CN102354107A

CN102354107A - On-line identification and control method for parameter of alternating current position servo system model

Info

Publication number: CN102354107A
Application number: CN2011101427369A
Authority: CN
Inventors: 李向国; 刘向红; 梅志千
Original assignee: Hohai University HHU
Current assignee: Changzhou Gugao Intelligent Equipment Technology Research Institute Co ltd
Priority date: 2011-05-30
Filing date: 2011-05-30
Publication date: 2012-02-15
Anticipated expiration: 2031-05-30
Also published as: CN102354107B

Abstract

The invention discloses an on-line identification and control method for model parameters of an AC servo system, using a model reference adaptive identification algorithm based on Lyapunov's (Lyapunov) stability theory to calculate the moment of inertia J and viscosity of the controlled object of the AC servo system The damping coefficient B is identified online. When the identification parameters converge, the position controller is designed online according to the values of J and B, and automatically switches to position control. The invention can greatly improve the efficiency of AC servo system design.

Description

A method for online identification and control of AC position servo system model parameters

技术领域 technical field

本发明涉及交流永磁同步电机伺服系统，特别涉及一种交流位置伺服系统模型参数在线辨识和控制方法，属于同步电机技术领域。The invention relates to an AC permanent magnet synchronous motor servo system, in particular to an online identification and control method for model parameters of an AC position servo system, and belongs to the technical field of synchronous motors.

背景技术 Background technique

一个新的交流伺服系统建立以后，其诸多系统参数都是未知的，而控制系统的控制器参数都是依据系统的模型参数来设计的。另外在许多控制问题中，面向的对象通常是不确定的，工作负载的改变会导致伺服系统模型参数的变化。因此，一个高性能的交流伺服系统不仅要求系统能对伺服指令做出快速、准确的响应，而且还要求当负载特征变化时，仍能保证系统具有良好的控制性能，这就要求伺服系统的控制器参数能够随负载特性作适当的调整。After a new AC servo system is established, many system parameters are unknown, and the controller parameters of the control system are designed according to the model parameters of the system. In addition, in many control problems, the object-oriented is usually uncertain, and the change of the workload will lead to the change of the parameters of the servo system model. Therefore, a high-performance AC servo system not only requires the system to respond quickly and accurately to servo commands, but also requires that the system still have good control performance when the load characteristics change, which requires the control of the servo system The parameters of the inverter can be adjusted appropriately according to the load characteristics.

交流伺服控制系统的设计方法一般分为三种，第一种是先离线辨识出系统模型参数，再根据辨识出的模型参数设计控制器参数，该方法效率比较低，并且离线辨识需要大量实验数据，要对多组数据进行处理才能得到系统的参数，计算量很大，并且当负载的变化导致系统模型参数变化时要重新进行离线参数辨识，增加了控制系统设计时间和工作量，专利申请号为200710024700.4名称为《一种交流位置伺服系统中干扰的观测和补偿方法》的中国专利介绍了参数变化等对被控对象控制性能的影响。第二种是先辨识出系统模型参数，再根据辨识出的模型参数在线设计控制器参数，并自动切换到位置控制。第三种是位置自适应控制算法，和第二种方法不同的是在控制系统运行过程中不断进行参数辨识和控制器的修改，此种方法系统设计比较复杂难于实现，并且对控制系统的硬件要求较高。The design methods of AC servo control systems are generally divided into three types. The first one is to identify the system model parameters offline first, and then design the controller parameters according to the identified model parameters. This method is relatively inefficient, and offline identification requires a large amount of experimental data. , it is necessary to process multiple sets of data to obtain the parameters of the system, which requires a large amount of calculation, and when the load changes cause the parameters of the system model to change, the offline parameter identification must be re-identified, which increases the design time and workload of the control system. Patent application number The 200710024700.4 Chinese patent titled "A Disturbance Observation and Compensation Method in AC Position Servo System" introduced the influence of parameter changes on the control performance of the controlled object. The second is to identify the system model parameters first, then design the controller parameters online according to the identified model parameters, and automatically switch to position control. The third is the position adaptive control algorithm, which is different from the second method in that parameter identification and controller modification are carried out continuously during the operation of the control system. Higher requirements.

发明内容 Contents of the invention

本发明要解决的技术问题在于，针对现有技术上的缺陷，提供一种交流位置伺服系统模型参数在线辨识和控制方法，以提高设计控制系统的效率。The technical problem to be solved by the present invention is to provide an AC position servo system model parameter online identification and control method to improve the efficiency of designing the control system in view of the defects in the prior art.

为解决上述技术问题，本发明提供一种交流位置伺服系统模型参数在线辨识和控制方法，其特征在于，包括以下步骤：In order to solve the above technical problems, the present invention provides a method for online identification and control of AC position servo system model parameters, which is characterized in that it includes the following steps:

1)设定交流伺服系统被控对象数学模型：利用一阶微分方程表示为

其中ω是系统输出速度，u是被控对象输入速度信号，J和B是交流伺服系统被控对象的模型参数，是未知参数，分别是转动惯量和粘性阻尼系数；1) Set the mathematical model of the controlled object of the AC servo system: use the first-order differential equation to express as

Where ω is the output speed of the system, u is the input speed signal of the controlled object, J and B are the model parameters of the controlled object of the AC servo system, which are unknown parameters, and are the moment of inertia and viscous damping coefficient respectively;

设定被控对象辨识的参考模型： $J_{m} {\overset{\cdot}{ω}}_{m} = - B_{m} ω_{m} + ω_ref,$ ω_ref是辨识输入的外部参考信号，ω_m为控制系统希望达到的控制性能指标，参数J_m和B_m分别为转动惯量和粘性阻尼系数在控制系统中希望达到的控制性能指标，均为正数；Set the reference model for plant identification: $J_{m} {\overset{&Center Dot;}{ω}}_{m} = - B_{m} ω_{m} + ω_ref,$ ω_ref is the external reference signal for identification input, ω _m is the control performance index that the control system hopes to achieve, and the parameters J _m and B _m are respectively the control performance index that the moment of inertia and viscous damping coefficient hope to achieve in the control system, both of which are positive numbers ;

2)在被控对象模型参考自适应控制系统中，将辨识的模型参数转动惯量J和粘性阻尼系数B的辨识值和其前一采样周期的转动惯量J和粘性阻尼系数B进行比较，直到它们的差值小于预先给定的性能指标ε时停止辨识，输出辨识的参数值J和B；2) In the model reference adaptive control system of the controlled object, compare the identified value of the identified model parameters moment of inertia J and viscous damping coefficient B with the moment of inertia J and viscous damping coefficient B of the previous sampling period until they When the difference between is less than the predetermined performance index ε, the identification is stopped, and the identification parameter values J and B are output;

3)根据步骤2)输出的被控对象辨识的参数值在线计算位置控制器，并自动切换到位置控制。3) Calculate the position controller online according to the parameter value of the controlled object identification output in step 2), and automatically switch to position control.

前述的一种交流位置伺服系统模型参数在线辨识和控制方法，其特征在于：在所述步骤2)中，被控对象辨识的参考模型和实际模型参数之间的跟踪偏差采用比例运算，控制规律为u＝θ_r(t)ω_ref-θ_y(t)ω，其中θ_r(t)和θ_y(t)是分别是t时刻的辨识值和参考模型参数的时变反馈增益，闭环系统函数为 $\overset{\cdot}{ω} = - (B + θ_{y}) ω / J + θ_{r} ω_ref / J;$ 跟踪偏差为e＝ω-ω_m，跟踪偏差的动态表达式为 $\overset{\cdot}{e} = \overset{\cdot}{ω} - {\overset{\cdot}{ω}}_{m} = - \frac{B_{m}}{J_{m}} e + (\frac{B_{m}}{J_{m}} - \frac{θ_{y}}{J} - \frac{B}{J}) ω + (\frac{θ_{r}}{J} - \frac{1}{J_{m}}) ω_ref .$ The aforesaid online identification and control method of AC position servo system model parameters is characterized in that: in the step 2), the tracking deviation between the reference model of the controlled object identification and the actual model parameters adopts proportional calculation, and the control law is u=θ _r (t)ω_ref-θ _y (t)ω, where θ _r (t) and θ _y (t) are the identification value at time t and the time-varying feedback gain of the reference model parameters, and the closed-loop system function for $\overset{&Center Dot;}{ω} = - (B + θ_{the y}) ω / J + θ_{r} ω_ref / J;$ Tracking deviation is e=ω-ω _m , and the dynamic expression of tracking deviation is $\overset{&Center Dot;}{e} = \overset{&Center Dot;}{ω} - {\overset{&Center Dot;}{ω}}_{m} = - \frac{B_{m}}{J_{m}} e + (\frac{B_{m}}{J_{m}} - \frac{θ_{the y}}{J} - \frac{B}{J}) ω + (\frac{θ_{r}}{J} - \frac{1}{J_{m}}) ω_ref .$

前述的一种交流位置伺服系统模型参数在线辨识和控制方法，其特征在于：在所述步骤2)中，利用李雅普诺夫稳定性判据判断被控对象模型参考自适应控制系统是否稳定，具体方法为：The aforesaid online identification and control method of AC position servo system model parameters is characterized in that: in the step 2), the Lyapunov stability criterion is used to judge whether the controlled object model reference adaptive control system is stable, specifically The method is:

李雅普诺夫 Lyapunov 函数为 $V (e, θ_{r}, θ_{y}) = \frac{1}{2} (e^{2} + \frac{J}{γ} {(\frac{θ_{y}}{J} + \frac{B}{J} - \frac{B_{m}}{J_{m}})}^{2} + \frac{J}{γ} {(\frac{θ_{r}}{J} - \frac{1}{J_{m}})}^{2}),$ 其中γ为自适应增益，当e＝0、控制器参数θ_r和θ_y等于它们的最优值时，李雅普诺夫函数V为零，V的导数为The Lyapunov function is $V (e, θ_{r}, θ_{the y}) = \frac{1}{2} (e^{2} + \frac{J}{γ} {(\frac{θ_{the y}}{J} + \frac{B}{J} - \frac{B_{m}}{J_{m}})}^{2} + \frac{J}{γ} {(\frac{θ_{r}}{J} - \frac{1}{J_{m}})}^{2}),$ where γ is the adaptive gain, when e=0, the controller parameters θ _r and θ _y are equal to their optimal values, the Lyapunov function V is zero, and the derivative of V is

$\frac{dV dV}{dt dt} = = e e \frac{de de}{dt dt} + + \frac{11}{γ γ} ((\frac{{θ θ}_{y the y}}{J J} + + \frac{B B}{J J} - - \frac{{B B}_{m m}}{{J J}_{m m}})) \frac{{dθ dθ}_{y the y}}{dt dt} + + \frac{11}{γ γ} ((\frac{{θ θ}_{r r}}{J J} - - \frac{11}{{J J}_{m m}})) \frac{{dθ dθ}_{r r}}{dt dt}$

$= = - - \frac{{B B}_{m m}}{{J J}_{m m}} {e e}^{22} + + \frac{11}{γ γ} ((\frac{{θ θ}_{y the y}}{J J} + + \frac{B B}{J J} - - \frac{{B B}_{m m}}{{J J}_{m m}})) ((\frac{{dθ dθ}_{y the y}}{dt dt} - - γωe γωe)) + + \frac{11}{γ γ} ((\frac{{θ θ}_{r r}}{J J} - - \frac{11}{{J J}_{m m}})) ((\frac{{dθ dθ}_{r r}}{dt dt} + + γeω γeω__ref ref))$

如果控制器参数根据自适应规律 $\frac{{dθ}_{r}}{dt} = - γeω_ref,$ $\frac{{dθ}_{y}}{dt} = γωe$ 进行更新，则得如果误差e不等于零，函数V就减小，可以得出误差将趋于零，判断出被控对象模型参考自适应控制系统是稳定的。自适应规律的差分方程为 $\frac{θ_{r} (k) - θ_{r} (k - 1)}{T_{s}} = - γe (k) ω_ref (k),$ $\frac{θ_{y} (k) - θ_{y} (k - 1)}{T_{s}} = γe (k) ω (k),$ 则转动惯量和粘性阻尼系数的差分方程为 $\frac{J (k) - J (k - 1)}{T_{s}} = - J_{m} γe (k) ω_ref (k),$ $\frac{B (k) - B (k - 1)}{T_{s}} = - B_{m} γe (k) ω_ref (k) - γe (k) ω (k),$ T_s为采样周期，θ_r(k)、θ_y(k)、e(k)、ω(k)、ω_ref(k)、J(k)、B(k)和θ_r(k-1)、θ_y(k-1)、J(k-1)、B(k-1)分别为第k个和第k-1个采样周期的值。If the controller parameters follow the adaptive law $\frac{{dθ}_{r}}{dt} = - γeω_ref,$ $\frac{{dθ}_{the y}}{dt} = γωe$ To update, you have to If the error e is not equal to zero, the function V will decrease, and it can be concluded that the error will tend to zero, and it is judged that the controlled object model reference adaptive control system is stable. The difference equation of the adaptive law is $\frac{θ_{r} (k) - θ_{r} (k - 1)}{T_{the s}} = - γe (k) ω_ref (k),$ $\frac{θ_{the y} (k) - θ_{the y} (k - 1)}{T_{the s}} = γe (k) ω (k),$ Then the difference equation of moment of inertia and viscous damping coefficient is $\frac{J (k) - J (k - 1)}{T_{the s}} = - J_{m} γe (k) ω_ref (k),$ $\frac{B (k) - B (k - 1)}{T_{the s}} = - B_{m} γe (k) ω_ref (k) - γe (k) ω (k),$ T _s is the sampling period, θ _r (k), θ _y (k), e(k), ω(k), ω_ref(k), J(k), B(k) and θ _r (k-1) , θ _y (k-1), J(k-1), B(k-1) are the values of the kth and k-1th sampling periods respectively.

前述的一种交流位置伺服系统模型参数在线辨识和控制方法，其特征在于：在所述步骤3)中，位置控制器采用PD控制，传递函数表示为G_c(s)＝K_p+K_ds，则位置环的闭环传递函数为 $Φ (s) = \frac{K_{p} + K_{d} s}{{Js}^{2} + (B + K_{d}) s + K_{p}},$ 根据二阶系统的标准形式得到ω_n ²＝K_p/J，2ζω_n＝(B+K_d)/J，所以

K_d＝2ζω_n-B，其中，K_P+K_ds为位置控制器，其中K_P为比例系数，K_d为微分系数，s为拉普拉斯变量；令ω_n表示位置环的期望自然频率，ζ表示位置环的期望阻尼比。The aforementioned online identification and control method for model parameters of an AC position servo system is characterized in that: in the step 3), the position controller adopts PD control, and the transfer function is expressed as G _c (s)=K _p +K _d s, then the closed-loop transfer function of the position loop is

Φ (the s) = \frac{K_{p} + K_{d} thes}{js},

According to the standard form of the second-order system Obtain ω _n ² =K _p /J, 2ζω _n =(B+K _d )/J, so

K _d =2ζω _n -B, where K _P +K _d s is the position controller, where K _P is the proportional coefficient, K _d is the differential coefficient, and s is the Laplace variable; let ω _n represent the expectation of the position loop The natural frequency, ζ represents the desired damping ratio of the position loop.

本发明的有益效果是，利用基于李雅普诺夫(Lyapunov)稳定性理论的模型参考自适应辨识算法，对交流伺服系统被控对象的模型参数转动惯量J和粘性阻尼系数B进行在线辨识，当辨识参数收敛后，根据J和B的值在线设计位置控制器，并自动切换到位置控制，大大提高系统设计的效率。The beneficial effect of the present invention is that, using the model reference adaptive identification algorithm based on Lyapunov (Lyapunov) stability theory, the model parameters moment of inertia J and viscous damping coefficient B of the controlled object of the AC servo system are identified online. After the parameters converge, the position controller is designed online according to the values of J and B, and automatically switches to position control, which greatly improves the efficiency of system design.

附图说明Description of drawings

图1为本发明的基于模型参数在线辨识和位置控制原理图；Fig. 1 is the schematic diagram of on-line identification and position control based on model parameters of the present invention;

图2为被控对象模型参数在线辨识和位置控制流程图；Fig. 2 is a flow chart of the online identification and position control of the model parameters of the controlled object;

图3为被控对象模型参考自适应控制系统的框图；Fig. 3 is a block diagram of the controlled object model reference adaptive control system;

图4为一阶系统的模型参考自适应辨识框图；Fig. 4 is a block diagram of the model reference adaptive identification of the first-order system;

图5为简化后的位置闭环原理框图；Fig. 5 is a schematic block diagram of the simplified position closed loop;

图6为位置控制输出跟踪曲线。Figure 6 is the position control output tracking curve.

具体实施方式 Detailed ways

下面结合附图和实施例对本发明进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

图1中

表示交流伺服系统被控对象数学模型，J和B是交流伺服系统被控对象的模型参数转动惯量和粘性阻尼系数，K_p+K_ds为位置控制器，θ_ref为系统的位置控制输入参考信号，ω_ref是辨识输入的外部参考信号。被控对象数学模型用一阶微分方程表示为

其中ω是系统输出速度，u是速度环输入。Figure 1

Indicates the mathematical model of the controlled object of the AC servo system, J and B are the model parameters of the controlled object of the AC servo system, the moment of inertia and the viscous damping coefficient, K _p + K _d s is the position controller, and θ_ref is the position control input reference signal of the system , ω_ref is the external reference signal for identification input. The mathematical model of the controlled object is expressed by a first-order differential equation as

Where ω is the system output speed, u is the speed loop input.

图2中 $\frac{J (k) - J (k - 1)}{T_{s}} = - J_{m} γe (k) ω_ref (k)$ 和 $\frac{B (k) - B (k - 1)}{T_{s}} = - B_{m} γe (k) ω_ref (k) - γe (k) ω (k)$ 为被控对象模型参数转动惯量和粘性阻尼系数自适应辨识的差分方程，ε为判断收敛的性能指标，将转动惯量J和粘性阻尼系数B的辨识值和其前一采样周期的值进行比较，直到它们的差值小于预先给定的性能指标ε时停止辨识，输出辨识的参数值J和B；根据J和B的值在线设计位置控制器，并自动切换到位置控制。Figure 2 $\frac{J (k) - J (k - 1)}{T_{the s}} = - J_{m} γ e (k) ω_ref (k)$ and $\frac{B (k) - B (k - 1)}{T_{the s}} = - B_{m} γ e (k) ω_ref (k) - γe (k) ω (k)$ is the difference equation for the adaptive identification of the controlled object model parameters moment of inertia and viscous damping coefficient, ε is the performance index for judging convergence, compare the identification value of moment of inertia J and viscous damping coefficient B with the value of the previous sampling period, Stop the identification until their difference is less than the predetermined performance index ε, and output the identified parameter values J and B; design the position controller online according to the values of J and B, and automatically switch to position control.

图3中

为被控对象辨识的参考模型，其中J_m和B_m是常数，ω_m为控制系统希望达到的控制性能指标，e表示每一个动态瞬间实际过程和参考模型之间的跟踪偏差，根据这个差异，不断的修改控制器参数，就可以使实际系统的控制性能指标尽可能接近参考模型，完成被控对象模型参数在线辨识。Figure 3

is the reference model for the identification of the controlled object, where J _m and B _m are constants, ω _m is the control performance index that the control system hopes to achieve, e represents the tracking deviation between the actual process and the reference model at each dynamic instant, according to the difference , and continuously modify the controller parameters, the control performance index of the actual system can be as close as possible to the reference model, and the online identification of the model parameters of the controlled object can be completed.

在自适应辨识系统中，假设系统参数J和B是未知的。所期望的系统的动态特性设为一阶参考模型 $J_{m} {\overset{\cdot}{ω}}_{m} = - B_{m} ω_{m} + ω_ref,$ ω_ref是输入的外部参考信号。参数J_m要求是严格正的，这样参考模型是稳定的。不失一般性，B_m也选为严格正数。参考模型可以用它的传递函数G表示为ω_m＝Gω_ref，其中 $G = \frac{1}{J_{m} s + B_{m}} .$ In an adaptive identification system, it is assumed that the system parameters J and B are unknown. The desired dynamic characteristics of the system are set as a first-order reference model $J_{m} {\overset{&Center Dot;}{ω}}_{m} = - B_{m} ω_{m} + ω_ref,$ ω_ref is the input external reference signal. The parameter J _m is required to be strictly positive so that the reference model is stable. Without loss of generality, B _m is also selected as a strictly positive number. The reference model can be expressed by its transfer function G as ω _m = Gω_ref, where $G = \frac{1}{J_{m} the s + B_{m}} .$

被控对象参考模型和实际模型参数之间的跟踪偏差要进行适当的运算，比较成熟的算法有比例控制和比例积分控制，本发明控制规律采用比例运算，因此选择控制规律u＝θ_r(t)ω_ref-θ_y(t)ω，其中θ_r和θ_y是时变反馈增益。闭环系统为 $\overset{\cdot}{ω} = - (B + θ_{y}) ω / J + θ_{r} ω_ref / J,$ 选择u＝θ_r(t)ω_ref-θ_y(t)ω为控制规律，很明显：它使得系统可以实现精确模型匹配。事实上，如果被控对象参数已知，让式 $\overset{\cdot}{ω} = - (B + θ_{y}) ω / J + θ_{r} ω_ref / J$ 和式 ${\overset{\cdot}{ω}}_{m} = \frac{- B_{m} ω_{m} + ω_ref}{J_{m}}$ 相等得： ${θ_{r}}^{*} = \frac{J}{J_{m}},$ ${θ_{y}}^{*} = \frac{B_{m} J}{J_{m}} - B,$ 即如果选择θ_r ^*，θ_y ^*这样的控制器参数，则闭环系统和参考模型的动态特性相同，从而有零跟踪误差。The tracking deviation between the controlled object reference model and the actual model parameters should be properly calculated. More mature algorithms have proportional control and proportional integral control. The control law of the present invention adopts proportional calculation, so the control law u= _θr (t )ω_ref-θ _y (t)ω, where θ _r and θ _y are time-varying feedback gains. The closed loop system is $\overset{\cdot}{ω} = - (B + θ_{the y}) ω / J + θ_{r} ω_ref / J,$ Choosing u=θ _r (t)ω_ref-θ _y (t)ω as the control law is obvious: it enables the system to achieve exact model matching. In fact, if the plant parameters are known, let $\overset{\cdot}{ω} = - (B + θ_{the y}) ω / J + θ_{r} ω_ref / J$ Japanese style ${\overset{\cdot}{ω}}_{m} = \frac{- B_{m} ω_{m} + ω_ref}{J_{m}}$ equal to: ${θ_{r}}^{*} = \frac{J}{J_{m}},$ ${θ_{the y}}^{*} = \frac{B_{m} J}{J_{m}} - B,$ That is, if the controller parameters such as θ _r ^* and θ _y ^* are selected, the dynamic characteristics of the closed-loop system and the reference model are the same, so there is zero tracking error.

现在我们选择参数θ_r和θ_y的自适应规律。记跟踪误差为e＝ω-ω_m，跟踪误差的动态表达式为 $\overset{\cdot}{e} = \overset{\cdot}{ω} - {\overset{\cdot}{ω}}_{m} = - \frac{B_{m}}{J_{m}} e + (\frac{B_{m}}{J_{m}} - \frac{θ_{y}}{J} - \frac{B}{J}) ω + (\frac{θ_{r}}{J} - \frac{1}{J_{m}}) ω_ref,$ 如果参数θ_r和θ_y等于它们的希望值θ_r ^*和θ_y ^*，则误差e就趋于零。引入Lyapunov函数 $V (e, θ_{r}, θ_{y}) = \frac{1}{2} (e^{2} + \frac{J}{γ} {(\frac{θ_{y}}{J} + \frac{B}{J} - \frac{B_{m}}{J_{m}})}^{2} + \frac{J}{γ} {(\frac{θ_{r}}{J} - \frac{1}{J_{m}})}^{2}),$ 当e＝0和控制器参数等于它们的最优值时，函数V为零。V的导数为Now we choose the adaptive law for the parameters _θr and _θy . Record the tracking error as e=ω-ω _m , and the dynamic expression of the tracking error is $\overset{&Center Dot;}{e} = \overset{&Center Dot;}{ω} - {\overset{&Center Dot;}{ω}}_{m} = - \frac{B_{m}}{J_{m}} e + (\frac{B_{m}}{J_{m}} - \frac{θ_{the y}}{J} - \frac{B}{J}) ω + (\frac{θ_{r}}{J} - \frac{1}{J_{m}}) ω_ref,$ If the parameters θ _r and θ _y are equal to their desired values θ _r ^* and θ _y ^* , the error e tends to zero. Introducing the Lyapunov function $V (e, θ_{r}, θ_{the y}) = \frac{1}{2} (e^{2} + \frac{J}{γ} {(\frac{θ_{the y}}{J} + \frac{B}{J} - \frac{B_{m}}{J_{m}})}^{2} + \frac{J}{γ} {(\frac{θ_{r}}{J} - \frac{1}{J_{m}})}^{2}),$ The function V is zero when e=0 and the controller parameters are equal to their optimal values. The derivative of V is

如果控制器参数根据自适应规律 $\frac{{dθ}_{r}}{dt} = - γeω_ref,$ $\frac{{dθ}_{y}}{dt} = γωe$ 进行更新，则得

因此只要误差e不等于零，函数V就减小，由此可以得出误差将趋于零，根据李雅普诺夫稳定性判据可以得到此系统是稳定的。If the controller parameters follow the adaptive law

\frac{{dθ}_{r}}{dt} = - γeω_ref,

\frac{{dθ}_{the y}}{dt} = γωe

To update, you have to

Therefore, as long as the error e is not equal to zero, the function V will decrease, and it can be concluded that the error will tend to zero. According to the Lyapunov stability criterion, the system is stable.

图4为一阶系统的模型参考自适应辨识框图，其中

是参考模型，

是被控对象的模型。调节时间t_s是反应一个系统动态特性的综合性指标，在本发明中就根据系统的调节时间t_s来确定参考模型中J_m和B_m的值。根据调节时间的计算公式，在本发明中选取所设计系统的调节时间为0.025秒，就可以得出J_m和B_m的值为0.00625和1，计算过程不再赘述。再根据

{θ_{r}}^{*} = \frac{J}{J_{m}},

{θ_{y}}^{*} = \frac{B_{m} J}{J_{m}} - B,

可得J＝θ_r ^*J_m，

B = \frac{B_{m} J}{J_{m}} - {θ_{y}}^{*} .

Figure 4 is a block diagram of the model reference adaptive identification of the first-order system, where

is the reference model,

is the model of the controlled object. The adjustment time t _s is a comprehensive index reflecting the dynamic characteristics of a system. In the present invention, the values of J _m and B _m in the reference model are determined according to the system adjustment time t _s . According to the calculation formula of the adjustment time, the adjustment time of the designed system is selected as 0.025 seconds in the present invention, and the values of J _m and B _m can be obtained as 0.00625 and 1, and the calculation process will not be repeated. Then according to

{θ_{r}}^{*} = \frac{J}{J_{m}},

{θ_{the y}}^{*} = \frac{B_{m} J}{J_{m}} - B,

It can be obtained that J＝θ _r ^* J _m ,

B = \frac{B_{m} J}{J_{m}} - {θ_{the y}}^{*} .

图5为简化后的位置闭环原理框图，本发明中位置控制器采用PD控制，其传递函数表示为G_c(s)＝K_p+K_ds，则位置环的闭环传递函数为 $Φ (s) = \frac{K_{p} + K_{d} s}{{Js}^{2} + (B + K_{d}) s + K_{p}},$ 令ω_n表示位置环的期望自然频率，ζ表示位置环的期望阻尼比，根据二阶系统的标准形式

可以得到ω_n ²＝K_p/J，2ζω_n＝(B+K_d)/J，所以K_d＝2ζω_n-B。Fig. 5 is the schematic block diagram of position closed-loop after simplification, position controller adopts PD control among the present invention, and its transfer function is expressed as G _c (s)=K _p +K _d s, then the closed-loop transfer function of position loop is

Φ (the s) = \frac{K_{p} + K_{d} the s}{{js}^{2} + (B + K_{d}) the s + K_{p}},

Let _ωn denote the desired natural frequency of the position loop and ζ the desired damping ratio of the position loop, according to the standard form of the second-order system

It can be obtained that ω _n ² =K _p /J, 2ζω _n =(B+K _d )/J, so _Kd = _2ζωn -B.

本发明根据转动惯量J和粘性阻尼系数B两个模型参数的辨识值，在线设计位置控制器，即将模型参数的辨识值和其前一采样周期的延迟值进行比较，直到它们的差值小于预先给定的性能指标时停止辨识，输出辨识的参数值，根据辨识值在线设计位置控制器，并自动切换到位置控制，跟踪的位置参考信号为单位阶跃信号，终值为1。According to the identification value of the two model parameters of moment of inertia J and viscous damping coefficient B, the present invention designs the position controller online, that is, the identification value of the model parameter is compared with the delay value of the previous sampling period until their difference is less than the preset When the performance index is given, the identification is stopped, the parameter value of identification is output, and the position controller is designed online according to the identification value, and automatically switches to position control. The tracked position reference signal is a unit step signal, and the final value is 1.

实验装置中交流永磁同步电机型号为MHMD042P1U，控制软件采用Mathworks公司生产的MATLAB2009a。试验时选择参考信号为ω_ref＝4sin100t。The model of the AC permanent magnet synchronous motor in the experimental device is MHMD042P1U, and the control software adopts MATLAB2009a produced by Mathworks. During the test, the reference signal is selected as ω_ref=4sin100t.

实验结果表明，模型参考自适应参数辨识方法可以正确的辨识控制系统的模型参数，根据辨识的被控对象模型参数在线设计位置控制器，并自动切换到位置控制，可以有效地提高控制系统的效率。以上已以较佳实施例公开了本发明，然其并非用以限制本发明，凡采用等同替换或者等效变换方式所获得的技术方案，均落在本发明的保护范围之内。The experimental results show that the model reference adaptive parameter identification method can correctly identify the model parameters of the control system, design the position controller online according to the identified model parameters of the controlled object, and automatically switch to position control, which can effectively improve the efficiency of the control system . The above has disclosed the present invention with preferred embodiments, but it is not intended to limit the present invention, and all technical solutions obtained by adopting equivalent replacement or equivalent transformation methods fall within the protection scope of the present invention.

Claims

1. An AC position servo system model parameter online identification and control method, is characterized in that, comprises the following steps:

1) Set the mathematical model of the controlled object of the AC servo system: use the first-order differential equation to express as

J \overset{\cdot}{ω} = - Bω + u,

Set the reference model for plant identification:

J_{m} {\overset{\cdot}{ω}}_{m} = - B_{m} ω_{m} + ω_ref,

ω_ref is the external reference signal for identification input, ω _m is the control performance index that the control system hopes to achieve, and the parameters J _m and B _m are respectively the control performance index that the moment of inertia and viscous damping coefficient hope to achieve in the control system, both of which are positive numbers ;

2) In the model reference adaptive control system of the controlled object, compare the identified value of the identified model parameters moment of inertia J and viscous damping coefficient B with the moment of inertia J and viscous damping coefficient B of the previous sampling period until they When the difference between is less than the predetermined performance index ε, the identification is stopped, and the identification parameter values J and B are output;

3) According to step 2), output the parameter value of the controlled object identification to calculate the position controller online, and automatically switch to position control.

2. A kind of AC position servo system model parameter online identification and control method according to claim 1, it is characterized in that: in said step 2), the tracking between the reference model and the actual model parameter of controlled object identification The deviation adopts proportional operation, and the control law is u=θ _r (t)ω_ref-θ _y (t)ω, where θ _r (t) and θ _y (t) are the identification value at time t and the time-varying parameters of the reference model Feedback gain, the closed-loop system function is

\overset{&Center Dot;}{ω} = - (B + θ_{the y}) ω / J + θ_{r} ω_ref / J;

Tracking deviation is e＝ω-ω _m , and the dynamic expression of tracking deviation is

\overset{&Center Dot;}{e} = \overset{\cdot}{ω} - {\overset{&Center Dot;}{ω}}_{m} = - \frac{B_{m}}{J_{m}} e + (\frac{B_{m}}{J_{m}} - \frac{θ_{the y}}{J} - \frac{B}{J}) ω + (\frac{θ_{r}}{J} - \frac{1}{J_{m}}) ω_ref .

3. A kind of AC position servo system model parameter online identification and control method according to claim 2, characterized in that: in said step 2), utilize the Lyapunov stability criterion to judge that the controlled object model refers to Whether the adaptive control system is stable, the specific method is:

The Lyapunov function is

V (e, θ_{r}, θ_{the y}) = \frac{1}{2} (e^{2} + \frac{J}{γ} {(\frac{θ_{the y}}{J} + \frac{B}{J} - \frac{B_{m}}{J_{m}})}^{2} + \frac{J}{γ} {(\frac{θ_{r}}{J} - \frac{1}{J_{m}})}^{2}),

where γ is the adaptive gain, when e=0, the controller parameters θ _r and θ _y are equal to their optimal values, the Lyapunov function V is zero, and the derivative of V is

\frac{dV dV}{dt dt} = = e e \frac{de de}{dt dt} + + \frac{11}{γ γ} ((\frac{{θ θ}_{y the y}}{J J} + + \frac{B B}{J J} - - \frac{{B B}_{m m}}{{J J}_{m m}})) \frac{{dθ dθ}_{y the y}}{dt dt} + + \frac{11}{γ γ} ((\frac{{θ θ}_{r r}}{J J} - - \frac{11}{{J J}_{m m}})) \frac{{dθ dθ}_{r r}}{dt dt}

= = - - \frac{{B B}_{m m}}{{J J}_{m m}} {e e}^{22} + + \frac{11}{γ γ} ((\frac{{θ θ}_{y the y}}{J J} + + \frac{B B}{J J} - - \frac{{B B}_{m m}}{{J J}_{m m}})) ((\frac{{dθ dθ}_{y the y}}{dt dt} - - γωe γωe)) + + \frac{11}{γ γ} ((\frac{{θ θ}_{r r}}{J J} - - \frac{11}{{J J}_{m m}})) ((\frac{{dθ dθ}_{r r}}{dt dt} + + γeω γeω__ref ref))

If the controller parameters follow the adaptive law

\frac{{dθ}_{r}}{dt} = - γeω_ref,

\frac{{dθ}_{the y}}{dt} = γωe

To update, you have to

If the error e is not equal to zero, the function V will decrease, and it can be concluded that the error will tend to zero, and it is judged that the controlled object model reference adaptive control system is stable, and the differential equation of the adaptive law is

\frac{θ_{r} (k) - θ_{r} (k - 1)}{T_{the s}} = - γ e (k) ω_ref (k),

\frac{θ_{the y} (k) - θ_{the y} (k - 1)}{T_{the s}} = γ e (k) ω (k),

Then the difference equation of moment of inertia and viscous damping coefficient is

\frac{J (k) - J (k - 1)}{T_{the s}} = - J_{m} γe (k) ω_ref (k),

\frac{B (k) - B (k - 1)}{T_{the s}} = - B_{m} γ e (k) ω_ref (k) - γe (k) ω (k),

where T _s is the sampling period, θ _r (k), θ _y (k), e(k), ω(k), ω_ref(k), J(k), B(k) and θ _r (k-1 ), θ _y (k-1), J(k-1), B(k-1) are the values of the kth and k-1th sampling period respectively.

4. A kind of AC position servo system model parameter online identification and control method according to claim 1, 2 or 3, characterized in that: in said step 3), the position controller adopts PD control, and the transfer function is expressed as G _c (s)=K _p +K _d s, then the closed-loop transfer function of the position loop is

Φ (the s) = \frac{K_{p} + K_{d} the s}{{js}^{2} + (B + K_{d}) the s + K_{p}},

K _d ＝2ζω _n -B, among them, K _p +K _d s is the position controller, K _p is the proportional coefficient, K _d is the differential coefficient, s is the Laplace variable; Let ω _n denote the expected nature of the position loop frequency, ζ represents the desired damping ratio of the position loop.