CN104102131B

Movatterモバイル変換

Info

Publication number: CN104102131B
Application number: CN201410280272.1A
Authority: CN
Inventors: 张乐; 李海生; 张日东; 吴锋; 邹洪波
Original assignee: Hangzhou Dianzi University
Current assignee: Hangzhou Dianzi University
Priority date: 2014-06-20
Filing date: 2014-06-20
Publication date: 2016-08-24
Anticipated expiration: 2034-06-20
Also published as: CN104102131A

Abstract

本发明提出了一种无穷时域优化的批次过程的线性二次容错控制方法。本发明通过结合状态变量和输出跟踪误差，建立了批次过程的扩展状态空间模型，进而在无限时域中设计控制器。该方法不仅保证了系统在未知扰动和执行器故障情况下有良好的跟踪性能，同时也保证了形式简单并满足实际工业过程的需要。The invention proposes a linear quadratic fault-tolerant control method of batch process optimized in infinite time domain. The invention establishes the extended state space model of the batch process by combining the state variable and the output tracking error, and then designs the controller in the infinite time domain. This method not only guarantees good tracking performance of the system in the case of unknown disturbances and actuator failures, but also ensures a simple form and meets the needs of actual industrial processes.

Description

Translated fromChinese

无穷时域优化的批次过程的线性二次容错控制方法A Linear Quadratic Fault-Tolerant Control Method for Batch Processes Optimized in Infinite Time Domain

技术领域technical field

本发明属于工业自动化技术领域，涉及一种无穷时域优化的批次过程的线性二次容错控制方法。The invention belongs to the technical field of industrial automation, and relates to a linear quadratic fault-tolerant control method of an infinite time-domain optimized batch process.

背景技术Background technique

随着社会的高速发展，人们对高品质批次生产的要求越来越高。这种高要求导致了生产需要在更加复杂的条件下操作，系统发生故障的概率也相应的增加了。在这些故障中，执行器故障是最常见的一种故障。由于存在摩擦、死区、饱和等特性，执行器在执行过程中不可避免地会出现一些故障，这导致它很难达到指定或理想的位置。如果故障没有被及时的检测并校正，生产性能必然会恶化，甚至会导致设备和人员的安全问题。因此，提出一种新的控制方法来解决执行器在执行过程中发生故障从而保证系统控制性能是十分必要的。With the rapid development of society, people's requirements for high-quality batch production are getting higher and higher. This high demand has led to the need for production to operate under more complex conditions, and the probability of system failure has increased accordingly. Among these failures, actuator failure is the most common one. Due to the characteristics of friction, dead zone, saturation, etc., the actuator will inevitably have some failures during the execution process, which makes it difficult for it to reach the specified or ideal position. If the failure is not detected and corrected in time, the production performance will inevitably deteriorate, and even cause safety problems for equipment and personnel. Therefore, it is necessary to propose a new control method to solve the failure of the actuator in the execution process so as to ensure the control performance of the system.

发明内容Contents of the invention

本发明的目的是针对批次生产过程中可能遇到执行器发生故障的问题，提出了一种无穷时域优化的批次过程的线性二次容错控制方法。该方法通过结合状态变量和输出跟踪误差，建立了批次过程的扩展状态空间模型，进而在无限时域中设计控制器。该方法不仅保证了系统在未知扰动和执行器故障情况下有良好的跟踪性能，同时也保证了形式简单并满足实际工业过程的需要。The purpose of the present invention is to propose a linear quadratic fault-tolerant control method for infinite time-domain optimized batch process aiming at the problem that the actuator may fail in the batch production process. The method builds an extended state-space model of the batch process by combining state variables and output tracking errors, and then designs the controller in the infinite time domain. This method not only guarantees good tracking performance of the system in the case of unknown disturbances and actuator failures, but also ensures a simple form and meets the needs of actual industrial processes.

本发明的技术方案是通过数据采集、模型建立、预测机理、优化等手段，确立了一种无穷时域优化的批次过程的线性二次容错控制方法，利用该方法可有效提高系统在未知扰动和执行器故障情况下的控制性能。The technical solution of the present invention is to establish a linear quadratic fault-tolerant control method for batch processes optimized in infinite time domain by means of data collection, model building, prediction mechanism, optimization, etc., which can effectively improve the system's performance in unknown disturbances. and control performance under actuator failure conditions.

本发明方法的步骤包括：The steps of the inventive method comprise:

步骤(1).建立被控对象的扩展状态空间模型，具体方法是：Step (1). Establish the extended state space model of the controlled object, the specific method is:

a.利用实时数据驱动的方法建立局部预测模型，具体方法是：建立批次过程的实时运行数据库，通过数据采集装置采集实时过程运行数据，将采集的实时过程运行数据作为数据驱动的样本集合其中，表示第i组工艺参数的输入值，y(i)表示第i组工艺参数的输出值，N表示采样总数；以该对象的实时过程运行数据集合为基础建立基于最小二乘算法的离散差分方程形式的局部受控自回归滑动平均模型：a. Use the real-time data-driven method to establish a local prediction model. The specific method is: establish a real-time operation database of the batch process, collect real-time process operation data through the data acquisition device, and use the collected real-time process operation data as a data-driven sample set in, Represents the input value of the i-th group of process parameters, y(i) represents the output value of the i-th group of process parameters, and N represents the total number of samples; based on the real-time process operation data set of the object, a discrete difference equation based on the least squares algorithm is established A locally controlled autoregressive moving average model of the form:

其中，y_L(k)表示k时刻局部预测模型的工艺参数的输出值，表示通过辨识得到的模型参数的集合，表示局部预测模型的工艺参数的过去时刻的输入和输出数据的集合，u(k-d-1)表示k-d-1时刻工艺参数对应的控制变量，d+1为实际过程的时滞，Τ为矩阵的转置符号。Among them, y_L (k) represents the output value of the process parameter of the local prediction model at time k, Represents the set of model parameters obtained through identification, Represents the collection of input and output data of the process parameters of the local prediction model in the past, u(kd-1) represents the control variable corresponding to the process parameters at kd-1 time, d+1 is the time lag of the actual process, and T is the matrix Transpose symbols.

采用的辨识手段为：The identification methods used are:

其中，和P为辨识中的两个矩阵，γ为遗忘因子，为单位矩阵。in, and P are two matrices in identification, γ is the forgetting factor, is the identity matrix.

b.利用a步骤中得到的系数，建立批次过程的差分方程模型，其形式为：b. Using the coefficients obtained in step a, establish a differential equation model for the batch process, which is in the form:

Δy(k)+HΔy(k-1)＝FΔu(k-d-1)Δy(k)+HΔy(k-1)=FΔu(k-d-1)

其中,Δ是差分算子，F,H为a步骤中通过辩识得到的参数，d为时滞项。Among them, Δ is the difference operator, F and H are the parameters obtained through identification in step a, and d is the delay term.

c.根据b步骤中的差分方程，建立批次过程的状态空间模型，形式如下：c. According to the difference equation in step b, establish a state-space model of the batch process, the form is as follows:

$\{\begin{matrix} Δx Δx ((k k + + 11)) = = {A A}_{m m} Δx Δx ((k k)) + + {B B}_{m m} Δu Δu ((k k)) \\ Δy Δy ((k k)) = = {C C}_{m m} Δx Δx ((k k)) \end{matrix}$

其中，in,

$Δx Δx ((k k + + 11)) = = (\begin{matrix} Δy Δy ((k k + + 11)) \\ Δu Δu ((k k)) \\ Δu Δu ((k k - - 11)) \\ \cdot \cdot \\ \cdot \cdot \\ \cdot \cdot \\ Δu Δu ((k k - - d d + + 11)) \end{matrix}),, Δx Δx ((k k)) = = (\begin{matrix} Δy Δy ((k k)) \\ Δu Δ u ((k k - - 11)) \\ Δu Δ u ((k k - - 22)) \\ \cdot \cdot \\ \cdot \cdot \\ \cdot \cdot \\ Δu Δ u ((k k - - d d)) \end{matrix})$

C_m＝(1 0 0 … 0)C_m = (1 0 0 ... 0)

其中,A_m为(d+1)×(d+1)阶矩阵,B_m为(d+1)×1阶矩阵,C_m为1×(d+1)阶矩阵。Among them, A_m is a (d+1)×(d+1) order matrix, B_m is a (d+1)×1 order matrix, and C_m is a 1×(d+1) order matrix.

d.将c步骤中得到的状态空间模型转换为包含状态变量和输出跟踪误差的扩展状态空间模型，形式如下：d. Convert the state-space model obtained in step c into an extended state-space model including state variables and output tracking errors, in the following form:

z(k+1)＝Az(k)+BΔu(k)＝Az(k)+Bu(k)-Bu(k-1)z(k+1)=Az(k)+BΔu(k)=Az(k)+Bu(k)-Bu(k-1)

式中，In the formula,

$z z ((k k + + 11)) = = [\begin{matrix} Δx Δx ((k k + + 11)) \\ e e ((k k + + 11)) \end{matrix}],, z z ((k k)) = = [\begin{matrix} Δx Δx ((k k)) \\ e e ((k k)) \end{matrix}]$

$A A = = (\begin{matrix} {A A}_{m m} & 00 \\ {C C}_{m m} {A A}_{m m} & 11 \end{matrix}),, B B = = [\begin{matrix} {B B}_{m m} \\ {C C}_{m m} {B B}_{m m} \end{matrix}]$

e(k)＝r(k)-y(k)e(k)=r(k)-y(k)

其中，r(k)为k时刻的理想输出值，e(k)为k时刻理想输出值与实际输出值之间的差值。Among them, r(k) is the ideal output value at time k, and e(k) is the difference between the ideal output value and the actual output value at time k.

步骤(2).设计被控对象的无穷时域优化的批次过程线性二次容错控制器，具体方法是：Step (2). Design the batch process linear quadratic fault-tolerant controller of the infinite time domain optimization of the controlled object, the specific method is:

a.选取批次处理过程的目标函数，形式如下：a. Select the objective function of the batch processing process, the form is as follows:

$\begin{matrix} J J = = {Σ Σ}_{k k = = {k k}_{00}}^{{k k}_{f f} - - 11} [[z z {((k k))}^{T T} Qz Qz ((k k)) + + Δu Δu {((k k))}^{T T} RΔu RΔu ((k k))]] + + z z {(({k k}_{f f}))}^{T T} Qz Qz (({k k}_{f f})) \\ Q Q = = diag diag {{{q q}_{j j 11},, {q q}_{j j 22},, \cdot \cdot \cdot \cdot \cdot \cdot,, {q q}_{jp jp + + q q - - 11},, {q q}_{je je}}} \end{matrix}$

其中，Q＞0,R＞0分别为过程状态的加权矩阵、输入加权矩阵，[k₀,k_f]为优化时域；q_j1,q_j2,…q_jp+q+1为过程状态的权重系数，q_je为输出跟踪误差的权重系数并且取q_je＝1。Among them, Q>0, R>0 are the weighting matrix of the process state and the input weighting matrix respectively, [k₀ , k_f ] is the optimization time domain; q_j1 , q_j2 ,…q_jp+q+1 are the process state Weight coefficient, q_je is the weight coefficient of the output tracking error and q_je =1.

b.利用庞特里亚金最小值原理将a步骤的目标函数写成如下形式：b. Use the Pontryagin minimum principle to write the objective function of step a as follows:

${H h}_{k k} = = [[z z {((k k))}^{T T} Qz Qz ((k k)) + + Δ Δ {u u}^{T T} ((k k)) RΔu RΔu ((k k))]] + + {p p}_{k k + + 11}^{T T} [[Az Az ((k k)) + + BΔu BΔu ((k k))]]$

其中，p_k+1为拉格朗日乘子。Among them, p_k+1 is the Lagrangian multiplier.

c.求并令其等于零，可得c. seek and set it equal to zero, we get

$Δu Δ u ((k k)) = = - - \frac{11}{22} {R R}^{- - 11} {B B}^{T T} {p p}_{k k + + 11}$

联合进一步可以得到joint further can be obtained

$\begin{matrix} Δu Δ u ((k k)) = = - - {R R}^{- - 11} {B B}^{T T} {[[I I + + {H h}_{{k k + + 11,, k k}_{f f}} {BR BR}^{- - 11} {B B}^{T T}]]}^{- - 11} {H h}_{{k k + + 11,, k k}_{f f}} Az Az ((k k)) \\ {H h}_{{k k,, k k}_{f f}} = = {A A}^{T T} [[I I + + {H h}_{{k k + + 11,, k k}_{f f}} {BR BR}^{- - 11} {B B}^{T T} {]]}^{- - 11} {H h}_{{k k + + 11,, k k}_{f f}} A A + + Q Q \\ = = {A A}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} A A - - {A A}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} B B {((R R + + {B B}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} B B))}^{- - 11} {B B}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} A A + + Q Q \\ {H h}_{{k k}_{f f},, {k k}_{f f}} = = Q Q \end{matrix}$

其中，R^-1表示输入加权矩阵的逆矩阵。Among them, R^-1 represents the inverse matrix of the input weighting matrix.

d.令k_f趋于正无穷，可得d. Let k_f tend to be positive infinity, we can get

Δu(k)＝-R^-1B^Τ[I+K_∞BR^-1B^Τ]^-1K_∞Az(k)Δu(k)=-R^-1 B^Τ [I+K_∞ BR^-1 B^Τ ]^-1 K_∞ Az(k)

K_∞＝A^Τ[I+K_∞BR^-1B^Τ]^-1K_∞A+QK_∞ ＝A^Τ [I+K_∞ BR^-1 B^Τ ]^-1 K_∞ A+Q

＝A^ΤK_∞A-A^ΤK_∞B(R+B^ΤK_∞B)^-1B^ΤK_∞A+Q=A^Τ K_∞ AA^Τ K_∞ B(R+B^Τ K_∞ B)^-1 B^Τ K_∞ A+Q

u(k)＝u(k-1)+Δu(k)u(k)=u(k-1)+Δu(k)

其中，K_∞为k_f趋于正无穷时的值。Among them, K_∞ is when k_f tends to positive infinity value.

e.将d步骤中得到的控制量u(k)作用于被控对象。e. Apply the control quantity u(k) obtained in step d to the controlled object.

f.在下一时刻，依照a到e的步骤继续求解新的控制量u(k+1)，依次循环。f. At the next moment, continue to solve the new control variable u(k+1) according to the steps from a to e, and cycle in turn.

本发明将将优化时域扩展到了无穷时域，提出了一种无穷时域优化的批次过程的线性二次容错控制方法。该方法弥补了传统线性二次控制方法的不足，有效地保证了系统在未知扰动和执行器故障情况下的良好跟踪性能。The invention extends the optimized time domain to the infinite time domain, and proposes a linear quadratic fault-tolerant control method for batch processes optimized in the infinite time domain. This method makes up for the shortcomings of the traditional linear quadratic control method, and effectively guarantees the good tracking performance of the system in the case of unknown disturbances and actuator failures.

具体实施方式detailed description

以注塑过程中注射速度的控制为例Taking the control of injection speed in the injection molding process as an example

注塑过程中注射速度的控制是一个典型的批次处理过程，调节手段为控制比例阀阀门的开度。The control of injection speed in the injection molding process is a typical batch process, and the adjustment method is to control the opening of the proportional valve.

步骤(1).建立注射过程的扩展状态空间模型，具体方法是：Step (1). Establish the extended state-space model of the injection process, the specific method is:

a.建立注射过程的实时运行数据库，通过数据采集装置采集实时过程运行数据将采集的实时过程运行数据作为数据驱动的样本集合其中，表示第i组比例阀阀门的开度，y(i)表示第i组实际输出的注射速度；以注射速度过程的实时过程运行数据集合为基础建立基于最小二乘算法的离散差分方程形式的局部受控自回归滑动平均模型：a. Establish a real-time operation database of the injection process, collect real-time process operation data through the data acquisition device, and use the collected real-time process operation data as a data-driven sample collection in, Indicates the opening degree of the i-th proportional valve, and y(i) indicates the actual output injection speed of the i-th group; based on the real-time process operation data set of the injection speed process, the local Controlled autoregressive moving average model:

其中，y_L(k)表示k时刻注射速度的实际输出值，θ表示通过辨识得到的模型参数的集合，表示注射过程局部预测模型的过去时刻的输入和输出数据的集合，u(k-d-1)表示k-d-1时刻注射过程中比例阀阀门的开度，d+1为对应注射过程的时滞，Τ为矩阵的转置符号。Among them, y_L (k) represents the actual output value of the injection speed at time k, θ represents the set of model parameters obtained through identification, Indicates the collection of input and output data of the local prediction model of the injection process in the past, u(kd-1) indicates the opening of the proportional valve in the injection process at kd-1 time, d+1 is the time lag of the corresponding injection process, Τ is the transpose symbol of the matrix.

采用的辨识手段为：The identification methods used are:

b.将a步骤中得到的注射过程模型转换为差分方程的形式：b. Convert the injection process model obtained in step a into the form of a differential equation:

Δy(k)+HΔy(k-1)＝FΔu(k-d-1)Δy(k)+HΔy(k-1)=FΔu(k-d-1)

c.选取状态变量,根据b步骤中的差分方程，建立注射过程的状态空间模型，形式如下：c. Select the state variable, according to the difference equation in step b, establish the state space model of the injection process, the form is as follows:

$\{\begin{matrix} Δx Δx ((k k + + 11)) = = {A A}_{m m} Δx Δx ((k k)) + + {B B}_{m m} Δu Δ u ((k k)) \\ Δy Δy ((k k)) = = {C C}_{m m} Δx Δx ((k k)) \end{matrix}$

其中，in,

$Δx Δx ((k k + + 11)) = = (\begin{matrix} Δy Δy ((k k + + 11)) \\ Δu Δ u ((k k)) \\ Δu Δ u ((k k - - 11)) \\ \cdot &Center Dot; \\ \cdot \cdot \\ \cdot \cdot \\ Δu Δ u ((k k - - d d + + 11)) \end{matrix}),, Δx Δx ((k k)) = = (\begin{matrix} Δy Δy ((k k)) \\ Δu Δu ((k k - - 11)) \\ Δu Δu ((k k - - 22)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ Δu Δu ((k k - - d d)) \end{matrix})$

C_m＝(1 0 0 … 0)C_m = (1 0 0 ... 0)

d.将c步骤中得到的注射过程的状态空间模型转换为包含状态变量和输出跟踪误差的扩展状态空间模型，形式如下：d. Convert the state-space model of the injection process obtained in step c into an extended state-space model including state variables and output tracking errors, in the following form:

式中，In the formula,

e(k)＝r(k)-y(k)e(k)=r(k)-y(k)

e(k)为k时刻理想注射速度值与实际注射速度值之间的差值。e(k) is the difference between the ideal injection speed value and the actual injection speed value at time k.

步骤(2).设计注射过程的无穷时域优化的批次过程线性二次容错控制器，具体方法是：Step (2). The batch process linear quadratic fault-tolerant controller of the infinite time domain optimization of the design injection process, the specific method is:

a.选取注射过程的目标函数，形式如下：a. Select the objective function of the injection process, the form is as follows:

$\begin{matrix} J J = = {Σ Σ}_{k k = = {k k}_{00}}^{{k k}_{f f} - - 11} [[z z {((k k))}^{T T} Qz Qz ((k k)) + + Δu Δu {((k k))}^{T T} RΔu RΔu ((k k))]] + + z z {(({k k}_{f f}))}^{T T} {Q Q}_{f f} z z (({k k}_{f f})) \\ Q Q = = diag diag {{{q q}_{j j 11},, {q q}_{j j 22},, \cdot \cdot \cdot \cdot \cdot \cdot,, {q q}_{jp jp + + q q - - 11},, {q q}_{je je}}} \end{matrix}$

其中，Q＞0,R＞0分别注射过程状态的加权矩阵、输入加权矩阵，[k₀,k_f]为注射过程的优化时域；q_j1,q_j2,…q_jp+q+1为注射速度过程状态的权重系数，q_je为输出跟踪误差的权重系数并且取q_je＝1。Among them, Q>0, R>0 are the weighting matrix of the injection process state and the input weighting matrix respectively, [k₀ ,k_f ] is the optimal time domain of the injection process; q_j1 ,q_j2 ,…q_jp+q+1 is The weight coefficient of the injection speed process state, q_je is the weight coefficient of the output tracking error and q_je =1.

c.求并令其等于零，可得c. seek and set it equal to zero, we get

联合 $p_{k} = 2 H_{{k, k}_{f}} z (k)$ 可得joint $p_{k} = 2 h_{{k, k}_{f}} z (k)$ Available

$\begin{matrix} Δu Δu ((k k)) = = - - {R R}^{- - 11} {B B}^{T T} {[[I I + + {H h}_{{k k + + 11,, k k}_{f f}} {BR BR}^{- - 11} {B B}^{T T}]]}^{- - 11} {H h}_{{k k + + 11,, k k}_{f f}} Az Az ((k k)) \\ {H h}_{{k k,, k k}_{f f}} = = {A A}^{T T} [[I I + + {H h}_{{k k + + 11,, k k}_{f f}} {BR BR}^{- - 11} {B B}^{T T} {]]}^{- - 11} {H h}_{{k k + + 11,, k k}_{f f}} A A + + Q Q \\ = = {A A}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} A A - - {A A}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} B B {((R R + + {B B}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} B B))}^{- - 11} {B B}^{T T} {H h}_{{k k + + 11,, k k}_{f f}} A A + + Q Q \\ {H h}_{{k k}_{f f},, {k k}_{f f}} = = Q Q \end{matrix}$

Δu(k)＝-R^-1B^T[I+K_∞BR^-1B^T]^-1K_∞Az(k)Δu(k)＝-R^-1 B^T [I+K_∞ BR^-1 B^T ]^-1 K_∞ Az(k)

K_∞＝A^T[I+K_∞BR^-1B^T]^-1K_∞A+QK_∞ ＝A^T [I+K_∞ BR^-1 B^T ]^-1 K_∞ A+Q

＝A^TK_∞A-A^TK_∞B(R+B^TK_∞B)^-1B^TK_∞A+Q＝A^T K_∞ AA^T K_∞ B(R+B^T K_∞ B)^-1 B^T K_∞ A+Q

u(k)＝u(k-1)+Δu(k)u(k)=u(k-1)+Δu(k)

e.将d步骤中得到的比例阀阀门开度u(k)作用于注塑机。e. Apply the valve opening u(k) of the proportional valve obtained in step d to the injection molding machine.

f.在下一时刻，依照a到e的步骤继续求解新的比例阀阀门的开度u(k+1)，并依次循环。f. At the next moment, continue to solve the opening degree u(k+1) of the new proportional valve according to the steps from a to e, and cycle in turn.