A method for controlling the speed of a gas turbine

Abstract

The present invention relates to a gas turbine speed control method, which uses fuel flow as input and gas turbine measured speed as state quantity to construct a system state equation of the gas turbine, uses a variable gain state observer to obtain a speed estimate, designs a speed controller based on high-order improved sliding mode control theory, uses the gas turbine set speed as a control target value, and performs robust control of the fuel flow in the presence of gas turbine modeling errors and external speed sampling interference according to the control law. The gas turbine speed control method of the present application has strong robustness to gas turbine modeling errors and external interference, has low dependence on model accuracy, and is not easy to diverge in control. In the presence of modeling errors and external disturbances, the state of the gas turbine can be correctly obtained and controlled.

Description

Technical Field

[0001] The invention relates to the technical field of gas turbines, in particular to a gas turbine speed control method based on a high-order improved sliding mode controller and a variable gain state observer. Background Art

[0002] A gas turbine is an internal combustion power machine that uses a continuously flowing gas as a working fluid to drive the impeller to rotate at high speed, converting the energy of the fuel into useful work. It is a rotating impeller heat engine. When the gas turbine enters the slow speed or above working condition, the air is compressed by the compressor and then enters the combustion chamber to mix with the fuel for combustion. The high-temperature and high-pressure gas generated drives the gas turbine and the power turbine to do work. Among them, the gas turbine drives the compressor to rotate through the rotating shaft to achieve the internal balance of the combustion engine; the power turbine drives the load to do work to achieve power output.

[0003] Gas turbines usually use closed-loop speed control to ensure stable operation by adjusting the fuel flow. However, the strong nonlinear characteristics of the gas turbine itself and the characteristic deviation caused by long-term operation inevitably lead to certain modeling errors. Since the speed sensor works in harsh environments such as high temperature, vibration, and oil mist, signal acquisition is often subject to external interference. Once the speed signal fluctuates due to modeling errors or external interference, the control system may malfunction, resulting in catastrophic consequences such as downgraded operating conditions and emergency shutdowns. Summary of the invention

[0004] In view of the shortcomings in the above-mentioned existing production technology, the applicant provides a gas turbine speed control method, which can effectively solve the technical problems and technical needs in the prior art that the state of the gas turbine cannot be correctly obtained and controlled due to modeling errors or when the speed sensor is subject to external interference, meet the use requirements, and can correctly obtain the state of the gas turbine and control it in the presence of modeling errors and external disturbances.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A gas turbine speed control method includes the following operation process:

[0007] S110: Fuel flow rate as input , the gas turbine speed is measured as a state quantity , also known as the output , the system state equation of the gas turbine is obtained based on the aerodynamic thermodynamic model of the gas turbine.

[0008]

[0009] The system state equation includes the nonlinear differentiable transfer function of the gas turbine ;

[0010] make Indicates the modeling error in the process of building the model. represents external interference; then we can define Lumped uncertainties representing modeling and external disturbances;

[0011] S120: Design of variable gain state observer based on gas turbine system state equation to obtain state quantity estimation and auxiliary estimated variables , ;

[0012] S130: State quantity estimation error based on state observer ,

[0013] Define extended sliding surface , and the sliding mode reaching law is designed as:

[0014] ,

[0015] In the above formula, is the symbolic function, , and are all normal numbers, It is a linear correction term used to improve the convergence speed of the system tracking error;

[0016] S140: Combined with the aerodynamic thermodynamic model of the gas turbine, determine the speed control law based on the high-order improved sliding mode structure; set the speed of the gas turbine As a state quantity The value of and the fuel flow rate are controlled according to the control law in the presence of modeling errors and external disturbances of the sensor.

[0017] Its further technical solution is:

[0018] The gas turbine speed control method includes gas turbine speed closed-loop control and power turbine speed closed-loop control. The speed sensor includes a gas turbine speed sensor and a power turbine speed sensor. The corresponding control amount can be selected according to the control requirements.

[0019] Speed ​​Estimation Error Based on State Observer , the variable gain observer is expressed as:

[0020]

[0021] in, express The derivative of , for complex systems with uncertain disturbances, the observer adjusts the gain , and To ensure sufficient observation accuracy;

[0022] In combination with the aerodynamic thermodynamic model of the gas turbine, the observation error is defined based on the estimated value of the state quantity , , , can be obtained

[0023]

[0024] Given gain , and The regulation rate is:

[0025]

[0026] in, , All are given adjustment coefficients;

[0027] From this, the observer error equation can be established

[0028]

[0029] make , the error equation can be expressed as:

[0030]

[0031] in, , , , , ,make ,because is a Hurwitz matrix, there exists is a positive symmetric matrix, satisfying

[0032]

[0033] in, For a positive symmetric matrix, define the quadratic Lyapunov function

[0034]

[0035] Combined with the aerodynamic thermodynamic model of the gas turbine, the gain is adjusted by selecting , and , so that the observer satisfies the following conditions

[0036]

[0037] Among them, take ,exist , the variable gain state observer is stable;

[0038] Design of extended sliding surface , thus, the given high-order improved sliding mode algorithm is:

[0039]

[0040] make , the above formula can be rewritten as

[0041]

[0042] In the formula, is the symbolic function, , and are all normal numbers, It is a linear correction term used to improve the convergence speed of the system tracking error;

[0043] The speed control rate based on high-order improved sliding mode control is determined as:

[0044] ;

[0045] in , , ;

[0046] Determining the high-order improved sliding mode speed control law also includes that the control rate adjustment coefficient satisfies:

[0047]

[0048] The gas turbine speed control method further includes:

[0049] When there is a modeling error of the gas turbine and external interference of the speed sensor sampling, the step of controlling the fuel flow rate according to the speed control rate of the gas turbine is performed;

[0050] Design the high-order improved sliding surface as , and there is

[0051]

[0052] in, for The derivative of

[0053] Given To set the speed, , , , then the system state equation can be rewritten as:

[0054] .

[0055] The beneficial effects of the present invention are as follows:

[0056] The present invention constructs the system state equation of the gas turbine with the fuel flow rate as the input quantity and the measured speed of the gas turbine as the state quantity, obtains the speed estimation value with the variable gain state observer, designs the speed controller based on the high-order improved sliding mode control theory, takes the set speed of the gas turbine as the control target value, and performs robust control on the fuel flow rate in the presence of gas turbine modeling errors and external speed sampling interference according to the control law. The gas turbine speed control method of the present invention has strong robustness to gas turbine modeling errors and external interferences, has low dependence on model accuracy and is not easy to diverge in control. In the presence of modeling errors and external disturbances, the state of the gas turbine can be correctly obtained and controlled.

[0057] When designing the speed control law, the present invention takes into account the large inertia and strong time lag of the gas turbine during actual operation. The controller output is usually difficult to directly fall on the sliding mode surface, but frequently switches on the sliding mode surface, which easily causes system chattering. Therefore, a high-order improved sliding mode control function is designed, and the discontinuous switching control term is applied to the high-order derivative of the sliding mode variable to construct a continuous control rate, which better suppresses the sliding mode control chattering and effectively improves the system stability.

[0058] Compared with traditional PID control, the gas turbine speed control method based on high-order improved sliding mode structure and variable gain state observer designed by the present invention has strong dependence on model accuracy and the control is prone to divergence when the speed sensor fails. The present application can quickly track the actual speed output, has a control effect with fast response speed and high control accuracy, and has stronger robustness and smaller overshoot in the presence of modeling errors and external interference of sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 The figure is a schematic diagram of the working principle of a dual-shaft gas turbine in one embodiment of the present invention.

[0060] Figure 2 It is a schematic diagram of a gas turbine speed control method based on a high-order improved sliding mode structure and a variable gain state observer in one embodiment of the present invention.

[0061] Figure 3 It is a system diagram of a dual-shaft gas turbine in one embodiment of the present invention.

[0062] Figure 4 This is a power turbine speed output curve of high-order improved sliding mode control and PID control in one embodiment of the present invention.

[0063] Figure 5This is an output curve when a rotation speed sensor of a power turbine fails in one embodiment of the present invention.

[0064] Figure 6 for Figure 5 The control error comparison curve of high-order improved sliding mode control and PID control corresponding to the case. DETAILED DESCRIPTION

[0065] The specific implementation of the present invention will be described below in conjunction with the accompanying drawings.

[0066] like Figure 1-Figure 6 As shown, is the compressor inlet air flow rate, , Indicates the compressor outlet pressure and temperature, is the fuel flow rate, , represents the gas turbine speed and outlet gas temperature, Indicates the speed of the power turbine. According to the operating principle of the gas turbine, the starting process usually uses a starting motor or high-pressure gas to drive the compressor components. At this moment, the engine is in an unstable transient state and generally adopts an open-loop control mode, which will not be discussed here. After the gas turbine enters the slow speed or above operating condition, the air is compressed by the compressor and then enters the combustion chamber to mix with the fuel and burn. The high-temperature and high-pressure gas generated drives the gas turbine and the power turbine to do work. Among them, the gas turbine drives the compressor to rotate through the rotating shaft to achieve the internal balance of the engine; the power turbine drives the load to do work to achieve power output.

[0067] S110, with fuel flow as input , the gas turbine speed is measured as a state quantity , also known as the output , based on the aerodynamic thermodynamic model of the gas turbine, the system state equation of the gas turbine is obtained. Indicates the modeling error in the process of building the model. represents external interference; then we can define Represents the lumped uncertainty of modeling and external disturbances.

[0068] Optionally, the gas turbine speed control method includes gas turbine speed closed-loop control and power turbine speed closed-loop control, and the speed sensor includes a gas turbine speed sensor and a power turbine speed sensor, and the corresponding control amount can be selected according to the control requirements.

[0069] S120, Design a variable gain state observer based on the system state equation of the gas turbine to obtain the estimated value of the state quantity and auxiliary estimated variables , .

[0070] S130, state quantity estimation error based on variable gain state observer , define the high-order improved sliding surface , and the sliding mode reaching law is designed as:

[0071] ,

[0072] In the formula, is the symbolic function, , and are all normal numbers, It is a linear correction term used to improve the convergence speed of the system tracking error.

[0073] S140, combined with the aerodynamic thermodynamic model of the gas turbine, determines the speed control law based on the high-order improved sliding mode structure; the speed is set by the gas turbine As a state quantity The value of and the fuel flow rate are controlled according to the control law in the presence of modeling errors and external disturbances of the sensor.

[0074] The gas turbine speed control method of the present application is a passive fault-tolerant control method, which is highly robust to modeling errors and external interferences, and is regarded as a lumped uncertainty in the design process, effectively avoiding the strong dependence of traditional control on model accuracy and the problem of easy control divergence when external interference occurs.

[0075] In order to more clearly illustrate the gas turbine speed control method based on the high-order improved sliding mode structure and the variable gain state observer of the present application, the examples of the present application are described in detail below in conjunction with the accompanying drawings.

[0076] Fuel flow rate as input , the gas turbine speed is measured as a state quantity , also known as the output , the system state equation of the gas turbine is obtained based on the aerodynamic thermodynamic model of the gas turbine.

[0077] (1)

[0078] The system state equation includes a nonlinear differentiable transfer function of the gas turbine , modeling errors in the process of building the model , external interference , gas turbine load power ;definition represents the lumped uncertainty of modeling and external disturbance. for The derivative of A , Bis a reversible matrix of known appropriate dimension obtained by fitting the aerodynamic thermodynamic model, and t is the time quantity.

[0079] S220, the system state equation based on the gas turbine can be written as:

[0080]

[0081] in, Represents the lumped uncertainty of modeling and external disturbances.

[0082] Determined based on gas turbine characteristics Satisfy the first assumption, the first assumption is: define a nonlinear function The derivative of , which satisfies the Lipschitz condition:

[0083] (2)

[0084] in, is a constant, Represents the norm of the function.

[0085] The uncertainty of the gas turbine state equation satisfies the second assumption, which is: , there is a constant , so that the lumped uncertainty satisfies:

[0086] (3)

[0087] In this embodiment, the variable gain state observer designed based on the gas turbine state equation is:

[0088] (4)

[0089] in, , , For complex systems with uncertain disturbances, there is often an initial error between the observer initial value and the actual value of the system, which can easily lead to a peak phenomenon in the observation error. Therefore, the observer adjustment gain is designed. , and To ensure sufficient observation accuracy, compensate for uncertainties such as modeling errors and external interference, and give constraints on the gain value. , and The regulation rate is:

[0090] (5)

[0091] in, , All are given adjustment coefficients.

[0092] S230, define the observer and measurement error , , for,

[0093]

[0094] From equation (5), equation (6) and assumption 2, we can get the observer error equation:

[0095] (6)

[0096] The gas turbine speed control method of the present application also includes: designing a high-order improved sliding mode controller based on the observation value of the variable gain state observer to achieve gas turbine speed control.

[0097] In the embodiment, the basic sliding surface is designed as,

[0098]

[0099] The given high-order improved sliding mode algorithm is:

[0100]

[0101] In the formula, is the symbolic function, , and are all normal numbers and satisfy , and , is a linear correction term used to improve the convergence speed of the system tracking error. The speed control law is obtained based on the sliding mode algorithm design:

[0102] (7)

[0103] in , , .

[0104] The following proves through Lyapunov function that the variable gain state observer and high-order improved sliding mode control law designed in this application make the gas turbine system stable.

[0105] (1) The proof process of the variable gain state observer includes:

[0106] make , then from formula (6) we can get

[0107]

[0108] in, , , , , .

[0109] make ,because is a Hurwitz matrix, there exists is a positive symmetric matrix, satisfying

[0110]

[0111] in, is a positive symmetric matrix. Define the quadratic Lyapunov function

[0112]

[0113] S240, yes Seeking guidance,

[0114]

[0115]

[0116] According to hypothesis 1,

[0117]

[0118] That is

[0119]

[0120] in, is a positive definite matrix The maximum eigenvalue of .

[0121] According to hypothesis 2,

[0122]

[0123] Available

[0124]

[0125]

[0126] in, , Therefore, if you want , that is,

[0127]

[0128] According to the Lyapunov stability theorem, by selecting the adjustment gain , and , so that the observer satisfies the following conditions

[0129]

[0130] exist , the variable gain state observer is stable.

[0131] (2) The process of proving that the speed control law makes the gas turbine system stable includes:

[0132] make , then it is easy to derive it

[0133]

[0134] Determine the second Lyapunov function ; and positive definite symmetric matrix The definition is

[0135]

[0136] Function The derivative is

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] in, .

[0144] Therefore, in the high-order improved sliding mode control formula (7), it can be guaranteed that , thus proving that the gas turbine system is stable.

[0145] In order to verify the effectiveness of the gas turbine speed control method designed in this application, the system state equation of the dual-shaft gas turbine is used as the gas turbine model, the gas turbine speed and the power turbine speed are used as the state quantities, and the interference effect is not considered. The model is normalized and the obtained parameter expressions include: , , , ,

[0146] The parameters of the gas turbine are set as follows: from the 0.25 working condition, the hydraulic dynamometer is used to simulate the load, and the power turbine speed control is adopted. When the power turbine speed is 2000r / min, it is suddenly increased to the 0.7 working condition at the 20th second. The power turbine is set to 2800r / min. The control effects of conventional PID control and high-order improved sliding mode controller are compared. Figure 3 It can be seen that both conventional PID control and high-order improved sliding mode control can track the set value, but the sliding mode control rate has better dynamic response speed and smaller overshoot, and basically no control chattering occurs.

[0147] In order to further verify the robustness of the high-order improved sliding mode control algorithm, a typical fault that occurs when the speed sensor is disturbed by external interference is selected to compare the control effects of different algorithms. The gas turbine is set to run at a constant speed of 2400r / min. seconds, the speed sensor Periodic disturbance fault ( Figure 5 ).

[0148] Figure 6 yes Figure 5 The control error comparison curve of high-order improved sliding mode control and PID control corresponding to the case.

[0149] Through the speed control error curve ( Figure 6 ) It can be seen that after the sensor periodic disturbance fault occurs, the system tends to be stable after the PID control performs speed regulation, but because the periodic disturbance always exists, the control error is large and the stabilization time is long. After the fault occurs, the speed tracking error of the high-order improved sliding mode control is reduced by about 50% compared with the PID control, and the overall robustness is good. In summary, the variable gain observer can quickly track the actual output, and the high-order improved sliding mode control algorithm based on the observer design has stronger robustness and smaller overshoot than the traditional control method.

[0150] The above description is an explanation of the present invention, not a limitation of the present invention. The scope of the present invention is defined in the claims. Any form of modification may be made within the scope of protection of the present invention.

Claims

1. A gas turbine speed control method, characterized in that: The following operation procedures are included: S110: With the fuel flow rate as the input u(t), the measured speed of the gas turbine as the state x(t), which is also the output y(t), the system state equation of the gas turbine is constructed based on the aerodynamic thermodynamic model of the gas turbine. The system state equation includes the nonlinear differentiable transfer function f(x, t) of the gas turbine; Let ΔA represent the modeling error in the process of building the model, and n(t) represent the external disturbance; define D(t) = ΔA f(x, t) + n(t) to represent the lumped uncertainty of modeling and external disturbance; S120: Design of variable gain state observer based on gas turbine system state equation to obtain state quantity estimation and auxiliary estimated variables S130: State quantity estimation error based on state observer Define extended sliding surface And the sliding mode reaching law is designed as: In the above formula, sgn(·) is the sign function, k1, k2 and k3 are all positive constants, and k3s is a linear correction term used to improve the convergence speed of the system tracking error; S140: Determine the speed control law based on the high-order improved sliding mode structure in combination with the aerodynamic thermodynamic model of the gas turbine; take the set speed x1(t) of the gas turbine as the value of the state quantity x(t), and control the fuel flow according to the control law in the presence of modeling errors and external interference of the speed sensor.

2. A gas turbine speed control method according to claim 1, characterized in that: The gas turbine speed control method includes a gas turbine speed closed-loop control and a power turbine speed closed-loop control, and the speed sensor includes a gas turbine speed sensor and a power turbine speed sensor.

3. A gas turbine speed control method according to claim 1, characterized in that: Speed ​​Estimation Error Based on State Observer The variable gain observer is expressed as: Where G(·) represents the derivative of f(·). For complex systems with uncertain disturbances, the observer adjusts gains β1, β2, and β3 to ensure sufficient observation accuracy. In combination with the aerodynamic thermodynamic model of the gas turbine, the observation error is defined based on the estimated value of the state quantity Available The regulation rates of given gains β1, β2 and β3 are: Among them, δ f >0,τ 1n >0, τ 2n >0 (n=1, 2, 3) are all given adjustment coefficients; From this, the observer error equation can be established make The error equation can be expressed as: in, R = [1 0 0], make Since β is a Hurwitz matrix, there exists a positive symmetric matrix Q0 that satisfies βQ0+Q0β T =-Q1 Among them, Q1 is a positive definite symmetric matrix, and the quadratic Lyapunov function is defined as Combined with the aerodynamic thermodynamic model of the gas turbine, by selecting the adjustment gains β1, β2 and β3, the observer meets the following conditions: Among them, take ζ∈(0,1), there exists The variable gain state observer is stable; Design of extended sliding surface Therefore, the given high-order improved sliding mode algorithm is: make The above formula can be rewritten as Where sgn(·) is the sign function, k1, k2 and k3 are all positive constants, and k3s is a linear correction term used to improve the convergence speed of the system tracking error; The speed control rate based on high-order improved sliding mode control is determined as: among them Λ=[-β1 A 1], Determining the high-order improved sliding mode speed control law also includes that the control rate adjustment coefficient satisfies: The gas turbine speed control method further includes: When there is a modeling error of the gas turbine and external interference of the speed sensor sampling, the step of controlling the fuel flow rate according to the speed control rate of the gas turbine is performed; Design the high-order improved sliding surface as And there is in, is the derivative of s(t); Given x d (t) is the set speed, let x1(t) = x(t), x2(t) = f(x, t), Then the system state equation can be rewritten as:

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