Fractional order adjusting method for water turbine system

Abstract

The invention provides a water turbine system fractional order adjustment method, which aims at a PI lambda controller of a water turbine system fractional order model, calculates stability domains of adjustment parameters kp and ki under different orders lambda based on real root and complex root boundaries, analyzes the rules of the stability domains, and uses the rules as boundaries to adjust the fractional order model of the water turbine system. And solving specific kp and ki parameters by using a frequency domain analysis method under the condition of adjusting the preset shear frequency omega c and the phase margin phi m, so that the fractional order controller PI lambda can achieve expected tracking performance and robustness. A simulation test shows that the control effect of the method is good, and compared with a swarm intelligence method based on an ITAE index, the analysis characteristic of the method enables the method to be easily realized through configuration, so that engineering application can be realized on a PLC or a DCS.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic turbine systems, and in particular to a fractional-order regulation method for hydraulic turbine systems. Background Art

[0002] In the wave of new technologies driving the construction of new power systems, the excellent peak-shaving and frequency-regulating performance of hydropower generation systems plays an effective role. Turbine regulation systems not only play the crucial role of regulating the output power of hydropower stations but also play a key role in the primary and secondary frequency regulation of the power grid. During the transient operation of hydropower units, operating parameters change significantly and rapidly. Conventional PID control laws are unable to adapt to these complex fluctuations, often hindering the full utilization of the hydropower unit's excellent characteristics.

[0003] The turbine system is a highly nonlinear non-minimum phase system composed of multiple nonlinear elements. Its natural elasticity and distribution characteristics have promoted the development of fractional-order modeling. From the perspective of amplitude-phase characteristics, the mathematical model of the turbine system usually has richer slope changes at the zero poles, rather than just integer multiples of ±20dB / dec. -λ For example (s is the Laplace operator, λ is the fractional order), its amplitude-frequency characteristic is 20lg|(jω) -λ |, a straight line with a slope of -20λdB / dec is shown in the Bode plot; its phase-frequency characteristic is ∠|(jω) -λ | = -πλ / 2, with the Bode plot showing a straight line with a constant value of -πλ / 2. Adjusting λ directly changes the amplitude-frequency and phase-frequency characteristics, demonstrating powerful dynamic performance.

[0004] The most commonly used method for existing turbine regulation is the integer-order regulation method based on integer-order models. Since the PID controller is a first-order integer, this method has poor adaptability to fractional-order objects with a wide range of orders. To better control fractional-order objects, fractional-order controllers have been introduced for fractional-order object models in the hope of achieving better control results. For example, in their research on fractional-order controller design, Zhang Dehu's team, using modern algorithms such as particle swarm and fuzzy algorithms, demonstrated strong adaptability to changing operating conditions, resulting in improved robustness of turbine systems under complex operating conditions.

[0005] However, existing regulation methods are mostly limited to integer-order turbine systems, employing integer-order or fractional-order regulation based on integer-order models. Furthermore, these methods lack analytical methods for parameter acquisition, hindering precise regulation. Therefore, developing an analytical method for determining the stability domain of regulation parameters and setting parameters for fractional-order systems, which can better adapt to the regulation needs of hydropower units in new power systems, is an urgent challenge. Summary of the Invention

[0006] In response to the above-mentioned problems, the present invention proposes a fractional-order regulation method for a turbine system, obtains parameter settings of a fractional-order controller, and uses the obtained parameters to enable the fractional-order controller to achieve better tracking and robustness.

[0007] The technical solutions adopted in the present invention are as follows:

[0008] A fractional-order regulation method for a hydraulic turbine system, characterized by comprising the following steps:

[0009] Step 1: Construct a fractional-order model of the turbine system, take the fractional-order model as the controlled object, and design its fractional-order controller;

[0010] Step 2: Draw the stability region of the fractional-order controller;

[0011] Step 3: Obtain the shear frequency and phase margin through frequency domain analysis method, and select the control parameter k in the stable domain according to the shear frequency and phase margin. p 、k i The dynamic performance of the fractional-order controller is tested by time domain analysis method;

[0012] Step 4: Based on the selected set of k i 、k p Parameters are used to adjust the turbine system.

[0013] Furthermore, the specific steps of step 1 include:

[0014] Step 11: Construct the fractional-order transfer function of the turbine system considering flow and capacity:

[0015]

[0016] Among them, G p (s) is the fractional-order transfer function of the turbine system considering flow and capacity; D(s) and N(s) are the input and output of the controlled object respectively; i D with i N is the highest fractional order of the output term of the transfer function,

[0017] Step 12: The designed fractional-order controller is:

[0018] G c (s) = k p +k i / s λ ,0<λ<2

[0019] Then the characteristic polynomial of the closed-loop system is:

[0020] Ψ(s)=sλ D(s)+(k p s λ +k i )N(s)=0

[0021] Among them, G c (s) is fractional-order PI λ Controller, k p 、k i is a set of control parameters, D(s) and N(s) are the input and output of the controlled object respectively.

[0022] Furthermore, the specific steps of step 2 include:

[0023] Step 21: Calculate the control parameter k by the following formula p 、k i :

[0024]

[0025] in,

[0026]

[0027] Where, α i , β i d i 、n i ,ω,λ,i D 、i N They represent the fractional order of flow, fractional order of flow capacity, input term coefficient, output term coefficient, frequency, fractional order of PI regulator, highest order of input term fractional order, and highest order of output term fractional order of the fractional order transfer function of the turbine system respectively;

[0028] Step 22: Based on the known parameter λ and the calculated k p 、k i Make the roots of the characteristic polynomial all on the left side of the complex plane, and draw the stable region of the fractional-order controller based on the complex root boundary at this time.

[0029] Furthermore, the specific steps of step 3 include:

[0030] Step 31: Use the frequency domain estimation method to obtain the control parameter k i 、k p The calculation formula of

[0031] Step 32: At a given shear frequency ω c Next, in the preset After the λ parameter, k is calculated according to the calculation formula in step 31. i 、k p ;

[0032] Step 33: According to k p 、k i Draw the phase margin contour of the controlled object and use the stability region boundary as the constraint condition;

[0033] Step 34: Select a set of k points on the phase margin contour line whose order is less than 1. i 、k p parameter.

[0034] Furthermore, the specific steps of step 31 include:

[0035] Step 311: Use the fractional order controller G c Written in frequency domain form:

[0036]

[0037] And the controller G c The amplitude and phase are:

[0038]

[0039] Step 312: Obtain the controlled object G through frequency domain analysis method p The shear frequency ω c and phase margin

[0040] Step 313: The controlled object G p The amplitude and phase of |G p (jω)| and ∠G p (jω), and let G c Meeting the phase margin G p Substituting the amplitude and phase into the above formula, we have:

[0041]

[0042] and,

[0043]

[0044] Step 314: Recorded as Rewrite the above formula as (k p k i ) form, then:

[0045]

[0046] Step 315: Substitute the above equation into equation (14) and set Ω = ω -λ 、Θ=|G p (jω)| -1 We can get ki The calculation formula is:

[0047]

[0048] Step 316: Substitute equation (17) back into equation (16) to obtain the control parameter k p The calculation formula of .

[0049] Furthermore, the specific steps of step 32 include:

[0050] Step 321: For a known controlled object, according to the known amplitude |G of the controlled object p (jω)| and phase ∠G p (jω), find the parameter with Θ;

[0051] Step 322: Preset parameters After λ, the control parameter k is calculated in sequence according to steps 315 and 316. i 、k p .

[0052] The beneficial effects of the present invention are:

[0053] First, the present invention introduces a fractional-order analysis method for a fractional-order controller supporting a fractional-order model object, which can perform analytical calculations on the stable domain of regulation, thereby reasonably selecting regulation parameters according to regulation requirements and obtaining the expected regulation effect.

[0054] Secondly, the present invention solves the common under- and over-regulation problems of conventional PID control laws in the peak regulation and frequency regulation of hydropower units through a fractional-order regulation method based on a fractional-order model. The given fractional-order PI control law is consistent with the fractional-order characteristics of the object, making the regulation process rapid, stable and accurate, thereby ensuring the peak regulation and frequency regulation of the hydropower units. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Schematic diagram of the closed loop of fractional-order controlled object and controller.

[0056] Figure 2 To fix α, β and T w Stability domain of different orders λ under the same conditions.

[0057] Figure 3 For fixed λ and T w Stability domains of different α and β orders under different conditions.

[0058] Figure 4 For different T under fixed α, β and λ orders w stability domain.

[0059] Figure 5Phase margin contours under different fractional order λ conditions

[0060] Figure 6 These are the contour lines of different phase margins under the same fractional order condition (λ=0.9).

[0061] Figure 7 is the specified shear frequency ω c =30 and phase margin The following equation (6) is the ramp response of the object at different fractional orders λ.

[0062] Figure 8 (a)-(b) are the specified shear frequencies ω c =40 and 50 and the phase margin Ramp response of different fractional orders λ.

[0063] Figure 9 Comparison between frequency domain method and swarm intelligence method.

[0064] Figure 10 Analysis of the stability domain and adjustment parameters of the fractional-order model for engineering examples.

[0065] Figure 11a-Figure 11b These are integer-order and fractional-order PI regulation examples respectively. DETAILED DESCRIPTION

[0066] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0067] 1. Fractional-order model of turbine system

[0068] The distributed flow in a pressurized pipeline is the main component of the elastic characteristics of the turbine system. The opening and closing of valves or guide vanes induces transient flow in the pipeline. Considering the compressibility of the fluid and the elasticity of the pipeline, and ignoring the influence of the pipe axis inclination and the flow resistance in the pipeline, the motion equation of the fluid in the pipeline is obtained according to Newton's law. This motion equation can be expressed in fractional order form:

[0069]

[0070] Where L0 represents the velocity per unit length of the pipe, L0 = Q0 / (gAH0), and g represents the acceleration due to gravity (m / s 2 ), A represents the cross-sectional area of ​​the pipe (m 2 ), Q and H are flow rate (m 3 / s) and pressure head (m), where the subscript 0 indicates the rated operating condition; q and h are their nominal values, respectively, and q = Q / Q0 and h = H / H0; x represents the axial coordinate; t represents time (s); and α represents the fractional order.

[0071] Similarly, the fractional order form of the continuity equation for fluid flow in a pipe is:

[0072]

[0073] Where C0 is the flow capacity per unit length of the pipe, C0=(gAH0) / (a 2 Q0), a is the water hammer wave velocity, approximately 1000m / s; β is the fractional order;

[0074] Perform Laplace transform on Equation (2) and differentiate Equation (1) with respect to x. According to the second-order homogeneous differential equation of H(x,s), the transfer function at the turbine inlet is obtained as follows:

[0075]

[0076] Among them, T e is the traveling wave time, T e =l / a, l is the length of the pressure water pipe, then T e is a fixed value; T w =(lQ) / (gAH) is the inertia time of water flow.

[0077] The ideal turbine transfer function operating at rated head and speed is:

[0078]

[0079] Substituting Equation (3) into Equation (4) yields the fractional-order mathematical model of the turbine system (including turbine and pressurized water pipe):

[0080]

[0081] By performing Maclaurin expansion on Equation (5), we can obtain the fractional-order transfer function of the turbine system considering flow velocity and flow capacity:

[0082]

[0083] Among them, D(s) and N(s) are the input and output of the controlled object respectively; i D with i N are the highest fractional orders of the input and output terms of the fractional transfer function of the turbine system,

[0084] 2. Parameter stability region of fractional-order PI controller

[0085] Although the introduction of the fractional-order method brings great flexibility to both the modeling method and the controller design, at the same time, the stability problem becomes prominent when selecting the controller parameters. In addition, the existence of flow capacity and flow rate is equivalent to the energy storage element in the hydraulic system. The control system transfer function contains complex poles. Before designing the adjustment method, the stability of the control system transfer function must be studied.

[0086] Considering the amplification effect of controller differentials on high-frequency disturbances, this step has been eliminated from most hydropower units' grid-connected regulation processes. Cheng Yuanchu confirmed through simulation that differential action significantly slows the decay of the rotor's rocking curve, resulting in small oscillations at the tail end of the transition process. Deng Wei, while optimizing speed regulator parameters, also found that reducing or even eliminating differential action significantly improves the damping of hydropower units and suppresses power system oscillations. Therefore, the present invention adopts a PI controller.

[0087] Typical fractional-order closed-loop control systems are Figure 1 As shown, where G p (s) is the transfer function of the controlled object (integer order or fractional order), G c (s) is fractional-order PI λ controller, r(t) is the input constant, e(t) is the deviation signal, u(t) and y(t) are the controller and system outputs respectively.

[0088] Fractional PI λ The controller is:

[0089] G c (s) = k p +k i / s λ ,0<λ<2 (7)

[0090] The characteristic polynomial of its closed-loop system is:

[0091] Ψ(s)=s λ D(s)+(k p s λ +k i )N(s)=0 (8)

[0092] (1) Stable domain calculation

[0093] If any set of parameters (k p ,k i ,λ) makes the roots of Equation (8) all on the left side of the complex plane, then the closed-loop system is BIBO stable. According to the D decomposition method, since i N >i D , infinite root boundary does not exist, then the parameter space Ψ can be divided into real root boundary and complex root boundary. According to the definition of real root, let s = 0, and calculate k i =0, then find the complex root boundary and get PIλ The stability region of the controller.

[0094] Let s = jω to construct the complex root boundary, we have:

[0095]

[0096] Apply Euler's formula:

[0097] (jω) α =ω α (cos(απ / 2)+jsin(απ / 2)) (9)

[0098] Substituting equation (9) into the above equation and setting its real and imaginary parts to 0, we can obtain:

[0099]

[0100] in,

[0101]

[0102] Observe formula (10), if the model structure and controller structure are given, then α, β and λ are all known, k p 、k i The formula is a function of ω. Besides trigonometric functions and arithmetic operations, it contains no complex calculations, making engineering configuration easy. However, full-frequency domain calculations are time-consuming, so a loop must be designed during configuration, or the stability envelope must be derived offline and then numerically regressed for use.

[0103] The above analytical method can quickly obtain the stable domain of the adjustment process, so that parameters can be safely selected within the stable domain according to the adjustment requirements (fast adjustment or stable adjustment).

[0104] (2) Changes in the stability domain

[0105] Considering the feasibility of online identification, formula (6) is selected as the fractional-order controlled object. If the α and β parameters are known, then PI λ The controller stability region mainly depends on the fractional order λ and the identification parameters n and d.

[0106] Select T e =1.0, T w =1.2, let α = 0.8, β = 0.8, select 6 orders equally spaced between λ = 0.2 and 1.2, calculate and draw the stable domain by formula (10), as shown in Figure 2 shown. Figure 2 Different values ​​of λ correspond to a k p (horizontal axis) and k i (vertical axis) envelope, any point on the line constitutes a (k p,k i ,λ) parameter group. As can be seen from the figure, as the fractional order λ decreases, PI λ The stability domain increases accordingly. The wider stability domain of the fractional order controller allows for greater room for parameter selection. The stability domain changes in k i The range is wider in the direction, and in k p Basically unchanged.

[0107] Take λ = 0.8, repeat the above test under different fractional orders α and β of the controlled object (let α = β for simplicity), calculate and draw the stability region, and get Figure 3 .from Figure 3 It can be seen from Figure 1 that when the fractional order of the controlled object decreases, the stability region increases accordingly.

[0108] The mechanical and electromagnetic characteristics of the turbine system generally do not change significantly during the maintenance interval. The dynamic characteristics are mainly related to the current operating conditions, that is, the head on the dam and the load. Its representative parameter is the hydraulic inertia T w , so the parameter T w Between 0.80 and 1.20, select 3 data with equal intervals, and still take λ=0.8 as an example to calculate the stable region, as shown in the following example: Figure 4 As shown. It can be seen that when the water head is small or the load is high (corresponding T w The larger the T, the smaller the stable domain. w As the value of θ decreases, the stable domain gradually becomes larger, and the amplitude of its expansion also increases gradually.

[0109] After clarifying the basic characteristics of the stable domain, we search for PI λ When the controller adjusts parameters, it already knows the boundaries of the selection process to ensure stable control. Choosing a smaller order λ results in a wider stability region, but the dynamic characteristics must meet engineering requirements, which translates into a question of selecting the adjustment parameters.

[0110] 3. Selection of fractional-order adjustment parameters

[0111] The main indicators of controller parameter design are tracking and robustness, so as to achieve the requirements of fast and stable regulation process and have strong adaptability to changes in working conditions. Similar to the tuning process of integer-order PI controller, the selection of fractional-order regulation parameters can also be based on the shear frequency ω c and phase margin Two aspects of the design, where the shear frequency ω c Approximately represents the rapidity of the regulation process, phase margin The present invention obtains the shear frequency and phase margin by frequency domain analysis method, and verifies the fractional order PI by time domain analysis method. λ Dynamic performance of the controller.

[0112] (1) Frequency domain estimation

[0113] According to formula (9), let PI λ Form Controller G c The frequency domain form of is written as:

[0114]

[0115] Controller G c The amplitude and phase are:

[0116]

[0117] The controlled object G p The amplitude and phase of |G p (jω)| and ∠G p (jω), let G c Meeting the phase margin Substituting it into equations (12)-(13) we have:

[0118]

[0119] And there are:

[0120]

[0121]

[0122] Brief Notes: for Rewrite Equation (15) as (k p / k i ) form, then:

[0123]

[0124] Substitute equation (16) into equation (14) and let Ω = ω -λ 、Θ=|G p (jω)| -1 We can get:

[0125]

[0126] Substituting formula (17) back into formula (16) yields k p , the formula is no longer listed.

[0127] (2) Phase margin contours

[0128] For a known controlled object, at a given shear frequency ω c Next, amplitude |G p (jω)| and phase ∠G p(jω) are known, then and Θ can be obtained, according to formula (16)-formula (17) in the preset After the λ parameter, k is calculated in sequence i 、k p .

[0129] Taking the fractional-order model shown in equation (6) as an example, the preset phase margin is In the common shear frequency range of engineering (from 0.2 to 1.2), calculate multiple groups of k i 、k p Parameters, draw the phase margin contours under different λ parameters, such as Figure 5 and combined with Figure 4 From the coordinate scale, we can see that the phase margin contours under the same order λ are included in the stable region. If the contours jump out of the stable region, the boundary of the stable region is used as a hard constraint.

[0130] A set of k corresponding to any point on the contour line i 、k p The parameters can make the fractional order controller PI λ The phase margin of the fractional-order controlled object is locked to a given Above. Figure 6 As shown, when When it increases, the contour line is close to k i 、k p The area enclosed by the coordinate axes becomes smaller.

[0131] On the phase margin contour, select φ from left to right m Parameters, the corresponding shear frequency gradually increases, by choosing φ m The corresponding control parameter k is obtained by i 、k p , thereby adjusting the control system to achieve satisfactory target tracking performance.

[0132] Select the shear frequency ω c =30, phase margin At λ=1 and above and below it, 5 orders are selected with an order difference of 0.05, and ramp excitation is implemented ( Figure 7 In SP), record as Figure 7 The response process is shown in the figure, where the right figure is the overall response, and the lower left and upper left figures are details such as the initial back-scaling and terminal overshoot. It is obvious from the figure that for fractional-order controlled objects, fractional-order PI λThe controller exhibits a variety of dynamic characteristics. Controllers with higher orders have faster response times and larger overshoots, while those with lower orders are just the opposite. The fractional-order integrator has different degrees of convolution of historical information, which results in different dynamic performances in the dynamic process and provides more options for simple PI controllers. In this case, since the shear frequencies are the same, the various ramp responses have similar dynamic tracking speeds. The main difference lies in the overshoot, with the 0.95-order controller having the best control effect. When the experiment is repeated with different shear frequencies (keeping the phase margin the same), the conclusions are similar, and the ramp responses are shown in Figure 2. Figure 8 , with the increase of shear frequency, the system tracking speed is accelerated, and the overshoot is also significantly increased. λ The controller shows a clear mitigating effect.

[0133] Therefore, when determining the adjustment parameters in engineering, if a larger shear frequency and a smaller phase margin are selected, the order λ<1 is better, which helps to alleviate overshoot; otherwise, set λ>1 to accelerate the adjustment.

[0134] (3) Comparison with swarm intelligence methods

[0135] In addition to the binary indicators of shear frequency and phase margin, ITAE, ISE, etc. can also be selected as comprehensive indicators of the control system response performance to obtain the optimal solution. In this case, swarm intelligence optimization methods such as particle swarm and genetic algorithm can be used for comparison. The parameters of each controller are shown in Table 1. Still taking the aforementioned fractional order model as an example (Equation (6)), the optimization is performed under the indicators such as ITAE and ISE. The PI established by the present invention is λ The controllers all have good performance; in comparison, the method based on frequency domain analysis can clearly specify the robustness index of the regulation process, which is unattainable by the integral performance type method (swarm intelligence optimization method) that uses ISE and ITAE indicators as optimization indicators. In addition, the frequency domain analysis method can be configured and implemented in PLC or DCS, which is easy to implement in engineering. The swarm intelligence method has high requirements for computing power and can generally only be performed offline. When the operating conditions change drastically (especially the characteristics of hydropower units vary greatly throughout the year), it will lead to inaccuracy. For the convenience of comparison, Figure 7 and Figure 8 The correlation curve and ITAE are plotted simultaneously in Figure 9 .

[0136] Table 1 Figure 9 Four types of PI λ Controller parameter list

[0137]

[0138] Example

[0139] In order to verify the effect of the present invention, an engineering example is used to illustrate it.

[0140] The second unit of a small- to medium-sized hydropower station has a rated capacity of 125 MW and is a Francis generator. Its design flow is 119.44 m³ / s, its rated head is 117 m, and its pipeline is 476 m long with a diameter of 4.6 m. In early summer, the head was insufficient. The industrial control system's online identification of a fractional-order model for the active power regulation process yielded the following results:

[0141]

[0142] Selecting λ = 0.9 can obtain better rapidity and smaller overshoot, and does not affect the robustness of the controlled object gain change. According to formula (10), the stability region analysis is carried out and the phase margin φ is selected. m The adjustment parameters are calculated using equations (16) and (17) for 30° and 60° and plotted on Figure 10 (solid and dashed lines), and plot λ = 1.0 and φ m =30° as a reference. It can be seen that Figure 10 The adjustment parameters are all within the corresponding λ stable domain, so any point in the adjustment parameter curve (corresponding to a shear frequency ω c ) corresponding to k p and k i Both can be used as regulator parameters. Note the shear frequency ω on the curve. c The value increases as you go to the right.

[0143] Select ω on the λ=0.9 curve c =0.314, corresponding to k p =1.2562, k i =0.1002 (hollow dots in the figure), and select ω on λ=1.0 c =0.314, corresponding to k p =1.2922, k i =0.0902 (hollow triangle in the figure), the two points are close, which is convenient for comparison. Plot the integer order and fractional order control processes respectively on Figure 11a (λ = 1.0) and Figure 11b (λ = 0.9), the regulation time for both operating conditions is 300s. Under different changes in the network active power command UMD, the performance of the active power output UL varies significantly (UFD in the figure is the reference curve of the 75% active power change rate. When UL falls to the left of UFD, it indicates an excellent regulation process).

[0144] Depend on Figure 11a-Figure 11bIt can be seen that the regulation effects of the two controllers are both excellent, and the fractional-order process is slightly better. However, the overshoot is obvious at the end of the integer-order regulation, while the overshoot is successfully suppressed under the action of the fractional order. It can also be seen from the measured trend of the guide vane opening GV that under the action of the fractional-order integral, there is little overshoot when approaching the target value, and there is almost no callback. This proves that the regulation method of the present invention can fit the fractional-order characteristics of the turbine system object and complete effective regulation with the fractional-order control law.

[0145] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A fractional-order regulation method for a hydraulic turbine system, characterized in that: The following steps are involved: Step 1: Construct a fractional-order model of the turbine system, take the fractional-order model as the controlled object, and design its fractional-order controller; Step 2: Draw the stability region of the fractional-order controller; Step 3: Obtain the shear frequency and phase margin through frequency domain analysis method, and select the control parameter k in the stable domain according to the shear frequency and phase margin. p 、k i The dynamic performance of the fractional-order controller is tested by time domain analysis method; Step 4: Based on the selected set of k i 、k p Parameters are used to adjust the turbine system.

2. The fractional-order regulation method for a hydraulic turbine system according to claim 1, wherein: The specific steps of step 1 include: Step 11: Construct the fractional-order transfer function of the turbine system considering flow and capacity: Among them, G p (s) is the fractional-order transfer function of the turbine system considering flow and capacity; D(s) and N(s) are the input and output of the controlled object respectively; i D with i N is the highest fractional order of the output term of the transfer function, α iN >...>α1>α0≥0, β iD >...>β1>β0≥0; Step 12: The designed fractional-order controller is: G c (s)=k p +k i / s λ ,0<λ<2 Then the characteristic polynomial of the closed-loop system is: Ψ(s)=s λ D(s)+(k p s λ +k i )N(s)=0 Among them, G c (s) is fractional-order PI λ Controller, k p 、k i is a set of control parameters, D(s) and N(s) are the input and output of the controlled object respectively.

3. The fractional-order regulation method for a hydraulic turbine system according to claim 1, wherein: The specific steps of step 2 include: Step 21: Calculate the control parameter k by the following formula p 、k i : in, Where, α i , β i d i 、n i ,ω,λ,i D 、i N They represent the fractional order of flow, fractional order of flow capacity, input term coefficient, output term coefficient, frequency, fractional order of PI regulator, highest order of input term fractional order, and highest order of output term fractional order of the fractional order transfer function of the turbine system respectively; Step 22: Based on the known parameter λ and the calculated k p 、k i Make the roots of the characteristic polynomial all on the left side of the complex plane, and draw the stable region of the fractional-order controller based on the complex root boundary at this time.

4. The fractional-order regulation method for a hydraulic turbine system according to claim 3, wherein: The specific steps of step 3 include: Step 31: Use the frequency domain estimation method to obtain the control parameter k i 、k p The calculation formula of Step 32: At a given shear frequency ω c Next, in the preset After the λ parameter, k is calculated according to the calculation formula in step 31. i 、k p ; Step 33: According to k p 、k i Draw the phase margin contour of the controlled object and use the stability region boundary as the constraint condition; Step 34: Select a set of k points on the phase margin contour line whose order is less than 1. i 、k p parameter.

5. The fractional-order regulation method for a hydraulic turbine system according to claim 4, characterized in that: The specific steps of step 31 include: Step 311: Use the fractional order controller G c Written in frequency domain form: And the controller G c The amplitude and phase are: Step 312: Obtain the controlled object G through frequency domain analysis method p The shear frequency ω c and phase margin Step 313: The controlled object G p The amplitude and phase of |G p (jω)| and ∠G p (jω), and let G c Meeting the phase margin G p Substituting the amplitude and phase into the above formula, we have: |G c (jω)G p (jω)|=1 and, Step 314: Recorded as Rewrite the above formula as (k p k i ) form, then: Step 315: Substitute the above equation into equation (14) and set Ω = ω -λ 、Θ=|G p (jω)| -1 We can get k i The calculation formula is: Step 316: Substitute equation (17) back into equation (16) to obtain the control parameter k p The calculation formula of .

6. The fractional-order regulation method for a hydraulic turbine system according to claim 4, characterized in that: The specific steps of step 32 include: Step 321: For a known controlled object, according to the known amplitude |G of the controlled object p (jω)| and phase ∠G p (jω), find the parameter with Θ; Step 322: Preset parameters After λ, the control parameter k is calculated in sequence according to steps 315 and 316. i 、k p .

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