CN114879505B - Pneumatic regulating valve control method based on quantitative feedback theory - Google Patents

Pneumatic regulating valve control method based on quantitative feedback theory Download PDF

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CN114879505B
CN114879505B CN202210590681.6A CN202210590681A CN114879505B CN 114879505 B CN114879505 B CN 114879505B CN 202210590681 A CN202210590681 A CN 202210590681A CN 114879505 B CN114879505 B CN 114879505B
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方星
夏勤
刘飞
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Abstract

本发明涉及一种基于定量反馈理论的气动调节阀控制方法,包括:建立气动调节阀系统的数学模型,考虑实际工况下系统模型参数的不确定性变化范围得到被控对象模板,设计鲁棒稳定性指标和跟踪性能指标;将气动调节阀系统的模型不确定性和性能指标要求等用定量的方式转化为控制边界,得到控制器的约束条件;根据控制器约束条件利用环路成形方法得到符合鲁棒性要求的反馈控制器和满足跟踪性能指标要求的前置滤波器。本发明通过利用已知对象模型及其不确定性信息,提高了气动调节阀系统的鲁棒性,使得气动调节阀系统在模型参数发生变化时的控制效果符合系统性能指标要求。

Figure 202210590681

The invention relates to a control method of a pneumatic control valve based on quantitative feedback theory, which includes: establishing a mathematical model of a pneumatic control valve system, considering the uncertainty range of system model parameters under actual working conditions to obtain a controlled object template, and designing a robust Stability index and tracking performance index; the model uncertainty and performance index requirements of the pneumatic control valve system are converted into control boundaries in a quantitative way, and the constraints of the controller are obtained; according to the constraints of the controller, the loop forming method is used to obtain A feedback controller that meets the requirements of robustness and a pre-filter that meets the requirements of the tracking performance index. The invention improves the robustness of the pneumatic control valve system by using the known object model and its uncertainty information, so that the control effect of the pneumatic control valve system meets the system performance index requirements when the model parameters change.

Figure 202210590681

Description

基于定量反馈理论的气动调节阀控制方法Control Method of Pneumatic Control Valve Based on Quantitative Feedback Theory

技术领域technical field

本发明涉及自动控制技术领域,尤其是指一种基于定量反馈理论的气动调节阀控制方法。The invention relates to the technical field of automatic control, in particular to a control method of a pneumatic regulating valve based on quantitative feedback theory.

背景技术Background technique

气动调节阀是现代工业过程控制系统中不可或缺的重要设备,其性能会直接影响到整个工业过程。而在实际生产过程中,气动调节阀又往往工作在复杂的环境中,容易受到外界干扰和内部等价干扰(包括模型不确定性、未建模动态等)的影响,因此,气动调节阀系统控制器的鲁棒性能要求就较高。Pneumatic control valves are indispensable and important equipment in modern industrial process control systems, and their performance will directly affect the entire industrial process. In the actual production process, pneumatic control valves often work in complex environments, and are easily affected by external disturbances and internal equivalent disturbances (including model uncertainty, unmodeled dynamics, etc.). Therefore, the pneumatic control valve system The robust performance requirements of the controller are higher.

目前,应用在气动调节阀系统中的控制算法主要有:常规PID控制方法和基于PID改进的控制方法,基于PID改进的控制算法有模糊-PID控制,灰色预测模糊-PID控制等。但是,基于PID控制的方法鲁棒性较差,不能够较好地满足该系统在外部干扰和模型不确定性下的性能指标要求,模型依赖性较强。基于PID改进的控制方法虽然能提高系统的鲁棒性,但都不能有效利用已知的对象模型及其不确定信息。At present, the control algorithms used in the pneumatic control valve system mainly include: conventional PID control method and improved control method based on PID. The improved control algorithm based on PID includes fuzzy-PID control, gray predictive fuzzy-PID control, etc. However, the method based on PID control has poor robustness, and cannot satisfy the performance index requirements of the system under external disturbance and model uncertainty, and has strong model dependence. Although the improved control methods based on PID can improve the robustness of the system, they cannot effectively utilize the known object model and its uncertain information.

发明内容Contents of the invention

为此,本发明所要解决的技术问题在于克服现有技术中的不足,提供一种基于定量反馈理论的气动调节阀控制方法,可以提高系统的鲁棒性、使得系统在模型参数发生变化时的控制效果符合系统性能指标要求。For this reason, the technical problem to be solved by the present invention is to overcome the deficiencies in the prior art, and provide a control method for pneumatic control valves based on quantitative feedback theory, which can improve the robustness of the system and make the system stable when the model parameters change. The control effect meets the system performance index requirements.

为解决上述技术问题,本发明提供了一种基于定量反馈理论的气动调节阀控制方法,包括以下步骤:In order to solve the above technical problems, the present invention provides a method for controlling a pneumatic control valve based on quantitative feedback theory, which includes the following steps:

步骤1:建立气动调节阀系统的数学模型;Step 1: Establish a mathematical model of the pneumatic control valve system;

步骤2:考虑实际工况下系统模型参数的不确定性变化范围,在所述气动调节阀系统的数学模型下得到被控对象模板,在所述被控对象模板下设计鲁棒稳定性指标和跟踪性能指标;Step 2: Considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system, and the robust stability index and track performance metrics;

步骤3:根据所述被控对象模板、鲁棒稳定性指标和跟踪性能指标得到复合边界,根据所述复合边界得到气动调节阀系统无控制器时的开环系统响应曲线;Step 3: Obtain the compound boundary according to the controlled object template, the robust stability index and the tracking performance index, and obtain the open-loop system response curve when the pneumatic control valve system has no controller according to the compound boundary;

步骤4:建立包含反馈控制器和前置滤波器的二自由度控制器,将所述二自由度控制器作用到所述气动调节阀系统中,调整所述二自由度控制器直到所述开环系统响应曲线满足性能要求,得到满足鲁棒稳定性指标和跟踪性能指标要求的气动调节阀系统。Step 4: Establish a two-degree-of-freedom controller including a feedback controller and a pre-filter, apply the two-degree-of-freedom controller to the pneumatic control valve system, and adjust the two-degree-of-freedom controller until the opening The response curve of the loop system meets the performance requirements, and a pneumatic control valve system that meets the requirements of the robust stability index and the tracking performance index is obtained.

作为优选的,所述气动调节阀系统的数学模型,包括智能定位器模块和阀门执行器模块,Preferably, the mathematical model of the pneumatic control valve system includes an intelligent positioner module and a valve actuator module,

所述智能定位器模块包括内部控制器、电气转换环节、气动放大环节和阀位反馈环节,所述电气转换环节和气动放大环节建模为二阶系统;The intelligent positioner module includes an internal controller, an electrical conversion link, a pneumatic amplification link and a valve position feedback link, and the electrical conversion link and the pneumatic amplification link are modeled as a second-order system;

所述阀门执行器模块包括密闭气室和阀杆运动环节,所述阀门执行器模块的机理模型分为气室气压转换环节、气压与力的转换环节和力与阀门执行器位移的转换环节;The valve actuator module includes an airtight air chamber and a valve stem movement link, and the mechanism model of the valve actuator module is divided into an air chamber air pressure conversion link, an air pressure and force conversion link, and a force and valve actuator displacement conversion link;

所述气动调节阀系统的传递函数G(s)=G1(s)G2(s)G3(s)G4(s),其中G1(s)为所述二阶系统的传递函数,G2(s)为所述气室气压转换环节的传递函数,G3(s)为所述气压与力的转换环节的传递函数,G4(s)为所述力与阀门执行器位移的转换环节的传递函数。The transfer function G(s) of the pneumatic regulating valve system=G 1 (s)G 2 (s)G 3 (s)G 4 (s), wherein G 1 (s) is the transfer function of the second-order system , G 2 (s) is the transfer function of the air pressure conversion link in the air chamber, G 3 (s) is the transfer function of the air pressure and force conversion link, and G 4 (s) is the force and valve actuator displacement The transfer function of the conversion link.

作为优选的,所述二阶系统的传递函数

Figure BDA0003667184470000031
其中,P1(s)为智能定位器模块的输出气压,x(s)是阀位输入,K是二阶系统增益,ξ是二阶系统阻尼系数,s是拉普拉斯算子,ω是二阶系统自然振荡频率;As preferably, the transfer function of the second-order system
Figure BDA0003667184470000031
Among them, P 1 (s) is the output air pressure of the intelligent positioner module, x (s) is the valve position input, K is the second-order system gain, ξ is the second-order system damping coefficient, s is the Laplacian operator, ω is the natural oscillation frequency of the second-order system;

所述气室气压转换环节的传递函数

Figure BDA0003667184470000032
其中P2(s)为经拉普拉斯变化后的输出气压P2,P1(s)为经拉普拉斯变化后的输入气压P1,Tv是气动阻容环节时间常数,s是拉普拉斯算子;The transfer function of the air pressure conversion link of the air chamber
Figure BDA0003667184470000032
Among them, P 2 (s) is the output air pressure P 2 changed by Laplace, P 1 (s) is the input air pressure P 1 changed by Laplace, T v is the time constant of the pneumatic resistance-capacitance link, s is the Laplacian operator;

所述气压与力的转换环节的传递函数

Figure BDA0003667184470000033
其中F(s)=P2(s)·AD,AD为气室内膜片的有效面积;The transfer function of the conversion link of the air pressure and force
Figure BDA0003667184470000033
Among them, F(s)=P 2 (s)· AD , where AD is the effective area of the diaphragm in the gas chamber;

所述力与阀门执行器位移的转换环节的传递函数

Figure BDA0003667184470000034
其中x(s)是阀位输入,m为执行机构运动部件的总质量,x为执行机构的输出位移,k为执行机构弹簧的弹性系数,b为执行机构的内摩擦阻尼。The transfer function of the conversion link between the force and valve actuator displacement
Figure BDA0003667184470000034
Where x(s) is the valve position input, m is the total mass of the moving parts of the actuator, x is the output displacement of the actuator, k is the spring coefficient of the actuator, and b is the internal friction damping of the actuator.

作为优选的,考虑实际工况下系统模型参数的不确定性变化范围,在所述气动调节阀系统的数学模型下得到被控对象模板,具体为:As preferably, considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system, specifically:

考虑实际工况下系统模型参数的不确定性变化范围,得到被控对象模板G1(s)、G2(s)、G3(s)和G4(s)实际表达式,将G4(s)中的执行机构运动部分质量m,弹簧弹性系数k和执行机构内摩擦阻尼b作为气动调节阀系统的不确定参数;Considering the uncertainty range of system model parameters under actual working conditions, the actual expressions of the controlled object templates G 1 (s), G 2 (s), G 3 (s) and G 4 (s) are obtained, and G 4 In (s), the mass m of the moving part of the actuator, the spring elastic coefficient k and the internal friction damping b of the actuator are used as uncertain parameters of the pneumatic control valve system;

经过实际测量得到不确定参数m、k和b的范围,选取范围内的m、k和b的一个值作为系统的标称参数,得到被控对象的传递函数G0(s);The range of uncertain parameters m, k and b is obtained through actual measurement, and a value of m, k and b within the range is selected as the nominal parameter of the system, and the transfer function G 0 (s) of the controlled object is obtained;

选择被控对象具有较大不确定性的频率作为频率阵列,根据气动调节阀系统的动态特性要求设置闭环系统阶跃响应的调节时间ts、上升时间tp、超调量σ、相角裕度

Figure BDA0003667184470000035
和幅值裕度KM。Select the frequency with greater uncertainty of the controlled object as the frequency array, and set the adjustment time t s , rise time t p , overshoot σ, and phase angle margin of the closed-loop system step response according to the dynamic characteristics of the pneumatic control valve system Spend
Figure BDA0003667184470000035
and amplitude margin K M .

作为优选的,所述鲁棒稳定性指标为:As preferably, the robust stability index is:

Figure BDA0003667184470000041
Figure BDA0003667184470000041

Figure BDA0003667184470000042
Figure BDA0003667184470000042

Figure BDA0003667184470000043
Figure BDA0003667184470000043

其中s=jω,L(jω)=C(jω)·G0(jω),C(jω)为待设计的反馈控制器,G0(jω)=G0(s)。Where s=jω, L(jω)=C(jω)·G 0 (jω), C(jω) is the feedback controller to be designed, G 0 (jω)=G 0 (s).

作为优选的,所述跟踪性能指标为:As preferably, the tracking performance index is:

Figure BDA0003667184470000044
Figure BDA0003667184470000044

其中D(jω)为需要设计的前置滤波器,Tu(jω)为跟踪性能的上界,Tl(jω)为跟踪性能的下界。Among them, D(jω) is the pre-filter to be designed, Tu (jω) is the upper bound of tracking performance, and T l (jω) is the lower bound of tracking performance.

作为优选的,根据所述被控对象模板、鲁棒稳定性指标和跟踪性能指标得到复合边界,具体为:Preferably, the composite boundary is obtained according to the controlled object template, the robust stability index and the tracking performance index, specifically:

在所述频率阵列上将被控对象模板根据所述鲁棒稳定性指标在Nichols图上建立鲁棒稳定性边界,On the frequency array, the controlled object template is established on the Nichols diagram according to the robust stability index, and a robust stability boundary is established,

在所述频率阵列上将被控对象模板根据所述跟踪性能指标在Nichols图上建立跟踪性能边界,On the frequency array, the controlled object template is set up on the Nichols diagram to track the performance boundary according to the tracking performance index,

将鲁棒稳定性边界和跟踪性能边界整合,得到复合边界。The robust stability bound and the tracking performance bound are integrated to obtain a composite bound.

作为优选的,所述调整所述二自由度控制器直到所述开环系统响应曲线满足性能要求,得到满足鲁棒稳定性指标和跟踪性能指标要求的气动调节阀系统,具体为:As a preference, the adjustment of the two-degree-of-freedom controller until the response curve of the open-loop system meets the performance requirements, so as to obtain a pneumatic control valve system that meets the requirements of the robust stability index and the tracking performance index, specifically:

调整所述反馈控制器直到所述开环系统响应曲线满足鲁棒稳定性指标的要求,将此时调整得到的反馈控制器带入所述气动调节阀系统中,得到满足鲁棒稳定性指标要求的气动调节阀系统;Adjusting the feedback controller until the response curve of the open-loop system meets the requirements of the robust stability index, and bringing the adjusted feedback controller into the pneumatic control valve system to meet the requirements of the robust stability index Pneumatic control valve system;

调整所述前置滤波器直到所述开环系统响应曲线满足跟踪性能指标的要求,将此时调整得到的前置滤波器带入所述气动调节阀系统中,得到满足跟踪性能指标要求的气动调节阀系统。Adjust the pre-filter until the response curve of the open-loop system meets the requirements of the tracking performance index, and bring the adjusted pre-filter into the pneumatic control valve system to obtain the pneumatic control valve system that meets the requirements of the tracking performance index. Regulating valve system.

作为优选的,所述调整所述反馈控制器直到所述开环系统响应曲线满足鲁棒稳定性指标的要求,具体为:Preferably, the adjustment of the feedback controller until the response curve of the open-loop system meets the requirements of the robust stability index, specifically:

在带二自由度控制器的气动调节阀系统中,通过调整反馈控制器的增益、零点与极点的方式,使得所述开环系统响应曲线满足:在所选择的频率点处位于对应跟踪性能边界上方,并且在高频处不与鲁棒稳定性边界相交。In the pneumatic control valve system with a two-degree-of-freedom controller, by adjusting the gain, zero and pole of the feedback controller, the response curve of the open-loop system satisfies: at the selected frequency point, it is located at the corresponding tracking performance boundary above and does not intersect the robust stability boundary at high frequencies.

作为优选的,将调整所述前置滤波器直到所述开环系统响应曲线满足跟踪性能指标的要求,具体为:Preferably, the pre-filter will be adjusted until the open-loop system response curve meets the requirements of the tracking performance index, specifically:

将二自由度控制器作用到气动调节阀系统中得到闭环系统跟踪边界响应曲线,通过调整前置滤波器的增益、零点与极点的方式,使得所述闭环系统跟踪边界响应曲线中闭环响应曲线的上界和下界围成的包络位于所述跟踪性能上界和所述跟踪性能下界之间。The two-degree-of-freedom controller is applied to the pneumatic control valve system to obtain the closed-loop system tracking boundary response curve. By adjusting the gain, zero point and pole of the pre-filter, the closed-loop system tracking boundary response curve in the closed-loop response curve The envelope formed by the upper bound and the lower bound is located between the upper bound of tracking performance and the lower bound of tracking performance.

本发明的上述技术方案相比现有技术具有以下优点:The above technical solution of the present invention has the following advantages compared with the prior art:

本发明通过QFT能够较好地处理被控对象不确定性的特点,利用已知的对象模型及其不确定性信息对气动调节阀系统进行控制器设计,将系统性能指标作为边界,利用多次试验的方法设计出使得包含不确定性的被控对象都满足系统性能指标要求,从而提高了气动调节阀系统的鲁棒性,使得气动调节阀系统在模型参数发生变化时的控制效果符合系统性能指标要求。The present invention can better deal with the characteristics of the uncertainty of the controlled object through QFT, use the known object model and its uncertainty information to design the controller of the pneumatic control valve system, use the system performance index as the boundary, and use multiple The experimental method is designed so that the controlled objects including uncertainties meet the system performance index requirements, thereby improving the robustness of the pneumatic control valve system, so that the control effect of the pneumatic control valve system is in line with the system performance when the model parameters change. Indicator requirements.

附图说明Description of drawings

为了使本发明的内容更容易被清楚的理解,下面根据本发明的具体实施例并结合附图,对本发明作进一步详细的说明,其中In order to make the content of the present invention more easily understood, the present invention will be described in further detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

图1是本发明的流程图;Fig. 1 is a flow chart of the present invention;

图2是本发明中气动调节阀系统的模块化结构示意图;Fig. 2 is a schematic diagram of the modular structure of the pneumatic regulating valve system in the present invention;

图3是本发明实施例中根据复合边界绘制的气动调节阀系统无控制器时的开环系统响应曲线;Fig. 3 is the open-loop system response curve when the pneumatic regulating valve system without a controller is drawn according to the compound boundary in the embodiment of the present invention;

图4是本发明实施例中带二自由度控制器的开环系统响应曲线;Fig. 4 is the open-loop system response curve with two degrees of freedom controller in the embodiment of the present invention;

图5是本发明实施例中的闭环系统跟踪边界响应曲线;Fig. 5 is the closed-loop system tracking boundary response curve in the embodiment of the present invention;

图6是本发明实施例中在标称状况下,将本发明与使用PID的方法进行对比的气动调节阀系统的闭环阶跃响应曲线图;Fig. 6 is a closed-loop step response curve diagram of the pneumatic control valve system comparing the present invention with the method using PID under the nominal condition in the embodiment of the present invention;

图7是本发明实施例中气动薄膜调节阀系统参数的变化在不确定设计范围内时,将本发明与使用PID的方法进行对比的气动调节阀系统的闭环阶跃响应曲线图;Fig. 7 is the closed-loop step response curve diagram of the pneumatic regulating valve system comparing the present invention with the method using PID when the variation of the parameters of the pneumatic film regulating valve system in the embodiment of the present invention is within the uncertain design range;

图8是本发明实施例中在模拟面对突发的极端工况的情况下,将本发明与使用PID的方法进行对比的气动调节阀系统的闭环阶跃响应曲线图。Fig. 8 is a closed-loop step response curve diagram of the pneumatic control valve system comparing the present invention with the method using PID in the case of simulating sudden extreme working conditions in the embodiment of the present invention.

具体实施方式Detailed ways

下面结合附图和具体实施例对本发明作进一步说明,以使本领域的技术人员可以更好地理解本发明并能予以实施,但所举实施例不作为对本发明的限定。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.

本发明针对气动调节阀系统在工业过程中受到的外界干扰和内部等价干扰的问题,提出了一种基于定量反馈理论(Quantitative Feedback Theory,QFT)的控制器设计方法。如图1流程图所示,本发明公开了一种基于定量反馈理论的气动调节阀控制方法,包括以下步骤:The invention proposes a controller design method based on Quantitative Feedback Theory (QFT) aiming at the external interference and internal equivalent interference that the pneumatic control valve system receives in the industrial process. As shown in the flow chart of Figure 1, the present invention discloses a method for controlling a pneumatic control valve based on quantitative feedback theory, which includes the following steps:

步骤1:针对气动调节阀系统在实际工业工程中受到的外界干扰和内部等价干扰,分析气动调节阀系统的工作流程,建立气动调节阀系统的数学模型。Step 1: According to the external interference and internal equivalent interference that the pneumatic control valve system receives in the actual industrial engineering, analyze the working process of the pneumatic control valve system, and establish the mathematical model of the pneumatic control valve system.

步骤1-1:如图2所示为气动调节阀系统的模块化结构示意图,所述气动调节阀系统的数学模型,按照气动调节阀的功能分区将系统划分为两个模块,包括智能定位器模块和阀门执行器模块,所述智能定位器模块包括内部控制器、电气转换环节、气动放大环节和阀位反馈环节(图2中为位移传感器),本实施例中阀位反馈环节(位移传感器)的传递函数为H(s)=1。所述电气转换环节和气动放大环节建模为二阶系统。所述阀门执行器模块包括密闭气室和阀杆运动环节,通过机理建模方法可得到该模块的数学模型。所述阀门执行器模块的机理模型分为气室气压转换环节、气压与力的转换环节和力与阀门执行器位移的转换环节。Step 1-1: As shown in Figure 2, it is a schematic diagram of the modular structure of the pneumatic control valve system. The mathematical model of the pneumatic control valve system divides the system into two modules according to the functional division of the pneumatic control valve, including the intelligent positioner module and a valve actuator module, the intelligent positioner module includes an internal controller, an electrical conversion link, a pneumatic amplification link and a valve position feedback link (displacement sensor in Fig. 2), and the valve position feedback link (displacement sensor ) transfer function is H(s)=1. The electrical conversion link and the pneumatic amplification link are modeled as second-order systems. The valve actuator module includes a closed air chamber and a valve stem movement link, and the mathematical model of the module can be obtained through a mechanism modeling method. The mechanism model of the valve actuator module is divided into the air pressure conversion link of the air chamber, the conversion link of air pressure and force, and the conversion link of force and valve actuator displacement.

步骤1-2:建立所述二阶系统的传递函数

Figure BDA0003667184470000071
其中,P1(s)为智能定位器模块的输出气压,x(s)是阀位输入,K是二阶系统增益,ξ是二阶系统阻尼系数,s是拉普拉斯算子,ω是二阶系统自然振荡频率。Step 1-2: Establish the transfer function of the second-order system
Figure BDA0003667184470000071
Among them, P 1 (s) is the output air pressure of the intelligent positioner module, x (s) is the valve position input, K is the second-order system gain, ξ is the second-order system damping coefficient, s is the Laplacian operator, ω is the natural oscillation frequency of the second-order system.

步骤1-3:建立所述气室气压转换环节的传递函数

Figure BDA0003667184470000072
其中P2(s)为经拉普拉斯变化后的输出气压P2,P1(s)为经拉普拉斯变化后的输入气压P1,Tv是气动阻容环节时间常数,s是拉普拉斯算子;Step 1-3: Establish the transfer function of the air pressure conversion link of the air chamber
Figure BDA0003667184470000072
Among them, P 2 (s) is the output air pressure P 2 changed by Laplace, P 1 (s) is the input air pressure P 1 changed by Laplace, T v is the time constant of the pneumatic resistance-capacitance link, s is the Laplacian operator;

传递函数G2(s)的推导过程为:The derivation process of the transfer function G 2 (s) is:

阀门执行器模块的气室可近似为阻容环节,根据理想气体等温状态下的弹性模量计算公式:The air chamber of the valve actuator module can be approximated as a resistance-capacity link, according to the calculation formula of the elastic modulus under the ideal gas isothermal state:

Figure BDA0003667184470000081
Figure BDA0003667184470000081

其中Kv,ΔP,ΔV和V分别为理想气体等温弹性模量,气室内压力变化值,压缩后气体体积的变化值和压缩前气体的体积,整理后得到

Figure BDA0003667184470000082
Among them, K v , ΔP, ΔV and V are the ideal gas isothermal elastic modulus, the change value of the pressure in the gas chamber, the change value of the gas volume after compression and the volume of the gas before compression.
Figure BDA0003667184470000082

Figure BDA0003667184470000083
并根据物料平衡关系式,
Figure BDA0003667184470000084
变为:make
Figure BDA0003667184470000083
And according to the material balance relation,
Figure BDA0003667184470000084
becomes:

Figure BDA0003667184470000085
Figure BDA0003667184470000085

其中Qi为气体流入流量,Qo为气体流出流量和P2为气室内的压强。Where Qi is the gas inflow flow rate, Qo is the gas outflow flow rate and P2 is the pressure inside the gas chamber.

在气体流速不高时,气体流量与压差之间有下列近似关系

Figure BDA0003667184470000086
其中P1为输入气压,Rv为导气气阻。由于气动薄膜执行机构的气室是封闭的,可知输出流量Qo=0。将
Figure BDA0003667184470000087
代入
Figure BDA0003667184470000088
中,经整理,并进行增量化处理后可得:When the gas flow rate is not high, there is the following approximate relationship between the gas flow rate and the pressure difference
Figure BDA0003667184470000086
Among them, P 1 is the input air pressure, and R v is the air guide air resistance. Since the air chamber of the pneumatic film actuator is closed, it can be seen that the output flow Q o =0. Will
Figure BDA0003667184470000087
substitute
Figure BDA0003667184470000088
Among them, after sorting and incremental processing, we can get:

Figure BDA0003667184470000089
Figure BDA0003667184470000089

其中ΔP2是输出气压变化量,ΔP1是输入气压变化量。Among them, ΔP 2 is the change of output air pressure, and ΔP 1 is the change of input air pressure.

为了简化模型的书写,将增量符号省略,可以得到:In order to simplify the writing of the model, the increment symbol is omitted to obtain:

Figure BDA00036671844700000810
Figure BDA00036671844700000810

其中Tv是气动阻容环节时间常数。Where T v is the time constant of the pneumatic resistance-capacitance link.

对上述一阶微分方程

Figure BDA00036671844700000811
进行拉氏变换,可得:For the above first order differential equation
Figure BDA00036671844700000811
Carrying out the Laplace transform, we can get:

Tv·sP2(s)+P2(s)=P1(s)T v ·sP 2 (s)+P 2 (s)=P 1 (s)

其中s是拉普拉斯算子,P2(s)是拉普拉斯变化后的P2。由此可得到气室气压转换环节的传递函数:Where s is the Laplacian operator, and P 2 (s) is P 2 after Laplacian transformation. From this, the transfer function of the gas pressure conversion link can be obtained:

Figure BDA0003667184470000091
Figure BDA0003667184470000091

步骤1-4:建立所述气压与力的转换环节的传递函数

Figure BDA0003667184470000092
其中F(s)=P2(s)·AD,AD为气室内膜片的有效面积。Steps 1-4: Establish the transfer function of the conversion link between air pressure and force
Figure BDA0003667184470000092
Wherein F(s)=P 2 (s)· AD , where AD is the effective area of the diaphragm in the gas chamber.

传递函数G3(s)的推到过程为:The derivation process of the transfer function G 3 (s) is:

气压与力转换环节是将气室内气压转换为执行机构推杆的拉力,力的大小F(t)与气室内膜片的有效面积AD有关,可以表示为:The air pressure and force conversion link is to convert the air pressure in the air chamber into the pulling force of the actuator push rod. The force F(t) is related to the effective area A D of the diaphragm in the air chamber, which can be expressed as:

F(t)=P2(t)ADF(t)=P 2 (t)A D ,

其中P2(t)是输出气压在时域中随时间变化的表达。where P 2 (t) is an expression of the output air pressure changing with time in the time domain.

该环节为比例环节,对F(t)进行拉氏变换得到:This link is a proportional link, and the Laplace transform of F(t) is obtained:

F(s)=P2(s)·ADF(s)=P 2 (s) · A D ,

将F(s)=P2(s)·AD转换为传递函数的形式,可得:Converting F(s)=P 2 (s)· AD into the form of transfer function, we can get:

Figure BDA0003667184470000093
Figure BDA0003667184470000093

步骤1-5:建立所述力与阀门执行器位移的转换环节的传递函数

Figure BDA0003667184470000094
其中x(s)是阀位输入,m为执行机构运动部件的总质量,x为执行机构的输出位移,k为执行机构弹簧的弹性系数,b为执行机构的内摩擦阻尼。Steps 1-5: Establish the transfer function of the conversion link between the force and the displacement of the valve actuator
Figure BDA0003667184470000094
Where x(s) is the valve position input, m is the total mass of the moving parts of the actuator, x is the output displacement of the actuator, k is the spring coefficient of the actuator, and b is the internal friction damping of the actuator.

传递函数G4(s)的推到过程为:The derivation process of the transfer function G 4 (s) is:

气动薄膜调节阀的位移转换环节可以近似为质量-弹簧-阻尼系统。根据牛顿第二定律得到气室输出力的系统方程为:The displacement conversion link of the pneumatic film regulating valve can be approximated as a mass-spring-damping system. According to Newton's second law, the system equation of the output force of the air chamber is:

Figure BDA0003667184470000101
Figure BDA0003667184470000101

在零初始条件下,进行拉氏变换,整理后可以得到气室输出力与阀杆位移的传递函数:Under the zero initial condition, the Laplace transform is carried out, and the transfer function of the output force of the air chamber and the displacement of the valve stem can be obtained after finishing:

Figure BDA0003667184470000102
Figure BDA0003667184470000102

步骤1-6:建立气动调节阀系统的传递函数G(s)=G1(s)G2(s)G3(s)G4(s),其中G1(s)为二阶系统的传递函数,G2(s)为气室气压转换环节的传递函数,G3(s)为气压与力的转换环节的传递函数,G4(s)为力与阀门执行器位移的转换环节的传递函数。Step 1-6: Establish the transfer function of the pneumatic control valve system G(s)=G 1 (s)G 2 (s)G 3 (s)G 4 (s), where G 1 (s) is the second-order system Transfer function, G 2 (s) is the transfer function of the air pressure conversion link of the air chamber, G 3 (s) is the transfer function of the conversion link of air pressure and force, G 4 (s) is the transfer function of the conversion link of force and valve actuator displacement Transfer Function.

步骤2:考虑实际工况下系统模型参数的不确定性变化范围,在气动调节阀系统的数学模型下得到被控对象模板,在被控对象模板下设计鲁棒稳定性指标和跟踪性能指标。Step 2: Considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system, and the robust stability index and tracking performance index are designed under the controlled object template.

步骤2-1:考虑实际工况下系统模型参数的不确定性变化范围,在气动调节阀系统的数学模型下得到被控对象模板。Step 2-1: Considering the uncertainty range of system model parameters under actual working conditions, the controlled object template is obtained under the mathematical model of the pneumatic control valve system.

步骤2-1-1:考虑实际工况下系统模型参数的不确定性变化范围,得到被控对象模板G1(s)、G2(s)、G3(s)和G4(s)实际表达式,本实施例中得到

Figure BDA0003667184470000103
G3(s)=65,
Figure BDA0003667184470000104
将G4(s)中的执行机构运动部分质量m,弹簧弹性系数k和执行机构内摩擦阻尼b作为气动调节阀系统的不确定参数;Step 2-1-1: Considering the uncertainty range of system model parameters under actual working conditions, obtain the controlled object templates G 1 (s), G 2 (s), G 3 (s) and G 4 (s) The actual expression, obtained in this example
Figure BDA0003667184470000103
G 3 (s)=65,
Figure BDA0003667184470000104
The mass m of the moving part of the actuator in G 4 (s), the spring elastic coefficient k and the internal friction damping b of the actuator are used as uncertain parameters of the pneumatic control valve system;

步骤2-1-2:经过实际测量得到不确定参数m、k和b的范围,本实施例中得到m∈[0.04 0.05]kg,k∈[8 10]N/mm,b∈[0.8 1]N/mm。选取范围内的m、k和b的一个值作为系统的标称参数,得到被控对象的传递函数G0(s);本实施例中选取m0=0.05kg,k0=10N/mm,b0=1N/mm,得到Step 2-1-2: Obtain the range of uncertain parameters m, k and b through actual measurement. In this embodiment, m∈[0.04 0.05]kg, k∈[8 10]N/mm, b∈[0.8 1 ] N/mm. Select a value of m, k and b within the range as the nominal parameter of the system to obtain the transfer function G 0 (s) of the controlled object; in this embodiment, select m 0 =0.05kg, k 0 =10N/mm, b 0 =1N/mm, get

Figure BDA0003667184470000111
Figure BDA0003667184470000111

步骤2-1-3:选择被控对象具有较大不确定性的频率作为频率阵列,根据气动调节阀系统的动态特性要求设置闭环系统阶跃响应的调节时间ts、上升时间tp、超调量σ、相角裕度

Figure BDA0003667184470000112
和幅值裕度KM。本实施例中选择的频率阵列ω=[0.01 0.05 0.1 0.5 1 5 10 50100 500 1000]rad/s,设置闭的环系统阶跃响应的调节时间ts≤2.5s,上升时间tp≤1.5s,超调量σ≤5%,相角裕度
Figure BDA0003667184470000113
幅值裕度KM≥5dB。Step 2-1-3: Select the frequency with greater uncertainty of the controlled object as the frequency array, and set the adjustment time t s , rise time t p , super Modulation σ, phase angle margin
Figure BDA0003667184470000112
and amplitude margin K M . The frequency array ω=[0.01 0.05 0.1 0.5 1 5 10 50100 500 1000]rad/s selected in this embodiment, the adjustment time t s of the step response of the closed loop system is set ≤2.5s, and the rise time t p ≤1.5s , overshoot σ≤5%, phase angle margin
Figure BDA0003667184470000113
Amplitude margin K M ≥ 5dB.

步骤2-2:在被控对象模板下设计鲁棒稳定性指标和跟踪性能指标。Step 2-2: Design robust stability indicators and tracking performance indicators under the template of the controlled object.

步骤2-2-1:建立鲁棒稳定性指标为:Step 2-2-1: Establish a robust stability index as:

Figure BDA0003667184470000114
Figure BDA0003667184470000114

Figure BDA0003667184470000115
Figure BDA0003667184470000115

Figure BDA0003667184470000116
Figure BDA0003667184470000116

其中s=jω,L(jω)=C(jω)·G0(jω),C(jω)为待设计的反馈控制器,G0(jω)=G0(s);Where s=jω, L(jω)=C(jω) G 0 (jω), C(jω) is the feedback controller to be designed, G 0 (jω)=G 0 (s);

本实施例中得到的具体鲁棒稳定性指标为:The specific robust stability index obtained in this embodiment is:

Figure BDA0003667184470000117
Figure BDA0003667184470000117

Figure BDA0003667184470000121
Figure BDA0003667184470000121

Figure BDA0003667184470000122
Figure BDA0003667184470000122

可以保证系统的最小幅值裕度KM为5.26dB,最小相位裕度

Figure BDA0003667184470000123
为49°,满足鲁棒稳定性要求。Can guarantee the minimum amplitude margin K M of the system is 5.26dB, the minimum phase margin
Figure BDA0003667184470000123
is 49°, which meets the requirement of robust stability.

步骤2-2-2:建立跟踪性能指标为:Step 2-2-2: Establish tracking performance indicators as:

Figure BDA0003667184470000124
Figure BDA0003667184470000124

其中D(jω)为需要设计的前置滤波器,Tu(jω)为跟踪性能的上界,Tl(jω)为跟踪性能的下界。Among them, D(jω) is the pre-filter to be designed, Tu (jω) is the upper bound of tracking performance, and T l (jω) is the lower bound of tracking performance.

本实施例中跟踪性能的上界

Figure BDA0003667184470000125
跟踪性能的下界
Figure BDA0003667184470000126
所选择的跟踪性能的上下界,保证了满足该上下界的闭环系统阶跃响应,其超调量不超过5%,上升时间不超过1.5秒,调节时间不超过2.5秒,符合跟踪性能要求。The upper bound of tracking performance in this example
Figure BDA0003667184470000125
Lower bound on tracking performance
Figure BDA0003667184470000126
The selected upper and lower bounds of the tracking performance ensure the step response of the closed-loop system meeting the upper and lower bounds. The overshoot does not exceed 5%, the rise time does not exceed 1.5 seconds, and the adjustment time does not exceed 2.5 seconds, which meets the tracking performance requirements.

定量反馈是指将性能指标量量化出生成响应边界对控制器设计进行约束,相关的指标还要输入扰动抑制指标,输出扰动抑制指标,灵敏度指标等,气动调节阀控制器设计时,本实施例中根据系统性能指标要求只选择了鲁棒稳定性指标和跟踪性能指标。Quantitative feedback refers to the quantification of performance indicators to generate response boundaries to constrain the controller design. Related indicators also need to input disturbance suppression indicators, output disturbance suppression indicators, sensitivity indicators, etc. When designing a pneumatic control valve controller, this embodiment According to the system performance index requirements, only the robust stability index and the tracking performance index are selected.

步骤3:根据被控对象模板、鲁棒稳定性指标和跟踪性能指标得到复合边界,根据复合边界得到气动调节阀系统无控制器时的开环系统响应曲线。Step 3: According to the controlled object template, the robust stability index and the tracking performance index, the composite boundary is obtained, and the open-loop system response curve of the pneumatic control valve system without a controller is obtained according to the composite boundary.

步骤3-1:根据被控对象模板、鲁棒稳定性指标和跟踪性能指标得到复合边界。Step 3-1: Obtain the compound boundary according to the controlled object template, robust stability index and tracking performance index.

步骤3-1-1:在所述频率阵列上将被控对象模板根据所述鲁棒稳定性指标在Nichols图上建立鲁棒稳定性边界,这是性能指标边界生成过程,以选取的频率阵列进行相应频率处边界生成,先以部分代替整体减少计算量,控制设计多次试验会保证全部频率满足要求。Step 3-1-1: On the frequency array, the controlled object template is established on the Nichols diagram according to the robust stability index, which is the performance index boundary generation process, and the selected frequency array To generate the boundary at the corresponding frequency, first replace the whole with part to reduce the amount of calculation, and control the design for multiple experiments to ensure that all frequencies meet the requirements.

步骤3-1-2:在所述频率阵列上将被控对象模板根据所述跟踪性能指标在Nichols图上建立跟踪性能边界。Step 3-1-2: On the frequency array, the controlled object template is used to establish a tracking performance boundary on the Nichols diagram according to the tracking performance index.

步骤3-1-3:将鲁棒稳定性边界和跟踪性能边界整合,得到复合边界。Step 3-1-3: Integrate the robust stability boundary and the tracking performance boundary to obtain a composite boundary.

由图3可以看出,未设计控制器时,系统开环频率响应曲线不符合系统性能指标边界要求,系统开环频率曲线与鲁棒稳定边界相交且相应频率点未处于跟踪性能边界上方。It can be seen from Figure 3 that when the controller is not designed, the system open-loop frequency response curve does not meet the boundary requirements of the system performance index, the system open-loop frequency curve intersects the robust stability boundary and the corresponding frequency point is not above the tracking performance boundary.

步骤3-2:根据复合边界得到气动调节阀系统无控制器时的开环系统响应曲线;本实施例中根据复合边界绘制的气动调节阀系统无控制器时的开环系统响应曲线如图3所示。Step 3-2: Obtain the open-loop system response curve of the pneumatic control valve system without a controller according to the composite boundary; the open-loop system response curve of the pneumatic control valve system without a controller drawn according to the composite boundary in this embodiment is shown in Figure 3 shown.

步骤4:建立包含反馈控制器和前置滤波器的二自由度控制器,将所述二自由度控制器作用到所述气动调节阀系统中,调整所述二自由度控制器直到所述开环系统响应曲线满足性能要求,得到满足鲁棒稳定性指标和跟踪性能指标要求的气动调节阀系统。Step 4: Establish a two-degree-of-freedom controller including a feedback controller and a pre-filter, apply the two-degree-of-freedom controller to the pneumatic control valve system, and adjust the two-degree-of-freedom controller until the opening The response curve of the loop system meets the performance requirements, and a pneumatic control valve system that meets the requirements of the robust stability index and the tracking performance index is obtained.

步骤4-1:使用QFT工具箱和环路成形方法建立包含反馈控制器和前置滤波器的二自由度控制器。Step 4-1: Use the QFT toolbox and the loop shaping method to build a two-degree-of-freedom controller including a feedback controller and a pre-filter.

步骤4-2:调整所述反馈控制器直到所述开环系统响应曲线满足鲁棒稳定性指标的要求。本实施例中,在如图4所示的带二自由度控制器的气动调节阀系统中,通过调整反馈控制器的增益、零点与极点的方式,使得所述开环系统响应曲线L0(jω)满足:在所选择的频率点处位于对应跟踪性能边界上方,并且在高频处L0(jω)不与鲁棒稳定性边界相交,此时调整得到的反馈控制器

Figure BDA0003667184470000141
Step 4-2: Adjusting the feedback controller until the response curve of the open-loop system meets the requirement of the robust stability index. In this embodiment, in the pneumatic regulating valve system with a two-degree-of-freedom controller as shown in FIG. 4 , the open-loop system response curve L 0 ( jω) satisfies: the selected frequency point is located above the corresponding tracking performance boundary, and L 0 (jω) does not intersect the robust stability boundary at high frequencies, then the adjusted feedback controller
Figure BDA0003667184470000141

步骤4-3:将此时调整得到的反馈控制器C(s)=C(jω)带入所述气动调节阀系统中,得到满足鲁棒稳定性指标要求的气动调节阀系统。本实施例中,图4中的0.01-1是左右贯通为跟踪性能边界,即0.01-1为低频处,图4中的5-10是鲁棒稳定椭圆为鲁棒稳定性边界,即5-10为高频处。从图4可以得到,开环系统响应曲线在所选择频率点处位于跟踪性能边界上方且与边界的距离很小,保证系统在设计前置滤波器时能满足跟踪性能要求。在高频处,开环系统响应曲线没有与鲁棒稳定性边界相交,从而保证系统的稳定性。Step 4-3: Bring the adjusted feedback controller C(s)=C(jω) into the pneumatic control valve system to obtain a pneumatic control valve system that meets the requirements of the robust stability index. In this embodiment, 0.01-1 in Fig. 4 is left and right through as the tracking performance boundary, that is, 0.01-1 is a low frequency place, and 5-10 in Fig. 4 is a robust stable ellipse, which is a robust stability boundary, that is, 5- 10 is the high frequency. It can be seen from Figure 4 that the response curve of the open-loop system is located above the tracking performance boundary at the selected frequency point and the distance from the boundary is very small, which ensures that the system can meet the tracking performance requirements when designing the pre-filter. At high frequencies, the open-loop system response curve does not intersect the robust stability boundary, thus ensuring the stability of the system.

步骤4-4:调整所述前置滤波器直到所述开环系统响应曲线满足跟踪性能指标的要求。本实施例中,将二自由度控制器作用到气动调节阀系统中得到如图5所示的闭环系统跟踪边界响应曲线,通过调整前置滤波器的增益、零点与极点的方式,使得闭环系统跟踪边界响应曲线中闭环响应曲线的上界和下界围成的包络位于所述跟踪性能上界Tu(s)=Tu(jω)和所述跟踪性能下界Tl(s)=Tl(jω)之间;此时调整得到的前置滤波器

Figure BDA0003667184470000142
Step 4-4: Adjusting the pre-filter until the response curve of the open-loop system meets the requirements of the tracking performance index. In this embodiment, the two-degree-of-freedom controller is applied to the pneumatic control valve system to obtain the closed-loop system tracking boundary response curve shown in Figure 5. By adjusting the gain, zero point and pole of the pre-filter, the closed-loop system The envelope formed by the upper bound and the lower bound of the closed-loop response curve in the tracking boundary response curve is located at the upper bound of the tracking performance T u (s) = T u (jω) and the lower bound of the tracking performance T l (s) = T l (jω); at this time, the adjusted pre-filter
Figure BDA0003667184470000142

步骤4-5:将此时调整得到的前置滤波器D(s)=D(jω)带入所述气动调节阀系统中,得到满足跟踪性能指标要求的气动调节阀系统。Step 4-5: Bring the adjusted pre-filter D(s)=D(jω) into the pneumatic control valve system to obtain a pneumatic control valve system that meets the requirements of the tracking performance index.

在上述反馈控制器C(s)和前置滤波器D(s)的作用下,气动调节阀系统满足鲁棒稳定性指标和跟踪性能指标的要求。Under the action of the above-mentioned feedback controller C(s) and pre-filter D(s), the pneumatic control valve system meets the requirements of robust stability index and tracking performance index.

本发明通过QFT能够较好地处理被控对象不确定性的特点,利用已知的对象模型及其不确定性信息对气动调节阀系统进行控制器设计,将系统性能指标作为边界,利用多次试验的方法设计出使得包含不确定性的被控对象都满足系统性能指标要求,从而提高了气动调节阀系统的鲁棒性,使得气动调节阀系统在模型参数发生变化时的控制效果符合系统性能指标要求。The present invention can better deal with the characteristics of the uncertainty of the controlled object through QFT, use the known object model and its uncertainty information to design the controller of the pneumatic control valve system, use the system performance index as the boundary, and use multiple The experimental method is designed so that the controlled objects including uncertainties meet the system performance index requirements, thereby improving the robustness of the pneumatic control valve system, so that the control effect of the pneumatic control valve system is in line with the system performance when the model parameters change. Indicator requirements.

为了进一步说明本发明的有益效果,本实施例中将使用本发明的气动调节阀系统和使用PID控制方法的气动调节阀系统进行对比。In order to further illustrate the beneficial effects of the present invention, in this embodiment, a comparison will be made between the pneumatic regulating valve system using the present invention and the pneumatic regulating valve system using the PID control method.

首先,在标称状况下将本发明与使用PID方法进行对比,在标称状况下气动调节阀系统的闭环阶跃响应曲线如图6所示。给定阀位信号为20mm时的闭环阶跃响应曲线(满量程为50mm),图6中虚线为使用PID方法,实线为使用本发明。从图6可以看出,在标称状况下,使用本发明的气动调节阀系统无超调(超调量(overshoot)是在阶跃输入作用下,被调量的瞬时最大偏差值Xmax与稳态值X(∞)之比,一般用百分比表示:超调量=[Xmax—X(∞)]/X(∞)×100%,此处调节最大瞬时值超出设定值20mm的百分比),而使用PID方法出现了一定的超调,可以看出本发明的鲁棒性优于PID控制方法;同时,使用本发明时,闭环系统满足设计过程中的各性能指标要求,因此本发明优于PID控制方法。First, compare the present invention with the PID method under nominal conditions, and the closed-loop step response curve of the pneumatic control valve system under nominal conditions is shown in FIG. 6 . The closed-loop step response curve (full scale is 50mm) when the given valve position signal is 20mm, the dotted line in Fig. 6 is to use the PID method, and the solid line is to use the present invention. As can be seen from Figure 6, under nominal conditions, the pneumatic control valve system of the present invention has no overshoot (the overshoot (overshoot) is the difference between the instantaneous maximum deviation value Xmax of the regulated quantity and the stable value under the action of a step input. The ratio of the state value X(∞) is generally expressed as a percentage: overshoot = [Xmax—X(∞)]/X(∞)×100%, where the percentage of the maximum instantaneous value exceeding the set value of 20mm is adjusted here), And use PID method to have occurred certain overshoot, it can be seen that the robustness of the present invention is better than PID control method; Simultaneously, when using the present invention, closed-loop system satisfies each performance index requirement in the design process, so the present invention is superior to PID control method.

接着,在气动薄膜调节阀系统参数的变化在不确定设计范围内时将本发明与使用PID方法进行对比。给定阀位信号为20mm时的闭环阶跃响应曲线(满量程为50mm),当气动薄膜调节阀系统参数的变化在不确定设计范围内时,即阀门执行器内摩擦阻尼b=0.8N/mm,弹簧的弹性系数k=8N/mm情况下,其闭环阶跃响应曲线如图7所示。此时,使用本发明的闭环阶跃响应曲线其超调量小于5%、上升时间小于1.5秒、调节时间小于2.5秒,控制系统仍然满足系统的性能指标要求。而使用PID方法的最大瞬时值接近25mm,闭环阶跃响应曲线其超调量为(25-20)/20×100%,远大于系统要求的5%,不满足系统的性能指标要求。本发明同样优于PID控制方法Next, the present invention is compared with the use of the PID method when the variation of the parameters of the pneumatic membrane regulating valve system is within the uncertain design range. Given the closed-loop step response curve when the valve position signal is 20mm (full scale is 50mm), when the change of the system parameters of the pneumatic film regulating valve is within the uncertain design range, that is, the internal frictional damping of the valve actuator b=0.8N/ mm, and the elastic coefficient k of the spring = 8N/mm, its closed-loop step response curve is shown in Figure 7. At this time, using the closed-loop step response curve of the present invention, the overshoot is less than 5%, the rise time is less than 1.5 seconds, and the adjustment time is less than 2.5 seconds, and the control system still meets the performance index requirements of the system. However, the maximum instantaneous value using the PID method is close to 25mm, and the overshoot of the closed-loop step response curve is (25-20)/20×100%, which is far greater than the 5% required by the system, which does not meet the performance index requirements of the system. The present invention is also superior to the PID control method

最后,在模拟面对突发的极端工况的情况下,将本发明与使用PID方法进行对比。在阀门执行器内摩擦阻尼和弹簧的弹性系数持续减小的实际工况下,当参数减小到b=0.7N/mm,k=7N/mm时,系统的闭环阶跃响应曲线如图8所示。从图8可以看出,使用PID方法的闭环阶跃响应曲线其超调量已达到38%严重超过系统性能要求的5%,其调节时间也已超过2.5秒,严重超过系统的性能指标要求;使用本发明的闭环阶跃响应曲线,其超调量仍小于5%,其上升时间仍小于1.5秒,其调节时间仍小于2.5秒,气动调节阀系统的性能指标仍符合设计要求。由上述分析可知,面对突发的极端工况,即系统的参数不确定性超出设计工况时,本发明的闭环系统仍然具有较强的鲁棒性,由此显示出本发明的实际工程应用价值。Finally, the present invention is contrasted with the use of the PID method in the case of simulations facing sudden extreme operating conditions. Under the actual working condition that the internal frictional damping of the valve actuator and the elastic coefficient of the spring continue to decrease, when the parameters are reduced to b=0.7N/mm, k=7N/mm, the closed-loop step response curve of the system is shown in Figure 8 shown. It can be seen from Figure 8 that the overshoot of the closed-loop step response curve using the PID method has reached 38%, seriously exceeding 5% of the system performance requirements, and its adjustment time has also exceeded 2.5 seconds, seriously exceeding the system performance index requirements; Using the closed-loop step response curve of the present invention, the overshoot is still less than 5%, the rise time is still less than 1.5 seconds, the adjustment time is still less than 2.5 seconds, and the performance index of the pneumatic control valve system still meets the design requirements. As can be seen from the above analysis, in the face of sudden extreme working conditions, that is, when the parameter uncertainty of the system exceeds the design working condition, the closed-loop system of the present invention still has strong robustness, which shows that the actual engineering of the present invention Value.

通过三种情况下的对比实验,进一步说明了本发明能够很好地控制气动调节阀系统,相比于传统的控制方法具有更好的鲁棒性,使得气动调节阀系统在模型参数发生变化时的控制效果符合系统性能指标要求。Through comparative experiments in three cases, it is further illustrated that the present invention can control the pneumatic control valve system well, and has better robustness compared with the traditional control method, so that the pneumatic control valve system can be controlled when the model parameters change. The control effect meets the system performance index requirements.

本领域内的技术人员应明白,本申请的实施例可提供为方法、系统、或计算机程序产品。因此,本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且,本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。Those skilled in the art should understand that the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器,使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present application is described with reference to flowcharts and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中,使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品,该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上,使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理,从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

显然,上述实施例仅仅是为清楚地说明所作的举例,并非对实施方式的限定。对于所属领域的普通技术人员来说,在上述说明的基础上还可以做出其它不同形式变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引申出的显而易见的变化或变动仍处于本发明创造的保护范围之中。Apparently, the above-mentioned embodiments are only examples for clear description, and are not intended to limit the implementation. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in various forms can also be made. It is not necessary and impossible to exhaustively list all the implementation manners here. However, the obvious changes or changes derived therefrom are still within the scope of protection of the present invention.

Claims (8)

1. A pneumatic control valve control method based on a quantitative feedback theory is characterized by comprising the following steps:
step 1: establishing a mathematical model of the pneumatic regulating valve system; the mathematical model of the pneumatic regulating valve system comprises an intelligent positioner module and a valve actuator module,
the intelligent locator module comprises an internal controller, an electrical conversion link, a pneumatic amplification link and a valve position feedback link, wherein the electrical conversion link and the pneumatic amplification link are modeled into a second-order system;
the valve actuator module comprises a closed air chamber and a valve rod movement link, and a mechanism model of the valve actuator module is divided into an air chamber air pressure conversion link, an air pressure and force conversion link and a force and valve actuator displacement conversion link;
transfer function G(s) = G of the pneumatically regulated valve system 1 (s)G 2 (s)G 3 (s)G 4 (s) in which G 1 (s) is the transfer function of the second order system, G 2 (s) is a transfer function of the air chamber air pressure conversion link, G 3 (s) is a transfer function of said conversion element of pressure and force, G 4 (s) is a transfer function of a conversion link of the force and valve actuator displacement;
transfer function of the second order system
Figure FDA0004000222180000011
Wherein, P 1 (s) is the output air pressure of the intelligent locator module, x(s) is the valve position input, K is the second-order system gain, ξ is the second-order system damping coefficient, s is the Laplacian operator, and ω is the second-order system natural oscillation frequency;
transfer function of air chamber air pressure conversion link
Figure FDA0004000222180000012
Wherein P is 2 (s) is the output pressure P after Laplace change 2 ,P 1 (s) is the input pressure P after Laplace change 1 ,T v Is the pneumatic resistance-capacitance link time constant, s is the laplace operator;
transfer function of the conversion link of the air pressure and the force
Figure FDA0004000222180000013
Wherein F(s) = P 2 (s)·A D ,A D Is the effective area of the diaphragm in the air chamber;
transfer function of the conversion link of the force and the displacement of the valve actuator
Figure FDA0004000222180000021
Wherein x(s) is valve position input, m is the total mass of the moving parts of the actuating mechanism, x is the output displacement of the actuating mechanism, k is the elastic coefficient of the spring of the actuating mechanism, and b is the internal friction damping of the actuating mechanism;
and 2, step: considering the uncertainty change range of system model parameters under the actual working condition, obtaining a controlled object template under the mathematical model of the pneumatic regulating valve system, and designing a robust stability index and a tracking performance index under the controlled object template;
and 3, step 3: obtaining a composite boundary according to the controlled object template, the robust stability index and the tracking performance index, and obtaining an open-loop system response curve when a pneumatic regulating valve system has no controller according to the composite boundary;
and 4, step 4: establishing a two-degree-of-freedom controller comprising a feedback controller and a pre-filter, acting the two-degree-of-freedom controller into the pneumatic regulating valve system, and regulating the two-degree-of-freedom controller until the response curve of the open-loop system meets the performance requirement to obtain the pneumatic regulating valve system meeting the requirements of robust stability index and tracking performance index.
2. The quantitative feedback theory-based pneumatic control valve control method according to claim 1, wherein: the method comprises the following steps of considering the uncertainty change range of system model parameters under the actual working condition, and obtaining a controlled object template under the mathematical model of the pneumatic regulating valve system, wherein the method specifically comprises the following steps:
the uncertainty change range of the system model parameters under the actual working condition is considered to obtain a controlled object template G 1 (s)、G 2 (s)、G 3 (s) and G 4 (s) actual expression, G 4 (s) the mass m of the moving part of the actuating mechanism, the elastic coefficient k of the spring and the friction damping b in the actuating mechanism are used as uncertain parameters of the pneumatic adjusting valve system;
obtaining the range of uncertain parameters m, k and b through actual measurement, selecting one value of m, k and b in the range as the nominal parameter of the system, and obtaining the transfer function G of the controlled object 0 (s);
Selecting the frequency with larger uncertainty of the controlled object as a frequency array, and setting the adjusting time t of the step response of the closed-loop system according to the dynamic characteristic requirement of the pneumatic adjusting valve system s Rising time t p Overshoot σ, phase angle margin
Figure FDA0004000222180000035
Sum amplitude margin K M
3. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 2, wherein: the robust stability index is as follows:
Figure FDA0004000222180000031
Figure FDA0004000222180000032
Figure FDA0004000222180000033
wherein s = j ω, L (j ω) = C (j ω) · G 0 (j ω), C (j ω) is the feedback controller to be designed, G 0 (jω)=G 0 (s)。
4. The quantitative feedback theory-based pneumatic control valve control method according to claim 3, wherein: the tracking performance indexes are as follows:
Figure FDA0004000222180000034
where D (j ω) is the pre-filter to be designed, T u (j ω) is an upper bound on tracking performance, T l (j ω) is the lower bound of tracking performance.
5. The quantitative feedback theory-based pneumatic control valve control method according to claim 2, wherein: obtaining a composite boundary according to the controlled object template, the robust stability index and the tracking performance index, specifically:
establishing a robust stability boundary on the Nichols diagram by using the controlled object template on the frequency array according to the robust stability index,
establishing a tracking performance boundary on the Nichols graph by using the controlled object template on the frequency array according to the tracking performance index,
and integrating the robust stability boundary and the tracking performance boundary to obtain a composite boundary.
6. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 4, wherein: the adjusting the two-degree-of-freedom controller until the response curve of the open-loop system meets the performance requirement to obtain the pneumatic regulating valve system meeting the requirements of robust stability index and tracking performance index specifically comprises the following steps:
adjusting the feedback controller until the response curve of the open loop system meets the requirement of the robust stability index, and bringing the feedback controller obtained by adjustment into the pneumatic regulating valve system to obtain the pneumatic regulating valve system meeting the requirement of the robust stability index;
and adjusting the prefilter until the response curve of the open loop system meets the requirement of the tracking performance index, and bringing the prefilter obtained by adjustment into the pneumatic regulating valve system to obtain the pneumatic regulating valve system meeting the requirement of the tracking performance index.
7. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 6, wherein: the adjusting the feedback controller until the response curve of the open loop system meets the requirement of the robust stability index specifically comprises:
in the pneumatic regulating valve system with the two-degree-of-freedom controller, the response curve of the open-loop system meets the following requirements by adjusting the gain, the zero and the pole of a feedback controller: located above the corresponding tracking performance boundary at the selected frequency points and not intersecting the robust stability boundary at high frequencies.
8. The pneumatic regulating valve control method based on the quantitative feedback theory as claimed in claim 6, wherein: the pre-filter is adjusted until the response curve of the open loop system meets the requirement of the tracking performance index, and the method specifically comprises the following steps:
and applying a two-degree-of-freedom controller to a pneumatic regulating valve system to obtain a closed loop system tracking boundary response curve, and enabling an envelope formed by an upper bound and a lower bound of the closed loop response curve in the closed loop system tracking boundary response curve to be positioned between the upper bound and the lower bound of the tracking performance by adjusting the gain, the zero and the pole of a pre-filter.
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