CN104483837B - Adaptive control method for reversible machinery group - Google Patents

Abstract

The present invention provides an adaptive control method for a reversible unit, comprising: S1, establishing a nonlinear mathematical model of each link in the reversible unit; S2, establishing a nonlinear mathematical model of the reversible unit according to the nonlinear mathematical model of each link; S3. Construct a three-dimensional matrix, and generate the 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; construct the expected output trajectory equation of the reversible unit, and generate the dynamic equation based on the actual output of the reversible unit And the expected output trajectory equation of the reversible unit generates a tracking error equation; S4, convert the tracking error equation into the control equation of the adaptive controller, generate the control quantity to adjust the control input of the reversible unit through the control equation of the adaptive controller, and An adaptive update mechanism is set up, and the control quantity of the adaptive controller is adjusted according to the output of the reversible unit and the adaptive update mechanism.

Description

Adaptive control method for reversible unit

technical field

The invention relates to the technical field of reversible unit control of a pumped storage power station, in particular to an adaptive control method for a reversible unit.

Background technique

For a long time, PID control and its improved control strategy based on linear control theory have been widely used in reversible units of pumped storage power plants. Due to the strong nonlinearity and non-minimum phase characteristics of the reversible unit, and the frequent switching of working conditions, the above linear control strategy faces the problems of deterioration of control quality and system stability, which seriously affects the safety, stability and stability of the reversible unit operation. dynamic performance.

At present, there are researches on nonlinear feedback control of reversible units based on differential geometry method. Although theoretically speaking, nonlinear feedback control can solve the nonlinear control problem of the reversible unit, it is necessary to accurately grasp the dynamic characteristics of the reversible unit, or to be able to establish a mathematical model that accurately describes the dynamic characteristics of the reversible unit control system. However, this condition is too harsh. For complex systems such as reversible units, the established mathematical model is only an approximation of the dynamic characteristics of the system, whether it is based on theoretical research or through model tests. It can certainly describe reversible units. Regulating the main characteristics of the system within a certain working range, but there must be a certain degree of uncertainty, which leads to the fact that the nonlinear feedback control has no practical application value.

In order to improve the regulation quality of the hydraulic turbine regulation system and meet its static and dynamic performance requirements, the nonlinear control methods represented by fuzzy control, neural network control and optimal control have been expanded in the study of hydroelectric unit control theory. The above-mentioned nonlinear control methods have made certain breakthroughs at the theoretical level, but there are still some deficiencies. For example, fuzzy control has the shortcomings of no basis for membership function assignment and difficult induction of fuzzy rules, while neural network control has shortcomings such as slow learning speed, long decision-making time, and easy convergence to local minimum points. However, the study of optimal control is limited to affine nonlinear systems, which need to solve Lie derivatives and partial differential equations, and the control law has strict requirements on the model, resulting in a large difference between theory and application.

Therefore, the existing control methods for reversible units cannot satisfy the safety, stability and good dynamic performance of reversible units.

Contents of the invention

In view of this, the present invention aims at the strong nonlinearity of the reversible unit, and proposes a nonlinear modeling method of the M-order polynomial of the three parameters of the pump turbine, so that the nonlinear mathematical model of the control system of the reversible unit satisfies the parameter linearization condition, An adaptive control method for a reversible unit capable of satisfying the safety, stability and good dynamic performance of the reversible unit operation is provided.

A reversible unit adaptive control method, the reversible unit adaptive control method includes the following steps:

S1. Establish mathematical models of actuators, power generators/motors, pressurized water systems, and pump turbines in reversible units, in which the 3-parameter M-degree polynomial nonlinear modeling of pump turbines is the key;

S2. Establish the nonlinear mathematical model of the reversible unit according to the mathematical models of the actuator, power generation/motor, pressurized water system, and pump turbine in the reversible unit; the nonlinear mathematical model of the reversible unit is composed of two known and a function of a smooth vector field with known structure and unknown parameters;

S3. Construct a three-dimensional matrix, and generate the 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; construct the expected output trajectory equation of the reversible unit, and generate the dynamic equation based on the actual output of the reversible unit And the expected output trajectory equation of the reversible unit generates the tracking error equation;

S4. Convert the tracking error equation into the control equation of the adaptive controller, generate the control quantity through the control equation of the adaptive controller to adjust the control input of the reversible unit, and set an adaptive update mechanism, which is used to control The smooth vector field with unknown parameters is estimated, and the control quantity of the adaptive controller is adjusted according to the output of the reversible unit and the adaptive update mechanism, so as to perform adaptive control on the transition process of the reversible unit of the pumped storage power station.

The self-adaptive control method of the reversible unit provided by the present invention establishes the nonlinear model of the reversible unit, and the nonlinear mathematical model of the reversible unit consists of two known functions and a smooth The function composition of the vector field, the nonlinear model of the reversible unit established in this way satisfies the parameter linearization conditions, so that the control does not need to know the specific torque, flow characteristics and self-regulation coefficient of the external load of the reversible unit, which overcomes the In the prior art, the parameter assignment in the function has no basis. Then the problem of the actual output tracking the expected output trajectory of the reversible unit is transformed into a tracking error problem. Then, by setting an adaptive update mechanism, the control quantity of the adaptive controller is adjusted according to the output of the reversible unit and the adaptive update mechanism, so as to perform adaptive control on the transition process of the reversible unit of the pumped storage power station, so that the reversible unit The tracking error gradually converges to zero.

Description of drawings

Fig. 1 is a structural block diagram of a reversible unit regulating system provided by an embodiment of the present invention;

Fig. 2 is a flowchart of an adaptive control method for a reversible unit provided in an embodiment of the present invention.

detailed description

The principle of the present invention is as follows, as shown in Figure 1, the reversible unit adjustment system adaptive controller 5 and the reversible unit, the reversible unit includes an actuator 1, a power generation/motor 2, a pressurized water system 3, and a water pump turbine 4 . Figure 1 shows the signal transmission of each link of the reversible unit regulation system, in which the control quantity u output by the adaptive controller 5 is the control input u of the actuator; the actuator 1 outputs the opening degree y to the pump turbine 4 and the adaptive controller 5. The pump turbine 4 outputs the torque to the generator/motor 2, and at the same time, the pump turbine 4 outputs the flow rate q to the pressurized water system 3; the generator/motor 2 simultaneously outputs the speed n to the adaptive controller 5 and the pump turbine 4; The water passing system 3 outputs the water pressure h to the water pump turbine 4 and the adaptive controller 5 .

The control quantity u output by the adaptive controller 5 is the control input u of the actuator, and the reversible unit is adjusted and controlled according to the control quantity u; the reversible unit feeds back the water pressure h, opening y and Speed n; the adaptive controller 5 updates the control quantity u output by the adaptive controller 5 according to the adaptive update mechanism and the received feedback water pressure h, opening y and speed n, thus completing the adaptive control of the reversible unit .

As shown in Figure 2, an embodiment of the present invention provides an adaptive control method for a reversible unit, and the adaptive control method for a reversible unit includes the following steps:

S1. Establish a mathematical model of the actuator 1, the generator/motor 2, the pressurized water system 3, and the pump turbine 4 in the reversible unit. The equilibrium operating point P ₀ ∈ (n=n ₀ ; Y=Y ₀ ; H=H ₀ ) of the reversible unit, M _t0 , Q ₀ are the moment and flow of the equilibrium operating point respectively, and the variables are defined as follows, n is The speed of the pump turbine, Y is the opening of the guide vane, H is the working water pressure, M _t is the torque of the unit, M _g is the load torque, and Q is the flow rate of the unit

Δn=nn ₀ , ΔY=YY ₀ , ΔH=HH ₀ , ΔM _t =M _t -M _t0 , ΔQ=QQ ₀

M _r is the torque rating, Q _r is the flow rating, H _r is the rated working water pressure, and Y _max is the maximum guide vane opening.

T _y is the inertial time constant of the servomotor, u is the control input, T _a is the inertial time constant of the generator/motor 2, e _n is the load self-regulation coefficient of the generator/motor 2, L is the length of the water diversion pipe, d is the diameter of the water diversion pipe, A is the area of the diversion pipe, a is the water hammer wave velocity, f is the friction coefficient, t is the time coefficient, T _w is the water flow inertia time constant; T _r is the water hammer wave reflection time, α is the loss coefficient,

The formula of the nonlinear mathematical model of actuator 1 is as follows:

The mathematical model of execution structure 1 is a known model.

The formula of the mathematical model of generator/motor 2 is as follows:

The mathematical model of the generator/motor 2 is a known model.

The steps of establishing the formula of the mathematical model of the pressurized water diversion system 3 are as follows:

S11a, establish the continuity equation and motion equation of the pressurized water diversion system 3 as follows:

S12a. Introduce the Laplacian operator s, transform the continuity equation and motion equation of the pressurized water diversion system 3 from the nonlinear partial differential form in the time domain to the linear ordinary differential equations in the s domain, and obtain the expression in the form of transfer function The formula of the model 3 of the pressurized water diversion system is as follows:

The model of the pressurized water diversion system 3 is a known model.

S13a. By ignoring the loss coefficient in the reversible unit, the function in the model formula of the pressurized water diversion system Taking the first Γ term of its Taylor expansion, the state space expression of model 3 of the pressurized water diversion system is obtained, as follows:

In the state space expression of the pressurized water diversion system model:

h＝[hh _e h ₁ h ₂ ... h _2r-1 ] ^T ∈ R ^2Γ ;

C _h =[1 0 ... 0] ^{∈R 2Γ} .

The steps to establish the formula of the pump-turbine nonlinear mathematical model are as follows:

S11b. According to the given equilibrium operating point P ₀ ∈ (n=n ₀ ; α=α ₀ ; H=H ₀ ) of the given reversible unit, perform Taylor series expansion on the torque characteristics and flow characteristics, and then intercept the former M degree polynomial and get the torque and flow characteristic expressions in the following form:

where the polynomial coefficients are unknown parameters x ₁ =x, x ₂ =y, x ₃ =h. In this way, the torque and flow characteristics can meet the conditions of parameter linearization.

S2. Establish the nonlinear mathematical model of the reversible unit according to the nonlinear mathematical models of the actuator 1, the power generation/motor 2, the pressurized water system 3, and the pump turbine 4 in the reversible unit; the nonlinear mathematical model of the reversible unit The model consists of two known functions and a function of a smooth vector field with known structure and unknown parameters.

S21. Select the state variable X, x=[x ₁ x ₂ x ₃ ] ^T =[xyh] ^T , where T is a transpose operation. In the expression of the state variable X and the following expressions, x ₁ =x, x ₂ =y, x ₃ =h.

S22. Based on the differential geometry theory of the smooth vector field, the nonlinear mathematical model of the reversible unit is established according to the nonlinear mathematical models of the actuator 1, the generator/motor 2, the pressurized water system 3, and the pump turbine 4 in the reversible unit, The formula of the nonlinear mathematical model of the reversible unit is as follows:

in,

S23. Bring the torque and flow characteristic expressions into the expression of F ₁ (x,t), and set e _n = θ ₀ at the same time, to get

Among them, F ₂ (x, t) and B are known functions, and F ₁ (x, t) describing the characteristics of the pump turbine 4 belongs to the known structure, but the parameter Function of unknown smooth vector field.

S3. Construct a three-dimensional matrix, and generate the 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; construct the expected output trajectory equation of the reversible unit, and generate the dynamic equation based on the actual output of the reversible unit And the expected output trajectory equation of the reversible unit generates the tracking error equation.

The step S3 includes the following sub-steps:

S31. Construct a one-dimensional output variable w=C(xx _e ), wherein C is a three-dimensional matrix, and C=[c ₁ c ₂ c ₃ ].

S32. Deriving w, and bringing in Obtain the actual output dynamic equation of the reversible unit in Where ρ(x,t)=CF ₂ (x,t), b=CB is a known function and constant; f(x,t)=-CF ₁ (x,t) is a function with known structure and unknown parameters.

Will Substituting into f(x,t)=-CF ₁ (x,t), we get

and let the parameter vector in:

Then f(x,t) can be written as

f(x,t)=η(x ₁ ,x ₂ ,x ₃ )θ; where: in:

Change the adaptive control of the reversible unit into: when the smooth vector field The sum function ρ(x,t)∈R is known, and the parameter vector unknown, and b≠0, that is, c ₂ ≠0, the output w(t) of the reversible unit regulation system tracks the desired output trajectory w _d (t)∈R.

S33, by deriving w _d (t) ∈ R, establishing the equation of the desired output trajectory w _d (t) ∈ R

Among them, k _d ∈ R ⁺ , so that the expected trajectory decays exponentially, so that the reversible unit regulation system has good dynamic performance; at this time w _d (0) = w (0).

S34. Define the tracking error e(t)= _wd (t)-w(t), and derive the tracking error function according to the error:

S4. Convert the tracking error equation into the control equation of the adaptive controller, generate the control quantity through the control equation of the adaptive controller to adjust the control input of the reversible unit, and set an adaptive update mechanism, which is used to control The smooth vector field with unknown parameters is estimated, and the control quantity of the adaptive controller is adjusted according to the output of the reversible unit and the adaptive update mechanism, so as to perform 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. For the actual output dynamic equation of the reversible unit, the input transformation is as follows

Then it will be transformed into the following formula according to the error function:

Then the tracking problem of the reversible unit regulation system is transformed into designing an adaptive controller u ₁ (t)∈R, so that the tracking error e(t)→0, and the real control variable u(t) of the system can be expressed as follows:

Obtaining the Governing Equations for the Adaptive Controller

Among them, k _e ∈ R ⁺ is the feedback gain, Represents the estimation of the unknown parameter θ; the control input of the reversible unit is adjusted by the control quantity generated by the control equation of the adaptive controller.

S42, setting an adaptive update mechanism, the formula of the adaptive update mechanism is as follows:

in, is a positive definite, diagonal update gain matrix, which can be taken as p∈R ⁺ , I is the unit matrix; the output of the reversible unit and the adaptive update mechanism adjust the control quantity of the adaptive controller, so as to perform adaptive control on the transition process of the reversible unit of the pumped storage power station. The formula for the adaptive update mechanism is a known formula.

The reversible unit adaptive control method provided by the embodiment of the present invention establishes a nonlinear model of the reversible unit, and the nonlinear mathematical model of the reversible unit consists of two known functions and a known structure and unknown parameters. The function composition of the smooth vector field, the nonlinear model of the reversible unit established in this way satisfies the parameter linearization conditions, so that the control does not need to know the specific torque value, flow characteristics and self-regulation of the external load of the reversible unit The coefficient overcomes the defect that the parameter assignment in the function has no basis in the prior art. Then the problem of the actual output of the reversible unit according to the expected output trajectory is transformed into a tracking error problem. And by transforming the tracking error equation into the control equation of the adaptive controller, the tracking problem is transformed into the equation problem of adaptive controller design. Then, by setting an adaptive update mechanism, the control quantity of the adaptive controller is adjusted according to the output of the reversible unit and the adaptive update mechanism, so as to perform adaptive control on the transition process of the reversible unit of the pumped storage power station, so that the reversible unit The tracking error gradually converges to zero.

By selecting the Lyapunov candidate function (Lyapunov function (Lyapunov function) can be used to prove the stability of a dynamical system or autonomous differential equation.) Select the Lyapunov candidate function as

can prove

Therefore, the tracking error of the reversible unit regulation system asymptotically converges to zero. It can be shown that the self-adaptive control method for the reversible unit provided by the embodiment of the present invention can make the operation of the reversible unit safe, stable and have good dynamic performance.

In all the above formulas, the same letters indicate the same parameters and variables.

Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other.

Professionals can further realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software or a combination of the two. In order to clearly illustrate the possible For interchangeability, in the above description, the composition and steps of each example have been generally described in terms of functionality. Whether these functions are executed by hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art may use different methods to implement the described functions for each specific application, but such implementation should not exceed the scope of the present invention.

The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be directly implemented by hardware, software modules executed by a processor, or a combination of both. Software modules can be placed in random access memory, internal memory, read-only memory, electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form known in the technical field in the storage medium.

It can be understood that those skilled in the art can make various other corresponding changes and modifications according to the technical concept of the present invention, and all these changes and modifications should belong to the protection scope of the claims of the present invention.

Claims (8)

1. a reversible unit adaptive control method, is characterized in that, described reversible unit adaptive control method comprises the steps: S1. Establish mathematical models of actuators, generators/motors, pressurized water systems, and pump turbines in reversible units; S2. Establish the nonlinear mathematical model of the reversible unit according to the mathematical models of the actuator, power generation/motor, pressurized water system, and pump turbine in the reversible unit; the nonlinear mathematical model of the reversible unit is composed of two known and a function of a smooth vector field with known structure and unknown parameters; S3. Construct a three-dimensional matrix, and generate the 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; construct the expected output trajectory equation of the reversible unit, and generate the dynamic equation based on the actual output of the reversible unit And the expected output trajectory equation of the reversible unit generates the tracking error equation; S4. Convert the tracking error equation into the control equation of the adaptive controller, generate the control quantity through the control equation of the adaptive controller to adjust the control input of the reversible unit, and set an adaptive update mechanism, which is used to control The smooth vector field with unknown parameters is estimated, and the control quantity of the adaptive controller is adjusted according to the output of the reversible unit and the adaptive update mechanism, so as to perform adaptive control on the transition process of the reversible unit of the pumped storage power station. 2. reversible unit adaptive control method as claimed in claim 1, the formula of the mathematical model of executive agency is as follows: Among them, T _y is the inertial time constant of the servomotor; u is the control input, and y is the relative value of the servomotor opening deviation. 3. the reversible unit adaptive control method as claimed in claim 2, is characterized in that, the formula of the mathematical model of generating/motor is as follows: Where x is the relative value of the speed deviation of the pump turbine, h is the relative value of the water pressure deviation of the pump turbine, T _a is the inertia time constant of the generator/motor, e _n is the load self-regulation coefficient of the generator/motor, M _g is the load moment of the pump-turbine, M _r is the torque rating, n ₀ , α ₀ , H ₀ are the speed of the pump-turbine at the equilibrium point, the opening of the guide vane and the working water pressure, respectively. 4. reversible unit self-adaptive control method as claimed in claim 3, is characterized in that, the step of setting up the formula of the mathematical model of pressurized water diversion system is as follows: S11a. Establish the continuity equation and motion equation of the pressurized water diversion system as follows: Among them, Q is the flow rate of the pump turbine, H is the working water pressure of the unit, L is the length of the water diversion pipe, d is the diameter of the water diversion pipe, A is the area of the water diversion pipe, a is the water shock wave velocity, f is the friction coefficient, and t is the time coefficient ; S12a. Introduce the Laplacian operator s, transform the continuity equation and motion equation of the pressurized water diversion system from the nonlinear partial differential form in the time domain to the linear ordinary differential equations in the s domain, and obtain the equations expressed in the form of transfer function The formula of the pressure diversion system model is as follows: Among them, T _w is the time constant of water flow inertia; T _r is the reflection time of water hammer wave; α is the loss coefficient; S13a. Definition By ignoring the loss coefficient in the reversible unit, the function in the model formula of the pressurized water diversion system Taking the first Γ term of its Taylor expansion, the state space expression of the pressurized water diversion system model is obtained, as follows: In the state space expression of the pressurized water diversion system model: h＝[hh _e h ₁ h ₂ ... h _2r-1 ] ^T ∈ R ^2Γ ; ${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccccccc}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; ...</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{{<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]<span\; class="notranslate">\; ;</span>$ C _h =[1 0 ... 0] ^{∈R 2Γ} . 5. reversible unit adaptive control method as claimed in claim 4, is characterized in that, the step of setting up the formula of water pump turbine mathematical model is as follows: S11b. According to the given equilibrium operating point P ₀ ∈ (n=n ₀ ; α=α ₀ ; H=H ₀ ) of the given reversible unit, perform Taylor series expansion on the torque characteristics and flow characteristics, and then intercept the former M degree polynomial and get the torque and flow characteristic expressions in the following form: Where n is the speed of the pump turbine, α is the opening of the guide vane, and H is the working water pressure; are the relative values of torque and flow deviation, respectively; Respectively, the relative values of rotational speed, servomotor opening and water pressure deviation; polynomial coefficient is an unknown parameter. 6. The reversible unit adaptive control method according to claim 5, wherein said step S2 comprises the following sub-steps: S21. Select the state variable X, x=[x ₁ x ₂ x ₃ ] ^T =[xyh] ^T , wherein T is a transpose operation; S22. Based on the differential geometry theory of the smooth vector field, the nonlinear mathematical model of the reversible unit is established according to the nonlinear mathematical models of the actuator, generator/motor, pressurized water system, and pump-turbine in the reversible unit. The formula of the nonlinear mathematical model is as follows: $\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; B</span>}\mathrm{<span\; class="notranslate">\; u</span>}$ in, S23. Bring the torque and flow characteristic expressions into the expression of F ₁ (x,t), and set e _n = θ ₀ at the same time, to get Among them, F ₂ (x,t) and B are known functions, and F ₁ (x,t) describing the characteristics of the pump turbine belongs to the known structure, but the parameters Function of unknown smooth vector field. 7. The reversible unit adaptive control method according to claim 6, wherein said step S3 comprises the following sub-steps: S31. Construct a one-dimensional output variable w=C(xx _e ), where C is a three-dimensional matrix, C=[c ₁ c ₂ c ₃ ]; S32. Deriving w, and bringing in Obtain the actual output dynamic equation of the reversible unit in Wherein ρ(x,t)=CF ₂ (x,t), b=CB is a known function and a constant; f(x,t)=-CF ₁ (x,t) is a function with known structure and unknown parameters; Will Substituting into f(x,t)=-CF ₁ (x,t), we get and let the parameter vector in: ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>$ Then f(x,t) can be written as f(x,t)=η(x ₁ ,x ₂ ,x ₃ )θ; where: in: ${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}$ Change the adaptive control of the reversible unit into: when the smooth vector field The sum function ρ(x,t)∈R is known, and the parameter vector unknown, and b≠0, that is, c ₂ ≠0, the output w(t) of the reversible unit regulation system can track the desired output trajectory w _d (t)∈R; S33, by deriving w _d (t) ∈ R, establishing the equation of the desired output trajectory w _d (t) ∈ R Among them, k _d ∈ R ⁺ , so that the expected trajectory decays exponentially, so that the reversible unit regulation system has good dynamic performance; at this time w _d (0) = w (0); S34. Define the tracking error e(t)= _wd (t)-w(t), and derive the tracking error function according to the error: $\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$ 8. The reversible unit adaptive control method according to claim 7, wherein said step S4 comprises the following sub-steps: S41. For the actual output dynamic equation of the reversible unit, the input transformation is as follows ${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>$ Then it will be transformed into the following formula according to the error function: Then the tracking problem of the reversible unit regulation system is transformed into designing an adaptive controller u ₁ (t)∈R, so that the tracking error e(t)→0, and the real control variable u(t) of the system can be expressed as follows: $\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$ Obtaining the Governing Equations for the Adaptive Controller ${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ Among them, k _e ∈ R ⁺ is the feedback gain, Represents the estimation of the unknown parameter θ; through the control equation of the adaptive controller, the control quantity is generated to adjust the control input of the reversible unit; S42, setting an adaptive update mechanism, the formula of the adaptive update mechanism is as follows: in, is a positive definite, diagonal update gain matrix, which can be taken as p∈R ⁺ , I is the unit matrix; the output of the reversible unit and the adaptive update mechanism adjust the control quantity of the adaptive controller, so as to perform adaptive control on the transition process of the reversible unit of the pumped storage power station.