CN105573125A

CN105573125A - Pneumatic system position adaption control method aiming at unknown control direction

Info

Publication number: CN105573125A
Application number: CN201610164275.8A
Authority: CN
Inventors: 任海鹏; 樊军涛
Original assignee: Xian University of Technology
Current assignee: Xian University of Technology
Priority date: 2016-03-22
Filing date: 2016-03-22
Publication date: 2016-05-11
Anticipated expiration: 2036-03-22
Also published as: CN105573125B

Abstract

The invention discloses a position self-adaptive control method of a pneumatic system aiming at an unknown control direction. The steps include: step 1) establishing a model of a pneumatic position servo system, and the control target is to make The displacement of the piston can track the required desired output; step 2) introduce the Nussbaum gain function, and set the adaptive controller of the pneumatic position servo system; step 3) limit the control signal; step 4) the pneumatic position servo system The values of the unknown model parameters are estimated, and the estimated results are used to update the parameters of the adaptive controller in real time. The computer sends the limited control signal to the proportional valve through the D/A converter, and adjusts the piston in the rodless cylinder in real time. displacement. The method of the invention does not need to know the direction of the control gain, does not need to add pressure detection hardware or software observation algorithm, has better tracking effect and higher control precision.

Description

A Pneumatic System Position Adaptive Control Method for Unknown Control Direction

技术领域technical field

本发明属于气动系统位置跟踪控制技术领域，涉及一种针对控制方向未知的气动系统位置自适应控制方法。The invention belongs to the technical field of pneumatic system position tracking control, and relates to a pneumatic system position self-adaptive control method aiming at unknown control direction.

背景技术Background technique

气动系统(即气动位置伺服系统)以其结构简单、功率体积比高、安全防爆、清洁和使用寿命长等特点，在工业自动化领域得到了广泛应用。但是，气动系统具有强非线性、参数时变性和模型不确定性，这些因素都增加了气动位置伺服系统的控制难度，如何提高气动位置伺服系统的轨迹跟踪性能，是当前气动位置伺服系统研究的一个重要方向。气动元件尤其是比例阀性价比的提高和微处理器速度的不断提高，给高性能气动跟踪控制系统带来了机遇。Pneumatic system (i.e. pneumatic position servo system) has been widely used in the field of industrial automation due to its simple structure, high power-to-volume ratio, safety and explosion-proof, cleanliness and long service life. However, the pneumatic system has strong nonlinearity, time-varying parameters, and model uncertainty. These factors have increased the control difficulty of the pneumatic position servo system. How to improve the trajectory tracking performance of the pneumatic position servo system is the current research topic of the pneumatic position servo system. an important direction. The improvement of the cost performance of pneumatic components, especially proportional valves, and the continuous improvement of microprocessor speed have brought opportunities to high-performance pneumatic tracking control systems.

气动位置伺服系统比例阀至气缸两侧输气管的连接顺序决定了控制作用的方向，实际中连接方向通常固定，但是对一些便携设备可能现场安装过程中出现失误导致控制方向不确定。现有的气动位置伺服系统的控制方法均需假设系统的控制增益符号已知，而当系统控制增益符号未知时，现有的很多控制方法很难实现有效控制。The connection sequence of the proportional valve of the pneumatic position servo system to the air pipes on both sides of the cylinder determines the direction of the control action. In practice, the connection direction is usually fixed, but for some portable devices, mistakes may occur during the on-site installation process, resulting in uncertain control direction. The existing control methods of the pneumatic position servo system all need to assume that the sign of the control gain of the system is known, and when the sign of the control gain of the system is unknown, many existing control methods are difficult to achieve effective control.

发明内容Contents of the invention

本发明的目的在于提供一种针对控制方向未知的气动系统位置自适应控制方法，解决了现有技术需要预先已知气动位置伺服系统控制增益的方向，而当系统控制增益符号(方向)未知时，现有的很多自适应控制方法难以实现的问题。The purpose of the present invention is to provide a kind of pneumatic system position self-adaptive control method for unknown control direction, solve the prior art need to know the direction of control gain of pneumatic position servo system in advance, and when the sign (direction) of system control gain is unknown , the problem that many existing adaptive control methods are difficult to realize.

本发明采用的技术方案是，一种针对控制方向未知的气动系统位置自适应控制方法，该方法按照以下步骤具体实施：The technical solution adopted by the present invention is a position adaptive control method for a pneumatic system whose control direction is unknown, and the method is specifically implemented according to the following steps:

步骤1、建立气动位置伺服系统的模型Step 1. Establish a model of the pneumatic position servo system

根据气动位置伺服系统的工作机理，忽略摩擦，同时进行线性化处理，得到线性化数学模型如式(1)所示：According to the working mechanism of the pneumatic position servo system, the friction is ignored, and the linearization process is carried out at the same time, and the linearized mathematical model is obtained as shown in formula (1):

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{x x}}_{11} = = {x x}_{22} \\ {\overset{\cdot &Center Dot;}{x x}}_{22} = = {x x}_{33} \\ {\overset{\cdot &Center Dot;}{x x}}_{33} = = {a a}_{11} {x x}_{11} + + {a a}_{22} {x x}_{22} + + {a a}_{33} {x x}_{33} + + b b u u \\ y the y = = {x x}_{11} \end{matrix},, - - - - - - ((11))$

其中x₁、x₂、x₃为系统状态变量，物理含义分别表示活塞(1)的位置、速度和加速度，分别对应为x₁、x₂、x₃的一阶导数，u为控制输入，a₁，a₂，a₃为未知模型参数，b为大小和方向均未知的系统控制增益，控制目标是在比例阀输出正、反两种连接方式时，使活塞的位移y都能跟踪所要求的期望输出y_d；Among them, x ₁ , x ₂ , and x ₃ are system state variables, and their physical meanings represent the position, velocity and acceleration of the piston (1) respectively, Corresponding to the first order derivatives of x ₁ , x ₂ , x ₃ respectively, u is the control input, a ₁ , a ₂ , a ₃ are unknown model parameters, b is the system control gain with unknown magnitude and direction, and the control target is at When the proportional valve outputs positive and negative connections, the displacement y of the piston can track the required desired output y _d ;

步骤2、引入Nussbaum增益函数，设置气动位置伺服系统的自适应控制器Step 2. Introduce the Nussbaum gain function to set up the adaptive controller of the pneumatic position servo system

对上述的式(1)选取自适应控制器，自适应控制器的模型表达式分别如式(2)和式(3)所示：The adaptive controller is selected for the above formula (1), and the model expressions of the adaptive controller are shown in formula (2) and formula (3):

$\overset{\cdot &Center Dot;}{ξ ξ} = = {z z}_{33} (({c c}_{33} {z z}_{33} + + {\overset{^^}{θ θ}}^{T T} ω ω)),, - - - - - - ((22))$

${u u}^{' '} = = N N ((ξ ξ)) (({c c}_{33} {z z}_{33} + + {\overset{^^}{θ θ}}^{T T} ω ω)),, - - - - - - ((33))$

其中N(ξ)为Nussbaum型偶函数，z₁＝x₁-y_d，z₂＝x₂-α₁，z₃＝x₃-α₂，θ＝[1a₁a₂a₃]^T为参数向量，为θ的估计值，为状态向量，为期望输出y_d的一阶导数，为α₁的一阶导数，为α₂的一阶导数，α₁、α₂、z₁、z₂、z₃为中间变量，c₁、c₂和c₃为设置参数；Where N(ξ) is a Nussbaum-type even function, z ₁ =x ₁ -y _d , z ₂ =x ₂ -α ₁ , z ₃ ＝x ₃ -α ₂ , θ＝[1a ₁ a ₂ a ₃ ] ^T is the parameter vector, is the estimated value of θ, is the state vector, is the first derivative of the expected output y _d , is the first derivative of α ₁ , is the first derivative of α ₂ , α ₁ , α ₂ , z ₁ , z ₂ , z ₃ are intermediate variables, c ₁ , c ₂ and c ₃ are setting parameters;

步骤3、对控制信号u′进行限幅，如式(4)：Step 3. Limit the control signal u′, as shown in formula (4):

$u u = = \{\begin{matrix} {U u}_{m m a a x x} & {u u}^{' '} > > {U u}_{m m a a x x} \\ {u u}^{' '} & - - {U u}_{max max} \leq \leq {u u}^{' '} \leq \leq {U u}_{m m a a x x} \\ - - {U u}_{m m a a x x} & {u u}^{' '} < < - - {U u}_{m m a a x x} \end{matrix},, - - - - - - ((44))$

U_max为控制量限幅值；U _max is the limit value of the control quantity;

步骤4、对气动位置伺服系统的未知模型参数的值进行估计Step 4. Estimate the values of the unknown model parameters of the pneumatic position servo system

未知模型参数的估计值参照式(5)进行计算：The estimated values of the unknown model parameters are calculated with reference to formula (5):

$\overset{\cdot \cdot}{\overset{^^}{θ θ}} = = {Γωz Γωz}_{33},, - - - - - - ((55))$

其中的Γ是正定矩阵，为自适应增益，为的一阶导数，Among them, Γ is a positive definite matrix, which is the adaptive gain, for The first derivative of ,

将式(5)估计得到的数值用于实时更新式(2)中的参数，计算机通过D/A转换器将经过限幅的控制信号输给比例阀，实时调节无杆气缸中活塞的位移y。Estimated by formula (5) The value is used to update the parameters in formula (2) in real time, and the computer sends the limited control signal to the proportional valve through the D/A converter to adjust the displacement y of the piston in the rodless cylinder in real time.

本发明的有益效果是，不需要预先已知系统控制增益的方向；不需要增加压力检测硬件或软件观测算法；不需要对象的模型的非线性项和不确定参数界，便能够实施有效控制；与现有一些控制方法相比，能够获得更好的跟踪效果和更高的控制精度。The beneficial effect of the present invention is that the direction of the system control gain does not need to be known in advance; the pressure detection hardware or software observation algorithm does not need to be added; the nonlinear term and the uncertain parameter boundary of the model of the object are not needed, and effective control can be implemented; Compared with some existing control methods, better tracking effect and higher control precision can be obtained.

附图说明Description of drawings

图1是本发明方法的控制对象(比例阀控制无杆气缸)的结构示意图；Fig. 1 is the structural representation of the control object (proportional valve control rodless cylinder) of the inventive method;

图2是采用本发明方法在比例阀正向连接时跟踪正弦信号的实验结果；Fig. 2 is the experimental result of tracking the sinusoidal signal when the proportional valve is connected in the forward direction by adopting the inventive method;

图3是采用本发明方法在比例阀正向连接时跟踪S曲线的实验结果；Fig. 3 is the experimental result of tracking the S-curve when the proportional valve is connected in the forward direction by adopting the method of the present invention;

图4是采用本发明方法在比例阀正向连接时跟踪多频正弦信号的实验结果；Fig. 4 is the experimental result of tracking the multi-frequency sinusoidal signal when the proportional valve is connected in the forward direction by adopting the inventive method;

图5是采用本发明方法在比例阀反向连接时跟踪正弦信号的实验结果；Fig. 5 is to adopt the inventive method to track the experimental result of sinusoidal signal when proportional valve reverse connection;

图6是采用本发明方法在比例阀反向连接时跟踪S曲线的实验结果；Fig. 6 is the experimental result of tracking the S curve when the proportional valve is reversely connected by adopting the method of the present invention;

图7是采用本发明方法在比例阀反向连接时跟踪多频正弦信号的实验结果；Fig. 7 is the experimental result of tracking the multi-frequency sinusoidal signal when the proportional valve is reversely connected by adopting the method of the present invention;

图8是采用滑模变结构方法1在比例阀正向连接时跟踪正弦信号的实验结果；Fig. 8 is the experimental result of tracking the sinusoidal signal when the proportional valve is connected in the forward direction by using the sliding mode variable structure method 1;

图9是采用滑模变结构方法1在比例阀正向连接时跟踪S曲线的实验结果；Fig. 9 is the experimental result of tracking the S-curve when the proportional valve is forward connected using the sliding mode variable structure method 1;

图10是采用滑模变结构方法1在比例阀正向连接时跟踪多频正弦信号的实验结果；Figure 10 is the experimental result of tracking multi-frequency sinusoidal signals when the proportional valve is connected in the forward direction using sliding mode variable structure method 1;

图11是采用滑模变结构方法1在比例阀反向连接时跟踪正弦信号的实验结果；Fig. 11 is the experimental result of tracking the sinusoidal signal when the proportional valve is reversely connected using the sliding mode variable structure method 1;

图12是采用滑模变结构方法1在比例阀反向连接时跟踪S曲线的实验结果；Fig. 12 is the experimental result of tracking the S-curve when the proportional valve is reversely connected using the sliding mode variable structure method 1;

图13是采用滑模变结构方法1在比例阀反向连接时跟踪多频正弦信号的实验结果；Fig. 13 is the experimental result of tracking the multi-frequency sinusoidal signal when the proportional valve is reversely connected using the sliding mode variable structure method 1;

图14是采用滑模变结构方法2在比例阀正向连接时跟踪正弦信号的实验结果；Fig. 14 is the experimental result of tracking the sinusoidal signal when the proportional valve is connected in the forward direction by adopting the sliding mode variable structure method 2;

图15是采用滑模变结构方法2在比例阀正向连接时跟踪S曲线的实验结果；Fig. 15 is the experimental result of tracking the S-curve when the proportional valve is forward connected using the sliding mode variable structure method 2;

图16是采用滑模变结构方法2在比例阀正向连接时跟踪多频正弦信号的实验结果；Fig. 16 is the experimental result of tracking the multi-frequency sinusoidal signal when the proportional valve is connected in the forward direction by adopting the sliding mode variable structure method 2;

图17是采用反步自适应方法1在比例阀正向连接时跟踪正弦信号的实验结果；Fig. 17 is the experimental result of tracking the sinusoidal signal when the proportional valve is connected in the forward direction by adopting backstep adaptive method 1;

图18是采用反步自适应方法1在比例阀正向连接时跟踪S曲线的实验结果；Fig. 18 is the experimental result of tracking the S-curve when the proportional valve is connected in the forward direction by adopting backstep adaptive method 1;

图19是采用反步自适应方法1在比例阀正向连接时跟踪多频正弦信号的实验结果；Fig. 19 is the experimental result of tracking the multi-frequency sinusoidal signal when the proportional valve is connected in the forward direction by adopting backstep adaptive method 1;

图20是采用反步自适应方法2在比例阀正向连接时跟踪正弦信号的实验结果；Fig. 20 is the experimental result of tracking the sinusoidal signal when the proportional valve is connected in the forward direction by adopting backstep adaptive method 2;

图21是采用反步自适应方法2在比例阀正向连接时跟踪S曲线的实验结果；Fig. 21 is the experimental result of tracking the S-curve when the proportional valve is connected in the forward direction by adopting backstep adaptive method 2;

图22是采用反步自适应方法2在比例阀正向连接时跟踪多频正弦信号的实验结果。Fig. 22 is the experimental result of tracking multi-frequency sinusoidal signals when the proportional valve is forward connected using the backstep adaptive method 2.

图中，1.活塞，2.负载，3.无杆气缸，4.位移检测仪，5.比例阀，6.计算机，7.减压阀，8.气泵，9.储气罐。In the figure, 1. Piston, 2. Load, 3. Rodless cylinder, 4. Displacement detector, 5. Proportional valve, 6. Computer, 7. Pressure reducing valve, 8. Air pump, 9. Air storage tank.

具体实施方式detailed description

下面结合附图和具体实施例对本发明进行详细说明。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

本发明的针对控制方向未知的气动系统位置自适应控制方法，按照以下步骤具体实施：The position adaptive control method of the pneumatic system for unknown control direction of the present invention is specifically implemented according to the following steps:

参照图1，本发明方法所依赖的气动位置伺服系统的结构是，无杆气缸3的活塞1与负载2固定连接，活塞1还与位移检测仪4对应接触，位置检测仪4的输出信号通过A/D转换器接入计算机6；无杆气缸3的气腔A侧和气腔B侧分别与比例阀5的两个出气端(即两个Po端)对应联通，比例阀5为三位五通比例伺服阀，按照两个出气端(即两个Po端)连接顺序的不同分别定义为正、反方向两种连接方式，比例阀5进气端(即Pu端)与储气罐9连通，储气罐9通过减压阀7与气泵8联通，计算机6通过D/A转换器与比例阀5连接，将控制器的输出信号发送给比例阀5。With reference to Fig. 1, the structure of the pneumatic position servo system that the method of the present invention relies on is that the piston 1 of the rodless cylinder 3 is fixedly connected with the load 2, the piston 1 is also in corresponding contact with the displacement detector 4, and the output signal of the position detector 4 passes through The A/D converter is connected to the computer 6; the side of the air chamber A and the side of the air chamber B of the rodless cylinder 3 are respectively connected with the two outlet ports of the proportional valve 5 (that is, the two Po ports), and the proportional valve 5 is three-position five Through the proportional servo valve, according to the difference in the connection sequence of the two gas outlets (that is, the two Po ports), it is defined as two connection modes in the forward and reverse directions. , the air storage tank 9 communicates with the air pump 8 through the pressure reducing valve 7, and the computer 6 connects with the proportional valve 5 through the D/A converter, and sends the output signal of the controller to the proportional valve 5.

假设上述的气动位置伺服系统满足如下条件：Assume that the above pneumatic position servo system meets the following conditions:

1)系统使用的工作介质(空气)为理想气体；1) The working medium (air) used in the system is an ideal gas;

2)气体流经阀口或其它节流口时的流动状态均为等熵绝热过程；2) The flow state of the gas flowing through the valve port or other throttle ports is an isentropic adiabatic process;

3)在同一容腔内气体压力和温度处处相等；3) The gas pressure and temperature in the same cavity are equal everywhere;

4)忽略泄漏；4) Ignore the leak;

5)活塞运动时，两腔内气体的变化过程均为绝热过程；5) When the piston moves, the change process of the gas in the two chambers is an adiabatic process;

6)气源压力和大气压力恒定；6) The air source pressure and atmospheric pressure are constant;

7)与系统动态特性相比，比例阀的惯性可以忽略。7) Compared with the dynamic characteristics of the system, the inertia of the proportional valve can be ignored.

其中x₁、x₂、x₃为系统状态变量，物理含义分别表示活塞1的位置、速度和加速度，分别对应为x₁、x₂、x₃的一阶导数，u为控制输入，a₁，a₂，a₃为未知模型参数，b为大小和方向(符号)均未知的系统控制增益，控制目标是在比例阀5输出正、反两种连接方式时，使活塞1的位移y都能跟踪所要求的期望输出y_d；Among them, x ₁ , x ₂ , and x ₃ are system state variables, and their physical meanings represent the position, velocity and acceleration of piston 1 respectively, Corresponding to the first-order derivatives of x ₁ , x ₂ , x ₃ respectively, u is the control input, a ₁ , a ₂ , a ₃ are unknown model parameters, b is the system control gain with unknown magnitude and direction (sign), and the control The goal is to make the displacement y of the piston 1 track the required desired output y _d when the proportional valve 5 outputs positive and negative connections;

$\overset{\cdot \cdot}{ξ ξ} = = {z z}_{33} (({c c}_{33} {z z}_{33} + + {\overset{^^}{θ θ}}^{T T} ω ω)),, - - - - - - ((22))$

其中N(ξ)＝ξ²cos(ξ)为Nussbaum型偶函数，z₁＝x₁-y_d，z₂＝x₂-α₁，z₃＝x₃-α₂，θ＝[1a₁a₂a₃]^T为参数向量，为θ的估计值，为状态向量，为期望输出y_d的一阶导数，为α₁的一阶导数，为α₂的一阶导数，α₁、α₂、z₁、z₂、z₃为中间变量，c₁、c₂和c₃为设置参数；Where N(ξ)=ξ ² cos(ξ) is a Nussbaum-type even function, z ₁ ＝x ₁ -y _d , z ₂ =x ₂ -α ₁ , z ₃ ＝x ₃ -α ₂ , θ＝[1a ₁ a ₂ a ₃ ] ^T is the parameter vector, is the estimated value of θ, is the state vector, is the first derivative of the expected output y _d , is the first derivative of α ₁ , is the first derivative of α ₂ , α ₁ , α ₂ , z ₁ , z ₂ , z ₃ are intermediate variables, c ₁ , c ₂ and c ₃ are setting parameters;

U_max为控制量限幅值，具体根据实际比例阀5和对象确定数值；U _max is the limit value of the control quantity, and the specific value is determined according to the actual proportional valve 5 and the object;

步骤4、对气动位置伺服系统(自适应控制器)的未知模型参数的值进行估计Step 4. Estimate the values of the unknown model parameters of the pneumatic position servo system (adaptive controller)

$\overset{\cdot &Center Dot;}{\overset{^^}{θ θ}} = = {Γωz Γωz}_{33},, - - - - - - ((55))$

将式(5)估计得到的数值用于实时更新式(2)中的参数，计算机6通过D/A转换器将经过限幅的控制信号输给比例阀5，实时调节无杆气缸3中活塞1的位移y，即成。Estimated by formula (5) The value is used to update the parameters in formula (2) in real time, and the computer 6 transmits the limited control signal to the proportional valve 5 through the D/A converter to adjust the displacement y of the piston 1 in the rodless cylinder 3 in real time.

实施例Example

第一，参照图1，选择各个部件的型号，构建气动位置伺服系统First, referring to Figure 1, select the model of each component to build a pneumatic position servo system

无杆气缸3选用FESTO公司DGPL-25-450-PPV-A-B-KF-GK-SV型号的无杆气缸；比例阀5选用型号MPYE-5-1/8-HF-010-B的三位五通比例阀；位移检测仪4选用型号MLO-POT-450-TLF的滑动电阻式直线位移检测仪；计算机6选用CPU为P21.2GHz的型号；通用数据采集卡选用的型号是PCI2306。计算机6内置的控制软件采用VB编制，通过显示屏显示出控制过程中相关变量的变化曲线。The rodless cylinder 3 is a rodless cylinder of the type DGPL-25-450-PPV-A-B-KF-GK-SV from FESTO; the proportional valve 5 is a three-position five of the model MPYE-5-1/8-HF-010-B The proportional valve is connected; the displacement detector 4 is a sliding resistive linear displacement detector of the model MLO-POT-450-TLF; the computer 6 is a CPU of P21.2GHz; the general data acquisition card is PCI2306. The built-in control software of the computer 6 is compiled by VB, and the change curve of the relevant variables in the control process is displayed through the display screen.

第二，设置气动位置伺服系统的控制目标Second, set the control target of the pneumatic position servo system

参考信号1为单频正弦信号：Reference signal 1 is a single-frequency sinusoidal signal:

y_d＝111.65sin0.5πt，(6)y _d =111.65sin0.5πt, (6)

参考信号2为S曲线信号：Reference signal 2 is an S-curve signal:

y_d＝-[55.825/(0.5π)²]sin0.5πt+[55.825/(0.5π)]t，(7)y _d =-[55.825/(0.5π) ² ] sin0.5πt+[55.825/(0.5π)]t, (7)

参考信号3为多频正弦信号：Reference signal 3 is a multi-frequency sinusoidal signal:

$\begin{matrix} {y the y}_{d d} = = 167.475 167.475 sin sin π π t t + + 167.475 167.475 sin sin 0.5 0.5 π π t t + + 167.475 167.475 sin sin ((22 π π t t / / 77)) \\ + + 167.475 167.475 sin sin ((π π t t / / 66)) + + 167.475 167.475 sin sin ((22 π π t t / / 1717)) \end{matrix},, - - - - - - ((88))$

第三，采用本发明方法通过式(2)-式(5)的自适应控制器进行实验The 3rd, adopt the inventive method to carry out experiment by the adaptive controller of formula (2)-formula (5)

设置各个参数的具体值，c₁＝c₂＝60，c₃＝0.1，Γ＝diag([0.010.010.01])，控制限幅U_max＝1.95V，当跟踪期望目标分别为式(6)-式(8)时，比例阀5输出为正方向连接时，跟踪曲线如图2、图3、图4所示。保持控制器参数不变，比例阀5输出反方向连接时，跟踪曲线如图5、图6、图7所示。可见，本发明方法不论对于伺服阀5正向连接还是反向连接都能够实现有效跟踪。Set the specific values of each parameter, c ₁ =c ₂ =60, c ₃ =0.1, Γ=diag([0.010.010.01]), control limit U _max =1.95V, when tracking the desired target is formula (6) - In formula (8), when the output of the proportional valve 5 is connected in the positive direction, the tracking curves are shown in Fig. 2, Fig. 3 and Fig. 4. Keeping the controller parameters unchanged, when the output of the proportional valve 5 is connected in the opposite direction, the tracking curves are shown in Figure 5, Figure 6, and Figure 7. It can be seen that the method of the present invention can realize effective tracking regardless of whether the servo valve 5 is connected in a forward direction or in a reverse direction.

第四，利用以下四种现有技术的控制方法进行对比试验The 4th, utilize the control method of following four kinds of prior art to carry out comparative test

一)滑模变结构方法11) Sliding mode variable structure method 1

滑模变结构方法1参照文献[T.Nguyen,J.Leavitt,F.Jabbari,J.E.Bobrow.AccurateSlide-ModeControlofPneumaticSystemsUsingLow-CostSolenoidValves.IEEE/ASMETransactionsonMechatronics,2007,12(2):216-219]，滑模变结构方法1的控制表达式为式(9)-式(10)：Sliding mode variable structure method 1 Refer to literature [T.Nguyen, J.Leavitt, F.Jabbari, J.E.Bobrow.AccurateSlide-ModeControlofPneumaticSystemsUsingLow-CostSolenoidValves.IEEE/ASMETransactionsonMechatronics,2007,12(2):216-219], sliding mode variable structure The control expression of method 1 is formula (9) - formula (10):

$S S = = \overset{\cdot\cdot \cdot\cdot}{y the y} - - {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{d d} + + 22 ζ ζ ω ω ((\overset{\cdot &Center Dot;}{y the y} - - {\overset{\cdot &Center Dot;}{y the y}}_{d d})) + + {ω ω}^{22} ((y the y - - {y the y}_{d d})),, - - - - - - ((99))$

u＝-k_s2sgn(S)，(10)u=-k _s2 sgn(S), (10)

该滑模变结构方法1针对开关阀控制气缸，实际的控制由式(10)给出，k_s2＝1，u＝1对应阀开，u＝-1对应阀关。取k_s2＝1.56伏控制比例阀5的开度幅值，控制器参数取ξ＝1，ω＝50，控制结果曲线如图8、图9、图10所示。保持控制器参数不变，比例阀5输出反方向连接时，控制结果曲线如图图11、图12、图13所示。由图11、图12、图13可知，滑模变结构方法1无法实现对参考信号的跟踪控制。The sliding mode variable structure method 1 is aimed at the on-off valve to control the cylinder, the actual control is given by formula (10), k _s2 =1, u=1 corresponds to the valve opening, and u=-1 corresponds to the valve closing. Take k _s2 =1.56 volts to control the opening amplitude of the proportional valve 5, and set the controller parameters to ξ=1, ω=50. The control result curves are shown in Fig. 8, Fig. 9 and Fig. 10 . Keeping the controller parameters unchanged, when the output of the proportional valve 5 is connected in the opposite direction, the control result curves are shown in Figure 11, Figure 12, and Figure 13. It can be seen from Fig. 11, Fig. 12 and Fig. 13 that the sliding mode variable structure method 1 cannot realize the tracking control of the reference signal.

二)滑模变结构方法22) Sliding mode variable structure method 2

滑模变结构方法2参照文献[GaryM.Bone,ShuNing.ExperimentalComparisonofPositionTrackingControlAlgorithmsforPneumaticCylinderActuators.IEEE/ASMETransactionsonMechatronics,2007,12(5):557-561]，该滑模变结构方法2的控制表达式为式(11)-式(14)：The sliding mode variable structure method 2 refers to the literature [GaryM.Bone, ShuNing.ExperimentalComparisonofPositionTrackingControlAlgorithmsforPneumaticCylinderActuators.IEEE/ASMETransactionsonMechatronics,2007,12(5):557-561], the control expression of the sliding mode variable structure method 2 is formula (11)- Formula (14):

$S S = = \overset{\cdot\cdot \cdot\cdot}{y the y} - - {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{d d} + + 22 λ λ ((\overset{\cdot &Center Dot;}{y the y} - - {\overset{\cdot &Center Dot;}{y the y}}_{d d})) + + {λ λ}^{22} ((y the y - - {y the y}_{d d})),, - - - - - - ((1111))$

${u u}_{e e q q} = = \frac{11}{{m m}_{00}} [[{\overset{\cdot\cdot\cdot \cdot\cdot\cdot}{y the y}}_{d d} + + {n no}_{22} \overset{\cdot\cdot \cdot\cdot}{y the y} + + {n no}_{11} \overset{\cdot \cdot}{y the y} + + {n no}_{00} y the y - - 22 λ λ ((\overset{\cdot\cdot \cdot\cdot}{y the y} - - {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{d d})) - - {λ λ}^{22} ((\overset{\cdot \cdot}{y the y} - - {\overset{\cdot \cdot}{y the y}}_{d d}))]],, - - - - - - ((1212))$

u_s＝-k_s1sat(S/φ)，(13)u _s =-k _s1 sat(S/φ), (13)

u′＝u_eq+u_s，(14)u'=u _eq +u _s , (14)

滑模变结构方法2实际的控制由式(14)给出，控制输出的限幅如式(4)给出，控制参数n₂＝29.5544，n₁＝218.436，n₀＝0，m₀＝5531.3305，λ＝50，k_s1＝2.44×10⁴，φ＝0.05，控制结果曲线如图14、图15、图16所示。保持控制器参数不变，比例阀5输出反方向连接时，类似于滑模控制方法1在比例阀5输出反向时的实验结果(参考图11、图12、图13)，该滑模变结构方法2无法实现对参考信号的跟踪控制。The actual control of sliding mode variable structure method 2 is given by formula (14), and the limit of the control output is given by formula (4), control parameters n ₂ =29.5544, n ₁ =218.436, n ₀ =0, m ₀ = 5531.3305, λ=50, k _s1 =2.44×10 ⁴ , φ=0.05, the control result curves are shown in Figure 14, Figure 15, and Figure 16. Keeping the controller parameters unchanged, when the output of the proportional valve 5 is connected in the opposite direction, it is similar to the experimental results of the sliding mode control method 1 when the output of the proportional valve 5 is reversed (refer to Figure 11, Figure 12, and Figure 13). Structural method 2 cannot realize the tracking control of the reference signal.

三)反步自适应方法13) Backstepping adaptive method 1

反步自适应方法1参照文献[RenHP,HuangC.AdaptiveBacksteppingControlofPneumaticServoSystem.InProceedingofthe2013IEEEInternationalSymposiumonIndustrialElectronics,Taibei,May28-31,2013:1-6]，反步自适应方法1的控制表达式为式(15)-式(16)：Backstepping adaptive method 1 refers to the literature [RenHP,HuangC.AdaptiveBacksteppingControlofPneumaticServoSystem.InProceedingofthe2013IEEEInternational Symposium on Industrial Electronics,Taibei,May28-31,2013:1-6], the control expression of backstepping adaptive method 1 is formula (15) - formula (16) :

${u u}^{' '} = = \frac{11}{\overset{^^}{b b}} ((- - {z z}_{22} - - {\overset{^^}{a a}}_{11} {z z}_{11} - - {\overset{^^}{a a}}_{11} {y the y}_{d d} - - {\overset{^^}{a a}}_{22} {z z}_{22} - - {\overset{^^}{a a}}_{22} {α α}_{11} - - {\overset{^^}{a a}}_{33} {α α}_{22} + + {\overset{\cdot \cdot}{α α}}_{22})),, - - - - - - ((1515))$

$\{\begin{matrix} \frac{11}{\overset{^^}{b b}} = = &Integral; &Integral; ((- - λ λ)) {z z}_{11} {y the y}_{d d} d d t t \\ {\overset{\cdot &Center Dot;}{\overset{^^}{a a}}}_{11} = = - - {β β}_{11} {z z}_{11} {x x}_{11} \\ {\overset{\cdot &Center Dot;}{\overset{^^}{a a}}}_{22} = = - - {β β}_{22} {z z}_{11} {x x}_{22} \\ {\overset{\cdot &Center Dot;}{\overset{^^}{a a}}}_{33} = = - - {β β}_{33} {z z}_{11} {x x}_{33} \end{matrix},, - - - - - - ((1616))$

该反步自适应方法1实际的控制由式(15)给出，控制输出的限幅如式(4)，控制器参数c₁＝c₂＝50，λ＝β₁＝β₂＝β₃＝1，控制结果曲线如图17、图18、图19所示。保持控制器参数不变，比例阀5输出反方向连接时，实验结果类似于滑模控制方法1在比例阀5输出反向时的实验结果(参考图11、图12、图13)，反步自适应方法1无法实现对参考信号的跟踪控制。The actual control of the backstepping adaptive method 1 is given by formula (15), the limit of the control output is as in formula (4), the controller parameters c ₁ =c ₂ =50, λ=β ₁ =β ₂ =β ₃ =1, the control result curves are shown in Figure 17, Figure 18, and Figure 19. Keeping the controller parameters unchanged, when the output of the proportional valve 5 is connected in the opposite direction, the experimental results are similar to the experimental results of the sliding mode control method 1 when the output of the proportional valve 5 is reversed (refer to Figure 11, Figure 12, and Figure 13), backstepping Adaptive method 1 cannot realize the tracking control of the reference signal.

四)反步自适应方法24) Backstepping Adaptive Method 2

反步自适应方法2参照文献[RenHP,HuangC.ExperimentalTrackingControlforPneumaticSystem.InProceedingofthe2013IEEE39thAnnualConferenceonIndustrialElectronicsSociety,Vienna,Austria,November10-13,2013:4126-4130]，反步自适应方法2的的控制表达式为式(17)-式(20)：Backstepping adaptive method 2 refers to the literature [RenHP,HuangC.ExperimentalTrackingControlforPneumaticSystem.InProceedingofthe2013IEEE39thAnnualConferenceonIndustrialElectronicsSociety,Vienna,Austria,November10-13,2013:4126-4130], the control expression of backstepping adaptive method 2 is formula (17)- (20):

$u u = = \overset{^^}{p p} \overset{&OverBar; &OverBar;}{u u},, - - - - - - ((1717))$

$\overset{&OverBar; &OverBar;}{u u} = = {α α}_{22} + + {\overset{\cdot\cdot\cdot \cdot\cdot\cdot}{y the y}}_{m m},, - - - - - - ((1818))$

$\overset{\cdot &Center Dot;}{\overset{^^}{p p}} = = - - γ γ sgn sgn (({m m}_{00})) \overset{&OverBar; &OverBar;}{u u} {z z}_{33},, - - - - - - ((1919))$

$\overset{\cdot &Center Dot;}{\overset{^^}{A A}} = = Γ Γ Φ Φ ((x x)) {z z}_{33},, - - - - - - ((2020))$

该反步自适应方法2实际的控制由式(17)给出，控制输出的限幅如式(4)，控制器参数c₁＝c₂＝50，λ＝1，Γ＝diag[111]，控制结果曲线参照图20、图21、图22所示。保持控制器参数不变，比例阀5输出反方向连接时，实验结果类似于滑模控制方法1在比例阀5输出反向时的实验结果(参考图11、图12、图13)，反步自适应方法2同样无法实现对参考信号的跟踪控制。The actual control of the backstepping adaptive method 2 is given by Equation (17), the limit of the control output is as Equation (4), the controller parameters c ₁ =c ₂ =50, λ=1, Γ=diag[111] , The control result curves are shown in Fig. 20, Fig. 21 and Fig. 22. Keeping the controller parameters unchanged, when the output of the proportional valve 5 is connected in the opposite direction, the experimental results are similar to the experimental results of the sliding mode control method 1 when the output of the proportional valve 5 is reversed (refer to Figure 11, Figure 12, and Figure 13), backstepping Adaptive method 2 also cannot realize the tracking control of the reference signal.

通过上述的四种现有控制技术的对比可见，本发明方法跟踪效果更好。尤其是在比例阀输出反方向连接时，现有四种控制方法的都失效，而本发明方法仍可实现对参考信号的有效跟踪控制。It can be seen from the comparison of the above four existing control technologies that the tracking effect of the method of the present invention is better. Especially when the output of the proportional valve is connected in the opposite direction, all the existing four control methods are invalid, but the method of the present invention can still realize the effective tracking control of the reference signal.

第五，为了更加直观的说明本发明方法的控制效果，在跟踪不同期望目标的情况下定量地计算了跟踪误差，误差定义为均方根误差，表达式如下：Fifth, in order to illustrate the control effect of the method of the present invention more intuitively, the tracking error is quantitatively calculated under the situation of tracking different desired targets, and the error is defined as the root mean square error, and the expression is as follows:

$R R M m S S E E. = = \sqrt{\frac{11}{{N N}_{22} - - {N N}_{11}} {Σ Σ}_{k k - - {N N}_{11}}^{{N N}_{22}} {e e}_{k k}^{22}},, - - - - - - ((21 twenty one))$

其中N₁为比较开始时刻，N₂为比较结束时刻，e_k＝y(kΔT)-y_d(kΔT)，ΔT为采样时间间隔，k表示采样时刻。为避免不同初值和随机干扰的影响，对每种参考信号的跟踪控制进行了多次试验，给出其中五次测试的实验结果。Where N ₁ is the comparison start time, N ₂ is the comparison end time, e _k =y(kΔT)-y _d (kΔT), ΔT is the sampling time interval, and k represents the sampling time. In order to avoid the influence of different initial values and random interference, several experiments are carried out on the tracking control of each reference signal, and the experimental results of five tests are given.

表1是本发明方法与现有四种控制方法在跟踪式(6)期望输出信号时的误差对比。Table 1 is the error comparison between the method of the present invention and the four existing control methods when tracking the expected output signal of formula (6).

表1本发明方法与现有控制方法在跟踪式(6)期望输出信号时的误差对比Table 1 The method of the present invention and the error contrast of existing control method when tracking formula (6) expected output signal

表2是本发明方法与现有四种控制方法在跟踪式(7)期望输出信号时的误差对比。Table 2 is the error comparison between the method of the present invention and the four existing control methods when tracking the expected output signal of formula (7).

表2本发明方法与现有控制方法在跟踪式(7)期望输出信号时的误差对比Table 2 The method of the present invention and the error contrast of existing control method when tracking formula (7) expected output signal

表3是本发明方法与现有四种控制方法在跟踪式(8)期望输出信号时的误差对比。Table 3 is the error comparison between the method of the present invention and the four existing control methods when tracking the expected output signal of formula (8).

表3本发明方法与现有控制方法在跟踪式(8)期望输出信号时的误差对比Table 3 The error comparison between the method of the present invention and the existing control method when tracking the expected output signal of formula (8)

对比上述表1、表2、表3中的数据，明显可见，在各种期望目标情况下，比例阀输出正、反两种连接方式时，本发明方法均能实现有效控制，且平均跟踪误差都小于现有的控制方法。Comparing the data in above Table 1, Table 2, and Table 3, it can be clearly seen that under various expected target situations, when the proportional valve outputs positive and negative connection modes, the method of the present invention can realize effective control, and the average tracking error are smaller than existing control methods.

Claims

1., for the pneumatic system position self-adaptation control method of controlling party to the unknown, it is characterized in that, the method is specifically implemented according to following steps:

Step 1, set up the model of Pneumatic Position Servo System

According to the working mechanism of Pneumatic Position Servo System, ignore friction, carry out linearization process simultaneously, obtain linear numerical modei such as formula shown in (1):

\{\begin{matrix} {\overset{\cdot}{x}}_{1} = x_{2} \\ {\overset{\cdot}{x}}_{2} = x_{3} \\ {\overset{\cdot}{x}}_{3} = a_{1} x_{1} + a_{2} x_{2} + a_{3} x_{3} + b u \\ y = x_{1} \end{matrix}, - - - (1)

Wherein x ₁, x ₂, x ₃for system state variables, physical meaning represents the position of piston (1), speed and acceleration respectively, correspond to x respectively ₁, x ₂, x ₃first order derivative, u is control inputs, a ₁, a ₂, a ₃for unknown model parameters, the Systematical control gain that sized by b and direction is all unknown, control objectives is when proportioning valve (5) exports positive and negative two kinds of connected modes, makes the displacement y of piston (1) can follow the tracks of required desired output y _d;

Step 2, introducing Nussbaum gain function, arrange the adaptive controller of Pneumatic Position Servo System

Choose adaptive controller to above-mentioned formula (1), the model expression of adaptive controller is respectively such as formula shown in (2) and formula (3):

\overset{\cdot}{ξ} = z_{3} (c_{3} z_{3} + {\hat{θ}}^{T} ω), - - - (2)

u^{'} = N (ξ) (c_{3} z_{3} + {\hat{θ}}^{T} ω), - - - (3)

Wherein N (ξ) is Nussbaum type even function, z ₁=x ₁-y _d, z ₂=x ₂-α ₁, z ₃=x ₃-α ₂, θ=[1a ₁a ₂a ₃] ^tfor parameter vector, for the estimated value of θ, for state vector, for desired output y _dfirst order derivative, for α ₁first order derivative, for α ₂first order derivative, α ₁, α ₂, z ₁, z ₂, z ₃for intermediate variable, c ₁, c ₂and c ₃for parameters;

Step 3, amplitude limit is carried out to control signal u ', such as formula (4):

u = \{\begin{matrix} U_{m a x} & u^{'} > U_{m a x} \\ u^{'} & - U_{m a x} \leq u^{'} \leq U_{m a x} \\ - U_{m a x} & u^{'} < - U_{m a x} \end{matrix}, - - - (4)

U _maxfor control output limitation value;

Step 4, the value of the unknown model parameters of Pneumatic Position Servo System to be estimated

The estimated value of unknown model parameters calculates with reference to formula (5):

\overset{\cdot}{\hat{θ}} = {Γωz}_{3}, - - - (5)

Γ is wherein positive definite matrix, is adaptive gain, for first order derivative,

Formula (5) estimation is obtained numerical value is used for the parameter in real-time update formula (2), control signal through amplitude limit is defeated by proportioning valve (5) by D/A converter by computing machine (6), regulates the displacement y of piston (1) in Rodless cylinder (3) in real time.

2. according to claim 1 for the pneumatic system position self-adaptation control method of controlling party to the unknown, it is characterized in that: in described step 1, the structure of controlled Pneumatic Position Servo System is, the piston (1) of Rodless cylinder (3) is fixedly connected with load (2), piston (1) also contacts with displacement detecting instrument (4) is corresponding, and the output signal of location detector (4) accesses computing machine (6) by A/D converter; The air cavity A side of Rodless cylinder (3) and air cavity B side respectively with two corresponding UNICOMs in outlet side of proportioning valve (5), proportioning valve (5) is 3 position-5 way proportional servo valve, positive and negative direction two kinds of connected modes are defined as respectively according to the difference of two outlet side orders of connection, proportioning valve (5) inlet end is communicated with gas-holder (9), gas-holder (9) is by reduction valve (7) and air pump (8) UNICOM, and computing machine (6) is connected with proportioning valve (5) by D/A converter.