CN108962410B - Active disturbance rejection control method for lead-cooled fast reactor power - Google Patents

Active disturbance rejection control method for lead-cooled fast reactor power Download PDF

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CN108962410B
CN108962410B CN201810669470.5A CN201810669470A CN108962410B CN 108962410 B CN108962410 B CN 108962410B CN 201810669470 A CN201810669470 A CN 201810669470A CN 108962410 B CN108962410 B CN 108962410B
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CN108962410A (en
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周世梁
沈聪
刘玉燕
刘凤鸣
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North China Electric Power University
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Abstract

The invention belongs to the technical field of nuclear power station control, and particularly relates to an active disturbance rejection control method for lead-cooled fast reactor power, which comprises the following steps: s1: obtaining a differential equation of the temperature of the lead-cooled fast reactor according to a neutron dynamics equation, and obtaining a reactivity feedback equation of the lead-cooled fast reactor according to the temperature feedback in the lead-cooled fast reactor and the rod position change of a control rod; s2: establishing an approximate single-group delayed neutron model for six groups of delayed neutrons in a neutron dynamic equation, and converting the model into a 2-order nonlinear model; s3: designing an active disturbance rejection controller based on a linear extended state observer by utilizing 2-order nonlinear model information; s4: and determining the active disturbance rejection control process of the lead-cooled fast reactor power control system by giving a controller bandwidth and an observer bandwidth.

Description

Active disturbance rejection control method for lead-cooled fast reactor power
Technical Field
The invention belongs to the technical field of nuclear power station control, and particularly relates to an active disturbance rejection control method for lead-cooled fast reactor power.
Background
Nuclear power plant units are highly complex nonlinear systems whose parameters are a function of operating power, nuclear fuel burnout, and control rod value, and vary over time. These factors must be taken into account especially when large power variations occur under load following conditions. Compared with a thermal reactor, the fast reactor has the advantages of high core enrichment, hard energy spectrum, small Doppler effect compared with the thermal reactor, short service life of instantaneous neutrons in the fast reactor, small delayed neutrons share, fast power change of the fast reactor under reactive disturbance, and requirement for a fast reactor control system to have better transient response characteristic. Most of the existing reactors are controlled by a conventional regulating system according to the parameter design of a basic load working point. A three-channel nonlinear controller usually adopted by a pressurized water reactor is actually a PID controller with nonlinear gain compensation, but if the three-channel nonlinear controller is applied to a fast reactor, the control effect is poor because target tracking and external disturbance suppression cannot be both considered.
Therefore, the tuning performance of conventional controllers is challenged under large load variation conditions. Many other advanced process control methods are also continuously available, such as fast reactor power control using an improved genetic programming method, and simulation results show that under the condition that the functional relationship between various reactivity feedbacks and reactivities generated by control rod actions is unclear, a prediction estimation function can be automatically generated through a training sample set, and the method has the advantages of fast convergence, high precision, no large fluctuation and oscillation in the control process, and well avoiding overshoot phenomenon. In the fast reactor power control based on the sliding mode control method, the result shows that the tracking output is insensitive to external interference and parameter uncertainty, and the sliding mode control observer is observed to have satisfactory performance under the condition that the parameters have uncertainty and interference, and shows more excellent power tracking and interference resistance compared with the traditional PID controller. Simulation results of the nuclear reactor power integral control system based on the Takagi-Sugeno fuzzy model show that the nuclear reactor power integral control system has better tracking characteristics, can realize zero steady-state tracking under the conditions of very small overshoot and few oscillations, and meets the operation safety requirements of the nuclear reactor. These control algorithms all achieve certain results, but because most of them have complex design structures and have the defects of difficult parameter setting and the like, they have not been widely used in engineering at present. Therefore, the research on a control strategy which is simple in structure, does not depend on a system model completely and has strong robustness has great practical significance for improving the performance of the conventional fast reactor power control system.
Disclosure of Invention
In order to solve the problems, the invention provides an active disturbance rejection control method for lead-cooled fast reactor power, which comprises the following steps:
s1: obtaining a differential equation of the temperature of the lead-cooled fast reactor according to a neutron dynamics equation, and obtaining a reactivity feedback equation of the lead-cooled fast reactor according to the temperature feedback in the lead-cooled fast reactor and the rod position change of a control rod;
s2: establishing an approximate single-group delayed neutron model for six groups of delayed neutrons in a neutron dynamic equation, and converting the model into a 2-order nonlinear model;
s3: designing an active disturbance rejection controller based on a linear extended state observer by utilizing 2-order nonlinear model information;
s4: and determining the active disturbance rejection control process of the lead-cooled fast reactor power control system by giving a controller bandwidth and an observer bandwidth.
The neutron dynamics equation is:
Figure BDA0001708719900000021
Figure BDA0001708719900000022
wherein t is time, n (t) is a neutron number function, rho (t) is a lead-cooled fast reactor reactivity feedback equation, beta is total effective delayed neutron share, lambda is invariable neutron average life, i is a delayed neutron group number, lambdad,iIs the i-th group of precursor nuclear decay constant, ci(t) is a function of the density of the i-th precursor nuclei, βiThe ratio of delayed neutrons in the ith group.
The lead-cooled fast reactor temperature comprises: the fuel temperature, the cladding temperature and the coolant average temperature respectively correspond to three differential equations as:
Figure BDA0001708719900000023
Figure BDA0001708719900000024
Figure BDA0001708719900000031
wherein M isfIs the fuel mass, CfIs the fuel heat capacity, T is the time, Tf(t) is fuel temperature, q (t) is reactor thermal power, kfcIs the heat transfer coefficient between the fuel and the cladding, Tc(t) is the cladding temperature, McIs the cladding quality, CcIs the cladding heat capacity, hclIs the heat transfer coefficient between the cladding and the coolant, Tl(t) is the average temperature of the lead inlet and outlet of the coolant, MlIs the mass of the coolant lead, ClIs the heat capacity of lead, gamma is the mass flow rate of lead, Tin(t) is the inlet temperature of lead.
The temperature feedback is a fuel doppler reactive feedback coefficient, an axial and radial expansion reactive feedback coefficient, and a coolant density reactive feedback coefficient.
The lead-cooled fast reactor reactivity feedback equation is as follows:
ρ(t)＝αD[Tf(t)-Tf0]+αZ[Tc(t)-Tc0]+αl[Tl(t)-Tl0]+αr[Tin(t)-Tin0]+αhΔhcr (6)
wherein rho (t) is a feedback equation of the reactivity of the lead-cooled fast reactor, alphaDIs the doppler reactivity feedback coefficient; alpha is alphazIs the axial expansion reactivity feedback coefficient; alpha is alpharIs the radial expansion reactivity feedback coefficient; alpha is alphalIs the coolant density reactive feedback coefficient; alpha is alphahIs the control rod differential value; t isf(T) is the fuel temperature, Tf0Is the fuel temperature at system equilibrium, Tc(T) is the cladding temperature, Tc0Is the temperature of the enclosure at system equilibrium, Tl(T) is the average temperature of the lead inlet and outlet of the coolant, Tl0Is the average temperature, T, of the lead inlet and outlet of the coolant at system equilibriumin(T) is the inlet temperature of lead, Tin0Is the inlet temperature of lead at system equilibrium, hcrIs the insertion depth of the control rod,. DELTA.hcrIs the amount of change in the insertion depth of the control rod.
The 2 nd order nonlinear model is:
Figure BDA0001708719900000032
wherein: n isrIs the relative neutron mass; zrIs the control rod speed, beta is the total effective delayed neutron fraction, Λ is the constant neutron average life, λ is the single group decay constant,
Figure BDA0001708719900000033
is the second derivative of the relative neutron variation,
Figure BDA0001708719900000034
is the first derivative of the variation in relative neutrons, δ nrIs the relative neutron variation, alphaDIs the Doppler reactive feedback coefficient, q0Is the thermal power of the reactor when the system is balanced; mfIs the fuel mass, CfIs the heat capacity of the fuel, nr0Relative neutron content at system equilibrium, GrControl rod value per unit length;
intermediate variables
Figure BDA0001708719900000035
Intermediate variables
Figure BDA0001708719900000036
Intermediate variables
Figure BDA0001708719900000037
Intermediate variables
Figure BDA0001708719900000041
kfcIs the heat transfer coefficient between the fuel and the cladding, Tf(T) is the fuel temperature, Tc(t) is the cladding temperature, rho (t) is the feedback equation of the reactivity of the lead-cooled fast reactor, alphazIs the axial expansion reactive feedback coefficient, alphalIs the coolant density reactive feedback coefficient;
Figure BDA0001708719900000042
is the first derivative of the temperature of the cladding,
Figure BDA0001708719900000043
is the first derivative of the coolant temperature, GrIs the value of the control rod per unit length.
The S3 specifically includes: expression of formula (26) as formula (27),
Figure BDA0001708719900000044
y and u are respectively output and input control quantities, g is a model uncertain factor, w is external disturbance of the system, and f is made to be g + w as total disturbance;
let the intermediate variable
Figure BDA0001708719900000045
The equation of state for equation (27) is:
Figure BDA0001708719900000046
wherein:
Figure BDA0001708719900000047
C＝(1 0 0)，
Figure BDA0001708719900000048
x1、x2and x3Are the three vectors in the expansion state matrix, A, B, C and E are the matrices defined in the expansion state equation, and h is the unknown perturbation. Wherein x is3F is the expanded state of the stent,
Figure BDA0001708719900000049
the linear extended state observer is then:
Figure BDA00017087199000000410
wherein z is an observation estimation item of x in the observer, L is observer gain, and the method is obtained by a pole allocation method:
Figure BDA00017087199000000411
Figure BDA00017087199000000412
l1、l2and l3Are the three vectors, ω, in the gain matrixoFor observer bandwidth, the observer tracks the following states:
Figure BDA00017087199000000413
z1、z2and z3Is three observations, y (t) is the system output, LESO is a linear extended state observer.
A controller:
Figure BDA0001708719900000051
f0(z1,z2) Is a function of the observed term in the controller design, u0Is the initial input.
The PD controller controls:
u0＝kp(r-z1)-kdz2
where r is a set value, the closed loop transfer function is:
Figure BDA0001708719900000052
the gain is then: coefficient of proportionality
Figure BDA0001708719900000053
Differential coefficient kd＝2ξωcS is a complex variable and ξ is the damping ratio.
The invention has the beneficial effects that: aiming at the problem that no simple controller capable of obtaining a good control effect exists in the current lead-cooled fast reactor object, an original model is converted into a nonlinear model suitable for designing an active disturbance rejection controller through derivation; model information is fully utilized, and the complex load of ESO is reduced; finally, the controller parameters can be easily obtained by simply adjusting the bandwidth, and compared with advanced control algorithms such as predictive control and fuzzy control, the control system has a simpler structure and a more excellent control effect.
Drawings
Fig. 1 is a schematic diagram of a linear active disturbance rejection structure without model information.
Fig. 2 is a schematic diagram of a linear active disturbance rejection controller structure with model information.
Detailed Description
The embodiments are described in detail below with reference to the accompanying drawings.
Summary and examples of applications of Linear Active Disturbance Rejection Control (LADRC) in many fields, including fast tool servo Control in precision lathes, variable frequency speed Control of asynchronous motors, uncertain time lag systems, ship heading Control, aircraft attitude Control, etc., all show great potential of the Active Disturbance Rejection Control technology. In the field of power generation, LADRC also obtains excellent control effect in simulation control of a main gas temperature control system of a thermal power plant, a circulating fluidized bed boiler combustion system and the like, and a linear active disturbance rejection device structure without model information is shown in figure 1. However, there is no research on applying the lacrc adjusted based on the bandwidth parameters using model information to the lead-cooled fast reactor power control.
In order to solve the above problems, the present invention provides an active disturbance rejection control method for lead-cooled fast reactor power, as shown in fig. 2, including:
s1: obtaining a differential equation of the temperature of the lead-cooled fast reactor according to a neutron dynamics equation, and obtaining a reactivity feedback equation of the lead-cooled fast reactor according to the temperature feedback in the lead-cooled fast reactor and the rod position change of a control rod;
s2: establishing an approximate single-group delayed neutron model for six groups of delayed neutrons in a neutron dynamic equation, and converting the model into a 2-order nonlinear model;
s3: designing an active disturbance rejection controller based on a linear extended state observer by utilizing 2-order nonlinear model information;
s4: and determining the active disturbance rejection control process of the lead-cooled fast reactor power control system by giving a controller bandwidth and an observer bandwidth.
The step S1 specifically includes:
1-1) assuming that the neutron flux in the reactor is independent of space, its spectrum is considered independent of neutron level, and the time-varying nature of the neutron density at each point is not correlated with spatial location. Approximately viewing the performance of the lead-cooled fast reactor as a 'point' without space measurement, and obtaining a neutron dynamics equation as follows:
Figure BDA0001708719900000061
Figure BDA0001708719900000062
wherein t is time, n (t) is a neutron number function, rho (t) is a lead-cooled fast reactor reactivity feedback equation, beta is total effective delayed neutron share, lambda is invariable neutron average life, i is a delayed neutron group number, lambdad,iIs the i-th group of precursor nuclear decay constant, ci(t) is a function of the density of the i-th precursor nuclei, βiThe ratio of delayed neutrons in the ith group.
1-2) obtaining three differential equations (3), (4) and (5) of the lead-cooled fast reactor with respect to the fuel temperature, the cladding temperature and the average temperature of the coolant according to the law of macroscopic energy conservation;
Figure BDA0001708719900000071
Figure BDA0001708719900000072
Figure BDA0001708719900000073
wherein M isfIs the fuel mass, CfIs the fuel heat capacity, T is the time, Tf(t) is fuel temperature, q (t) is reactor thermal power, kfcIs the heat transfer coefficient between the fuel and the cladding, Tc(t) is the cladding temperature, McIs the cladding quality, CcIs the cladding heat capacity, hclIs the heat transfer coefficient between the cladding and the coolant, Tl(t) is the average temperature of the lead inlet and outlet of the coolant, MlIs the mass of the coolant lead, ClIs the heat capacity of lead, gamma is the mass flow rate of lead, Tin(t) is the inlet temperature of lead.
1-3) feeding back temperature in the lead-cooled fast reactor according to the fuel Doppler effect reactivity feedback coefficient, the axial and radial expansion reactivity feedback coefficients and the coolant density reactivity feedback coefficient, wherein the temperature feedback is constant and is calculated by an average value. In addition, reactivity feedback brought by the rod position change of the control rod is considered, and the obtained reactivity feedback equation of the lead-cooled fast reactor is as follows:
ρ(t)＝αD[Tf(t)-Tf0]+αZ[Tc(t)-Tc0]+αl[Tl(t)-Tl0]+αr[Tin(t)-Tin0]+αhΔhcr(16)
wherein rho (t) is a feedback equation of the reactivity of the lead-cooled fast reactor, alphaDIs the doppler reactivity feedback coefficient; alpha is alphazIs the axial expansion reactivity feedback coefficient; alpha is alpharIs the radial expansion reactivity feedback coefficient; alpha is alphalIs the coolant density reactive feedback coefficient; alpha is alphahIs the control rod differential value; t isf(T) is the fuel temperature, Tf0Is the fuel temperature at system equilibrium, Tc(T) is the cladding temperature, Tc0Is the temperature of the enclosure at system equilibrium, Tl(T) is the average temperature of the lead inlet and outlet of the coolant, Tl0Is the average temperature, T, of the lead inlet and outlet of the coolant at system equilibriumin(T) is the inlet temperature of lead, Tin0Is the inlet temperature of lead at system equilibrium, hcrIs the insertion depth of the control rod,. DELTA.hcrIs the amount of change in the insertion depth of the control rod.
In the design of a control system, a constant is taken as β 319 pcm; Λ 8.0659 × 10-7s；λ＝0.081958s；αD＝-0.15pcm K-1；q0＝300MWth；Mf＝2132kg；Cf＝375.5Jkg-1K-1；nr0＝1；Gr＝αh＝138pcm cm-1。
The step S2 specifically includes:
firstly, the six groups of delayed neutrons in (1) and (2) are approximated to a single group of delayed neutrons to establish an approximate model.
A single set of delayed neutron contributions β, defined as:
Figure BDA0001708719900000081
a single set of decay constants, λ, defined as:
Figure BDA0001708719900000082
according to the following steps:
Figure BDA0001708719900000083
obtaining:
Figure BDA0001708719900000084
according to the form of the 2 nd order power differential equation, the equation is ultimately:
Figure BDA0001708719900000085
normalizing the neutron number n:
Figure BDA0001708719900000086
substituting (7) and (8) into (1):
Figure BDA0001708719900000087
assuming that the initial precursor-nucleus density is unchanged, the steady-state initial conditions and (2) are given as follows:
Figure BDA0001708719900000088
therefore:
Figure BDA0001708719900000089
substituting (13) into (1) and (2) yields:
Figure BDA00017087199000000810
Figure BDA00017087199000000811
wherein the content of the first and second substances,
Figure BDA00017087199000000812
by taking the derivative of (14), the following can be obtained:
Figure BDA00017087199000000813
substituting (6) and (15) into (17) to obtain
Figure BDA00017087199000000814
Setting:
Figure BDA0001708719900000091
δnr＝nr-nr0 (30)
from (20) can be obtained:
Figure BDA0001708719900000092
substituting (19), (20) and (21) into (18) yields:
Figure BDA0001708719900000093
substituting (14) into (22) to obtain:
Figure BDA0001708719900000094
from (3) can be obtained:
Figure BDA0001708719900000095
substituting (24) into (22) to obtain:
Figure BDA0001708719900000096
Figure BDA0001708719900000097
wherein:
Figure BDA0001708719900000098
Figure BDA0001708719900000099
the S3 specifically includes: expression of formula (26) as formula (27),
Figure BDA00017087199000000910
y and u are respectively output and input control quantities, g is a model uncertain factor, w is external disturbance of the system, and f is made to be g + w as total disturbance;
let the intermediate variable
Figure BDA00017087199000000911
The equation of state for equation (27) is:
Figure BDA00017087199000000912
wherein:
Figure BDA0001708719900000101
C＝(1 0 0)，
Figure BDA0001708719900000102
x1、x2and x3Are the three vectors in the expansion state matrix, A, B, C and E are the matrices defined in the expansion state equation, and h is the unknown perturbation. Wherein x is3F is the expanded state of the stent,
Figure BDA0001708719900000103
the linear extended state observer is then:
Figure BDA0001708719900000104
wherein z is an observation estimation item of x in the observer, L is observer gain, and the method is obtained by a pole allocation method:
Figure BDA0001708719900000105
Figure BDA0001708719900000106
l1、l2and l3Are the three vectors, ω, in the gain matrixoFor observer bandwidth, the observer tracks the following states:
Figure BDA0001708719900000107
z1、z2and z3Is three observations, y (t) is the system output, and LESO is a linear extended state observer.
A controller:
Figure BDA0001708719900000108
f0(z1,z2) Is a function of the observed term in the controller design, u0Is the initial input.
The PD controller controls:
u0＝kp(r-z1)-kdz2
where r is a set value, the closed loop transfer function is:
Figure BDA0001708719900000109
the gain is then: coefficient of proportionality
Figure BDA00017087199000001011
Differential coefficient kd＝2ξωcS is a complex variable and ξ is the damping ratio.
The S4 is specifically when:
Figure BDA00017087199000001010
ω c and ωoSetting is needed, and the following rules are followed in the actual setting process:
1) for controller bandwidth omegacIn other words, ωcThe larger the system response speed is, the better the anti-interference effect and the sensitivity to parameter change are, but the more serious oscillation and overshoot are brought along with the reduction of the stability;
2) for observer bandwidth omegaoIn other words, ωoThe larger the ESO, the stronger the observation ability, the noise to the sensorThe higher the sensitivity of (c); therefore, ωoGradually increasing from a smaller value until the observation precision meets the requirement;
ωcand ωoThe error index is determined by multiple tests and comprehensive comparison on the premise of ensuring the stability of the controller, and the upper error bound of the observer and the controller and the bandwidth omega thereofcAnd ωoInversely, the wider the bandwidth, the smaller the error, and the lower the stability.
The present invention is not limited to the above embodiments, and any changes or substitutions that can be easily made by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (4)

1. An active disturbance rejection control method for lead-cooled fast reactor power is characterized by comprising the following steps:
s1: obtaining a differential equation of neutron density of a lead-cooled fast reactor and a precursor concentration of delayed neutrons according to reactor neutron dynamics, obtaining a differential equation of fuel temperature, cladding temperature and coolant average temperature according to reactor core heat transfer and heat balance, and obtaining a reactivity feedback equation of the lead-cooled fast reactor according to temperature feedback in the lead-cooled fast reactor and rod position change of a control rod; the differential equation of the neutron density and the delayed neutron precursor nucleus concentration is as follows:
Figure FDA0002910091570000011
Figure FDA0002910091570000012
wherein t is time, n (t) is a neutron number function, rho (t) is a lead-cooled fast reactor reactivity feedback equation, beta is total effective delayed neutron share, lambda is invariable neutron average life, and i is a delayed neutron group number，λd，iIs the i-th group of precursor nuclear decay constant, ci(t) is a function of the density of the i-th precursor nuclei, βiThe proportion of the delayed neutrons in the ith group; the differential equations for the fuel temperature, cladding temperature, and coolant average temperature are:
Figure FDA0002910091570000013
Figure FDA0002910091570000014
Figure FDA0002910091570000015
wherein M isfIs the fuel mass, CfIs the fuel heat capacity, T is the time, Tf(t) is fuel temperature, q (t) is reactor thermal power, kfcIs the heat transfer coefficient between the fuel and the cladding, Tc(t) is the cladding temperature, McIs the cladding quality, CcIs the cladding heat capacity, hclIs the heat transfer coefficient between the cladding and the coolant, Tl(t) is the average temperature of the lead inlet and outlet of the coolant, MlIs the mass of the coolant lead, ClIs the heat capacity of lead, gamma is the mass flow rate of lead, Tin(t) is the inlet temperature of lead; the lead-cooled fast reactor reactivity feedback equation is as follows:
ρ(t)＝αD[Tf(t)-Tf0]+αZ[Tc(t)-Tc0]+α1[T1(t)-Tl0]+αr[Tin(t)-Tin0]+αhΔhcr (6)
wherein rho (t) is a feedback equation of the reactivity of the lead-cooled fast reactor, alphaDIs the doppler reactivity feedback coefficient; alpha is alphazIs the axial expansion reactivity feedback coefficient; alpha is alpharIs the radial expansion reactivity feedback coefficient; alpha is alphalIs the coolant density reactive feedback coefficient；αhIs the control rod differential value; t isf(T) is the fuel temperature, Tf0Is the fuel temperature at system equilibrium, Tc(T) is the cladding temperature, Tc0Is the temperature of the enclosure at system equilibrium, Tl(T) is the average temperature of the lead inlet and outlet of the coolant, Tl0Is the average temperature, T, of the lead inlet and outlet of the coolant at system equilibriumin(T) is the inlet temperature of lead, Tin0Is the inlet temperature of lead at system equilibrium, hcrIs the insertion depth of the control rod,. DELTA.hcrIs the amount of change in the insertion depth of the control rod;
s2: establishing an approximate single-group delayed neutron model for six groups of delayed neutrons in a neutron dynamic equation, and converting the model into a 2-order nonlinear model;
s3: designing an active disturbance rejection controller based on a linear extended state observer by utilizing 2-order nonlinear model information;
s4: and determining the active disturbance rejection control process of the lead-cooled fast reactor power control system by giving a controller bandwidth and an observer bandwidth.
2. The active disturbance rejection control method for lead-cooled fast reactor power of claim 1, wherein the temperature feedback is a fuel doppler reactive feedback coefficient, an axial and radial expansion reactive feedback coefficient and a coolant density reactive feedback coefficient.
3. The active disturbance rejection control method for the lead-cooled fast reactor power according to claim 1 or 2, wherein the 2 nd order nonlinear model is:
Figure FDA0002910091570000021
wherein: n isrIs the relative neutron mass; zrIs the control rod speed, beta is the total effective delayed neutron fraction, Λ is the constant neutron average life, λ is the single group decay constant,
Figure FDA0002910091570000022
is the second derivative of the relative neutron variation,
Figure FDA0002910091570000023
is the first derivative of the variation in relative neutrons, δ nrIs the relative neutron variation, alphaDIs the Doppler reactive feedback coefficient, q0Is the thermal power of the reactor when the system is balanced; mfIs the fuel mass, CfIs the heat capacity of the fuel, nr0Relative neutron content at system equilibrium, GrIs the value of the control rod per unit length;
intermediate variables
Figure FDA0002910091570000031
Intermediate variables
Figure FDA0002910091570000032
Intermediate variables
Figure FDA0002910091570000033
Intermediate variables
Figure FDA0002910091570000034
kfcIs the heat transfer coefficient between the fuel and the cladding, Tf(T) is the fuel temperature, Tc(t) is the cladding temperature, rho (t) is the feedback equation of the reactivity of the lead-cooled fast reactor, alphazIs the axial expansion reactive feedback coefficient, alphalIs the coolant density reactive feedback coefficient,
Figure FDA0002910091570000035
is the first derivative of the temperature of the cladding,
Figure FDA0002910091570000036
is the first derivative of the coolant temperature.
4. The active disturbance rejection control method for the lead-cooled fast reactor power according to claim 3, wherein the S3 specifically includes: the formula (7) is expressed in the form of the formula (8),
Figure FDA0002910091570000037
y and u are respectively output and input control quantities, g is a model uncertain factor, w is external disturbance of the system, and f is made to be g + w as total disturbance;
let the intermediate variable
Figure FDA0002910091570000038
The equation of state for equation (8) is:
Figure FDA0002910091570000039
wherein:
Figure FDA00029100915700000310
C＝(1 0 0)，
Figure FDA00029100915700000311
x1、x2and x3Are the three vectors in the expansion state matrix, A, B, C and E are the matrices defined in the expansion state equation, h is the unknown perturbation;
wherein x is3F is the expanded state of the stent,
Figure FDA00029100915700000312
the linear extended state observer is then:
Figure FDA00029100915700000313
wherein z is an observation estimation item of x in the observer, L is observer gain, and the method is obtained by a pole allocation method:
Figure FDA0002910091570000041
Figure FDA0002910091570000042
l1、l2and l3Are the three vectors, ω, in the gain matrixoFor observer bandwidth, the observer tracks the following states:
Figure FDA0002910091570000043
z1、z2and z3Is three observations, y (t) is the system output, LESO is the linear extended state observer;
designing a controller:
Figure FDA0002910091570000044
f0(z1，z2) Is a function of the observed term in the controller design, u0Is the initial input;
the PD controller controls:
u0＝kp(r-z1)-kdz2
where r is a set value, the closed loop transfer function is:
Figure FDA0002910091570000045
wherein the proportionality coefficient
Figure FDA0002910091570000046
ωcFor controller bandwidth, the differential coefficient kd＝2ξωcS is a complex variable and ξ is the damping ratio.
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