A Nonlinear Predictive Function Control Method for Fractional-Order Hydropower Turbine Regulation System

Abstract

This invention discloses a nonlinear predictive function control method for a fractional-order turbine regulating system, belonging to the field of automatic control technology. First, a sudden load model of the turbine regulating system is introduced, incorporating fractional calculus and dynamic turbine transfer coefficients. Then, based on the series characteristics of the turbine regulating system, a predictive function controller based on a time-varying nonlinear state-space model is designed, effectively improving the unit's speed and stability. The fractional-order model part employs an improved Oustaloup approximation method and an optimal model order reduction algorithm, enabling efficient computer simulation calculations.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and more specifically to a nonlinear predictive function control method for a fractional-order turbine regulating system. Background Technology

[0002] Currently, in order to achieve the "dual carbon" goal, the proportion of hydropower in renewable energy power generation systems is gradually increasing as the energy structure is continuously optimized and upgraded. Hydropower stations are increasingly handling peak loads, which increases the number of unit regulation operations and the occurrence of unstable operating conditions. The turbine regulation system plays a crucial role in stably and safely regulating the output frequency of the hydropower station; however, during certain transient processes, turbine operating parameters change dramatically and rapidly. In such cases, poor control mechanisms severely impact the operational quality of the hydropower station and can even lead to accidents in the hydropower machinery. Furthermore, research on turbine regulation systems primarily focuses on linear predictive function control; however, most turbine regulation systems in actual production are nonlinear.

[0003] Therefore, under unfavorable conditions for turbine regulation, it is essential to provide an effective control strategy for the turbine regulation system to ensure that the hydropower station can maintain stable operation when the turbine regulation system parameters change rapidly and significantly. Summary of the Invention

[0004] In view of this, the present invention provides a nonlinear predictive function control method for a fractional-order turbine regulating system. First, a sudden load model of the turbine regulating system is introduced, incorporating fractional-order calculus and dynamic turbine transfer coefficients. Then, based on the series characteristics of the turbine regulating system, a predictive function controller based on a time-varying nonlinear state-space model is designed, effectively improving the speed and stability of the unit. The fractional-order model part is processed using an improved Oustaloup approximation method and an optimal model order reduction algorithm, enabling the model to be efficiently calculated using computer simulation.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A nonlinear predictive function control method for a fractional-order hydraulic turbine regulating system includes the following steps:

[0007] Step 1: Establish mathematical models of each component of the fractional-order turbine regulating system according to their characteristics, and establish an overall model of the fractional-order turbine regulating system under sudden load based on the mathematical models.

[0008] Step 2: Simplify the fractional-order hydraulic servo system model based on the improved Oustaloup approximation method and the optimal model order reduction algorithm;

[0009] Step 3: Generate an integer-order nonlinear time-varying state-space model of the turbine regulating system based on the simplified fractional-order hydraulic servo system model;

[0010] Step 4: Design the nonlinear predictive function controller for the fractional-order turbine regulating system based on the nonlinear time-varying state-space model;

[0011] Step 5: Simulate the nonlinear predictive function controller and optimize its control performance.

[0012] Furthermore, the fractional-stage turbine regulating system comprises three subsystems: a hydraulic servo system, a turbine section, and a generator. The mathematical modeling process for each component of the fractional-stage turbine regulating system is as follows: a mathematical model of the hydraulic servo system is established based on fractional calculus; the transfer function of the turbine section is established based on the elastic water hammer condition in the pressure pipeline; and a first-order linear model is used for the generator model.

[0013] Furthermore, the transfer function of the turbine unit section is:

[0014]

[0015] In the formula, h w T is the characteristic coefficient of the pressure pipeline; r Let e ​​be the elastic water hammer time constant, and e be the turbine transmission coefficient. e qy Let e ​​be the transfer function of flow rate with respect to guide vane opening. qh Let e ​​be the transfer function of flow rate with respect to head. my Let e ​​be the transfer function of the turbine for the guide vane opening. mh Let be the transfer function of the turbine to the water head, which is determined by trigonometric functions and exponents.

[0016] Furthermore, based on the aforementioned mathematical model, the differential equation expression for the overall fractional-order turbine regulating system model under sudden load is as follows:

[0017]

[0018] Where z1, z2, and z3 are intermediate variables in the turbine section model, ω is the turbine speed, and m t This refers to the turbine torque.

[0019] Furthermore, the improved Oustaloup approximation method in step 2 includes:

[0020] The selected fitting frequency range is [ω] b ω h The improved Oustaloup approximation expression is as follows:

[0021]

[0022] Where α is the order of the fractional order, 0 < α < 1, ω' m =ω b (ω h / ω b ) (2m-1-α) / 2M For zero, ω m =ω b (ω h / ω b ) (2m-1+α) / 2M Let M be the pole, M be the selected order, and b and d be two adjustable parameters, typically b = 10 and d = 9.

[0023] Furthermore, the optimal model reduction algorithm in step 2 includes:

[0024] The degradation error signal e is obtained based on the integer high-order model and the degradation model. r (t);

[0025] Based on the order reduction error signal e r (t) Define the objective function, which is:

[0026]

[0027] In the formula ω r (t) represents the error signal weights;

[0028] Define the undetermined parameter vector θ = [λ1, λ2, ..., λ k ,ζ1,ζ2,…,ζ q+1 If ,] then for a given class of input signals, the error signal of the reduced-order model can be defined. Therefore, an optimal objective function for order reduction is defined as follows:

[0029]

[0030] The fractional differential operator s can be obtained by fitting the objective function of the optimal price reduction. α An approximate integer low-order transfer function model is used to simplify the fractional-order hydraulic servo system model.

[0031] Furthermore, step 3 also includes: the simplified fractional-order hydraulic servo system model is transformed into differential equations, and the remaining part of the model is combined to obtain the integer-order form of the nonlinear time-varying state-space model of the turbine regulating system.

[0032] Furthermore, step 4 specifically includes:

[0033] Discretize the nonlinear time-varying state-space model of the integer-order hydro-turbine regulation system as a prediction model:

[0034]

[0035] Where, x m (k-1) represents the state variable at time k-1, u(k-1) represents the control variable at time k-1, and g m (k) is the state variable at time k, G m (k)∈R 6×6 H is the state coefficient matrix. m (k)∈R 6×1 For the control coefficient matrix, Q m (k)∈R 1×6 This is the output coefficient matrix.

[0036] As can be seen from the above technical solution, compared with the prior art, this invention discloses a nonlinear predictive function control method for a fractional-order turbine regulating system. First, it introduces a sudden load model of the turbine regulating system using fractional-order calculus and dynamic turbine transfer coefficients. Then, based on the series characteristics of the turbine regulating system, a predictive function controller based on a time-varying nonlinear state-space model is designed, effectively improving the unit's speed-performance and stability. This invention also studies the stability and robustness of the closed-loop system, where the fractional-order model part employs an improved Oustaloup approximation method and an optimal model order reduction algorithm to enable efficient computer simulation calculations. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0038] Figure 1 This is a flowchart of the nonlinear predictive function control of the fractional-order turbine regulating system of the present invention.

[0039] Figure 2 This is a schematic diagram of the operating principle of the turbine regulating system of the present invention.

[0040] Figure 3 This is a schematic diagram of the price reduction error signal principle of the model of this invention.

[0041] Figure 4 This is a schematic diagram of the control principle framework of the fractional-order nonlinear prediction function of the present invention.

[0042] Figure 5The figure shows the unit step response curves of three fractional-order models of the hydraulic servo system.

[0043] Figure 6 The figures show the unit step response curves of the original fractional-order model and the approximate reduced-order model, where (a) α = 0.9 and (b) α = 0.8.

[0044] Figure 7 The figures show the free response curve and FNPFC control response curve of the turbine regulating system under initial values, where (a) the initial value is ω-t; and (b) the initial value is m. t -t; (c) The initial value is yt.

[0045] Figure 8 The following are response curves of the turbine regulating system under initial values ​​during model matching: (a) initial value is ω-t; (b) initial value is m. t -t; (c) The initial value is yt.

[0046] Figure 9 The following are the variable response curves of the turbine regulating system under model mismatch: (a) order ω-t; (b) order et; (c) order yt; (d) order m. t -t.

[0047] Figure 10 The following are the response curves of the turbine regulating system under a step signal: (a) order is ω-t; (b) order is m. t -t; (c) The order is yt. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] This invention discloses a nonlinear predictive function control method for a fractional-order turbine regulating system, such as... Figure 1 As shown, it includes the following steps:

[0050] Step 1: Based on the characteristics of each component of the fractional-order turbine regulating system, establish mathematical models of each component of the fractional-order turbine regulating system, and establish an overall model of the fractional-order turbine regulating system under sudden load based on the mathematical models.

[0051] The operating principle of the turbine regulating system is as follows: Figure 2As shown, the fractional-order nonlinear model of the turbine regulating system during the sudden load surge includes three subsystems: the hydraulic servo system, the turbine section, and the generator. In the turbine section model, a dynamically changing turbine transmission coefficient is introduced to represent its irregular changes after the sudden load surge. The fractional-order characteristics are reflected in the hydraulic servo system model.

[0052] A mathematical model of the hydraulic servo system is established based on fractional calculus. The dynamic characteristics of the hydraulic servo system after incorporating fractional calculus are expressed as follows:

[0053]

[0054] In the formula, T y y is the relay response time, y is the relay stroke, and u is the control input. Let a be a fractional Caputo differential operator, t be the upper and lower bounds of the operator, and α be the fractional order.

[0055] Considering the case of elastic water hammer in the pressure pipeline, the transfer function of the turbine section is established as follows:

[0056]

[0057] In the formula, h w T is the characteristic coefficient of the pressure pipeline; y The time constant is the elastic water hammer time constant. During the sudden load transition process, it is assumed that the turbine parameters are in a state of continuous fluctuation. Trigonometric functions and exponents are introduced to establish the expression for the change of the turbine transmission coefficient.

[0058]

[0059] e mw e my e mh e qw e qy e qh These are the transmission coefficients of turbine torque and flow rate to rotational speed, guide vane opening, and head, respectively.

[0060] Single-unit operation is the most unfavorable situation for the dynamic characteristics of the turbine regulation system. In order to simplify the analysis and to ensure that the nonlinearity of the generator part has little impact on the control effect, a first-order linear model is selected as the mathematical model of the generator part.

[0061]

[0062] In the formula, T a e is the generator's inertial time constant. n =e g -e x e xe is the partial derivative of the turbine torque with respect to the rotational speed, also known as the turbine self-regulation coefficient; g It is the partial derivative of the generator torque with respect to the rotational speed, also known as the generator self-adjustment coefficient.

[0063] Based on the models of each subsystem, an overall fractional-order turbine regulating system model under sudden load is established, and its differential equation expression is as follows:

[0064]

[0065] Where z1, z2, and z3 are intermediate variables in the turbine section model, ω is the turbine speed, and m t This refers to the turbine torque.

[0066] Step 2: Simplify the fractional-order hydraulic servo system model based on the improved Oustaloup approximation method and the optimal model reduction algorithm.

[0067] The selected fitting frequency range is [ω b ω h The improved Oustaloup approximation is as shown in equation (6):

[0068]

[0069] Where α is the order of the fractional order, 0 < α < 1, ω′ m =ω b (ω h / ω b ) (2m-1-α) / 2M For zero, ω m =ω b (ω h / ω b ) (2m-1+α) / 2M Let M be the pole, M be the selected order, and b and d be two adjustable parameters, typically b = 10 and d = 9.

[0070] The idea behind the optimal model degradation algorithm is as follows: Figure 3 As shown.

[0071] Assume the higher-order integer model is

[0072]

[0073] v1...v n With a1...a n All are coefficients.

[0074] The reduced-order model is

[0075]

[0076] ζ1...ζ q+1 With λ1...λk All are coefficients.

[0077] Based on the order reduction error signal e r (t) Define the objective function as shown in equation (9):

[0078]

[0079] In the formula ω r (t) represents the error signal weight.

[0080] Define an undetermined parameter vector θ = [λ1, λ2, ..., λ k ,ζ1,ζ2,...,ζ q+1 If ,] then for a given class of input signals, the error signal of the reduced-order model can be defined. Therefore, an optimal objective function for order reduction is defined:

[0081]

[0082] By minimizing the objective function (10), the fractional differential operator s can be obtained. α An approximate integer low-order transfer function model is used to obtain a simplified fractional-order hydraulic servo system model.

[0083] Step 3: Generate an integer-order nonlinear time-varying state-space model of the turbine regulating system based on the simplified fractional-order hydraulic servo system model.

[0084] Using the algorithm described in step 2, a simplified transfer function model of the hydraulic servo system can be obtained, which is equivalent to transforming T... y Fit to a new T' y Transforming it into a differential equation and combining it with other parts of the model, we can obtain the following integer-order nonlinear time-varying state-space model of the turbine regulating system:

[0085]

[0086] in,

[0087]

[0088] C = [0 0 0 1 0 0];

[0089] Where x is the system state variable; u is the system control variable; and g is the system output variable; Let x be the first derivative; A′(t) be the coefficient matrix of the system's state variables; B′(t) be the coefficient matrix of the system's control variables; and C be the coefficient matrix of the system's output variables.

[0090] Step 4: Design the nonlinear predictive function controller for the fractional-order turbine regulation system based on the nonlinear time-varying state-space model.

[0091] Discretize model (11) as a prediction model, as shown in equation (12):

[0092]

[0093] Where x m (k-1) represents the state variable at time k-1, u(k-1) represents the control variable at time k-1, and x m (k) is the first derivative of g, where g is the derivative of g. m (k) is the state variable at time k, G m (k)∈R 6×6 H is the state coefficient matrix. m (k)∈R 6×1 For the control coefficient matrix, Q m (k)∈R 1×6 This is the output coefficient matrix.

[0094] basis functions {f k The system output can be viewed as a weighted linear combination of basis functions acting on the controlled object's response. Therefore,

[0095]

[0096] In the formula, the number of basis functions is J; μ j (k) are the linear weighting coefficients of the basis functions, obtained through optimization calculation; f kj (i) is a basis function at t = iT s The value of T s Where is the sampling period, and P is the prediction time domain length.

[0097] Choose a step response function as the basis function, as shown in equation (14):

[0098] f k1 (0)=f k2 (1) = ... = f kJ (P-1) (14)

[0099] The model state variable x is obtained by mathematical induction from equation (12). m (k+i)

[0100] x m (k+i)=G m (k)G m (k+1)...G m (k+i-1)x m (k)+G m(k)G m (k+1)...G m (k+i-2)H m (k)u(k)+G m (k)G m (k+1)…G m (k+i-3)H m (k+1)u(k+1)+…+G m (k)H m (k+i-2)u(k+i-2)+H m (k+i-1)u(k+i-1) (15)

[0101] The predicted output g at time k+i can then be derived. m (k+i):

[0102]

[0103] Where μ(k)=[μ1(k),μ2(k),…,μ J (k)],l k (i)=[l k1 (i),l k2 (i),…,l kJ (i)] T ,

[0104] Step 5: Simulate the nonlinear predictive function controller and optimize its control performance.

[0105] The principle of fractional nonlinear predictive function control (FNPFC) for turbine regulating systems is as follows: Figure 4 As shown.

[0106] The prediction model can include almost any form of parametric and nonparametric model. This invention introduces a nonlinear time-varying state-space model of the entire system as the prediction model. The output of the prediction model is represented as the free response output g. l and forced response output g f sum:

[0107] g m (k)=g l (k)+g f (k) (17)

[0108] The optimization calculation is divided into error compensation and rolling optimization.

[0109] Error compensation takes into account the presence of disturbances and irregular changes in parameters in practical applications, and calculates the actual output g of the system. p With the output g of the prediction model mThe error value between the two values ​​is added to the predicted output as compensation to improve control accuracy. Let the error at time k represent the error at time k+i in the future.

[0110] e(k+i)=g p (k)-g m (k) (18)

[0111] The corrected actual process prediction output is

[0112] g p (k+i)=g m (k+i)+e(k+i) (19)

[0113] Rolling optimization solves for the control input u by optimizing a certain objective function, so that the output of the prediction process in the time domain is as close as possible to the reference trajectory. A reference trajectory is set to avoid drastic changes in the control input and large overshoot, allowing the system output to smoothly reach the setpoint along this trajectory. A first-order exponential function is chosen as the reference trajectory.

[0114] g r (k+i)=g s (k+i)-β i (g s (k)-g p (k)) (20)

[0115] In the formula, g r For reference trajectory; g s g p These output the set value and the actual value, respectively. T is the attenuation coefficient, 0 < β < 1, representing how quickly the reference trajectory approaches the set value. c The reference trajectory time constant.

[0116] The most commonly used quadratic performance index function is chosen as the objective function, which represents minimizing the sum of squared errors between the prediction process output and the reference trajectory. As shown in the equation:

[0117]

[0118] In the formula, k s It is the number of fitted points in the prediction time domain P; p i These are the selected fitting points.

[0119] The parameter values ​​of the turbine regulating system of this invention are shown in Table 1.

[0120] Table 1. Parameter values ​​of the turbine regulating system

[0121]

[0122] In this invention, the feasibility and effectiveness of the Oustaloup approximation method and the optimal model order reduction algorithm are first verified. Then, the control performance of the FNPFC controller under different fractional orders, model matching, model mismatch and step signals is studied under a given initial signal.

[0123] The system order was selected for three cases: 1, 0.9, and 0.8, and the fitting frequency range was selected as (10^35)^25. -3 10 3 To maintain consistency with the original model's order, the numerator and denominator orders of the reduced-order hydraulic servo system model were set to q = 0 and k = 1. The unit step response curves of the three fractional-order models of the hydraulic servo system are shown below. Figure 5 As shown, the response curve becomes flatter as the order decreases. The unit step responses of the original fractional-order model and the approximate reduced-order model are as follows: Figure 6 As shown, the approximate simplified models of the two fractional-order models have allowable errors, and the approximation results meet the requirements.

[0124] In the study of the control performance of the turbine regulating system, the initial system value is set as x = [0 0 0 0.001 0 0]. T Taking an integer-order hydraulic servo system model as an example, the response curves of the system variables of the turbine regulating system under the initial value are simulated to test the ability of each variable of the turbine regulating system to stabilize to the set value under FNPFC control. Figure 7 The free response curve and FNPFC control response curve of the turbine regulating system under this initial value are shown. ω is the final output of the turbine regulating system, u directly acts on y, and m t This is an intermediate output variable. When the controller is not involved in regulation, the relay output y is 0, and the torque m is... t As the rotational speed ω initially deviates from its stable value, reaches a peak, and then slowly approaches a stable state, accompanied by fluctuations caused by the nonlinear time-varying turbine transmission coefficient, the FNPFC control strategy can effectively regulate the transient process of the turbine regulation system. The accuracy of the model of the servo actuator in the hydraulic servo system, acting as the actuator, has a non-negligible impact on the response process of each variable. Figure 7 The numerical experimental system shown also has an order α of 1, 0.9, and 0.8, respectively, and the initial system value is x = [0000.00100]. T The aim was to observe the influence of fractional order on the control effect. Figure 8 The response curves of the turbine regulating system under these initial values ​​are shown during model matching. The transient response of ω is almost uniform, and the speed regulation is unaffected. The key difference lies in the change in the control inputs acting on the servo, which alters y and m. t The responses show significant differences; as the order decreases, y and m... tThe smaller the maximum deviation during the response process, the smoother the curve, and the smaller the difference in stabilization time. This indicates that the action performance of relays of different orders is inconsistent. Adjusting the speed under the same initial value requires different relay stroke settings. In the opening adjustment mode, it is necessary to focus on the influence of the relay order on the opening setting.

[0125] Considering that the parameters of the FNPFC controller predictive model are preset in practice, and the changes in operating conditions are unknown, the predictive model will not adjust automatically, resulting in a mismatch. Assuming the system parameters of the predictive model are ideal, let e be taken as... qh =0.5, e y =1, e=0.7. The actual model changes to equation (5) after a sudden increase in load. Figure 9 The variable response curves of the turbine regulating system under model mismatch are shown, with the initial system value set to x = [0 0 0 0.001 0 0]. T It is obvious that m t The fluctuations in ω are more frequent and severe than during model matching. This is because tracking errors arise when the control input calculated from the predictive model is applied to the actual model. The overall trend is that the system gradually stabilizes amidst continuous fluctuations. This can be seen from... Figure 8 (b) Observing the tracking error during the transition process, the initial error was relatively large, but then it decreased rapidly. Compared to the smaller amplitude of the unbiased tracking relay action during model matching, m t The adjustment amplitude is not significant, which leads to a large maximum deviation of ω and a long settling time. FNPFC can still maintain good tracking performance even under severe model mismatch and will not experience uncontrolled adjustment.

[0126] Table 2 compares the settling time and maximum deviation of the turbine regulating system response under FNPFC control strategy with and without model matching, providing a direct observation of the controller's performance. The ω-response curves show significant differences after model mismatch, with ω, y, and m... t Both the maximum deviation and the settling time have increased to some extent.

[0127] Table 2 Comparison of Model Matching and Model Mismatch Control Performance

[0128]

[0129] Figure 10 The response curve of the turbine regulating system under a step signal is shown. The initial system value is x = [0 0 00 0 0]. T, the ω set value is 0. A rotational speed step signal with an amplitude of 0.01 is applied at t = 2s, and this rotational speed step signal is withdrawn at t = 32s. Observe the transient characteristics of the variables of the hydraulic turbine governing system reaching a new steady state under FNPFC control. When 2s < t < 32s, ω rises to around 0.01 in a short time, accompanied by stable fluctuations. Due to the fluctuations of the transfer coefficient of the hydraulic turbine during this transient process, the response curves of each state variable cannot reach the set value at a constant value and fluctuate around it with a very small amplitude, and no unstable divergence phenomenon occurs, indicating that the response curve of the hydraulic turbine governing system with parametric nonlinear time-varying characteristics will inevitably show continuous fluctuations under a step signal. When the step signal disappears, the FNPFC controller can act quickly, and the variables of the hydraulic turbine governing system can all quickly return to the set value with a small overshoot value. Similar to the above simulation experiment, when matching the model, the order of the hydraulic servo system has little effect on the regulation of rotational speed, and the laws of the response curves of other system variables are also consistent with the above simulation experiment.

[0130] Table 3 specifically shows the relevant indexes of the response of the hydraulic turbine governing system when applying and withdrawing the step signal. The regulation time required for the system transient process and the maximum deviation are very small in both cases, indicating that the FNPFC control strategy can stably regulate the hydraulic turbine governing system when the external signal changes.

[0131] Table 3 Step Response Results of Hydraulic Turbine Governing System

[0132]

[0133]

[0134] In this specification, each embodiment is described in a progressive manner. The key points of each embodiment are the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0135] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A nonlinear predictive functional control method for a fractional order hydro-turbine governing system, characterized in that, Comprise the following steps: Step 1, the mathematical model of each component of the fractional order hydraulic turbine governing system is established according to the characteristics of each component of the fractional order hydraulic turbine governing system respectively, the fractional order hydraulic turbine governing system includes hydraulic servo system, hydraulic turbine unit section, generator three subsystems; It comprises: the mathematical model of the hydraulic servo system is established based on fractional calculus; The transfer function of the hydraulic turbine unit section is established according to the elastic water hammer of the pressure pipeline: ； wherein is a characteristic coefficient of the pressure conduit; is an elastic water hammer time constant, e is a transfer coefficient of the water turbine, , is a transfer function of the flow rate to the guide vane opening, is a transfer function of the flow rate to the water head, is a transfer function of the water turbine to the guide vane opening, is a transfer function of the water turbine to the water head, determined from trigonometric functions and exponentials; The generator adopts a first-order linear model; The overall fractional order hydraulic turbine governing system model under sudden load is established based on the mathematical model: ； wherein , and are intermediate variables of the hydraulic turbine section model, is the hydraulic turbine speed, is the hydraulic turbine torque, is the characteristic coefficient of the pressure conduit; is the elastic water hammer time constant, e is the hydraulic turbine transfer coefficient, , is the flow to guide vane opening transfer function, is the flow to head transfer function, is the hydraulic turbine to guide vane opening transfer function, is the hydraulic turbine to head transfer function, determined from trigonometric and exponential functions; T y is the servomotor reaction time, y is the servomotor stroke, u is the control input, is the fractional order Caputo differential operator a , t is the upper and lower line of the operation operator, α is the fractional order; T a is the generator inertia time constant, , e x is the partial derivative of the hydraulic turbine torque to the speed, also known as the hydraulic turbine self-regulation coefficient; e g is the partial derivative of the generator torque to the speed, also known as the generator self-regulation coefficient; Step 2, the fractional order hydraulic servo system model is simplified based on the improved Oustaloup approximation method and the optimal model reduction algorithm, comprising: The selected fitting frequency range is The improved Oustaloup approximation expression is then as follows: ； wherein is the order of the fractional order, , ω h is the maximum value of the fitting frequency, is the zero, is the pole, is the selected order, , are two adjustable parameters; Obtaining a degradation error signal from an integer higher order model and a degradation model , According to the reduced error signal defining an objective function, the objective function being: ； In the formula is the error signal weight; Define the vector of unknown parameters The error signal of the reduced order model is then defined for a given input signal The objective function for optimal reduction is thus defined as ； fitting a fractional differential operator by the optimal reduced-order objective function an approximate integer low-order transfer function model, and further simplifying the fractional order hydraulic servo system model; Step 3, the integer order form of the hydraulic turbine governing system nonlinear time-varying state space model is generated according to the simplified fractional order hydraulic servo system model, the simplified fractional order hydraulic servo system model is converted into a differential equation, and the integer order form of the hydraulic turbine governing system nonlinear time-varying state space model is obtained by combining the remaining part model; Step 4, the integer order form of the hydraulic turbine governing system nonlinear time-varying state space model is discretized as a prediction model; Step 5, the nonlinear predictive function controller is simulated, and the control performance is optimized.

2. The method according to claim 1, wherein, The step 4 specifically comprises: ； wherein is a state variable at time t, is a control variable at time t, is a state variable at time t, is a state variable coefficient matrix, is a control variable coefficient matrix, is an output variable coefficient matrix.

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