide vane angle.

[0015] The system (1) can be discretized as:

[0016] where A d , B d , C d and D d are discretized matrices, x(k) represents the current system state, x(k+1) represents the next system state, y(k) represents the current output value, and u(k) represents the value of the current control input.

[0017] Then the present application introduces an extended state where u(k-1) represents the value of the control input at the previous time, and then the system (2) can be converted into:

[0018]

[0019] where and C de =(C d D d ) represent system matrices, x e (k), x e (k+1) are introduced augmented state variables, and Δu(k) represents the change in the current control input.

[0020] According to the discrete system (3), the present application can obtain the prediction of the system:

[0021]

[0022] where

[0023]

[0024]

[0025] where A x , B x , C x , D y represent system matrices, X(k) represents the current system state, Y(k) represents the current output value, ΔU(k) represents the change in the current control input value, N y and N u represent the prediction time domain and the control time domain, respectively, y r (k+i), i=1, 2,..., N y represents the reference trajectory of the output from the current time to the i-th step in the future, and Δu(k+i), i=1, 2,..., N y -1 represents the change in the control input from the current time to the i-th step in the future.

[0026] The present application then considers a tracking problem, which is to set a reference signal y r , which represents the output signal to be tracked. In order to minimize the error between the actual output of the engine and the desired output, the problem can be formulated as the following optimization problem:

[0027]

[0028] where N y and N u represent the prediction horizon and the control horizon, respectively; P and Q are weight matrices; h is the sampling interval; the notation (t+ih), i = j, k represents the prediction of the relevant variable after i samplings from the current time t; the subscripts max and min represent the maximum and minimum limits of the relevant variable, respectively. In MPC, the reference value is always given by y r (k+j) = y(k) + (y ref - y(k))(l - e -jh / τ ), where y ref is the target value and τ is a time constant, such that the tracking reference y r becomes a smooth curve.

[0029] Applying the system (4) to the cost function (5), the minimum value optimization problem can be obtained as:

[0030]

[0031] Let M(k) = C y x e (k) - y r (k), it can be derived from (6) that which can be further converted to the following quadratic programming:

[0032]

[0033] Note that the matrices C y and D y should be calculated using the corresponding rows in C and D. For example, if C t x = y t , C t should be used to derive C y . Finally, the optimization problem (5) can be converted to the quadratic programming (7) with the constraint A i ΔU(k) ≤ b(k), where

[0034] This quadratic programming is easy to solve by applying some traditional optimization methods. However, when using traditional MPC methods, the optimization problem is solved at every sampling instant, which leads to excessive computational burden. Therefore, the present invention will focus on the design of event-triggered mechanism to reduce the number of solving optimization problems.

[0035] Second step, design event-triggered mechanism

[0036] The main idea of event-triggered control is to design a threshold to check whether the control strategy should be updated or whether the sampling information should be updated. In EMPC, the threshold is used to determine whether the optimization problem should be solved to obtain a new control input sequence.

[0037] Consider ||y t (t)-y r (t)||≥δ, where δ is a threshold. If the error between the tracking output and the given reference output y r exceeds the threshold, the event is triggered and the optimization problem (5) should be solved to derive a new control input sequence. When the event is not triggered, the values in the control input sequence obtained by solving the optimization problem previously are uploaded one by one directly without re-solving the optimization problem. Specifically:

[0038] Suppose at time t k , the event is triggered, by solving the optimization problem, the control input sequence u(t k ), u(t k +h), …, u(t k +(N u -1)h) is obtained and the first value u(t k ) is updated to the controller. At the next sampling instant t k +h, if the event is not triggered, the second value u(t k +h) is updated to the controller. If the event is not triggered before uploading the last value of the control input sequence, the values of the optimized control input sequence are uploaded one by one to the controller repeatedly. If the event is still not triggered at the next sampling instant t k +N u h, a zero-order holder (ZOH) is taken to hold the last input value, i.e. u(t k +N u h) = u(t k +(N u -1)h). In this way, the solving of the optimization problem will not be performed again before the event is triggered. Therefore, this strategy will reduce the control effect to some extent. Therefore, the present invention introduces a dynamic forced triggering mechanism to improve the control effect. Consider the following dynamic forced triggering interval related to the reference change.

[0039]

[0040] wherein T n is a positive integer, is a normal number, n∈Z + According to different change trends of the reference trajectory, different forced triggering intervals are provided. Therefore, the overall event triggering mechanism is as follows:

[0041]

[0042] The beneficial effects of the present application are:

[0043] The present application is directed to an aero-engine control system, on the basis of a model predictive control algorithm, a dynamic forced triggering mechanism is proposed, a dynamic forced triggering interval is designed, and an event-triggered model predictive control algorithm (EMPC) is formed. The EMPC algorithm is used to control the engine transition state process, and the transition state control law design under the constraint condition is realized. While basically guaranteeing the tracking effect of the control method, the number of solving optimization problems is greatly reduced, and the calculation resources are saved. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is the realization of EMPC control scheme in Simulink;

[0045] Figure 2 is the preset reference trajectory;

[0046] Figure 3 is the surge margin SM f change;

[0047] Figure 4 is the temperature T change;

[0048] Figure 5 is the speed tracking curve under EMPC control;

[0049] Figure 6 is the speed tracking error curve under EMPC control;

[0050] Figure 7 is the comparison chart of MPC and EMPC event triggering times. DETAILED DESCRIPTION

[0051] In order to make the method problems solved by the present application, the method scheme adopted and the method effects achieved more clear, the present application will be further described in detail below in combination with the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application. In addition, it should be noted that, in order to facilitate description, only the parts related to the present application are shown in the drawings, but not all the contents.

[0052] The invention is based on a nonlinear model of a certain type of dual-spool turbofan engine, and the control structure diagram is as shown in Figure 1 .

[0053] First, design the MPC control strategy of the aero-engine model

[0054] Consider the aero-engine model given in the following form

[0055]

[0056] where x(t)∈R n represents the system state, u∈R m control input, y∈R k represents the output. A, B, C, and D represent constant matrices with appropriate dimensions. The output here includes the tracking output y t , such as the speed of the fan or the core engine, and the limited output y l , such as the fan surge margin, turbine inlet temperature, etc. The control input can be composed of fuel flow, nozzle area, and guide vane angle.

[0057] The system (1) can be discretized as:

[0058]

[0059] where A d , B d , C d , and D d are discretized matrices, x(k) represents the current system state, x(k+1) represents the next system state, y(k) represents the current output value, and u(k) represents the current control input value.

[0060] Then the invention introduces an extended state Then the system (10) can be converted to

[0061]

[0062] where and C de = (C d D d ) represent the system matrix, x e (k), x e (k+1) is the augmented state variable introduced, and Δu(k) represents the change of the current control input.

[0063] According to the discrete system (11), the invention can derive the prediction of the system:

[0064]

[0065] wherein

[0066]

[0067] A, B, C, and D x , respectively x , respectively x , respectively y denotes a system matrix, X(k) denotes a current system state, Y(k) denotes a current output value, ΔU(k) denotes a variation of a current control input value, N y and N u represent a prediction horizon and a control horizon, respectively, y r (k+i), i = 1, 2,..., N y denotes a reference trajectory from a current time to an i-th future output, Δu(k+i), i = 1, 2,..., N y -1 denotes a variation of a control input from a current time to an i-th future control input.

[0068] The present application then considers a tracking problem, in which a reference signal y r is given, which represents an output signal to be tracked. In order to minimize an error between an actual output of the engine and a desired output, the problem can be expressed as the following optimization problem:

[0069]

[0070] wherein N y and N u represent a prediction horizon and a control horizon, respectively; P and Q are weight matrices; h is a sampling interval; y r (t+ih), i = j, k denotes a prediction of a relevant variable after i times of sampling from a current time t; and subscripts max and min denote maximum and minimum limits of the relevant variable, respectively. In the MPC, a reference value is always given by y ref (k+j) = y(k) + (y -jh / τ - y(k))(1 - e ref ), where y r is a target value and τ is a time constant, so that the tracking reference y y becomes a smooth curve.

[0071] By applying the system (12) to the cost function (13), a minimum value optimization problem

[0072]

[0073] Let M(k) = C e x r(k), which can be derived from (14) It can be further converted to the following quadratic programming:

[0074]

[0075] Note that the matrix C y and D y should be calculated using the corresponding rows in C t and D t , respectively. For example, if C t x = y y , then C i should be derived using C t . Finally, the optimization problem (13) can be converted to a quadratic programming (15) with constraints A r ΔU(k)≤b(k), where

[0076] This quadratic programming can be easily solved by applying some traditional optimization methods. However, when using traditional MPC methods, the optimization problem is solved at every sampling instant, which leads to excessive computational burden. Therefore, the present invention will focus on the design of an event-triggered mechanism to reduce the number of times the optimization problem is solved.

[0077] Second step, design an event-triggered mechanism

[0078] The main idea of event-triggered control is to design a threshold to check whether the control strategy should be updated or whether the sampling information should be updated. In EMPC, the threshold is used to determine whether the optimization problem should be solved to obtain a new control input sequence.

[0079] Consider ||y t (t)-y r (t)||≥δ, where δ is a threshold. If the error between the tracking output and the given reference output y r exceeds the threshold, an event is triggered and the optimization problem (13) should be solved to derive a new control input sequence. When the event is not triggered, the control input sequence obtained from the previous optimization problem is directly uploaded without re-solving the optimization problem. Specifically: assume that at time t k , the event is triggered and by solving the optimization problem, the control input sequence u(t k ), u(t k +h), …, u(t k +(N u -1)h) is obtained and the first value u(t k ) is updated to the controller. At the next sampling instant t k +h, if the event is not triggered, the second value u(t k+h) Update to the controller. If no event is triggered before the last value of the uploaded control input sequence, repeat the upload of the optimized control input sequence values ​​to the controller one by one. If the event occurs at the next sampling time t k +N u If h is still not triggered, a zero-order hold (ZOH) is used to hold the last input value, i.e., u(t). k +N u h)=u(t k +(N u -1)h). Thus, the optimization problem will not be solved before the event is triggered. Therefore, this strategy will reduce the control effect to some extent. Therefore, this invention introduces a dynamic forced triggering mechanism to improve the control effect. Consider the following dynamic forced triggering interval related to reference changes.

[0080]

[0081] Where T n It is a positive integer. For positive constants, n∈Z + Different forced trigger intervals are provided based on the different changing trends of the reference trajectory. Therefore, the overall event triggering mechanism is as follows:

[0082]

[0083] The following is a simulation application of this invention on an actual engine model:

[0084] The goal is to control the rotational speed of the low-pressure turbine in the JT9D aero engine. l To track Figure 2 The preset reference trajectory is shown below. Note that the reference trajectory includes three different transients: two acceleration phases and one deceleration phase. Assume the aircraft engine is operating stably at point A on the reference trajectory, and then a transient acceleration phase begins at point B, lasting 0.5 seconds. The control input is the fuel-air ratio r. fa The outputs are the temperature T after the high-pressure turbine and the fan surge margin SM. f During transient processes, this invention requires T ≤ 2150R and SM. f ≥15%. The EMPC control scheme with the event-triggered mechanism designed in this patent is applied to the JT9D aero-engine. H is set to 0.01s, N... y =N u =3h, σ=1. The dynamic trigger interval is designed as follows:

[0085]

[0086] The main idea is that if the reference trajectory accelerates with a certain acceleration, the trigger interval is increased to reduce the computational burden, but if the speed of the reference trajectory switches to a steady state or a small transient state, the trigger interval is shortened to reduce the possible overshoot caused by system inertia. Then, the simulation results are shown in Figure 5 Due to the strong constraint management ability of the MPC method, the temperature T after the high-pressure turbine and the fan surge margin SM f do not exceed their limits during the transient period. The tracking results and tracking errors are shown in Figure 5 and Figure 6 It can be observed that the EMPC method with (16) achieves good control effect, and the total tracking error is less than 0.25%. In order to further compare, the trigger time generated by the algorithm is shown in Figure 7 , where the red dots represent the trigger time, and the blue dots represent the event trigger time. It is pointed out that when the EMPC method is applied, the computational burden is significantly reduced: thanks to the dynamic trigger mechanism, it is not necessary to frequently solve the optimization problem when using strategy (16).

[0087] It can be seen from the above that the transition state control law method of the aero-engine proposed by the present application is effective and feasible, which greatly reduces the number of solving optimization problems while basically ensuring the tracking effect of the control method, saves computing resources. And it has universality and can be applied to the transition state control law optimization of other types of engines.

[0088] The above-described embodiments only express the implementation of the present application, but cannot be interpreted as a limitation on the scope of the patent of the present application. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which all belong to the protection scope of the present application.

Claims

1. An aero-engine transition state control method based on event-triggered model predictive control, characterized in that, The method comprises the following steps: The first step is to design an MPC control strategy for an aero-engine model The aero-engine model is given as follows: where x(t) e R n represents the system state, u e R m is the control input, y e R k represents the output; A, B, C and D are constant matrices with appropriate dimensions; the output includes the tracking output y t and the constrained output y l ; the control input can be composed of fuel flow, nozzle area and guide vane angle; The system (1) can be discretized as: where A d , B d , C d , and D d are discretized matrices, x(k) represents the current time system state, x(k+1) represents the next time system state, y(k) represents the current output value, and u(k) represents the current control input value. The extended state is then introduced where u(k - 1) denotes the value of the control input at the previous time instant, then the system (2) is transformed into: wherein and C de = (C d D d ) represents the system matrix, x e (k), x e (k+1) is the introduced augmented state variable, and Δu(k) represents the change in the current control input. According to the discrete system (3), the prediction of the system is obtained: wherein wherein A x , B x , C x , and D y represent a system matrix, X(k) represents a current system state, Y(k) represents a current output value, ΔU(k) represents a change amount of a current control input value, N y and N u represent a prediction time domain and a control time domain, respectively, y r (k+i), i=1, 2,..., N y represents a reference trajectory output from the current time to the i-th step in the future, and Δu(k+i), i=1, 2,..., N y -1 represents a change amount of the control input from the current time to the i-th step in the future. Then consider a tracking problem, pre-set a reference signal y r , which represents the output signal to be tracked; in order to minimize the error between the actual output of the engine and the expected output, the problem is expressed as the following optimization problem: s.t.u min ≤u(t+jh)≤u max y min ≤ y l (t + kh)≤ y max where N y and N u represent the prediction and control horizons, respectively; P and Q are weight matrices; h is the sampling interval; the expression (t+ih), i = j, k represents the prediction of the relevant variable after i samples from the current time t; the subscripts max and min represent the maximum and minimum limits of the relevant variable, respectively; in the MPC, the reference value is always given by y r (k+j) = y(k) + (y ref -y(k))(l-e -jh / τ ), where y ref is the target value and τ is the time constant, such that the tracking of the reference y r becomes a smooth curve; The system (4) is applied to the cost function (5), and a minimum value optimization problem is obtained: Let M(k) = C y x e (k)-y r (k), it follows from (6) that which can be further converted into the following quadratic program: Finally, the optimization problem (5) is converted into a quadratic program with constraints A i ΔU(k)≤b(k) of the form (7), where The second step is to design an event-triggered mechanism The main idea of event-triggered control is to design a threshold to check whether the control strategy should be updated or whether the sampling information should be updated; in EMPC, the threshold is used to determine whether the optimization problem should be solved to obtain a new control input sequence; Consider ||y t (t)-y r (t)||≥δ, where δ is a threshold value; if the error between the tracking output and the given reference output y r is beyond the threshold value, an event is triggered and the optimization problem (5) should be solved to derive a new sequence of control inputs; when the event is not triggered, the values in the previously solved sequence of control inputs are directly uploaded one by one without re-solving the optimization problem.

2. The method of claim 1, wherein, The second step is specifically as follows: Suppose at time t k , an event is triggered, by solving the optimization problem, the control input sequence u(t k ), u(t k +h), …, u(t k +(N u -1)h) is obtained, and the first value u(t k ) is updated to the controller; at the next sampling time t k +h, if the event is not triggered, the second value u(t k +h) is updated to the controller; if the event is not triggered before the last value of the control input sequence is uploaded, the optimized control input sequence values are uploaded to the controller one by one repeatedly; if the event is still not triggered at the next sampling time t k +N u h, a zero-order holder (ZOH) is taken to keep the last input value, i.e. u(t k +N u h) = u(t k +(N u -1)h). Before the event trigger, the optimization problem will not be solved again, and the control effect will be reduced; therefore, a dynamic forced triggering mechanism is introduced to improve the control effect; the following dynamic forced triggering interval related to the reference change is considered where T n is a positive integer, is a normal number, n∈Z + According to different change trends of the reference trajectory, different forced triggering intervals are provided; therefore, the overall event triggering mechanism is as follows:

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