CN104483837B - Adaptive control method for reversible machinery group - Google Patents
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Abstract
本发明提供一种可逆式机组自适应控制方法,包括:S1、建立可逆式机组中各环节的非线性数学模型;S2、根据各环节的非线性数学模型建立可逆式机组的非线性数学模型;S3、构造一个三维矩阵,并根据三维矩阵以及可逆式机组的非线性数学模型生成可逆式机组实际输出的动态方程;构造可逆式机组的期望输出轨迹方程,并根据可逆式机组实际输出的动态方程以及可逆式机组的期望输出轨迹方程生成跟踪误差方程;S4、将跟踪误差方程转换为自适应控制器的控制方程,通过自适应控制器的控制方程生成控制量调节可逆式机组的控制输入,并设置一自适应更新机制,根据可逆式机组的输出以及自适应更新机制调整自适应控制器的控制量。
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
技术领域technical field
本发明涉及抽水蓄能电站的可逆式机组控制技术领域,尤其是一种可逆式机组自适应控制方法。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.
背景技术Background technique
长期以来,抽水蓄能电站的可逆式机组广泛采用了以线性控制理论为基础的PID控制及其改进的控制策略。由于可逆式机组呈现强非线性和非最小相位特性,并且工况转换频繁,导致了上述线性控制策略面临控制品质恶化和系统稳定性的问题,严重地影响了可逆式机组运行的安全稳定性和动态性能。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.
目前,出现了以微分几何方法为基础的可逆式机组非线性反馈控制的研究。虽然从理论上说,非线性反馈控制可以解决可逆式机组的非线性控制问题,但需要精确掌握可逆式机组的动态特性,或者说能够建立精确描述可逆式机组控制系统动态特性的数学模型。然而这种条件过于苛刻,对于可逆式机组这类复杂系统而言,无论是采用理论研究还是通过模型试验的方法,所建立的数学模型只是系统动态特性的一种近似,固然可以描述可逆式机组调节系统在一定工作范围内的主要特性,但必然存在某种程度的不确定性,因而导致了非线性反馈控制不具有实际应用的价值。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.
为了改善水轮机调节系统的调节品质,满足其静态和动态性能要求,以模糊控制、神经网络控制及最优控制为代表性的非线性控制方法在水电机组控制理论研究中得到拓展。上述非线性控制方法在理论层面均取得了一定突破,然而也存在一些不足。比如模糊控制存在隶属度函数赋值没有依据、模糊规则归纳困难的缺点,神经网络控制则存在学习速度慢、决策时间长、容易收敛到局部最小点等缺陷。而最优控制研究局限于仿射非线性系统,需要求解李导数和偏微分方程组,且控制规律对模型要求严格,导致理论与应用之间的差异较大。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.
因此现有的可逆式机组控制方法无法满足可逆式机组运行的安全稳定性和良好的动态性能。Therefore, the existing control methods for reversible units cannot satisfy the safety, stability and good dynamic performance of reversible units.
发明内容Contents of the invention
有鉴于此,本发明针对可逆式机组的强非线性,提出了水泵水轮机3参数的M次多项式的非线性建模方法,进而使可逆式机组控制系统的非线性数学模型满足参数线性化条件,提供一种能够满足可逆式机组运行的安全稳定性和良好的动态性能的可逆式机组自适应控制方法。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.
一种可逆式机组自适应控制方法,所述可逆式机组自适应控制方法包括如下步骤:A reversible unit adaptive control method, the reversible unit adaptive control method includes the following steps:
S1、建立可逆式机组中执行机构、发电/电动机、有压过水系统、水泵水轮机的数学模型,其中水泵水轮机的3参数M次多项式非线性建模是关键;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、根据可逆式机组中执行机构、发电/电动机、有压过水系统、水泵水轮机的数学模型建立可逆式机组的非线性数学模型;所述可逆式机组的非线性数学模型由两个已知的函数和一个结构已知、参数未知的光滑向量场的函数构成;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、构造一个三维矩阵,并根据三维矩阵以及可逆式机组的非线性数学模型生成可逆式机组实际输出的动态方程;构造可逆式机组的期望输出轨迹方程,并根据可逆式机组实际输出的动态方程以及可逆式机组的期望输出轨迹方程生成跟踪误差方程;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、将跟踪误差方程转换为自适应控制器的控制方程,通过自适应控制器的控制方程生成控制量调节可逆式机组的控制输入,并设置一自适应更新机制,自适应更新机制用于对参数未知的光滑向量场进行估计,根据可逆式机组的输出以及自适应更新机制调整自适应控制器的控制量,从而对抽水蓄能电站的可逆式机组过渡过程进行自适应控制。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.
本发明提供的可逆式机组自适应控制方法,通过建立可逆式机组的非线性模型,而所述可逆式机组的非线性数学模型由两个已知的函数和一个结构已知、参数未知的光滑向量场的函数构成,这样建立的可逆式机组的非线性模型满足参数线性化条件,从而使得控制时不需要知道可逆式机组的具体的转矩、流量特性以及外部负载的自调节系数,克服了现有技术中函数中参数赋值没有依据的缺陷。然后将可逆式机组的的实际输出跟踪期望输出轨迹的问题转化为跟踪误差问题。而后通过设置一自适应更新机制,根据可逆式机组的输出以及自适应更新机制调整自适应控制器的控制量,从而对抽水蓄能电站的可逆式机组过渡过程进行自适应控制,使得可逆式机组的跟踪误差逐步收敛于零。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.
附图说明Description of drawings
图1是本发明实施方式提供的可逆式机组调节系统结构框图;Fig. 1 is a structural block diagram of a reversible unit regulating system provided by an embodiment of the present invention;
图2是本发明实施方式提供的可逆式机组自适应控制方法流程图。Fig. 2 is a flowchart of an adaptive control method for a reversible unit provided in an embodiment of the present invention.
具体实施方式detailed description
本发明的原理如下,如图1所示,可逆式机组调节系统自适应控制器5以及可逆式机组,可逆式机组包括执行机构1、发电/电动机2、有压过水系统3、水泵水轮机4。图1表示可逆式机组调节系统各个环节的信号传递,其中自适应控制器5输出的控制量u为执行机构的控制输入u;执行机构1将开度y输出给水泵水轮机4以及自适应控制器5;水泵水轮机4输出力矩给发电/电动机2,同时水泵水轮机4输出流量q给有压过水系统3;发电/电动机2将转速n同时输出给自适应控制器5以及水泵水轮机4;有压过水系统3将水压h输出给水泵水轮机4以及自适应控制器5。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 .
其中自适应控制器5输出的控制量u为执行机构的控制输入u,根据控制量u对可逆式机组进行调节控制;而可逆式机组向自适应控制器5反馈水压h、开度y以及转速n;自适应控制器5根据自适应更新机制以及接收到的反馈水压h、开度y以及转速n更新自适应控制器5输出的控制量u,从而完成对可逆式机组的自适应控制。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 .
如图2所示,本发明实施例提供一种可逆式机组自适应控制方法,所述可逆式机组自适应控制方法包括如下步骤: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、建立可逆式机组中执行机构1、发电/电动机2、有压过水系统3、水泵水轮机4的数学模型。可逆式机组的平衡工况点P0∈(n=n0;Y=Y0;H=H0),Mt0,Q0分别为平衡工况点的力矩和流量,定义如下变量,n为水泵水轮机的转速,Y为导叶开度,H为工作水压,Mt为机组力矩,Mg为负载力矩,Q为机组过机流量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=n-n0,ΔY=Y-Y0,ΔH=H-H0,ΔMt=Mt-Mt0,ΔQ=Q-Q0 Δn=nn 0 , ΔY=YY 0 , ΔH=HH 0 , ΔM t =M t -M t0 , ΔQ=QQ 0
Mr为转矩额定值,Qr为流量额定值,Hr为额定工作水压,Ymax为最大导叶开度。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.
Ty为接力器惯性时间常数,u为控制输入,Ta为发电/电动机2的惯性时间常数,en为发电/电动机2负载自调节系数,L为引水管道长度,d为引水管道直径,A为引水管道面积,a为水击波速,f为摩阻系数,t为时间系数,Tw为水流惯性时间常数;Tr为水锤波反射时间,α为损失系数, 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,
其中执行机构1的非线性数学模型的公式如下:The formula of the nonlinear mathematical model of actuator 1 is as follows:
执行结构1的数学模型为已知模型。 The mathematical model of execution structure 1 is a known model.
发电/电动机2的数学模型的公式如下:The formula of the mathematical model of generator/motor 2 is as follows:
发电/电动机2的数学模型为已知模型。 The mathematical model of the generator/motor 2 is a known model.
建立有压引水系统3的数学模型的公式的步骤如下:The steps of establishing the formula of the mathematical model of the pressurized water diversion system 3 are as follows:
S11a、建立有压引水系统3的连续方程和运动方程如下:S11a, establish the continuity equation and motion equation of the pressurized water diversion system 3 as follows:
S12a、引入拉普拉斯算子s,将有压引水系统3的连续方程和运动方程从时域的非线性偏微分形式转化为s域的线性常微分方程组,得到用传递函数形式表达的有压引水系统3模型的公式,如下: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:
有压引水系统3的模型为已知模型。 The model of the pressurized water diversion system 3 is a known model.
S13a、通过忽略可逆式机组中的损失系数,对有压引水系统模型公式中函数取其泰勒展开式的前Γ项,获得有压引水系统模型3的状态空间表达式,如下: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:
有压引水系统模型的状态空间表达式中: In the state space expression of the pressurized water diversion system model:
h=[h he h1 h2 … h2r-1]T∈R2Γ;h=[hh e h 1 h 2 ... h 2r-1 ] T ∈ R 2Γ ;
Ch=[1 0 … 0]∈R2Γ。C h =[1 0 ... 0] ∈R 2Γ .
建立水泵水轮机非线性数学模型的公式的步骤如下:The steps to establish the formula of the pump-turbine nonlinear mathematical model are as follows:
S11b、根据给定的可逆式机组的平衡工况点P0∈(n=n0;α=α0;H=H0),将力矩特性和流量特性做泰勒级数展开,然后截取前M次多项式并得到如下形式的力矩、流量特性表达式: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:
其中多项式系数为未知参数x1=x,x2=y,x3=h。这样,力矩和流量特性就可以满足参数线性化的条件。 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、根据可逆式机组中执行机构1、发电/电动机2、有压过水系统3、水泵水轮机4的非线性数学模型建立可逆式机组的非线性数学模型;所述可逆式机组的非线性数学模型由两个已知的函数和一个结构已知、参数未知的光滑向量场的函数构成。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、选取状态变量X,x=[x1 x2 x3]T=[x y h]T,其中T为转置运算。在状态变量X的表达式及以下表达式中,x1=x,x2=y,x3=h。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、基于光滑向量场的微分几何理论,根据可逆式机组中执行机构1、发电/电动机2、有压过水系统3、水泵水轮机4的非线性数学模型建立可逆式机组的非线性数学模型,可逆式机组的非线性数学模型的公式如下: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:
其中, in,
S23、将力矩、流量特性表达式带入F1(x,t)的表达式中,同时令en=θ0,得 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
其中,F2(x,t)以及B为已知函数,描述水泵水轮机4特性的F1(x,t)属于结构已知,但参数未知的光滑向量场的函数。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、构造一个三维矩阵,并根据三维矩阵以及可逆式机组的非线性数学模型生成可逆式机组实际输出的动态方程;构造可逆式机组的期望输出轨迹方程,并根据可逆式机组实际输出的动态方程以及可逆式机组的期望输出轨迹方程生成跟踪误差方程。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.
所述步骤S3包括如下子步骤:The step S3 includes the following sub-steps:
S31、构造一维输出变量w=C(x-xe),其中,C为三维矩阵,C=[c1 c2 c3]。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、对w求导,并带入中获得可逆式机组实际输出动态方程其中ρ(x,t)=CF2(x,t),b=CB为已知函数和常数;f(x,t)=-CF1(x,t)为结构已知,参数未知函数。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.
将代入到f(x,t)=-CF1(x,t)中,获得Will Substituting into f(x,t)=-CF 1 (x,t), we get
并令参数向量其中:and let the parameter vector in:
则f(x,t)可写为Then f(x,t) can be written as
f(x,t)=η(x1,x2,x3)θ;其中:其中:f(x,t)=η(x 1 ,x 2 ,x 3 )θ; where: in:
将可逆式机组的自适应控制变为:当光滑向量场和函数ρ(x,t)∈R已知,参数向量未知,且b≠0即c2≠0条件下,使得可逆式机组调节系统的输出w(t)跟踪期望输出轨迹wd(t)∈R。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、通过对wd(t)∈R求导,建立期望输出轨迹wd(t)∈R的方程S33, by deriving w d (t) ∈ R, establishing the equation of the desired output trajectory w d (t) ∈ R
其中,kd∈R+,以使期望轨迹成指数衰减,从而可逆式机组调节系统有良好的动态性能;此时wd(0)=w(0)。 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、定义跟踪误差e(t)=wd(t)-w(t),对根据误差求导得跟踪误差函数:S34. Define the tracking error e(t)= wd (t)-w(t), and derive the tracking error function according to the error:
S4、将跟踪误差方程转换为自适应控制器的控制方程,通过自适应控制器的控制方程生成控制量调节可逆式机组的控制输入,并设置一自适应更新机制,自适应更新机制用于对参数未知的光滑向量场进行估计,根据可逆式机组的输出以及自适应更新机制调整自适应控制器的控制量,从而对抽水蓄能电站的可逆式机组过渡过程进行自适应控制。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.
所述步骤S4包括如下子步骤:The step S4 includes the following sub-steps:
S41、对可逆式机组实际输出动态方程如下输入变换S41. For the actual output dynamic equation of the reversible unit, the input transformation is as follows
则将根据误差函数转化为如下公式: Then it will be transformed into the following formula according to the error function:
则可逆式机组调节系统的跟踪问题转化为设计自适应控制器u1(t)∈R,使跟踪误差e(t)→0,而系统真正控制量u(t)则可有以下表达公式: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:
获得自适应控制器的控制方程Obtaining the Governing Equations for the Adaptive Controller
其中,ke∈R+为反馈增益,表示对未知参数θ的估计;通过自适应控制器的控制方程生成控制量调节可逆式机组的控制输入。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、设置一自适应更新机制,自适应更新机制的公式如下:S42, setting an adaptive update mechanism, the formula of the adaptive update mechanism is as follows:
其中,为正定、对角的更新增益矩阵,可取p∈R+,I为单位矩阵;可逆式机组的输出以及自适应更新机制调整自适应控制器的控制量,从而对抽水蓄能电站的可逆式机组过渡过程进行自适应控制。自适应更新机制的公式为已知公式。 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.
本发明实施例提供的可逆式机组自适应控制方法,通过建立可逆式机组的非线性模型,而所述可逆式机组的非线性数学模型由两个已知的函数和一个结构已知、参数未知的光滑向量场的函数构成,这样建立的可逆式机组的非线性模型就满足了参数线性化条件,从而使得控制时不需要知道可逆式机组的具体转矩值、流量特性以及外部负载的自调节系数,克服了现有技术中函数中参数赋值没有依据的缺陷。然后将可逆式机组的的实际输出根据期望输出轨迹的问题转化为跟踪误差问题。并通过将跟踪误差方程转换为自适应控制器的控制方程实现了将跟踪问题转化为自适应控制器的设计的方程问题。而后通过设置一自适应更新机制,根据可逆式机组的输出以及自适应更新机制调整自适应控制器的控制量,从而对抽水蓄能电站的可逆式机组过渡过程进行自适应控制,使得可逆式机组的跟踪误差逐步收敛于零。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.
通过选取李雅普诺夫候选函数(李雅普诺夫函数(Lyapunov function)可以用来证明一动力系统或自治微分方程稳定性。)选取李雅普诺夫候选函数为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
可以证明can prove
因此,可逆式机组调节系统的跟踪误差渐近收敛于零。可以说明本发明实施例提供的可逆式机组自适应控制方法可以使得可逆式机组运行具有安全稳定性和良好的动态性能。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.
在上述所有公式中,相同的字母表示相同参数与变量。In all the above formulas, the same letters indicate the same parameters and variables.
本说明书中各个实施例采用递进的方式描述,每个实施例重点说明的都是与其他实施例的不同之处,各个实施例之间相同相似部分互相参见即可。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.
专业人员还可以进一步意识到,结合本文中所公开的实施例描述的各示例的单元及算法步骤,能够以电子硬件、计算机软件或者二者的结合来实现,为了清楚地说明硬件和软件的可互换性,在上述说明中已经按照功能性一般性地描述了各示例的组成及步骤。这些功能究竟以硬件还是软件方式来执行,取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能,但是这种实现不应超过本发明的范围。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.
结合本文中所公开的实施例描述的方法或算法的步骤可以直接用硬件、处理器执行的软件模块,或者二者的结合来实施。软件模块可以置于随机储存器、内存、只读存储器、电可编程ROM、电可檫除可编程ROM、寄存器、硬盘、可移动磁盘、CD-ROM、或技术领域内所公知的任意其他形式的存储介质中。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.
可以理解的是,对于本领域的普通技术人员来说,可以根据本发明的技术构思做出其它各种相应的改变与变形,而所有这些改变与变形都应属于本发明权利要求的保护范围。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.
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