阅读说明：本技术 一种变参双幂趋近律的水轮机组微分预测滑模控制方法 (Variable-parameter double-power approximation law differential prediction sliding mode control method for hydraulic turbine set ) 是由 李江峰 向凤红 张洪亮 王永斌 唐浩轩 王彦杰 于 2021-09-02 设计创作，主要内容包括：本发明涉及水轮机组控制技术领域,尤其涉及一种变参双幂趋近律的水轮机组微分预测滑模控制方法。本发明实时获取机组控制器输出、导叶开度、水轮机力矩及电机转速信息；将获取信息及时反馈至滑模控制器中,更新控制器输出；考虑到PID控制方法鲁棒性差,运用滑模控制理论设计控制器,以提高抗扰能力；设计出参数根据状态自调整的新型双幂次趋近律,提高了系统响应时间且削弱控制输入抖振；将实际电机转速通过微分控制器引出反向叠加到控制器输出,预测系统偏差。本发明所提出的控制方法满足机组系统抗扰动、响应速度及减震的要求,具有较好的动态性能及稳态精度。(The invention relates to the technical field of hydraulic turbine unit control, in particular to a hydraulic turbine unit differential prediction sliding mode control method based on a variable parameter double power approximation law. The method comprises the steps of acquiring information of output of a unit controller, opening of a guide vane, torque of a water turbine and rotating speed of a motor in real time; feeding back the acquired information to the sliding mode controller in time, and updating the output of the controller; considering that the PID control method is poor in robustness, a sliding mode control theory is applied to design a controller so as to improve the anti-interference capability; designing a novel double-power approximation law with parameters self-adjusted according to states, improving the response time of the system and weakening control input buffeting; and leading out the actual motor rotating speed through a differential controller and superposing the actual motor rotating speed to the controller output in a reverse direction, and predicting the system deviation. The control method provided by the invention meets the requirements of disturbance resistance, response speed and shock absorption of the unit system, and has better dynamic performance and steady-state precision.)

1. A differential prediction sliding mode control method of a variable parameter double power approach law for a hydraulic turbine set is characterized by comprising the following steps:

s1, establishing a mathematical model of the hydraulic turbine set, and obtaining a state equation of the hydraulic turbine set system according to the transfer function of each module in the hydraulic turbine set, wherein the hydraulic turbine set comprises three modules, namely an actuating mechanism, a hydraulic turbine, a water diversion system, a generator and a load;

s2, designing a self-adaptive variable-parameter double-power approximation law sliding mode controller according to the mathematical model of the hydro-turbine set in S1;

and S3, setting a target value of the rotating speed of the motor, controlling the rotating speed of the motor by using the sliding mode controller, acquiring the output of the sliding mode controller, the guide vane opening of the water turbine, the torque of the water turbine and the rotating speed of the motor in the control process, feeding the obtained values back to the input end of the sliding mode controller to form a closed loop, leading out the rotating speed of the motor through a differential controller, reversely superposing the rotating speed of the motor to the output of the sliding mode controller, and acting on an execution mechanism to stabilize the output of the water turbine set system in a target range.

2. The differential prediction sliding-mode control method for the hydraulic turbine unit according to claim 1, characterized in that in step S1, an actuating mechanism G is adopted_hWater turbine and water diversion system G_tAnd generator and load G_pThe transfer function of (a) is:

in the formula, T_yIs the time constant of the main servomotor, T_wIs the water flow inertia time constant, T_aAs unit inertia time constant, e_nThe comprehensive self-adjusting coefficient of the hydroelectric generating set is obtained, and S is a complex variable of a transfer function;

the corresponding state space equation is obtained from the transfer function:

in the formula, u is the output of the sliding mode controller, y is the opening degree of the guide vane, M_tIs the water turbine moment, and x is the actual rotating speed of the motor.

3. The differential prediction sliding-mode control method for the hydro-turbine unit according to claim 1, characterized in that: the design process of the sliding mode controller in step S2 is as follows:

s21, the output u of the sliding mode controller and the guide vane opening y are led into a linear sliding mode surface, and a new sliding mode surface S is designed as follows:

wherein e ═ x_d-x，x_dThe target rotating speed of the motor is shown, c and b are parameters, c is greater than 0, and b is a negative number;

s22 is obtained by deriving equations (2) and (3):

wherein the content of the first and second substances,

the sliding mode control process of the S23 is divided into an approaching process and a sliding mode, when the system reaches the sliding mode surface, the system is in the sliding mode stage, at the moment, S is 0, and the equivalent control law obtained by the formula (4) is as follows:

s24, using the double power approach law and the enhanced approach law, designing the double power approach law which can self-adjust the approach parameter according to the state variable as follows:

wherein upsilon is₁、υ₂、a、i、k₁、k₂Are all parameters, v₁＞0，υ₂＞0，0＜a＜1，0＜k₁＜1，0＜k₂1, i is greater than 0, e is a natural constant, sgn () is a sign function;

s25, when the system is in the approach process, the switching control law is:

s36, obtaining a final sliding mode control law as follows:

4. the differential prediction sliding-mode control method for the hydro-turbine unit according to claim 1, characterized in that: in step S3, the actual rotation speed is led out by the differential controller and added to the controller output in the opposite direction, and the actual rotation speed and the sliding mode controller act on the executing mechanism together, and the transfer function of the differential controller is as follows:

wherein k is_dTo gain, T_nIs the differential decay time constant.

Technical Field

The invention relates to the technical field of hydraulic turbine unit control, in particular to a hydraulic turbine unit differential prediction sliding mode control method based on a variable parameter double power approximation law.

Background

Along with the rapid development of China, the power consumption requirements of industrial manufacturing and resident life are gradually expanded, and the hydroelectric power generation industry is rapidly developed. Meanwhile, users also put forward higher requirements on the quality of electric energy, and hydraulic power plants also have higher targets on the quality and the efficiency of power generation. The key of hydroelectric generation is the control of frequency, and the frequency is determined by the speed of the rotating speed of the water turbine, so that the quality of electric energy can be improved by controlling the rotating speed of the water turbine.

In actual operation, fluctuations in load and water power and interference from external factors present challenges to the control performance of the unit. PID control is the most classical control method of a traditional hydraulic turbine set, and the result is simple and easy to operate. However, the hydraulic turbine set is a complex nonlinear system, and the PID with fixed structural parameters is difficult to obtain stable control effect in the working condition.

Disclosure of Invention

In order to solve the problems of large vibration, low response speed of a control system and poor robustness of the existing hydraulic turbine unit, the invention provides a differential prediction sliding mode control method of the hydraulic turbine unit with variable parameter double power approximation law, which comprises the following steps:

s1, establishing a mathematical model of the hydraulic turbine set, and obtaining a state equation of the hydraulic turbine set system according to the transfer function of each module in the hydraulic turbine set, wherein the hydraulic turbine set comprises three modules, namely an actuating mechanism, a hydraulic turbine, a water diversion system, a generator and a load;

actuating mechanism G_hWater turbine and water diversion system G_tAnd generator and load G_pThe transfer function of (a) is:

in the formula, T_yIs the time constant of the main servomotor, T_wIs the water flow inertia time constant, T_aAs unit inertia time constant, e_nThe comprehensive self-adjusting coefficient of the hydroelectric generating set is obtained, and S is a complex variable of a transfer function;

the corresponding state space equation is obtained from the transfer function:

in the formula, u is the output of the sliding mode controller, y is the opening degree of the guide vane, M_tIs the water turbine moment, and x is the actual rotating speed of the motor.

S2, designing a self-adaptive variable-parameter double-power approximation law sliding mode controller according to the mathematical model of the hydro-turbine set in S1; the design process of the sliding mode controller is as follows:

s21, the output u of the sliding mode controller and the guide vane opening y are led into a linear sliding mode surface, and a new sliding mode surface S is designed as follows:

wherein e ═ x_d-x，x_dThe target rotating speed of the motor is shown, c and b are parameters, c is greater than 0, and b is a negative number;

s22 is obtained by deriving equations (2) and (3):

wherein the content of the first and second substances,

the sliding mode control process of the S23 is divided into an approaching process and a sliding mode, when the system reaches the sliding mode surface, the system is in the sliding mode stage, at the moment, S is 0, and the equivalent control law obtained by the formula (4) is as follows:

s24, using the double power approach law and the enhanced approach law, designing the double power approach law which can self-adjust the approach parameter according to the state variable as follows:

wherein upsilon is₁、υ₂、a、i、k₁、k₂Are all parameters, v₁＞0，υ₂＞0，0＜a＜1，0＜k₁＜1，0＜k₂1, i is greater than 0, e is a natural constant, sgn () is a sign function;

s25, when the system is in the approach process, the switching control law is:

s36, obtaining a final sliding mode control law as follows:

and S3, setting a target value of the rotating speed of the motor, controlling the rotating speed of the motor by using the sliding mode controller, acquiring the output of the sliding mode controller, the guide vane opening of the water turbine, the torque of the water turbine and the rotating speed of the motor in the control process, feeding the obtained values back to the input end of the sliding mode controller to form a closed loop, leading out the rotating speed of the motor through a differential controller, reversely superposing the rotating speed of the motor to the output of the sliding mode controller, and acting on an execution mechanism to stabilize the output of the water turbine set system in a target range. The transfer function of the differential controller is:

wherein k is_dTo gain, T_nIs the differential decay time constant.

Compared with the prior art, the invention has the beneficial effects that:

1. the variable parameter double power approach law sliding mode control method is adopted, so that the problems of low response speed of a unit, fixed structural parameters and output buffeting of the controller can be effectively solved; in addition, through a differential feedback device, the error can be effectively predicted, the inertia response speed is increased, and the overshoot of the system is reduced.

2. Compared with a PID controller, the sliding mode control is insensitive to disturbance and has stronger robustness due to purposeful change of the structure along with the state.

Drawings

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the description will be briefly introduced below.

FIG. 1 is a schematic block diagram of a differential prediction sliding mode control principle of a hydraulic turbine set.

Detailed Description

In order to make the technical solution and advantages of the present invention clearer, the present invention is further described in detail below with reference to the accompanying drawings in combination with specific embodiments.

Example (b): a differential prediction sliding mode control method of a hydraulic turbine set with variable parameter double power approximation law is further explained by combining the attached drawings.

As shown in fig. 1, the control target quantity is the rotating speed of the motor, the controller is divided into a sliding mode controller and a differential controller, the executing mechanism is a hydraulic control servomotor, and the control objects are a water turbine, a water diversion system, a generator and a load. In the control process of the sliding mode controller, the output of the controller, the opening degree of the guide vane, the torque of the water turbine and the rotating speed of the motor are fed back to the sliding mode controller to be used as control quantities.

The control method comprises the following steps:

and S1, obtaining a system state equation according to the transfer function of the modules in the hydraulic turbine set. The hydraulic turbine set comprises three modules, namely a hydraulic actuating mechanism, a water turbine, a water diversion system, a generator and a load. The hydraulic actuating mechanism can output a measurable quantity of the opening of a guide vane of the water turbine, the water turbine and the water diversion system can output a measurable quantity of the moment of the water turbine, and the generator and the load can measure power, frequency, voltage and current and the like. The quality of electric energy is usually measured by frequency, the rotating speed of the motor is an important factor for determining the stability of the frequency, and therefore the rotating speed is selected as a target control quantity.

Actuating mechanism G_hWater turbineAnd a water diversion system G_tAnd the transfer function of the generator and load Gp is:

in the formula, T_yIs the time constant of the main servomotor, T_wIs the water flow inertia time constant, T_aAs unit inertia time constant, e_nThe comprehensive self-adjusting coefficient of the hydroelectric generating set is obtained, and S is a complex variable of a transfer function; taking fig. 1 as a reference, the transfer function is converted to obtain a state space equation of the system as follows:

in the formula, u is the output of the sliding mode controller, y is the opening degree of the guide vane, M_tIs the water turbine moment, and x is the actual rotating speed of the motor.

According to a mathematical model of a hydraulic turbine set in S1, a self-adaptive variable-parameter double-power approximation law sliding mode controller is designed S21, the sliding mode controller outputs u, the guide vane opening degree y is led into a linear sliding mode surface, a new sliding mode surface S is designed, and the input target rotating speed of the motor is x_dIf the actual output speed is x, the error is defined as e ═ x_d-x. The basic sliding mode control can only ensure that the rotating speed and the power of the motor are stable within a target range in a short time, and cannot ensure the opening of the guide vane and the stability of the output of the sliding mode controller. Therefore, the linear sliding mode surface is used as a base, the guide vane opening and the controller are introduced into the sliding mode surface design, and the defined sliding mode surface is as follows:

wherein c and b are parameters, c is more than 0, because the opening degree of the guide vane is a feedback quantity, and b is a negative number;

s22 is obtained by deriving equations (2) and (3):

wherein the content of the first and second substances,

the sliding mode control process of the S23 is divided into an approaching process and a sliding mode, when the system reaches the sliding mode surface, the system is in the sliding mode stage, at the moment, S is 0, and the equivalent control law obtained by the formula (4) is as follows:

s24 is affected by the discontinuous switching characteristic controlled by the sliding mode, the limited speed of the system when the moving point reaches the switching surface, the inertia, etc., and the moving point can not slide exactly according to the predetermined track, but buffet near the switching surface. The approach law is the main method for solving the buffeting problem, and can well adjust the convergence rate. When the system motion point is in the approaching process and does not reach the sliding mode, a double-power approaching law and an enhanced approaching law are applied, and the double-power approaching law capable of self-adjusting approaching parameters according to state variables is designed as follows:

wherein upsilon is₁、υ₂、a、i、k₁、k₂Are all parameters, v₁＞0，υ₂＞0，0＜a＜1，0＜k₁＜1，0＜k₂1, i is greater than 0, e is a natural constant, sgn () is a sign function; the design principle is as follows: when the system is far away from the sliding form (s > 1), there are:υ₁the term denominator approaches 1, upsilon₂Term denominator approach k₂，υ₂The item approach parameter is larger and plays a leading role; when the system is close to slidingWhen the surface of the die is molded (s is more than or equal to 0 and less than or equal to 1), the ratio ofυ₁Term denominator approach k₁，υ₂The term denominator approaches 1, upsilon₁The item approach parameter is larger and plays a leading role; the approach speeds of both terms are zero when the system reaches the sliding mode. The designed control law has larger approaching speed no matter at the near sliding mode surface or the far sliding mode surface, and meanwhile, when the system state approaches the sliding mode, smaller control gain is ensured, so that buffeting is weakened.

S25, when the system is in the approach process, the switching control law is:

s36, obtaining a final sliding mode control law as follows:

in order to verify the stability of the sliding mode controller, a Lyapunov function is selected as follows:

by substituting equations (5) and (7) by deriving equation (10), the following can be obtained:

it can be seen that the system is able to converge in a limited time.

And S3, setting a target value of the rotating speed of the motor, controlling the rotating speed of the motor by using the sliding mode controller, acquiring the output of the sliding mode controller, the guide vane opening of the water turbine, the torque of the water turbine and the rotating speed of the motor in the control process, feeding the obtained values back to the input end of the sliding mode controller to form a closed loop, leading out the rotating speed of the motor through a differential controller, reversely superposing the rotating speed of the motor to the output of the sliding mode controller, and acting on an execution mechanism to stabilize the output of the water turbine set system in a target range.

For the inputs of the derivative controller: the actual rotating speed of the unit is used as the input of a differentiator instead of the rotating speed error. Under special conditions, the given rotating speed value needs to be changed according to the setting of the given rotating speed value, and then the given rotating speed change curve can be used as a reference model of the set rotating speed curve. When the given rotation speed is changed together with the actual rotation speed, the differentiator predicts the deviation value of the rotation speed and loses meaning. Therefore, the actual motor rotating speed is led out by the differential controller and is reversely superposed to the controller output to jointly act on the hydraulic actuating mechanism. The transfer function of the differential controller is:

wherein k is_dTo gain, T_nIs the differential decay time constant.

The above embodiments are merely illustrative of the technical ideas and features of the present invention, but the scope of the present invention is not limited thereto. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.