CN113669163A - Cascade gas turbine rotating speed control method based on active disturbance rejection control - Google Patents

Abstract

The purpose of the present invention is to provide a cascade gas turbine speed control method based on active disturbance rejection control, including an outer loop controller and an inner loop controller, the outer loop controller is a first-order linear active disturbance rejection controller, and the inner loop controller It is a second-order linear ADRR controller, the outer-loop first-order linear ADRR controller includes a proportional controller Kp _out and an extended state observer ESO _out , and the outer-loop first-order linear ADRR controller includes a proportional-differential controller Kp _in , Kd _in and the extended state observer ESO _in . The technical scheme of the present invention adopts the cascade control method to realize the closed-loop control of the gas turbine speed, and the inner loop adopts the second-order linear active disturbance rejection controller, and the outer loop adopts the first-order linear active disturbance rejection controller, which can ensure the high-voltage rotor speed and power. The disturbance-free control of the turbine speed, and the anti-saturation effect of the controller can be realized.

Description

A Cascade Gas Turbine Speed Control Method Based on Active Disturbance Rejection Control

technical field

The invention relates to a gas turbine control method, in particular to a gas turbine rotational speed control method.

Background technique

Gas turbines have the advantages of high power density, strong fuel adaptability and high efficiency, and are widely used in aviation aircraft, marine propulsion, combined cycle power generation and other fields. With the rise of emerging technologies such as electronic power technology, measurement and control technology, advanced control technology, and artificial intelligence technology, the control of gas turbines will be further improved. How to use emerging technologies to improve the performance of gas turbines and solve the problem of restricting the development of gas turbines has become an urgent problem to be solved in the development of gas turbines. Especially in the application of ship propulsion, it is imminent to realize the low energy consumption and low pollution of gas turbine propulsion.

Marine gas turbines can be used for both driving and power generation. The multi-purpose features lead to differences in the control methods of gas turbines. Especially in the process of gas turbine power generation, the grid-connected control requirements of the gas turbine are high, and the speed control is required to be precise and the fluctuation error is small. On the other hand, due to the numerous working modes of gas turbines and the limitations of exhaust temperature and rotational speed, it is required to realize bumpless switching during mode switching. Due to the complex thermal process of gas turbines, with the characteristics of nonlinearity and large time delay, traditional proportional-integral control is difficult to achieve precise control of gas turbines. It is urgent to find an advanced control method that can solve the above problems of gas turbines.

Active Disturbance Rejection Control (ADRC) is an advanced control technology that has emerged in recent years. It estimates the total disturbance of the system through Extended State Observer (ESO), and converts the control object into an integral series connection. type, and then compensated by the control rate to achieve disturbance-free control. There are many disturbances in the operation process of gas turbine, such as sudden change of load and nonlinear time delay of fuel generator, which seriously affect the control of gas turbine. The application of ADRC technology to gas turbines will be able to solve the characteristics of gas turbines such as sensitivity to disturbances, nonlinearity, time delay, etc., especially to achieve disturbance-free switching and tracking control of gas turbines, which can significantly improve the operating performance of gas turbines.

For ships powered or propelled by gas turbines, the application of active disturbance rejection control technology can solve the difficulties of high speed control requirements for grid-connected power generation and no disturbance in speed control during propulsion. It has good adaptability to the disturbance of the gas turbine ship navigation environment to the disturbance of the gas turbine, the combustion in the combustion chamber, the disturbance of the fuel generator, and the air intake flow of the compressor. Compared with the traditional proportional integral control, the control process is more stable. Therefore, it is of great research significance to apply ADRC technology in the field of marine gas turbines, and it is urgent to propose a new gas turbine ADRC technology scheme to achieve precise and stable control of gas turbines.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a cascade gas turbine based on active disturbance rejection control, which can solve the problems of non-linearity and delay in the working process of the gas turbine, which lead to difficulty in control, and realize multi-mode operation switching without disturbance control, so as to realize the precise control of the gas turbine rotational speed. Speed control method.

The object of the present invention is achieved in this way:

The invention is a method for controlling the rotational speed of a cascade gas turbine based on active disturbance rejection control, which is characterized by comprising an outer loop controller and an inner loop controller, the outer loop controller is a first-order linear active disturbance rejection controller, and the inner loop controller is a first-order linear active disturbance rejection controller. It is a second-order linear ADRR controller, the outer-loop first-order linear ADRR controller includes a proportional controller Kp _out and an extended state observer ESO _out , and the inner-loop second-order linear ADRR controller includes a proportional-differential controller Kp _in , Kd _in and the extended state observer ESO _in .

The present invention can also include:

1. The design of the outer loop first-order linear active disturbance rejection controller includes the following steps:

其中

为动力涡轮转子转速导数，n_g为燃气发生器转速，m_a为燃气轮机执行器输出燃气量，J_P为动力涡轮转动惯量，f₁为表征燃气轮机动力涡轮输出非线性的函数；The gas turbine power turbine speed is expressed as:

in

is the rotational speed derivative of the power turbine rotor, n _g is the rotational speed of the gas generator, m _a is the output gas volume of the gas turbine actuator, J _P is the moment of inertia of the power turbine, and f ₁ is a function that characterizes the nonlinear output of the gas turbine power turbine;

其中，z₁＝n_p，z₂＝f，C＝[1 0]，L＝[β₁ β₂]^T，

B＝[b₀ 0^T，β₁、β₂、b₀为控制器参数整定值；The extended state observer ESO _out in the outer loop first-order linear active disturbance rejection controller is designed as:

Wherein, z ₁ =n _p , z ₂ =f, C=[1 0], L=[β ₁ β ₂ ] ^T ,

B=[b ₀ 0 ^T , β ₁ , β ₂ , b ₀ are controller parameter setting values;

The control rate of the controller Kp _out is designed as u ₀ =K _p (n _p,r -z ₁ ), and the output of the controller is n _g,r =(u ₀ -z ₂ )/b ₀ , where n _g,r is the gas The generator reference input speed is the reference input of the inner loop second-order linear active disturbance rejection controller.

2. The design of the inner loop second-order linear active disturbance rejection controller includes the following steps:

其中

为燃气发生器转速二次导数，

为燃气发生器转速一次导数，n_g为燃气发生器转速，m_a为燃气轮机执行器输出燃气量，J_g为燃气发生器转动惯量，f₂为表征燃气轮机燃气发生器转速输出非线性的函数；The rotational speed of the gas turbine gas generator is expressed as:

in

is the second derivative of the gas generator speed,

is the first derivative of the rotational speed of the gas generator, n _g is the rotational speed of the gas generator, m _a is the output gas volume of the gas turbine actuator, J _g is the moment of inertia of the gas generator, and f ₂ is a function that characterizes the output nonlinearity of the rotational speed of the gas generator of the gas turbine;

其中，

b₁为控制器参数整定值；The expanded state observer ESO _{in in} the inner-loop second-order linear ADRC controller is designed as:

in,

b ₁ is the controller parameter setting value;

控制器输出为

其中m_c为燃气轮机执行机构参考输入燃料量即积分控制器的参考输入。The control rate of the controller _Kpin is designed as

The controller output is

Where m _c is the reference input fuel quantity of the gas turbine actuator, that is, the reference input of the integral controller.

3. The first input of the outer ring expansion state observer ESO _out is the measured value of the rotational speed of the gas turbine gas generator, and the second input is the measured value of the rotational speed of the power turbine; the input of the inner ring expanded state observer ESO _in is the measured value of the fuel quantity of the gas turbine actuator, The second input is the gas generator rotational speed measurement.

4. The outer loop control feedback value is the estimated value of the power turbine speed output by the expansion state observer ESO _out , and the inner loop control feedback value is the estimated value of the gas generator speed and its derivative output by the expansion state observer ESO _in .

The advantages of the present invention are:

1. The present invention provides a method for controlling the rotational speed of a cascade gas turbine based on active disturbance rejection control, wherein the outer loop is a first-order linear active disturbance rejection controller, the inner loop is a second-order linear active disturbance rejection controller, and the gas turbine actuator is controlled as: Integral controller. The obvious technical effects are as follows: the application of the active disturbance rejection control method can effectively improve the disturbance immunity of the gas turbine and ensure the disturbance-free control of the gas turbine working mode switching.

2. This control method adopts the cascade control scheme, which can realize the decoupling of the speed of the fuel generator and the speed of the power turbine. The influence of the disturbance on the speed of the power turbine; other disturbances affecting the speed of the power turbine are controlled by the outer loop ADRC.

3. The inner loop is the second-order active disturbance rejection controller scheme, which can control the high-order change of the fuel generator speed, effectively control the impact of the combustion process on the speed fluctuation, and avoid the use of a low-order controller to affect the high-order speed signal. The disadvantage of imprecise control. The outer loop adopts a first-order active disturbance rejection controller, which corresponds to the first-order inertial characteristics of the power turbine speed output, which not only reduces the operation of the controller, accelerates the operation speed, but also combines its output characteristics to achieve effective and precise control.

4. The first input of the outer ring expansion state observer ESO _out described in the present invention is the measured value of the rotational speed of the gas turbine gas generator, not the output value of the outer ring controller, and the second input is the measured value of the rotational speed of the power turbine; the inner ring expansion state observation The input of the generator ESO _in is the measured value of the fuel quantity of the gas turbine actuator, not the output value of the inner loop controller, and the second input is the measured value of the rotational speed of the gas generator. The scheme can effectively avoid the saturation of the two controllers, realize the limitation of the fuel quantity of the gas turbine and the rotation speed of the fuel generator, and avoid the disadvantage that the expansion state observer is difficult to estimate accurately due to the input of the controller.

5. The present invention is not only applicable to gas turbine power generation control, but also to gas turbine ship propulsion control.

Description of drawings

FIG. 1 is a schematic structural diagram of the present invention.

Detailed ways

The present invention will be described in more detail below in conjunction with the accompanying drawings:

Referring to Fig. 1, a method for controlling the rotational speed of a cascade gas turbine based on ADRC of the present invention includes an outer loop first-order linear ADRC controller 1, an inner loop second-order linear ADRC controller 2, a gas turbine actuator and a control 3, fuel generator 4, power turbine 5, load 6.

The outer-loop first-order linear ADRC includes proportional controller Kp _out and extended state observer ESO _out , and the outer-loop first-order linear ADRC includes proportional-differential controllers Kp _in , Kd _in and extended state observer ESO _in .

The design of the outer loop first-order linear ADRC controller includes the following steps:

其中

为动力涡轮转子转速导数，n_g为燃气发生器转速，m_a为燃气轮机执行器输出燃气量，J_P为动力涡轮转动惯量，f₁为表征燃气轮机动力涡轮输出非线性的函数。The gas turbine power turbine speed is expressed as:

in

is the derivative of the rotor speed of the power turbine, n _g is the speed of the gas generator, m _a is the output gas volume of the gas turbine actuator, J _P is the moment of inertia of the power turbine, and f ₁ is a function that characterizes the nonlinear output of the power turbine of the gas turbine.

The extended state observer ESO _out in the outer loop first-order linear active disturbance rejection controller is designed as:

其中，z₁＝n_p，z₂＝f，C＝[1 0]，L＝[β₁ β₂]^T，

B＝[b₀0]^T。β₁，β₂，b₀，为控制器参数整定值。

Wherein, z ₁ =n _p , z ₂ =f, C=[1 0], L=[β ₁ β ₂ ] ^T ,

B=[b ₀ 0] ^T . β ₁ , β ₂ , b ₀ are controller parameter setting values.

The control rate of the controller Kp _out is designed as u ₀ =K _p (n _p,r -z ₁ ), and the controller output is n _g,r =(u ₀ -z ₂ )/b ₀ . Among them, n _{g, r} is the reference input speed of the gas generator, that is, the reference input of the inner loop second-order linear active disturbance rejection controller.

The design of the inner-loop second-order linear ADRC controller includes the following steps:

其中

为燃气发生器转速二次导数，

为燃气发生器转速一次导数，n_g为燃气发生器转速，m_a为燃气轮机执行器输出燃气量，J_g为燃气发生器转动惯量，f₂为表征燃气轮机燃气发生器转速输出非线性的函数。The gas turbine gas generator speed is expressed as:

in

is the second derivative of the gas generator speed,

is the first derivative of the rotational speed of the gas generator, n _g is the rotational speed of the gas generator, m _a is the output gas volume of the gas turbine actuator, J _g is the moment of inertia of the gas generator, and f ₂ is a function that characterizes the nonlinearity of the rotational speed output of the gas generator of the gas turbine.

其中，

b₁，为控制器参数整定值。The extended state observer ESO _{in in} the outer loop first-order linear active disturbance rejection controller is designed as:

in,

b ₁ , is the controller parameter setting value.

控制器输出为

其中m_c为燃气轮机执行机构参考输入燃料量即积分控制器的参考输入。The control rate of the controller _Kpin is designed as

The controller output is

Where m _c is the reference input fuel quantity of the gas turbine actuator, that is, the reference input of the integral controller.

The outer loop controller is a first-order active disturbance rejection controller, which matches the first-order inertial link of the power turbine speed. The inner loop controller is a second-order active disturbance rejection controller, which matches the requirements of the limit of the speed rise rate of the gas generator, and at the same time considers the combustion process to affect the high-order output of the speed, so as to achieve precise control of the high-order signal of the speed.

The first input of the outer ring expansion state observer ESO _out is the measured value of the gas turbine gas generator speed, not the output value of the outer ring controller, and the second input is the measured value of the power turbine speed; the input of the inner ring expansion state observer ESO _in is the gas turbine. The fuel quantity measurement of the actuator, not the output value of the inner loop controller, the second input is the speed measurement value of the gas generator.

The outer loop control feedback value is the estimated value of the power turbine speed output by the expansion state observer ESO _out , and the inner loop control feedback value is the estimated value of the gas generator speed and its derivative output by the expansion state observer ESO _in .

The gas turbine fuel injection actuator is integral control.

The design method of the present invention mainly comprises the following steps:

其中，

b₁，为控制器参数整定值。其扩张状态观测器的输入为执行器实际燃料量、动力涡轮转速及转速导数，其输出为动力涡轮速及转速导数的估计值。First, the inner-loop second-order linear ADRC is designed. Since the ADRC can realize model-free control, it is only necessary to design the control rate and the expansion state observer. Therefore, for the expansion state of the inner-loop ADRC The observer is designed to

in,

b ₁ , is the controller parameter setting value. The input of the expanded state observer is the actual fuel quantity of the actuator, the rotational speed of the power turbine and the derivative of the rotational speed, and the output is the estimated value of the speed of the power turbine and the derivative of the rotational speed.

将矩阵的特征方程写为

将扩张状态观测器带宽配置在

则

可以得出

The parameter tuning law of the extended state observer adopts the bandwidth tuning method, and the expression of the extended observer is rearranged as

Write the characteristic equation of the matrix as

Configure the expanded state observer bandwidth at

but

can be drawn

控制器输出为

将控制器等效为二阶无零点的传递函数为

因此，控制器带宽

设计为：

ξ＝0.707。The second-order linear active disturbance rejection control rate is designed as

The controller output is

The controller is equivalent to a second-order zero-free transfer function as

Therefore, the controller bandwidth

Designed to:

ξ=0.707.

扩张状态观测器带宽

系统参数b₁。内环控制方案为，通过燃料计量器测量燃气轮机执行机构输出的燃料量，作为扩张状态观测器的第一输入；通过转速传感器测量燃气发生器转速及计算转速一次导数，将燃气发生器转速及转速的一次导数作为扩张状态观测器的第二及第三输入；扩张状态观测器输出燃气发生器转速及转速的一次导数的估计值作为反馈值，与外环一阶线性自抗扰控制器的输出值一同得到设计的控制率，输出燃气轮机执行机构的燃料喷射参考量，燃气轮机执行机构通过积分控制位置闭环进行控制。最后针对燃气轮机燃料发生器转速内环进行参数整定，直到满足其控制性能要求。To sum up, after pole configuration and bandwidth tuning, the parameter that needs to be designed for the inner-loop linear second-order ADRC controller is the controller bandwidth.

Expanded State Observer Bandwidth

System parameter b ₁ . The inner loop control scheme is to measure the amount of fuel output by the gas turbine actuator through the fuel gauge as the first input of the expansion state observer; measure the rotational speed of the gas generator and calculate the first derivative of the rotational speed by the rotational speed sensor, and calculate the rotational speed of the gas generator and the rotational speed. As the second and third inputs of the expansion state observer; the expansion state observer outputs the estimated value of the gas generator speed and the first derivative of the speed as the feedback value, which is related to the output of the first-order linear active disturbance rejection controller of the outer loop. The designed control rate is obtained together with the value, and the fuel injection reference quantity of the gas turbine actuator is output, and the gas turbine actuator is controlled by the integral control position closed-loop. Finally, the parameters of the inner loop of the gas turbine fuel generator speed are adjusted until the control performance requirements are met.

其中，z₁＝n_p，z₂＝f，C＝[1 0]，L＝[β₁ β₂]^T，

B＝[b₀ 0]^T。β₁，β₂，b₀，为控制器参数整定值。扩张状态观测器的输入为燃料发生器实际测量转速、动力涡轮实际测量转速。Secondly, the first-order linear active disturbance rejection controller of the outer loop is designed, and the expression of its extended state observer is:

Wherein, z ₁ =n _p , z ₂ =f, C=[1 0], L=[β ₁ β ₂ ] ^T ,

B=[b ₀ 0] ^T . β ₁ , β ₂ , b ₀ are controller parameter setting values. The input of the expansion state observer is the actual measured rotational speed of the fuel generator and the actual measured rotational speed of the power turbine.

将矩阵的特征方程写为

将扩张状态观测器带宽配置在ω₀，则

可以得出β₁＝2ω₀，β₂＝ω₀ ²。Its parameter tuning law also adopts the bandwidth tuning method, and rearranges the expression of the extended observer as

Write the characteristic equation of the matrix as

If the bandwidth of the extended state observer is configured at ω ₀ , then

It can be concluded that β ₁ =2ω ₀ and β ₂ =ω ₀ ² .

The first-order linear active disturbance rejection control rate is designed as u ₀ =K _p (n _p,r -z ₁ ), and the controller output is n _g,r =(u ₀ -z ₂ )/b ₀ . Therefore, the controller bandwidth is designed as ω _c , K _p =ω _c .

To sum up, after pole configuration and bandwidth tuning, the parameters to be designed for the outer-loop linear first-order ADRC controller are the controller bandwidth ω _c , the extended state observer bandwidth ω ₀ , and the system parameter b ₀ . The outer loop control scheme is to measure the rotational speed of the fuel generator and the rotational speed of the power turbine as the first and second input quantities of the outer loop expansion state observer. The control rate is formed, and the output value of the controller is represented as the rotational speed of the fuel generator, that is, the reference value of the controller in the inner loop of the system.

It should be noted that the bandwidth parameter of the inner loop controller is generally larger than the bandwidth parameter of the outer loop controller to ensure that the inner loop system is faster and more stable.

Claims (5)

1. a cascade gas turbine rotational speed control method based on active disturbance rejection control is characterized in that: comprise outer loop controller and inner loop controller, outer loop controller is first-order linear active disturbance rejection controller, inner loop controller It is a second-order linear ADRR controller, the outer-loop first-order linear ADRR controller includes a proportional controller Kp _out and an extended state observer ESO _out , and the inner-loop second-order linear ADRR controller includes a proportional-differential controller Kp _in , Kd _in and the extended state observer ESO _in . 2. A kind of cascade gas turbine rotational speed control method based on ADRC according to claim 1, is characterized in that: the outer loop first-order linear ADRC design comprises the following steps: The gas turbine power turbine speed is expressed as:

in

is the rotational speed derivative of the power turbine rotor, n _g is the rotational speed of the gas generator, m _a is the output gas volume of the gas turbine actuator, J _P is the moment of inertia of the power turbine, and f ₁ is a function that characterizes the nonlinear output of the gas turbine power turbine; The extended state observer ESO _out in the outer loop first-order linear active disturbance rejection controller is designed as:

Wherein, z ₁ =n _p , z ₂ =f, C=[1 0], L=[β ₁ β ₂ ] ^T ,

B=[b ₀ 0] ^T , β ₁ , β ₂ , and b ₀ are controller parameter setting values; The control rate of the controller Kp _out is designed as u ₀ =K _p (n _p,r -z ₁ ), and the output of the controller is n _g,r =(u ₀ -z ₂ )/b ₀ , where n _g,r is the gas The generator reference input speed is the reference input of the inner loop second-order linear active disturbance rejection controller. 3. A kind of cascade gas turbine rotational speed control method based on ADRC according to claim 1 is characterized in that: the inner loop second-order linear ADRC design comprises the following steps: The rotational speed of the gas turbine gas generator is expressed as:

in

is the second derivative of the gas generator speed,

is the first derivative of the rotational speed of the gas generator, n _g is the rotational speed of the gas generator, m _a is the output gas volume of the gas turbine actuator, J _g is the moment of inertia of the gas generator, and f ₂ is a function that characterizes the output nonlinearity of the rotational speed of the gas generator of the gas turbine; The expanded state observer ESO _{in in} the inner-loop second-order linear ADRC controller is designed as:

in,

b ₁ is the controller parameter setting value; The control rate of the controller _Kpin is designed as

The controller output is

Where m _c is the reference input fuel quantity of the gas turbine actuator, that is, the reference input of the integral controller. 4. A kind of cascade gas turbine rotational speed control method based on active disturbance rejection control according to claim 1, it is characterized in that: the first input of the outer ring expansion state observer ESO _out is the gas turbine gas generator rotational speed measurement value, the second The input is the measured value of the rotational speed of the power turbine; the input of the inner ring expansion state observer ESO _in is the measured value of the fuel quantity of the gas turbine actuator, and the second input is the measured value of the rotational speed of the gas generator. 5. A method for controlling the rotational speed of a cascade gas turbine based on active disturbance rejection control according to claim 1, wherein the outer loop control feedback value is the estimated value of the power turbine rotational speed output by the expanded state observer ESO _out , and the inner loop The control feedback value is the estimated value of the rotational speed of the gas generator and the estimated value of its derivative output by the expansion state observer ESO _in .

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