CN104483837B - Adaptive control method for reversible machinery group - Google Patents
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Abstract
The invention provides an adaptive control method for a reversible machinery group. The adaptive control method comprises the following steps: S1) establishing a nonlinear mathematic model of each link in the reversible machinery group; S2) according to the nonlinear mathematic model of each link, establishing a nonlinear mathematic model of the reversible machinery group; S3) constructing a three-dimensional matrix, generating a dynamic equation which is practically output from the reversible machinery group according to the three-dimensional matrix and the nonlinear mathematic model of the reversible machinery group, constructing an expected output track equation of the reversible machinery group, and generating a tracking error equation according to the dynamic equation which is practically output from the reversible machinery group and the expected output track equation of the reversible machinery group; S4) converting the track error equation into a control equation of an adaptive controller, generating a control amount via the control equation of the adaptive controller to regulate the control input of the reversible machinery group, setting an adaptive updating mechanism, and regulating the control amount of the adaptive controller according to the output of the reversible machinery group and the adaptive updating mechanism.
Description
Technical Field
The invention relates to the technical field of reversible unit control of pumped storage power stations, in particular to a reversible unit self-adaptive control method.
Background
For a long time, the reversible unit of the pumped storage power station widely adopts the PID control based on the linear control theory and the improved control strategy thereof. The reversible unit has strong nonlinearity and non-minimum phase characteristics, and frequent working condition conversion, so that the linear control strategy has the problems of poor control quality and system stability, and the safety stability and the dynamic performance of the operation of the reversible unit are seriously influenced.
At present, the study of the nonlinear feedback control of reversible units based on differential geometry methods has emerged. Although theoretically, the nonlinear feedback control can solve the nonlinear control problem of the reversible unit, the dynamic characteristics of the reversible unit need to be accurately mastered, or a mathematical model capable of accurately describing the dynamic characteristics of the reversible unit control system needs to be established. However, such conditions are too harsh, for a complex system such as a reversible unit, no matter a theoretical research method or a model test method is adopted, the established mathematical model is only an approximation of the dynamic characteristics of the system, so that the main characteristics of the reversible unit adjusting system in a certain working range can be described, but certain uncertainty exists, and therefore, the nonlinear feedback control has no practical application value.
In order to improve the regulation quality of a water turbine regulation system and meet the requirements of static and dynamic performances of the water turbine regulation system, a nonlinear control method taking fuzzy control, neural network control and optimal control as representatives is developed in the research of a hydroelectric generating set control theory. The nonlinear control method makes certain breakthrough in the theoretical level, but has some defects. For example, fuzzy control has the defects that membership function assignment is not based and fuzzy rule induction is difficult, and neural network control has the defects of low learning speed, long decision time, easy convergence to a local minimum point and the like. The optimal control research is limited to an affine nonlinear system, a lie derivative and a partial differential equation set need to be solved, and the control rule has strict requirements on a model, so that the difference between theory and application is large.
Therefore, the existing reversible unit control method cannot meet the requirements of safe stability and good dynamic performance of the operation of the reversible unit.
Disclosure of Invention
In view of the above, the invention provides a nonlinear modeling method of an M-th order polynomial of parameters of a pump turbine 3 for strong nonlinearity of a reversible unit, so that a nonlinear mathematical model of a reversible unit control system meets a parameter linearization condition, and provides a reversible unit self-adaptive control method capable of meeting the safety stability and good dynamic performance of operation of the reversible unit.
A reversible unit self-adaptive control method comprises the following steps:
s1, establishing mathematical models of an actuating mechanism, a power generation/motor, a pressure water passing system and a pump turbine in the reversible unit, wherein the nonlinear modeling of a 3-parameter M-th-order polynomial of the pump turbine is a key point;
s2, establishing a nonlinear mathematical model of the reversible unit according to mathematical models of an actuating mechanism, a power generation/motor, a pressure water passing system and a water pump turbine in the reversible unit; the nonlinear mathematical model of the reversible unit consists of two known functions and a function of a smooth vector field with known structure and unknown parameters;
s3, constructing a three-dimensional matrix, and generating a dynamic equation of the actual output of the reversible unit according to the three-dimensional matrix and the nonlinear mathematical model of the reversible unit; constructing an expected output trajectory equation of the reversible unit, and generating a tracking error equation according to a dynamic equation of actual output of the reversible unit and the expected output trajectory equation of the reversible unit;
and S4, converting the tracking error equation into a control equation of an adaptive controller, generating a control input for controlling the quantity regulation reversible unit through the control equation of the adaptive controller, setting a self-adaptive updating mechanism, estimating a smooth vector field with unknown parameters by the self-adaptive updating mechanism, and adjusting the control quantity of the adaptive controller according to the output of the reversible unit and the self-adaptive updating mechanism, thereby performing adaptive control on the transition process of the reversible unit of the pumped storage power station.
The invention provides a reversible unit self-adaptive control method, which is characterized in that a nonlinear model of a reversible unit is established, the nonlinear mathematical model of the reversible unit is composed of two known functions and a function of a smooth vector field with known structure and unknown parameters, and the nonlinear model of the reversible unit established in the way meets the condition of parameter linearization, so that the specific torque and flow characteristics of the reversible unit and the self-adjusting coefficient of an external load are not required to be known during control, and the defect that parameter assignment in the function in the prior art is not based is overcome. And then the problem that the actual output of the reversible unit tracks the expected output track is converted into a tracking error problem. And then, a self-adaptive updating mechanism is arranged, and the control quantity of the self-adaptive controller is adjusted according to the output of the reversible unit and the self-adaptive updating mechanism, so that the self-adaptive control is carried out on the transition process of the reversible unit of the pumped storage power station, and the tracking error of the reversible unit gradually converges to zero.
Drawings
Fig. 1 is a block diagram of a reversible unit adjustment system according to an embodiment of the present invention;
fig. 2 is a flowchart of a reversible unit adaptive control method according to an embodiment of the present invention.
Detailed Description
The principle of the invention is as follows, as shown in fig. 1, a reversible unit adjusting system self-adaptive controller 5 and a reversible unit, wherein the reversible unit comprises an actuating mechanism 1, a power generation/motor 2, a pressure water passing system 3 and a pump turbine 4. Fig. 1 shows the signaling of the individual elements of a reversible aggregate control system, the control variable u output by the adaptive controller 5 being the control input u of the actuator; the actuating mechanism 1 outputs the opening degree y to a water pump turbine 4 and an adaptive controller 5; the pump turbine 4 outputs torque to the generator/motor 2, and the pump turbine 4 outputs flow q to the pressure water passing system 3; the generator/motor 2 simultaneously outputs the rotating speed n to the adaptive controller 5 and the pump turbine 4; the pressure water-passing system 3 outputs the water pressure h to the water pump turbine 4 and the self-adaptive controller 5.
The control quantity u output by the self-adaptive controller 5 is the control input u of the actuating mechanism, and the reversible unit is adjusted and controlled according to the control quantity u; the reversible unit feeds back the water pressure h, the opening degree y and the rotating speed n to the self-adaptive controller 5; and the self-adaptive controller 5 updates the control quantity u output by the self-adaptive controller 5 according to the self-adaptive updating mechanism and the received feedback water pressure h, the opening degree y and the rotating speed n, so that the self-adaptive control of the reversible unit is completed.
As shown in fig. 2, an embodiment of the present invention provides a reversible unit adaptive control method, where the reversible unit adaptive control method includes the following steps:
s1, establishingThe mathematical model of an actuating mechanism 1, a power generation/motor 2, a pressure water passing system 3 and a pump turbine 4 in the reversible unit. Balance operating point P of reversible unit0∈(n＝n0；Y＝Y0；H＝H0)，Mt0,Q0The moment and the flow of the balance working point are respectively defined as the following variables, n is the rotating speed of the pump turbine, Y is the opening degree of the guide vane, H is the working water pressure, M istFor unit moment, MgIs the load moment, Q is the unit flow
Δn＝n-n0，ΔY＝Y-Y0,ΔH＝H-H0,ΔMt＝Mt-Mt0,ΔQ＝Q-Q0
MrFor torque rating, QrTo a flow rating, HrFor rated working water pressure, YmaxIs the maximum guide vane opening.
TyIs the inertial time constant of the servomotor, u is the control input, TaIs an inertia time constant of the generator/motor 2, enFor the generator/motor 2 load self-adjusting coefficient, L is the penstock length, d is the penstock diameter, A is the penstock area, a is the water shock wave velocity, f is the friction coefficient, T is the time coefficient, T is the time coefficientwIs the water flow inertia time constant; t isrThe water hammer reflection time, α the loss factor,
the formula of the nonlinear mathematical model of the actuator 1 is as follows:
the mathematical model of the implementation structure 1 is a known model.
The formula of the mathematical model of the generator/motor 2 is as follows:
the mathematical model of the generator/motor 2 is a known model.
The steps of establishing a formula of a mathematical model of the pressure water diversion system 3 are as follows:
s11a, establishing a continuous equation and a motion equation of the pressure water diversion system 3 as follows:
s12a, introducing Laplace operator S, converting a continuous equation and a motion equation of the pressure water diversion system 3 from a time domain nonlinear partial differential form into an S domain linear ordinary differential equation set, and obtaining a formula of a pressure water diversion system 3 model expressed by a transfer function form, wherein the formula comprises the following components:
the model of the pressure water diversion system 3 is a known model.
S13a, neglecting loss coefficients in the reversible unit, applying functions in a model formula of a pressure water diversion systemTaking the antecedent of the Taylor expansion to obtain a state space expression of the pressure diversion system model 3, as follows:
in the state space expression of the pressure diversion system model:
h＝[h heh1h2… h2r-1]T∈R2；
Ch＝[1 0 … 0]∈R2。
the method for establishing the formula of the nonlinear mathematical model of the pump turbine comprises the following steps:
s11b, according to the balance operating point P of the given reversible unit0∈(n＝n0；α＝α0；H＝H0) And performing Taylor series expansion on the torque characteristic and the flow characteristic, then intercepting the previous M-degree polynomial and obtaining a torque and flow characteristic expression in the following form:
wherein the polynomial coefficientFor an unknown parameter x1＝x,x2＝y,x3H. Thus, the torque and flow characteristics can satisfy the condition of parameter linearization.
S2, establishing a nonlinear mathematical model of the reversible unit according to the nonlinear mathematical models of an actuating mechanism 1, a generator/motor 2, a pressure water passing system 3 and a pump turbine 4 in the reversible unit; the nonlinear mathematical model of the reversible unit is composed of two known functions and a function of a smooth vector field with known structure and unknown parameters.
S21, selecting a state variable X, X ═ X1x2x3]T＝[x y h]TWhere T is the transpose operation. In the expression of the state variable X and the following expressions, X1＝x,x2＝y,x3＝h。
S22, based on the differential geometric theory of the smooth vector field, establishing a nonlinear mathematical model of the reversible unit according to the nonlinear mathematical models of an actuating mechanism 1, a power generation/motor 2, a pressure water passing system 3 and a pump turbine 4 in the reversible unit, wherein the formula of the nonlinear mathematical model of the reversible unit is as follows:
wherein,
s23, substituting the expression of the torque and flow rate characteristics into F1In the expression of (x, t), let e at the same timen＝θ0To obtain
Wherein, F2(x, t) and B are known functions, F, which describe the behavior of the pump turbine 41(x, t) is of known structure, but the parametersFunction of the unknown smooth vector field.
S3, constructing a three-dimensional matrix, and generating a dynamic equation of the actual output of the reversible unit according to the three-dimensional matrix and the nonlinear mathematical model of the reversible unit; and constructing an expected output trajectory equation of the reversible unit, and generating a tracking error equation according to a dynamic equation of actual output of the reversible unit and the expected output trajectory equation of the reversible unit.
The step S3 includes the following sub-steps:
s31, constructing one-dimensional output variable w ═ C (x-x)e) Wherein C is a three-dimensional matrix, and C ═ C1c2c3]。
S32, deriving w and bringing inIn-process obtaining reversible unit actual output dynamic equationWhere ρ (x, t) ═ CF2(x, t), b ═ CB is a known function and constant; f (x, t) ═ CF1(x, t) is a function with known structure and unknown parameters.
Will be provided withSubstituted into f (x, t) ═ CF1(x, t) to obtain
And order the parameter vectorWherein:
then f (x, t) can be written as
f(x,t)＝η(x1,x2,x3) Theta; wherein:wherein:
the self-adaptive control of the reversible unit is changed into: when smooth vector fieldThe sum function ρ (x, t) ∈ R is known, the parameter vectorUnknown, and b ≠ 0, i.e., c2Not equal to 0, the output w (t) of the reversible unit regulating system is made to track the expected output trajectory wd(t)∈R。
S33, passing pair wd(t) ∈ R is derived to establish the desired output trajectory wd(t) ∈ R equation
Wherein k isd∈R+So that the expected track is exponentially attenuated, and the reversible unit regulating system has good dynamic performance; at this time wd(0)＝w(0)。
S34, defining tracking error e (t) wd(t) -w (t), deriving a tracking error function from the error:
and S4, converting the tracking error equation into a control equation of an adaptive controller, generating a control input for controlling the quantity regulation reversible unit through the control equation of the adaptive controller, setting a self-adaptive updating mechanism, estimating a smooth vector field with unknown parameters by the self-adaptive updating mechanism, and adjusting the control quantity of the adaptive controller according to the output of the reversible unit and the self-adaptive updating mechanism, thereby performing adaptive control on the transition process of the reversible unit of the pumped storage power station.
The step S4 includes the following sub-steps:
s41, converting the actual output dynamic equation of the reversible unit as follows
Then the following equation will be translated from the error function:
the tracking problem of the reversible unit adjustment system is translated into designing the adaptive controller u1(t) ∈ R, so that the tracking error e (t) → 0, and the real system control amount u (t) can have the following expression:
obtaining control equations for adaptive controllers
Wherein k ise∈R+In order to feed back the gain, the gain is,representing an estimate of an unknown parameter theta; and generating control input of the control quantity adjusting reversible unit through a control equation of the self-adaptive controller.
S42, setting a self-adaptive updating mechanism, wherein the formula of the self-adaptive updating mechanism is as follows:
wherein,for positive definite, diagonal update of gain matrix, it is advisablep∈R+I is an identity matrix; the output of the reversible unit and a self-adaptive updating mechanism adjust the control quantity of the self-adaptive controller, so that the self-adaptive control is carried out on the transition process of the reversible unit of the pumped storage power station. The formula of the adaptive update mechanism is a known formula.
According to the reversible unit self-adaptive control method provided by the embodiment of the invention, the nonlinear model of the reversible unit is established, and the nonlinear mathematical model of the reversible unit is composed of two known functions and a function of a smooth vector field with a known structure and unknown parameters, so that the established nonlinear model of the reversible unit meets the condition of parameter linearization, the specific torque value, the flow characteristic and the self-adjusting coefficient of an external load of the reversible unit are not required to be known during control, and the defect that parameter assignment in the function in the prior art is not based is overcome. And then converting the actual output of the reversible unit into a tracking error problem according to the problem of the expected output track. And the tracking problem is converted into the equation problem of the design of the adaptive controller by converting the tracking error equation into the control equation of the adaptive controller. And then, a self-adaptive updating mechanism is arranged, and the control quantity of the self-adaptive controller is adjusted according to the output of the reversible unit and the self-adaptive updating mechanism, so that the self-adaptive control is carried out on the transition process of the reversible unit of the pumped storage power station, and the tracking error of the reversible unit gradually converges to zero.
Lyapunov candidate function is selected as a Lyapunov candidate function (Lyapunov function) which can be used to prove the stability of a power system or an autonomous differential equation)
Can prove that
The tracking error of the reversible unit regulating system therefore converges asymptotically to zero. The reversible unit self-adaptive control method provided by the embodiment of the invention can ensure that the reversible unit has safe stability and good dynamic performance in operation.
In all the above formulas, the same letter represents the same parameter and variable.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in random access memory, read only memory, electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable magnetic disk, a CD-ROM, or any other form of storage medium known in the art.
It is understood that various other changes and modifications may be made by those skilled in the art based on the technical idea of the present invention, and all such changes and modifications should fall within the protective scope of the claims of the present invention.
Claims (8)
1. The adaptive control method of the reversible unit is characterized by comprising the following steps:
s1, establishing mathematical models of an actuating mechanism, a power generation/motor, a pressure water passing system and a water pump turbine in the reversible unit;
s2, establishing a nonlinear mathematical model of the reversible unit according to mathematical models of an actuating mechanism, a power generation/motor, a pressure water passing system and a water pump turbine in the reversible unit; the nonlinear mathematical model of the reversible unit consists of two known functions and a function of a smooth vector field with known structure and unknown parameters;
s3, constructing a three-dimensional matrix, and generating a dynamic equation of the actual output of the reversible unit according to the three-dimensional matrix and the nonlinear mathematical model of the reversible unit; constructing an expected output trajectory equation of the reversible unit, and generating a tracking error equation according to a dynamic equation of actual output of the reversible unit and the expected output trajectory equation of the reversible unit;
and S4, converting the tracking error equation into a control equation of an adaptive controller, generating a control input for controlling the quantity regulation reversible unit through the control equation of the adaptive controller, setting a self-adaptive updating mechanism, estimating a smooth vector field with unknown parameters by the self-adaptive updating mechanism, and adjusting the control quantity of the adaptive controller according to the output of the reversible unit and the self-adaptive updating mechanism, thereby performing adaptive control on the transition process of the reversible unit of the pumped storage power station.
2. The reversible machine-group adaptive control method according to claim 1, wherein the mathematical model of the actuator has the following formula:
wherein T isyIs the servomotor inertia time constant; u is the control input, and y is the relative value of the aperture deviation of the servomotor.
3. The adaptive control method of a reversible machine set according to claim 2, wherein the mathematical model of the generator/motor is formulated as follows:
wherein x is the relative value of the rotational speed deviation of the pump turbine, h is the relative value of the water pressure deviation of the pump turbine, and TaIs the inertia time constant of the generator/motor, enThe coefficients are self-adjusted for the generator/motor load,Mgfor the pump turbine load moment, MrFor torque rating, n0,α0,H0The rotating speed, the guide vane opening degree and the working water pressure of the water pump turbine at the balance working condition point are respectively.
4. The adaptive control method of the reversible unit according to claim 3, wherein the step of establishing the formula of the mathematical model of the pressure diversion system is as follows:
s11a, establishing a continuous equation and a motion equation of the pressure water diversion system as follows:
q is the flow of the pump turbine, H is the working water pressure of the unit, L is the length of the water conduit, d is the diameter of the water conduit, A is the area of the water conduit, a is the water shock wave speed, f is the friction coefficient, and t is the time coefficient;
s12a, introducing Laplace operator S, converting a continuous equation and a motion equation of the pressure water diversion system from a time domain nonlinear partial differential form into an S domain linear ordinary differential equation set, and obtaining a formula of a pressure water diversion system model expressed by a transfer function form, wherein the formula comprises the following components:
wherein, TwIs the water flow inertia time constant; t isrThe reflection time of the water hammer wave is α is a loss coefficient;
s13a, definitionBy neglecting the loss coefficient in the reversible unit, the function in the model formula of the pressure water diversion system is subjected toTaking the antecedent of the Taylor expansion to obtain a state space expression of the pressure diversion system model, and the method comprises the following steps:
in the state space expression of the pressure diversion system model:
h＝[h heh1h2… h2r-1]T∈R2；
Ch＝[1 0 … 0]∈R2。
5. the adaptive control method for the reversible unit according to claim 4, wherein the step of establishing the formula of the mathematical model of the pump turbine comprises the following steps:
s11b, according to the balance operating point P of the given reversible unit0∈(n＝n0；α＝α0；H＝H0) And performing Taylor series expansion on the torque characteristic and the flow characteristic, then intercepting the previous M-degree polynomial and obtaining a torque and flow characteristic expression in the following form:
wherein n is the rotating speed of the pump turbine, α is the opening degree of the guide vane, and H is the working water pressure;respectively are torque and flow deviation relative values; respectively are relative values of the rotating speed, the opening degree of the servomotor and the water pressure deviation; polynomial coefficientAre unknown parameters.
6. The adaptive control method for the reversible unit according to claim 5, wherein the step S2 comprises the following sub-steps:
s21, selecting a state variable X, X ═ X1x2x3]T＝[x y h]TWherein T is a transposition operation;
s22, based on the differential geometric theory of the smooth vector field, establishing a nonlinear mathematical model of the reversible unit according to the nonlinear mathematical models of an actuating mechanism, a power generation/motor, a pressure water passing system and a pump turbine in the reversible unit, wherein the formula of the nonlinear mathematical model of the reversible unit is as follows:
wherein,
s23, substituting the expression of the torque and flow rate characteristics into F1In the expression of (x, t), let e at the same timen＝θ0To obtain
Wherein, F2(x, t) and B are known functions, F, describing the behavior of the pump turbine1(x, t) is of known structure, but the parametersFunction of the unknown smooth vector field.
7. The adaptive control method for the reversible unit according to claim 6, wherein the step S3 comprises the following sub-steps:
s31, constructing one-dimensional output variable w ═ C (x-x)e) Wherein C is a three-dimensional matrix, and C ═ C1c2c3]；
S32, deriving w and bringing inIn-process obtaining reversible unit actual output dynamic equationWhere ρ (x, t) ═ CF2(x, t), b ═ CB is a known function and constant; f (x, t) ═ CF1(x, t) is a function with known structure and unknown parameters;
will be provided withSubstituted into f (x, t) ═ CF1(x, t) to obtain
And order the parameter vectorWherein:
then f (x, t) can be written as
f(x,t)＝η(x1,x2,x3) Theta; wherein:wherein:
the self-adaptive control of the reversible unit is changed into: when smooth vector fieldThe sum function ρ (x, t) ∈ R is known, the parameter vectorUnknown, and b ≠ 0, i.e., c2Not equal to 0, the output w (t) of the reversible unit regulating system is made to track the expected output trajectory wd(t)∈R；
S33, passing pair wd(t) ∈ R is derived to establish the desired output trajectory wd(t) ∈ R equation
Wherein k isd∈R+So that the expected track is exponentially attenuated, and the reversible unit regulating system has good dynamic performance; at this time wd(0)＝w(0)；
S34, defining tracking error e (t) wd(t) -w (t), deriving a tracking error function from the error:
8. the adaptive control method for the reversible unit according to claim 7, wherein the step S4 comprises the following sub-steps:
s41, converting the actual output dynamic equation of the reversible unit as follows
Then root will beThe error function is converted into the following formula:
the tracking problem of the reversible unit adjustment system is translated into designing the adaptive controller u1(t) ∈ R, so that the tracking error e (t) → 0, and the real system control amount u (t) can have the following expression:
obtaining control equations for adaptive controllers
Wherein k ise∈R+In order to feed back the gain, the gain is,representing an estimate of an unknown parameter theta; generating control input of a control quantity adjusting reversible unit through a control equation of an adaptive controller;
s42, setting a self-adaptive updating mechanism, wherein the formula of the self-adaptive updating mechanism is as follows:
wherein,for positive definite, diagonal update of gain matrix, it is advisablep∈R+I is an identity matrix; output and adaptation of reversible unitsThe new mechanism adjusts the control quantity of the self-adaptive controller, thereby carrying out self-adaptive control on the reversible unit transition process of the pumped storage power station.
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| CN103795088A (en) * | 2013-10-16 | 2014-05-14 | 华北电力大学（保定） | Load curve quantization-based pumped storage power station optimized dispatching method |
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| CN103699938A (en) * | 2013-10-10 | 2014-04-02 | 华北电力大学（保定） | Power generation planning method for power system with pumped storage power station |
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