Fuel gas generator online optimization and negative regulation constraint control system design method based on model predictive control

Abstract

The invention provides a gas generator online optimization and negative regulation constraint control system design method based on model predictive control, which realizes real-time online optimization and control of a gas flow regulation system under the condition of meeting gas flow negative regulation constraint. The control system is mainly composed of two parts, the first part is a prediction model obtaining layer, on the premise that an execution mechanism is considered, the actual working state of a gas generator in each control period serves as a steady state point, a small deviation linearization model near the current steady state point is established in real time, and the small deviation linearization model serves as a prediction model to be provided for a controller; and the second part is a control rule decision-making layer which is composed of a model prediction controller. The controller obtains the optimal control quantity of the current control period by solving a constrained quadratic programming problem on the basis of the prediction model of the current control period under the condition of considering the gas flow negative regulation constraint, and effective control over the gas flow regulation system is achieved.

Description

Technical Field

[0001] The invention provides a method for designing a gas generator online optimization and negative regulation constraint control system based on model predictive control, belonging to the technical field of control and simulation of a gas flow regulating system of a solid rocket ramjet engine. Background Art

[0002] The working performance of a solid rocket ramjet engine is closely related to the air-fuel ratio in the afterburner. Effective control of the gas flow rate can stabilize the air-fuel ratio within the required range, thus ensuring good engine performance and thrust regulation capabilities.

[0003] At present, there are many kinds of gas flow control methods, the most common ones are variable combustion surface type, variable combustion rate type, non-blocking type and blocking type. Among them, the blocking type regulation scheme changes the throat area of ​​the gas generator by controlling the movement of the gas flow control valve, thereby adjusting the pressure and gas flow. This scheme is flexible to adjust and has a large adjustment range. It has become the most widely used gas flow regulation scheme. The blocking type gas flow regulation system has strong time-varying and nonlinearity. The document "Research on a Pressure Control Algorithm for a Flow-Adjustable Gas Generator" designs a feedforward adaptive PID controller to effectively overcome the adverse effects of the system variable parameter characteristics on the control. However, this document does not consider the negative regulation phenomenon of gas flow. The document "Optimization Control of Flow Regulation of Gas Generators for Solid-state Engines" points out that the negative regulation phenomenon of gas flow will seriously affect the performance of the engine and even cause the engine to stall. How to effectively consider nonlinearity in the design of the control system and introduce gas flow negative regulation constraints is the key to improving the performance of the control system. Model predictive control is a control method that uses a predictive model to optimize the dynamic trajectory of the system, which can handle various variable constraints in the control process. For nonlinear systems, directly using nonlinear models as prediction models can significantly improve control accuracy, but this method easily introduces complex nonlinear optimization problems and is difficult to meet the real-time requirements of the control system.

[0004] The present invention takes the actual working state of the gas generator as the steady-state point, establishes the linearized state space model of the gas flow regulation system in each control cycle in real time under the premise of considering the actuator, and designs a model predictive controller. While introducing the negative regulation constraint of the gas flow, the real-time online optimization of the gas flow regulation system is realized, effectively reducing the amount of calculation and improving the performance of the control system. Summary of the invention

[0005] In order to solve the problems of system nonlinearity and time-varying, realize effective control of the gas flow regulation system and suppress the negative regulation of gas flow, the present invention proposes a gas generator online optimization and negative regulation constraint control design method based on model predictive control.

[0006] The technical solution of the present invention:

[0007] A design method for online optimization and negative regulation constraint control system of gas generator based on model predictive control. The control system mainly consists of two parts. The first part is the prediction model acquisition layer, and the second part is the control law decision layer.

[0008] The specific steps are as follows:

[0009] S1. Prediction model acquisition layer

[0010] Taking the actual working state of the current control cycle of the gas generator as the steady-state point, a small deviation linearization model of the gas flow regulation system near the steady-state point of the current control cycle is established in real time and continuously. The small deviation linearization model is obtained by Taylor expansion, expressed in the form of a state space equation, and provided to the model predictive controller as a prediction model. The specific steps are as follows:

[0011] S1.1 When the gas generator of a choked solid rocket ramjet engine is operating, the combustion process satisfies the following zero-dimensional interior ballistic differential equation:

[0012]

[0013] Among them, p c and q mf are the internal pressure and gas flow rate of the gas generator, V g and A t are the free volume and throat area of ​​the gas generator, V gini is the initial throat area, α and n are the burning rate coefficient and pressure index of the propellant, 0<n<1, C * and ρ b are the characteristic velocity and density of the propellant, A b is the burning surface area of ​​the propellant, Γ is the specific heat ratio function;

[0014] The S1.2 gas flow regulation system adopts pressure closed-loop control and uses a servo motor as an actuator. The servo motor changes the throat area of ​​the gas generator by adjusting the opening of the gas flow control valve, thereby changing the pressure and adjusting the gas flow. When working, the actuator is approximately an inertia link.

[0015]

[0016] Where u is the input quantity, T a is the time constant of the actuator;

[0017] S1.3 Based on S1.1-S1.2, the nonlinear differential equation model of the gas flow control system with actuator is obtained:

[0018]

[0019] When the system is in a stable state, the steady-state pressure p c0 , gas flow q mf0 , throat area A t0 , the input quantity u0 satisfies the following relationship

[0020]

[0021] S1.4 is based on S1.3, at a certain steady-state point (p c0 ,A t0 ,q mf0 ,u0) and free volume V g0 Taylor expansion is used to perform small deviation linearization nearby, and the steady-state relationship is used to simplify it, that is, the transfer function model of the gas flow regulation system is obtained:

[0022]

[0023]

[0024] in, is the transfer function of pressure and throat area, is the transfer function of gas flow and throat area, G a (s) is the transfer function of throat area and input quantity, Δp c (s), Δq mf (s), ΔA t (s), Δu(s) are the Laplace transforms of pressure increment, gas flow increment, throat area increment, and input increment, respectively, and s is a complex variable;

[0025]

[0026] S1.5 is based on S1.4. The gas flow regulation system is a second-order system. The gas generator pressure and throat area are taken as state quantities, and the gas generator pressure is taken as the output quantity. The small deviation linearized state space equation of the gas flow regulation system near a certain steady-state point is obtained:

[0027]

[0028] in,

[0029] Δx=[Δp c ,ΔA t ] T , whose elements are the increments of the state quantity relative to the steady-state point, Δp c , ΔA t are the increments of pressure and throat area relative to the steady state point, is the first-order derivative of Δx;

[0030] Δy=Δpc , whose elements are the increments of the output relative to the steady-state point;

[0031] Δu is the increment of input relative to the steady-state point;

[0032] C = [1 0];

[0033] S1.6 is based on S1.5, and discretizes the small deviation linearized state space equation of the gas flow control system. The sampling period of the discretization is the same as the control period of the control system, which is T s The discretized state space equation is expressed as:

[0034]

[0035] Among them, k represents the kth control cycle, A d , B d , C d is the discretized parameter matrix;

[0036] Δx(k)=[Δp c (k),ΔA t (k)] T It represents the increment of the state quantity of the kth control cycle relative to the steady-state point, Δp c (k), ΔA t (k) respectively represent the increments of pressure and throat area relative to the steady-state point in the kth control cycle;

[0037] Δy(k)=Δp c (k) represents the increment of the output of the kth control cycle relative to the steady-state point;

[0038] Δu(k) represents the increment of the input quantity of the kth control cycle relative to the steady-state point;

[0039] Simplifying it into the form of absolute quantity, the state space equation can be expressed as:

[0040]

[0041] Where x0 = [p c0 ,A t0 ] T , x0 and u0 are steady-state values;

[0042] x(k)=[p c (k),A t (k)] T represents the state quantity of the kth control cycle, p c (k), A t (k) respectively represent the pressure and throat area of ​​the kth control cycle;

[0043] y(k)=p c (k) indicates the output of the kth control cycle;

[0044] u(k) represents the input quantity of the kth control cycle; I is the unit matrix;

[0045] S1.7 In each control cycle, the internal pressure of the gas generator is measured in real time by the sensor as the pressure steady-state point p of the current control cycle. c0_k , A is calculated based on the S1.3 steady-state relationship t0_k ,q mf0_k 、u 0_k The free volume V of the current control cycle g0_k Use the following formula to estimate:

[0046]

[0047] Based on S1.6, using the steady-state point (p c0_k ,A t0_k ,q mf0_k ,u 0_k ) and V g0_k , the small deviation linearized state space equation near the steady-state point of the current control period is calculated in real time and provided as a prediction model to the model predictive controller for trajectory optimization;

[0048] S2. Control law decision layer

[0049] Based on the prediction model of the current control cycle obtained in step S1, a model predictive controller for the gas generator pressure closed loop is constructed. The model predictive controller constructs the objective function based on the difference between the output and the set value, and the difference between the input and the set value. The input limit of the system and the negative adjustment limit of the gas flow are used as constraints. The optimal control vector of the current control cycle is obtained by solving the constrained quadratic programming problem online. The specific steps are as follows:

[0050] S2.1 obtains the steady-state point (p c0_k ,A t0_k ,q mf0_k ,u 0_k ) and V g0_k The state space equation of the gas flow control system nearby is:

[0051]

[0052] Among them, A d_k , B d_k , C d_k is the parameter matrix calculated in control cycle k;

[0053] p set_k =(IA d_k )x 0_k -B d_k u 0_k , x 0_k =[p c0_k ,A t0_k ] T ;

[0054] Taking the prediction time domain and control time domain of the model predictive controller as N, the prediction formulas for the state sequence and output sequence are as follows:

[0055]

[0056] in,

[0057] x′(k)=[p c ′(k),A t ′(k)] T represents the measured data of the state quantity in the control cycle k, p c ′(k), A t ′(k) represent the measured values ​​of pressure and throat area in control period k, respectively;

[0058] represents the state prediction at time k+i in control cycle k, They represent the predicted values ​​of pressure and throat area at time k+i in control cycle k respectively;

[0059] represents the output prediction for time k+i in control cycle k,

[0060] represents the input prediction at time k+i in control cycle k;

[0061]

[0062] S2.2 designs the online optimization objective function as follows:

[0063]

[0064] Among them, y r 、u r is the set value, R and Q are weighting coefficients;

[0065] Based on S2.1, the online optimization objective function can be simplified as:

[0066]

[0067] in,

[0068] After expansion, merging and removing the constant terms that have no effect on J, the online optimization objective function is simplified to the following quadratic form:

[0069]

[0070] in,

[0071] S2.3 is based on S2.1, with input restriction constraints

[0072]

[0073] Can be simplified to

[0074]

[0075] in,

[0076] u min 、u max are the lower and upper limits of the input quantity respectively;

[0077] S2.4 When the gas generator is working, the gas flow will produce negative regulation phenomenon, that is, in the initial stage of flow regulation, the gas flow will have a change trend opposite to the expected regulation direction. Define the concepts of absolute negative regulation and relative negative regulation, respectively, with R a and R us Absolute negative regulation refers to the maximum change in gas flow in the opposite direction of the expected result, and relative negative regulation refers to the ratio of absolute negative regulation to the difference between the steady-state flow and the initial flow in the flow regulation cycle.

[0078] For the gas flow regulation system, the following gas flow negative regulation limit constraints are introduced:

[0079]

[0080] in,

[0081] q mf_ini Indicates the initial value of the gas flow rate in the current regulation cycle, q mf_end Indicates the final value of the gas flow rate in the current regulation cycle;

[0082] SIG=sign(q mf_end -q mf_ini ), indicating the expected change direction of the gas flow rate in the current regulation cycle;

[0083] It represents the predicted value of gas flow at time k+i in control cycle k;

[0084] R us_set is the relative negative adjustment constraint value, set to the pressure measurement value p of the current control period c ′(k) and estimated free volume V g0_k Function:

[0085] R us_set =aV g0_k +bp c ′(k)+c

[0086] Among them, a, b, and c are all setting parameters, a>0, b>0. As the pressure and free volume increase, the negative adjustment phenomenon intensifies, and R us_set becomes larger, relaxing the constraint value of the relative negative adjustment.

[0087] When the S2.5 gas generator is working, the gas flow cannot be measured directly. Based on S1, the gas flow is estimated using the following relationship:

[0088]

[0089] in,

[0090] The actual measured value p in the current control cycle c ′(k), A t ′(k) is Taylor expanded and high-order small quantities are ignored. The gas flow estimation formula is simplified to:

[0091]

[0092] S2.6 is based on S2.4-S2.5, and the gas flow negative adjustment limit constraint is simplified to:

[0093]

[0094] After simplification, the gas flow negative adjustment limit constraint is recorded as:

[0095]

[0096] in,

[0097]

[0098] Based on S2.1, the gas flow negative regulation limit constraint is simplified to:

[0099]

[0100] Among them, A neq_U =A neq_X BU , b neq_U =b neq_X -A neq_X A X x′(k)-A neq_X P X ;

[0101] S2.7 is based on S2.2-S2.3 and S2.6, and constructs the following optimization problem for the gas flow regulation system:

[0102]

[0103] According to the objective function and constraints, rolling optimization is achieved by solving the constrained quadratic programming problem online and building a model predictive controller. Take the first element of the optimal control quantity sequence As the actual control quantity of the current control cycle, it acts on the actual controlled system.

[0104] Beneficial effects of the present invention:

[0105] (1) The present invention proposes a method for online optimization and negative regulation constraint control design of a gas generator based on model predictive control. For the acquisition of the prediction model, the nonlinear model is not directly used, but the actual working state of each control cycle of the gas generator is used as the steady-state point, and the small deviation linearized state space model near the current steady-state point is obtained in real time through Taylor expansion as the prediction model. Compared with directly using the nonlinear model as the prediction model and solving the nonlinear optimization problem online, the present invention can reduce the complexity and calculation time of the optimization problem and improve the real-time performance of the control system.

[0106] (2) In the process of designing the model predictive controller, the present invention introduces a negative regulation constraint for the negative regulation phenomenon of the gas flow rate. Negative regulation of the gas flow rate may cause a significant change in the afterburner pressure and engine thrust of the solid rocket ramjet engine, and even cause the engine to enter a subcritical state, threatening the stability of the engine. To this end, the present invention introduces a negative regulation constraint of the gas flow rate in the controller design, and simplifies it into a linear inequality constraint through Taylor expansion, which not only ensures the realization of the negative regulation constraint, but also reduces the solution time of the optimization problem, thereby improving the real-time performance of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 It is the control principle diagram of the present invention.

[0108] Figure 2 is the gas generator pressure p under the square wave command signal c Change curve.

[0109] Figure 3is the gas flow rate q under square wave command signal mf Change curve.

[0110] Figure 4 is the low pressure section (0.5-5MPa) gas generator pressure p c Change curve.

[0111] Figure 5 The gas flow rate q in the low pressure section (0.5-5MPa) mf Change curve.

[0112] Figure 6 The gas generator pressure p is the full pressure section (0.5-10MPa) c Change curve.

[0113] Figure 7 The gas flow rate q in the full pressure section (0.5-10MPa) mf Change curve. DETAILED DESCRIPTION

[0114] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0115] This embodiment is a design method for online optimization and negative regulation constraint control system of a gas generator based on model predictive control. The principle is as follows: Figure 1 As shown, the specific steps include:

[0116] Step 1: Prediction model acquisition layer

[0117] Taking the actual working state of the current control cycle of the gas generator as the steady-state point, a small deviation linearization model of the gas flow regulation system near the steady-state point of the current control cycle is established in real time and continuously. The small deviation linearization model is obtained by Taylor expansion, expressed in the form of a state space equation, and provided to the model predictive controller as a prediction model. The specific steps are as follows:

[0118] Step 1.1: The gas flow regulating system in this embodiment adopts a choke type regulating scheme, using a sliding disc valve as a gas flow regulating valve. When the gas generator is working, the actuator adjusts the angle of the sliding disc valve to change the throat area, thereby adjusting the pressure and gas flow.

[0119] When the gas generator of a choked solid rocket ramjet engine is working, the combustion process satisfies the following zero-dimensional interior ballistic differential equation:

[0120]

[0121] Among them, p c and q mf are the internal pressure and gas flow rate of the gas generator, V gand A t are the free volume and throat area of ​​the gas generator, V gini is the initial throat area, α and n are the burning rate coefficient and pressure index of the propellant, 0<n<1, C * and ρ b are the characteristic velocity and density of the propellant, A b is the burning surface area of ​​the propellant, Γ is the specific heat ratio function;

[0122] Step 1.2: The gas flow regulation system adopts pressure closed-loop control and uses a servo motor as an actuator. The servo motor changes the throat area of ​​the gas generator by adjusting the opening of the gas flow control valve, thereby changing the pressure and adjusting the gas flow. When working, the actuator is approximately an inertia link.

[0123]

[0124] Where u is the input quantity, T a is the time constant of the actuator;

[0125] In this embodiment, T a =0.1;

[0126] Step 1.3: Based on formulas (1)-(2), the nonlinear differential equation model of the gas flow control system with actuator is obtained:

[0127]

[0128] When the system is in a stable state, the steady-state pressure p c0 , gas flow q mf0 , throat area A t0 , the input quantity u0 satisfies the following relationship

[0129]

[0130] Step 1.4: Based on step 1.3, at a steady-state point (p c0 ,A t0 ,q mf0 ,u0) and free volume V g0 Taylor expansion is used to perform small deviation linearization nearby, and the steady-state relationship is used to simplify it, that is, the transfer function model of the gas flow regulation system is obtained:

[0131]

[0132] in, is the transfer function of pressure and throat area, is the transfer function of gas flow and throat area, G a(s) is the transfer function of throat area and input quantity, Δp c (s), Δq mf (s), ΔA t (s), Δu(s) are the Laplace transforms of pressure increment, gas flow increment, throat area increment, and input increment, respectively, and s is a complex variable;

[0133]

[0134] Step 1.5: Based on step 1.4, the gas flow regulation system is a second-order system. The gas generator pressure and throat area are taken as state quantities, and the gas generator pressure is taken as the output quantity. The small deviation linearized state space equation of the gas flow regulation system near a certain steady-state point is obtained:

[0135]

[0136] in,

[0137] Δx=[Δp c ,ΔA t ] T , whose elements are the increments of the state quantity relative to the steady-state point, Δp c , ΔA t are the increments of pressure and throat area relative to the steady state point, is the first-order derivative of Δx;

[0138] Δy=Δp c , whose elements are the increments of the output relative to the steady-state point;

[0139] Δu is the increment of input relative to the steady-state point;

[0140] C = [1 0];

[0141] Step 1.6: Based on step 1.5, the small deviation linearized state space equation of the gas flow control system is discretized. The sampling period of the discretization is the same as the control period of the control system, which is T s The discretized state space equation is expressed as:

[0142]

[0143] Among them, k represents the kth control cycle, A d , B d , C d is the discretized parameter matrix;

[0144] Δx(k)=[Δp c (k),ΔA t (k)]T It represents the increment of the state quantity of the kth control cycle relative to the steady-state point, Δp c (k), ΔA t (k) respectively represent the increments of pressure and throat area relative to the steady-state point in the kth control cycle;

[0145] Δy(k)=Δp c (k) represents the increment of the output of the kth control cycle relative to the steady-state point;

[0146] Δu(k) represents the increment of the input quantity of the kth control cycle relative to the steady-state point;

[0147] In this embodiment, T s =0.01s;

[0148] Simplifying it into the form of absolute quantity, the state space equation can be expressed as:

[0149]

[0150] Where x0 = [p c0 ,A t0 ] T , x0 and u0 are steady-state values;

[0151] x(k)=[p c (k),A t (k)] T represents the state quantity of the kth control cycle, p c (k), A t (k) respectively represent the pressure and throat area of ​​the kth control cycle;

[0152] y(k)=p c (k) indicates the output of the kth control cycle;

[0153] u(k) represents the input quantity of the kth control cycle;

[0154] I is the identity matrix;

[0155] Step 1.7: In each control cycle, use the sensor to measure the internal pressure of the gas generator in real time as the pressure steady-state point p of the current control cycle c0_k , A is calculated based on the steady-state relationship of formula (4) t0_k ,q mf0_k 、u 0_k The free volume V of the current control cycle g0_k Use the following formula to estimate:

[0156]

[0157] Based on step 1.6, using the steady-state point (p c0_k ,A t0_k ,q mf0_k ,u 0_k ) and V g0_k , the small deviation linearized state space equation near the steady-state point of the current control cycle can be calculated in real time and provided to the model predictive controller as a prediction model for trajectory optimization;

[0158] Step 2: Control Law Decision Layer

[0159] Based on the prediction model of the current control cycle obtained in step 1, the model predictive controller of the gas generator pressure closed loop is constructed. The model predictive controller constructs the objective function with the difference between the output and the set value, and the difference between the input and the set value. The input limit of the system and the negative adjustment limit of the gas flow are used as constraints. The optimal control vector of the current control cycle is obtained by solving the constrained quadratic programming problem online. The specific steps are as follows:

[0160] Step 2.1: Based on step 1, we can get the steady-state point (p c0_k ,A t0_k ,q mf0_k ,u 0_k ) and V g0_k The state space equation of the gas flow control system nearby is:

[0161]

[0162] Among them, A d_k , B d_k , C d_k is the parameter matrix calculated in control cycle k;

[0163] p set_k =(IA d_k )x 0_k -B d_k u 0_k , x 0_k =[p c0_k ,A t0_k ] T ;

[0164] Taking the prediction time domain and control time domain of the model predictive controller as N = 10, the prediction formulas of the state sequence and output sequence are as follows:

[0165]

[0166] in,

[0167] x′(k)=[p′ c (k),A′ t(k)] T represents the measured data of the state quantity in the control cycle k, p′ c (k), A′ t (k) respectively represent the measured values ​​of pressure and throat area in control period k;

[0168] represents the state prediction at time k+i in control cycle k, They represent the predicted values ​​of pressure and throat area at time k+i in control cycle k respectively;

[0169] represents the output prediction for time k+i in control cycle k,

[0170] represents the input prediction at time k+i in control cycle k;

[0171]

[0172] Step 2.2: Design the online optimization objective function as:

[0173]

[0174] Among them, y r 、u r is the set value, R and Q are weighting coefficients;

[0175] In this embodiment, R=1×10 -12 , Q = 9 × 10 6 ;

[0176] Based on step 2.1, the online optimization objective function can be simplified as:

[0177]

[0178] in,

[0179] After expansion, merging and removing the constant terms that have no effect on J, the online optimization objective function is simplified to the following quadratic form:

[0180]

[0181] in,

[0182] Step 2.3: Based on step 2.1, for input restriction constraints

[0183]

[0184] Can be simplified to

[0185]

[0186] in,

[0187] u min 、u max are the lower and upper limits of the input quantity respectively;

[0188] In this embodiment, take u min =1.3481×10 -5 m 3 、u max =8.0424×10 -4 m 3 ;

[0189] Step 2.4: When the gas generator is working, the gas flow will produce negative regulation phenomenon, that is, in the initial stage of flow regulation, the gas flow will have a trend of change opposite to the expected regulation direction. Define the concepts of absolute negative regulation and relative negative regulation, respectively, with R a and R us Absolute negative regulation refers to the maximum change in gas flow in the opposite direction of the expected result, and relative negative regulation refers to the ratio of absolute negative regulation to the difference between the steady-state flow and the initial flow in the flow regulation cycle.

[0190] For the gas flow regulation system, the following gas flow negative regulation limit constraints are introduced:

[0191]

[0192] in,

[0193] q mf_ini Indicates the initial value of the gas flow rate in the current regulation cycle, q mf_end Indicates the final value of the gas flow rate in the current regulation cycle;

[0194] SIG=sign(q mf_end -q mf_ini ), indicating the expected change direction of the gas flow rate in the current regulation cycle;

[0195] It represents the predicted value of gas flow at time k+i in control cycle k;

[0196] R us_set is the relative negative adjustment constraint value, set to the pressure measurement value p of the current control period c ′(k) and estimated free volume V g0_k Function:

[0197] R us_set =aV g0_k +bp c ′(k)+c (20)

[0198] Among them, a, b, and c are all setting parameters, a>0, b>0. As the pressure and free volume increase, the negative adjustment phenomenon intensifies, and R us_set becomes larger, relaxing the constraint value of the relative negative adjustment.

[0199] In this embodiment, a=2.2021, b=1×10 -8 , c = -0.005833;

[0200] Step 2.5: When the gas generator is working, the gas flow cannot be measured directly. Based on step 1, the gas flow is estimated using the following relationship:

[0201]

[0202] in,

[0203] The actual measured value p in the current control cycle c ′(k), A t ′(k) is Taylor expanded and high-order small quantities are ignored. The gas flow estimation formula is simplified to:

[0204]

[0205] Step 2.6: Based on steps 2.4 and 2.5, the gas flow negative adjustment limit constraint is simplified to:

[0206]

[0207] After simplification, the gas flow negative adjustment limit constraint is recorded as:

[0208]

[0209] in,

[0210]

[0211] Based on step 2.1, the gas flow negative regulation limit constraint is simplified to:

[0212]

[0213] Among them, A neq_U =A neq_X B U , b neq_U =b neq_X -A neq_XA X x′(k)-A neq_X P X ;

[0214] Step 2.7 Based on formulas (16), (18) and (25), the following optimization problem is constructed for the gas flow regulation system:

[0215]

[0216] According to the objective function and constraints, rolling optimization is achieved by solving the constrained quadratic programming problem online and building a model predictive controller. Take the first element of the optimal control quantity sequence As the actual control quantity of the current control cycle, it acts on the actual controlled system.

[0217] In order to further illustrate the control effect of the model predictive controller in this embodiment, the following simulation experiment is conducted to verify the effectiveness of the method in the present invention.

[0218] In order to verify the tracking ability of the control system to the square wave signal and observe the relationship between the negative adjustment of the gas flow and the simulation time, a square wave command signal is set, the simulation time is set to 90s, and its pressure value alternates between 0.5MPa and 3MPa, and the duration is 10s. c Change curve and gas flow q mf The change curve is as Figure 2 , Figure 3 shown.

[0219] By observation Figure 2 and Figure 3 , it can be seen that both pressure and gas flow can follow the changes of set values, and the control system has a short adjustment time. As the simulation time increases, the free volume becomes larger, the dynamic characteristics of the system slow down, and the adjustment time increases. In this process, the control system can relax the constraints on the negative adjustment intensity, and the negative adjustment constraints show an increasing trend. In the early stage of simulation, the free volume is small, the dynamic response of the system is fast, and a certain overshoot phenomenon occurs. The maximum pressure overshoot and gas flow overshoot are 3.3660% and 5.7493% respectively. The overshoot is small, which meets the design requirements of the control system.

[0220] In order to verify the control effect of the gas generator when it is working normally within the low-pressure adjustment range, a step command signal is set, the simulation time is set to 90s, the step amount is 1MPa, the change range is 0.5-5MPa, and the duration is 10s. c Change curve and gas flow q mf The change curve is as Figure 4 , Figure 5 shown.

[0221] By observation Figure 4 and Figure 5 It can be seen that the pressure and gas flow of the gas generator can follow the changes of the set value well. Under normal working conditions, the gas flow shows obvious negative regulation phenomenon, and the negative regulation phenomenon is aggravated with the increase of free volume and working pressure. The model predictive controller can effectively constrain the negative regulation within the set range, and the control effect is good. During the simulation process, the maximum pressure overshoot and gas flow overshoot are 1.7076% and 5.0660% respectively. The overshoot is small, which meets the design requirements of the control system.

[0222] In order to verify the control effect of the control system when the gas generator works normally within the entire pressure regulation range, a step command signal is set, the simulation time is set to 90s, the step amount is 2MPa, the range is 0.5-10MPa, and the duration is 10s. c Change curve and gas flow q mf The change curve is as Figure 6 , Figure 7 shown.

[0223] By observation Figure 6 and Figure 7 It can be seen that in the entire pressure regulation range, both the pressure and the gas flow rate can follow the changes of the set value well. Compared with the low-pressure regulation range, the overshoot is slightly increased, and the maximum pressure overshoot and gas flow overshoot are 1.9710% and 6.8970% respectively, but they are still within the acceptable range and meet the design requirements of the control system.

Claims

1. A method for designing an online optimization and negative regulation constraint control system for a gas generator based on model predictive control, characterized in that: The control system mainly consists of two parts. The first part is the prediction model acquisition layer, and the second part is the control law decision layer. The specific steps are as follows: S1. Prediction model acquisition layer Taking the actual working state of the current control cycle of the gas generator as the steady-state point, a small deviation linearization model of the gas flow regulation system near the steady-state point of the current control cycle is established in real time and continuously; The small deviation linearization model is obtained through Taylor expansion, expressed in the form of state space equations, and provided to the model predictive controller as a prediction model; S2. Control law decision layer Based on step S1, the prediction model of the current control cycle is obtained, and a model predictive controller of the gas generator pressure closed loop is constructed; the model predictive controller constructs an objective function with the difference between the output and the set value, and the difference between the input and the set value, and takes the input limit of the system and the negative adjustment limit of the gas flow as constraints, and obtains the optimal control vector of the current control cycle by solving the constrained quadratic programming problem online.

2. A method for designing a gas generator online optimization and negative regulation constraint control system based on model predictive control according to claim 1, characterized in that: Step S1 is specifically as follows: S1.1 When the gas generator of a choked solid rocket ramjet engine is working, the combustion process satisfies the following zero-dimensional interior ballistic differential equation: Among them, p c and q mf are the internal pressure and gas flow rate of the gas generator, V g and A t are the free volume and throat area of ​​the gas generator, V gini is the initial throat area, α and n are the burning rate coefficient and pressure index of the propellant, 0<n<1, C * and ρ b are the characteristic velocity and density of the propellant, A b is the burning surface area of ​​the propellant, Γ is the specific heat ratio function; S1.2 Gas flow regulation system adopts pressure closed-loop control and uses servo motor as actuator; the servo motor changes the throat area of ​​the gas generator by adjusting the opening of the gas flow regulating valve, thereby changing the pressure and adjusting the gas flow; when working, the actuator is approximately an inertia link Where u is the input quantity, T a is the time constant of the actuator; S1.3 Based on S1.1-S1.2, the nonlinear differential equation model of the gas flow control system with actuator is obtained: When the system is in a stable state, the steady-state pressure p c0 , gas flow q mf0 , throat area A t0 , the input quantity u0 satisfies the following relationship S1.4 is based on S1.3, at a certain steady-state point (p c0 ,A t0 ,q mf0 ,u0) and free volume V g0 Taylor expansion is used to perform small deviation linearization nearby, and the steady-state relationship is used to simplify it, that is, the transfer function model of the gas flow regulation system is obtained: in, is the transfer function of pressure and throat area, is the transfer function of gas flow and throat area, G a (s) is the transfer function of throat area and input quantity, Δp c (s), Δq mf (s), ΔA t (s), Δu(s) are the Laplace transforms of pressure increment, gas flow increment, throat area increment, and input increment, respectively, and s is a complex variable; S1.5 is based on S1.

4. The gas flow regulation system is a second-order system. The gas generator pressure and throat area are taken as state quantities, and the gas generator pressure is taken as the output quantity. The small deviation linearized state space equation of the gas flow regulation system near a certain steady-state point is obtained: in, Δx=[Δp c ,ΔA t ] T , whose elements are the increments of the state quantity relative to the steady-state point, Δp c , ΔA t are the increments of pressure and throat area relative to the steady state point, is the first-order derivative of Δx; Δy=Δp c , whose elements are the increments of the output relative to the steady-state point; Δu is the increment of input relative to the steady-state point; S1.6 is based on S1.5, and discretizes the small deviation linearized state space equation of the gas flow control system. The sampling period of the discretization is the same as the control period of the control system, which is T s ; The discretized state space equation is expressed as: Among them, k represents the kth control cycle, A d , B d , C d is the discretized parameter matrix; Δx(k)=[Δp c (k),ΔA t (k)] T It represents the increment of the state quantity of the kth control cycle relative to the steady-state point, Δp c (k), ΔA t (k) respectively represent the increments of pressure and throat area relative to the steady-state point in the kth control cycle; Δy(k)=Δp c (k) represents the increment of the output of the kth control cycle relative to the steady-state point; Δu(k) represents the increment of the input quantity of the kth control cycle relative to the steady-state point; Simplifying it into the form of absolute quantity, the state space equation can be expressed as: Where x0 = [p c0 ,A t0 ] T , x0 and u0 are steady-state values; x(k)=[p c (k),A t (k)] T represents the state quantity of the kth control cycle, p c (k), A t (k) respectively represent the pressure and throat area of ​​the kth control cycle; y(k)=p c (k) indicates the output of the kth control cycle; u(k) represents the input quantity of the kth control cycle; I is the identity matrix; S1.7 In each control cycle, the internal pressure of the gas generator is measured in real time by the sensor as the pressure steady-state point p of the current control cycle. c0_k , A is calculated based on the S1.3 steady-state relationship t0_k ,q mf0_k 、u 0_k ; Free volume V of the current control cycle g0_k Use the following formula to estimate: Based on S1.6, using the steady-state point (p c0_k ,A t0_k ,q mf0_k ,u 0_k ) and V g0_k , the small deviation linearized state space equation near the steady-state point of the current control period can be calculated in real time and provided as a prediction model to the model predictive controller for trajectory optimization.

3. A method for designing a gas generator online optimization and negative regulation constraint control system based on model predictive control according to claim 2, characterized in that: Step S2 is specifically as follows: S2.1 obtains the steady-state point (p c0_k ,A t0_k ,q mf0_k ,u 0_k ) and V g0_k The state space equation of the gas flow control system nearby is: Among them, A d_k , B d_k , C d_k is the parameter matrix calculated in control cycle k; p set_k =(I-A d_k )x 0_k -B d_k u 0_k ,x 0_k =[p c0_k ,A t0_k ] T ; Taking the prediction time domain and control time domain of the model predictive controller as N, the prediction formulas for the state sequence and output sequence are as follows: in, x′(k)=[p c ′(k),A t ′(k)] T represents the measured data of the state quantity in the control cycle k, p c ′(k), A t ′(k) represent the measured values ​​of pressure and throat area in control period k, respectively; represents the state prediction at time k+i in control cycle k, They represent the predicted values ​​of pressure and throat area at time k+i in control cycle k respectively; represents the output prediction for time k+i in control cycle k, represents the input prediction at time k+i in control cycle k; S2.2 designs the online optimization objective function as follows: Among them, y r 、u r is the set value, R and Q are weighting coefficients; Based on S2.1, the online optimization objective function can be simplified as: in, After expansion, merging and removing the constant terms that have no effect on J, the online optimization objective function is simplified to the following quadratic form: in, S2.3 is based on S2.1, with input restriction constraints Can be simplified to in, u min 、u max are the lower and upper limits of the input quantity respectively; S2.4 When the gas generator is working, the gas flow will produce negative regulation phenomenon, that is, in the initial stage of flow regulation, the gas flow will produce a trend of change opposite to the expected regulation direction; define the concepts of absolute negative regulation and relative negative regulation, respectively expressed as R a and R us Indicates; Absolute negative regulation refers to the maximum change in gas flow in the opposite direction of the expected result, and relative negative regulation refers to the ratio of absolute negative regulation to the difference between steady-state flow and initial flow in the flow regulation cycle; For the gas flow regulation system, the following gas flow negative regulation limit constraints are introduced: in, q mf_ini Indicates the initial value of the gas flow rate in the current regulation cycle, q mf_end Indicates the final value of the gas flow rate in the current regulation cycle; SIG=sign(q mf_end -q mf_ini ), indicating the expected change direction of the gas flow rate in the current regulation cycle; It represents the predicted value of gas flow at time k+i in control cycle k; R us_set is the relative negative adjustment constraint value, set to the pressure measurement value p of the current control period c ′(k) and estimated free volume V g0_k Function: R us_set =aV g0_k +bp c ′(k)+c Among them, a, b, and c are all setting parameters, a>0, b>0; with the increase of pressure and free volume, the negative adjustment phenomenon intensifies, R us_set becomes larger, relaxing the constraint value of the relative negative adjustment; When the S2.5 gas generator is working, the gas flow cannot be measured directly; based on S1, the gas flow is estimated using the following relationship: in, The actual measured value p in the current control cycle c ′(k), A t ′(k) is Taylor expanded and high-order small quantities are ignored. The gas flow estimation formula is simplified to: S2.6 is based on S2.4-S2.5, and the gas flow negative adjustment limit constraint is simplified to: After simplification, the gas flow negative adjustment limit constraint is recorded as: in, Based on S2.1, the gas flow negative regulation limit constraint is simplified to: Among them, A neq_U = A neq_X B U , b neq_U = b neq_X - A neq_X A X x′(k)- A neq_X P X ; S2.7 is based on S2.2-S2.3 and S2.6, and constructs the following optimization problem for the gas flow regulation system: According to the objective function and constraints, rolling optimization is achieved by solving the constrained quadratic programming problem online and building a model predictive controller; based on the optimal control quantity sequence obtained by optimization Take the first element of the optimal control quantity sequence As the actual control quantity of the current control cycle, it acts on the actual controlled system.

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