CN101339409B - Identification Method of Digital-to-Analog and Analog-to-Digital Conversion Card Based on Equivalent Model Transformation - Google Patents

Abstract

A digital-analog and analog-to-digital conversion card identification method based on equivalent model transformation in the field of industrial control technology, the steps are: using Simulink and xPCTarget to build a test platform for digital-to-analog conversion cards and analog-to-digital conversion cards for semi-physical simulation The series test of the digital-to-analog conversion card and the analog-to-digital conversion card in the control system obtains accurate input and output test data through pure digital signal input and storage; based on the principle of equivalent model transformation, an equivalent model after the two are connected in series is established , using the input and output test data collected under the test platform to identify the equivalent model, in which the curve fitting and normal distribution verification methods are used to obtain the constant value drift and quantization error of the digital-to-analog conversion card and the analog-to-digital conversion card, and based on the prediction The error minimization method is used to obtain the conversion delay model. The invention can replace the digital-to-analog conversion card and the analog-to-digital conversion card by the equivalent model, and can design the control algorithm off-line to improve the performance of the control system.

Description

Identification Method of Digital-to-Analog and Analog-to-Digital Conversion Card Based on Equivalent Model Transformation

technical field

The invention relates to a digital-analog and analog-to-digital conversion card identification method in the technical field of industrial control, in particular to a digital-to-analog and analog-to-digital conversion card identification method based on equivalent model conversion.

Background technique

In the process of industrial control system design, a semi-physical simulation control system usually includes analog-to-digital conversion cards, digital-to-analog conversion cards, signal processing boards, controllers, drive circuits, controlled objects and other monitoring units. In order to obtain reliable control performance, semi-physical control systems need to be mathematically modeled and simulated. In system modeling, the analog-to-digital conversion and digital-to-analog conversion parts are often ignored or only considered as a gain link. However, according to the basic principles of digital-to-analog conversion and analog-to-digital conversion, the signal conversion process will not only produce constant drift and quantization errors, but also produce conversion delays, that is, after the signal passes through digital-to-analog and analog-to-digital conversion, its phase and amplitude The value property will change. When the performance of the digital-to-analog conversion card and analog-to-digital conversion card used in the control system is poor, it will have a greater impact on the control signal. Especially for the precise semi-physical simulation control system, a large control error will be generated, which may even lead to the divergence of the control system. In order to improve the performance of the semi-physical simulation control system, it is necessary to carry out mathematical modeling on the digital-to-analog and the analog-to-digital conversion card.

After searching the documents of the prior art, it was found that in Tsinghua University's doctoral thesis "Research on DC Electrostatic Support System with Variable Structure Support and Stiffness Compensation" (September 2002, pages 60-64), the method with time delay and The model of the characteristics of the zero-order keeper approximates the process of digital-to-analog and analog-to-digital conversion, where the delay link represents the time consumed by the analog-to-digital conversion and digital-to-analog conversion, and the zero-order keeper describes the process of holding the analog signal, and the approximate model Bring in the closed-loop control system to redesign the controller to improve the performance of the control system. Since the time constants in the model are approximate, they often cannot reflect the conversion delay of the actual analog-to-digital conversion and digital-to-analog conversion card, so the accuracy of the model is not very high. Moreover, for multi-channel digital-to-analog conversion cards and analog-to-digital conversion cards, there will be differences in the conversion delay of each channel, and such differences are usually not given in the corresponding manuals. In addition, although the causes of quantization errors are discussed in the literature, and methods to reduce quantization errors are given, the impact of constant drift is not mentioned. In fact, for digital-to-analog conversion cards and analog-to-digital conversion cards, constant value drift has a greater impact on the stability of the control system than quantization errors. It can not only reduce the performance of the control system, but even cause the control system to diverge.

Contents of the invention

Aiming at the problems existing in the prior art, the invention proposes an identification method for digital-analog and analog-to-digital conversion cards based on equivalent model transformation. According to the characteristics of the semi-physical simulation control system, the digital-to-analog conversion card and the analog-to-digital conversion card are connected in series for unified identification. Using Simulink (a modular simulation modeling platform developed by Maxworks) and xPCTarget (a real-time simulation modeling toolbox developed by Maxworks) to establish a digital-to-analog conversion card and an analog-to-digital conversion card test platform. Using the test data, the equivalent models of the digital-to-analog conversion card and the analog-to-digital conversion card are identified. The equivalent model includes conversion delay, constant value drift and quantization error, and can accurately simulate the working characteristics of the digital-to-analog conversion card and the analog-to-digital conversion card connected in series. In the semi-physical simulation control system design, the control engineer can use the equivalent model obtained by the identification method to replace the digital-to-analog conversion card and the analog-to-digital conversion card to establish a simulation model of the control system. Furthermore, various optimization algorithms can be used to redesign the controller to improve the performance of the control system.

The present invention is achieved through the following technical solutions, and the present invention comprises the following steps:

The first step is to use Simulink and xPCTarget to build a test platform for digital-analog conversion cards and analog-to-digital conversion cards, which is used for serial testing of digital-analog conversion cards and analog-to-digital conversion cards in semi-physical simulation. Through pure digital signal input and Storage to obtain accurate input and output test data;

In the second step, based on the principle of equivalent model transformation, the equivalent model of the series connection of the digital-to-analog conversion card and the analog-to-digital conversion card is established. This model includes constant value drift, quantization error and conversion delay. Then use the input and output test data collected under the test platform to identify the equivalent model, including constant value drift identification, quantization error identification and conversion delay identification, in which the digital-to-analog conversion is obtained by curve fitting and normal distribution verification method The constant value drift and quantization error of the card and the analog-to-digital conversion card, and the conversion delay model is obtained based on the method of minimizing the prediction error, and finally the equivalent model is verified to complete the entire identification process.

Described establishment of the test platform of digital-to-analog conversion card and analog-to-digital conversion card, the steps are as follows:

①Software installation: The test platform is established based on the host-target model, so two PCs are required. A host is used for model building, code generation and data analysis; a target machine is used for real-time operation of the test model and data collection, where the target machine can be an ordinary PC, PC104 or an industrial control board. Install the Matlab development environment on the host computer, including Simulink, xPCTarget, Real Time Workshop (a real-time code generation toolbox developed by Maise Walker), Curve Fitting (a curve fitting toolbox developed by Maise Walker) and System Identification (a toolbox developed by Mais Walker). System Identification Toolbox developed by Swerk Corporation), the above toolbox can be purchased through Maeswork Corporation. Use the xPCTarget toolbox to generate a real-time operating system and install it on the target machine.

②Hardware connection

Communication between the host computer and the target computer: Based on the TCP/IP protocol, the host computer and the target computer are connected through a network cable in the LAN to realize the communication between the two. In this way, the code of the host machine can be downloaded to the target machine, and the test data of the target machine can be uploaded to the host machine.

③Install the digital-to-analog conversion card and the analog-to-digital conversion card: connect the conversion card with the target machine according to the interface form of the conversion card. For example, if the conversion card is a PCI interface, insert the conversion card into the PCI slot of the target machine. In order to identify the model after the digital-to-analog conversion card and the analog-to-digital conversion card are connected in series, the analog output and analog input channels of the two are connected with wires.

④ Test model establishment

The test model of digital-to-analog conversion card and analog-to-digital conversion is established under Simulink. The model includes a standard digital signal source, digital-to-analog conversion card interface module, analog-to-digital conversion card interface module and data acquisition module. Usually the I/O library of xPCTarget provides a variety of interface modules for conversion cards. If there is no corresponding interface module, the user can simply modify it under xPCTarget referring to other interface modules of conversion cards to create the required interface module.

⑤Test data collection:

On the host computer, use the Real Time Workshop toolbox to compile the test model and generate real-time code. Then download the real-time code to the target machine. The user defines the running time, sampling period, etc. according to the requirements, and then performs real-time simulation. During the simulation process, the data is stored in the memory of the target computer, and must be uploaded to the host computer after the simulation is completed.

The identification of the constant value drift refers to subtracting the reference input signal from the output results of the analog-to-digital conversion card and the digital-to-analog conversion card in the test data under Matlab to obtain the residual value of the two. A smooth curve can be obtained by fitting the residual curve using the Fourier series. In order to improve the accuracy of the fitting without taking too much time, an eighth-order Fourier series is used.

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; n\&omega;x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; n\&omega;x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Here a ₀ , a _n , b _n are Fourier level coefficients, and ω is the fundamental frequency. The mean value of the fitted curve can be obtained by using the Data Statistics tool in Matlab. This mean value is the constant value drift of the digital-to-analog conversion card and the analog-to-digital conversion card.

The quantization error identification refers to: on the basis of constant value drift identification, the fitting curve is subtracted from the residual value, and the difference between the two represents the quantization error of the digital-to-analog conversion card and the analog-to-digital conversion card. It should be noted that this error may contain some circuit noise. The normal distribution method is used to verify the distribution characteristics of this part of the difference. During the verification process, the normplot (X) command in Matlab is used to draw the data distribution graph, where X represents the difference data set. If the data obeys the normal distribution, the obtained graph is approximately a straight line, and then use the normfit(X, alpha) command to obtain the mean and variance of the difference data set at the (1-alpha)% confidence level. If it obeys other distributions, the graph contains curve segments, and other distribution verification methods are required.

The conversion delay identification refers to: since the digital-to-analog conversion card and the analog-to-digital conversion card have delay and zero-order hold characteristics, the conversion delay model of the two can be obtained through corresponding simplified processing:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; delay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; as</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bs</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, K, a, and b respectively represent the parameters to be identified in the model. Use the SystemIdentification toolbox in Matlab for identification. First, the process model identification method based on the minimum prediction error is adopted; then, according to the structure of the conversion delay model, a model containing only one pole and zero is selected; and then the interval of the parameters to be identified in the model is set: K ∈ (0, inf); a ∈ ( 0, inf); b ∈ (0, inf). In addition, the number N of recursive execution of the identification process is selected, and N is a natural number.

Described equivalent model verification refers to: under Simulink, constant drift, quantization error and conversion delay model are combined to form the equivalent model of digital-to-analog conversion card and analog-to-digital conversion card, and the equivalent model is put into real test In the model, the interface modules of the substituted digital-to-analog conversion card and analog-to-digital conversion card, that is, there are no actual digital-to-analog conversion cards and analog-to-digital conversion cards in the test model. Use Real Time Workshop to generate the code of the new test model, and download it to the target machine for real-time operation, and upload the new test results to the host machine after the operation is completed. Compare the test results obtained under the new test model with the test results of the real test model including the analog-to-digital conversion card and the digital-to-analog conversion card. If the mean value of the difference between the two is approximately zero, it means that the equivalent model can accurately simulate the digital-to-analog conversion card. and the constant value drift of the analog-to-digital conversion card; if the difference between the two has no obvious trend item, it means that the equivalent model can accurately simulate the conversion delay characteristics of the digital-to-analog conversion card and the analog-to-digital conversion card.

In order to identify the equivalent model after the digital-to-analog conversion card and the analog-to-digital conversion card are connected in series, the present invention establishes a new test platform based on the host-target mode, which does not require an external standard power supply and high-precision test equipment. Accurate input and output test data are obtained through pure digital signal input and storage, and a series of toolboxes provided by Matlab are used to identify equivalent models. In this way, in the semi-physical simulation control system design, the control engineer can use the equivalent model obtained by the identification method to replace the digital-to-analog conversion card and the analog-to-digital conversion card to establish a simulation model of the control system. Furthermore, various optimization algorithms can be used to redesign the controller to improve the performance of the control system.

Description of drawings

FIG. 1 is a structural block diagram of a test platform for a digital-to-analog conversion card PCI1720U and an analog-to-digital conversion card PCI1710HG according to an embodiment of the present invention.

Fig. 2 is a schematic diagram of a sinusoidal reference signal according to an embodiment of the present invention.

Fig. 3 is a schematic diagram of the semi-physical simulation control system transfer function in the embodiment of the present invention;

Among them: (a) is the system transfer function before equivalent transformation, (b) is the system transfer function after equivalent transformation.

Fig. 4 is the four-channel curve fitting schematic diagram that adopts Fouier series method to obtain of the embodiment of the present invention;

Among them: (a) is the curve fitting of channel 1, (b) is the curve fitting of channel 2, (c) is the curve fitting of channel 3, (d) is the curve fitting of channel 4; (a)～ The upper graphs of (d) represent curve fitting, the dotted line represents the actual residual, and the solid line represents the fitted curve; the lower graphs of (a) to (d) represent the difference between the actual residual and the fitted curve .

5 is a verification diagram of quantization error distribution obtained by using the normal distribution method according to an embodiment of the present invention;

Where: (a) is the quantization error distribution of channel 1, (b) is the quantization error distribution of channel 2, (c) is the quantization error distribution of channel 3, and (d) is the quantization error distribution of channel 4.

Fig. 6 is a schematic diagram of the output result difference between the new test model and the actual test model including the digital-to-analog conversion card and the equivalent model of the analog-to-digital conversion card according to the embodiment of the present invention;

Among them: (a) is the difference value of channel 1, (b) is the difference value of channel 2, (c) is the difference value of channel 3, and (d) is the difference value of channel 4.

Detailed ways

The following describes the excellent model identification effect shown by an embodiment of the present invention with reference to the accompanying drawings. It should be pointed out that the present invention is not limited to the following embodiments. This embodiment is implemented on the premise of not departing from the basic spirit of the present invention and not exceeding the scope involved in the essence of the present invention. The digital-analog and The analog-to-digital conversion identification method is applicable to various types of digital-to-analog conversion cards and analog-to-digital conversion cards, and can be widely used in semi-physical simulation control processes in industries such as aerospace, automobiles, and machinery.

Embodiment: Aiming at Advantech's digital-to-analog conversion card PCI1720U and analog-to-digital conversion card PCI1710HG, which are often used in a semi-physical simulation control system, the identification method of digital-to-analog and analog-to-digital conversion card based on equivalent model transformation is adopted, and the specific implementation steps are introduced .

1). Software installation:

This embodiment is based on the host-target machine mode, and a PC is used as the host machine, and a PC equipped with a floppy drive is used as the target machine. Install the Matlab development environment on the host, including toolboxes such as Simulink, xPCTarget, Real Time Workshop, Curve Fitting, and System Identification. Use the xPCTarget toolbox to generate a real-time operating system for starting the target machine. Then connect the host machine and the target machine to the LAN respectively through the network cable.

2). Hardware connection:

The PCI digital-to-analog conversion card and the PCI analog-to-digital conversion card used in the embodiment are respectively PCI1720U and PCI1710HG of Advantech. The two conversion cards are based on the PCI bus, and they can be directly inserted into the two PCI slots of the target machine, and then use their own cables to connect the conversion cards with their wiring boards. In order to identify the four I/O channels, use four wires to connect the four analog output ports on the analog output terminal board and the four analog input ports on the analog input terminal board. In addition, the target machine and the host are connected to the router through the RJ45 network cable, and the communication between the target machine and the host is based on the TCP/IP protocol. The built test platform is shown in Figure 1.

3). Build a test model:

The test model of analog-to-digital conversion card and digital-to-analog conversion is established under Simulink. The model contains a sinusoidal reference signal with an amplitude of 5V and a frequency of 100HZ. This signal is used as the input of the four channels of the PCI1720U interface module in the test model. Through the external hardware connection, the four-channel analog output signal of the digital-to-analog conversion card is used as the four-channel analog input signal of the analog-to-digital conversion card, and then the digital signal acquisition is realized through the PCI1710HG interface module in the test model.

4). Test data collection:

On the host computer, use the Real Time Workshop toolbox to compile the test model and generate real-time code. The real-time code is then downloaded to the target machine and real-time simulation is performed. In the experiment, the real-time running time is set to 4000s, the sampling period is 0.002s, etc., and a total of 2e ⁶ samples are collected. Since the model discretization process is included in the test model compilation, and the discretization time set in the test model discretization process is 1e ^-8 s, the sinusoidal signal only runs for 0.02 s, as shown in Figure 2.

5). Establish equivalent models of digital-to-analog conversion card and analog-to-digital conversion card based on equivalent transformation

In order to verify the validity of the equivalent model of PCI1720U and PCI1710HG in the semi-physical simulation control system, a classic semi-physical simulation control system model is established. As shown in Figure 3. Among them, C(s): transfer function of the controller; G _D/A (s): equivalent transfer function of the digital-to-analog conversion card PCI1720U; k: equivalent link of the power drive circuit, generally in the form of constant gain; F(s) : The equivalent transfer function of the signal processing circuit; P(s): The equivalent transfer function of the controlled object; G _A/D (s): The equivalent transfer function of the analog-to-digital conversion card PCI1710HG.

According to Figure 3(a), the transfer function of the closed-loop control system can be obtained:

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In Figure 3(b), since the series model G(s) of PCI1720U and PCI1710HG is included, the transfer function of its closed-loop control system can be written as:

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Substituting G(s)=G _D/A (s)G _A/D (s) into formula (2), it can be seen that T′ _C (s)=T _C (s). Therefore, the equivalent model of PCI1720U and PCI1710HG in series will not affect the stability of the semi-physical simulation control system, and the equivalent model G(s) after series can be uniformly identified. The equivalent model includes constant drift, quantization error, and transition delay. Using the test data obtained in steps 1-4, the equivalent models of PCI1720U and PCI1710HG are identified in the host computer's Matlab environment.

5). Constant drift identification:

First, the sinusoidal reference signal is subtracted from the output results of the four channels to obtain the residual value of the four channels, as shown in the upper dotted line of each channel in Figure 4. It can be seen that the curve includes constant value drift, quantization noise and conversion delay caused by the phase deviation. Use the eighth-order Fourier series to fit the residual curve to obtain the four channels

The fitting curve is shown as the solid line in the upper figure of each channel in Figure 4. The mean value of the fitted curve can be calculated by using the data statistics tool in Matlab. The mean value is the constant value drift of the digital-to-analog conversion card PCI1720U and the analog-to-digital conversion card PCI1710HG. The constant drift of the four channels is shown in Table 1.

Table 1. The conversion error after the digital-to-analog conversion card and the analog-to-digital conversion card are connected in series

6). Quantization error identification:

考虑到转换过程中二者的量化误差不相关性，它们串联后的量化误差应为0.0024V。可以看出实际量化误差比理想值(0.0024V)大，这是由于转换过程中量化误差叠加了电路噪声。注意这里所提到的量化误差均指其标准差。On the basis of step 5, subtract the residual value from the fitting curve data to obtain the quantization error of the digital-to-analog conversion card and the analog-to-digital conversion card during the conversion process, as shown in the lower figure of (a)-(d) in Figure 4 shown. It should be noted that part of the circuit noise is included in this error. The normal distribution method was used to verify this part of the difference. During the verification process, the normplot (X) command in Matlab is used to draw the data distribution graph, where X represents the difference data set. As shown in Figure 5, the graph (indicated by "+") represents the verification graph of the distribution of the quantization error. It can be seen that the graphs of the four channels are approximately a straight line, which indicates that the quantization error is approximately a normal distribution. Then use the normfit(X, alpha) command to obtain the mean and variance of the difference set at the (1-alpha)% confidence level. Since the mean value of the quantization error is close to zero, it can be ignored, and only the variance value is calculated here. As shown in Table 1. In the experiment, the D/A resolution of the analog-to-digital conversion card PCI1710HG is 12 bits, the input range is [-10V, 10V], and the gain is 0.5; the A/D resolution of the digital-to-analog conversion card PCI20U is 12 bits, and the input range is [-10V, 10V] , with a gain of 0.5. For the rounding type PCI1710HG and PCI1720U, the quantization error of both is

Considering the irrelevance of the quantization errors of the two in the conversion process, the quantization error after they are connected in series should be 0.0024V. It can be seen that the actual quantization error is larger than the ideal value (0.0024V), which is due to the circuit noise superimposed by the quantization error during the conversion process. Note that the quantization error mentioned here refers to its standard deviation.

7). Conversion delay identification

Judging from the working mechanism of PCI1720U and PCI1710HG, both of them have retention characteristics inside. The zero-order keeper characteristics of the two are represented by (a) and (b) in formula (3).

$\left.\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; G</span>}}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; G</span>}}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Combined with their respective transition delay time constants, the complete model structures of PCI1720U and PCI1710HG can be represented by (a) and (b) in equation (4):

$\left.\begin{array}{c}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In principle, this model structure embodies the conversion delay characteristics of analog-to-digital conversion and digital-to-analog conversion boards, but the parameters cannot be obtained directly. In order to improve the accuracy of identification, the model needs to be simplified. Firstly, the second-order Taylor series is used to simplify the model structure. The simplified form of the digital-to-analog conversion card is as follows:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="k"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="e\; T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="1"\; label="e\; T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{{\mathrm{<span\; class="notranslate">\; </span>}}_{}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; \&ap;</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In formula (5), T' ₁ =T ₁ +T _D/A , k ₁ is the digital-to-analog conversion gain.

Neglecting the second-order term in the denominator, further arrangement can be obtained:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="b"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">b</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Among them a ₁ , b ₁ , K _D/A are the model coefficients of PCI1720U.

Through similar simplification, the model of the digital-to-analog conversion card PCI1710HG can be obtained:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Among them a ₂ , b ₂ , K _A/D are the model coefficients of PCI1710HG.

According to the serial characteristics of PCI1720U and PCI1710HG, the conversion delay model of the two can be obtained after ignoring the second-order item:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; delay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="b"\; filenames="H2008100416670E00011.png"\; state="\{\{state\}\}">b</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; as</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bs</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

In formula (8), K=K ₁ K ₂ , a=a ₁ +a ₂ , b=b ₁ +b ₂ .

It can be seen that the transition delay characteristics of PCI1720U and PCI1710HG can be represented by a model containing only one pole and zero.

On the basis of step 5, the constant value drift is subtracted from the test data, and then the sinusoidal reference signal and test data are used as the input and output data sets of the identification method. Use the SystemIdentification toolbox in Matlab for identification. First, the process model identification method based on the minimum prediction error is adopted; then, according to the structure of the conversion delay model, a model containing only one pole and zero is selected; and then the interval of the parameters to be identified in the model is set: K ∈ (0, inf); a ∈ ( 0, inf); b ∈ (0, inf)

Equation 9 represents the identification results of the four channels.

$\left.\begin{array}{c}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.99405</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.0053732</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.0053731</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.9981</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.022858</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.022866</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.99684</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.0041722</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.0041722</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.99539</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.29686</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.29612</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

To validate the simplified model structure proposed in Section II, several other model structures are used for comparison. The model structures in Table 2 are represented as follows:

Table 2. Identification accuracy (%) of different model structures

P1D: Contains a pole and pure delay section

P2D: Contains two poles and a pure delay link

P1DZ: Contains a pole, zero and pure delay element

P1Z: Contains a pole, zero and pure delay

Table 2 shows the four-channel identification results obtained after 20 recursions using the PEM method. It can be seen that among the four model structures, the P1Z model structure can achieve the highest recognition accuracy, which shows that the P1Z model structure is effective. In addition, compared with several other structures, the P1Z model structure is a relatively simple linear model, which can simplify the model of the control system and facilitate system modeling and simulation in the modeling design of the control system.

8). Establish the equivalent model of PCI1720U and PCI1710HG connected in series

Under Simulink, a constant module is used to represent the constant value drift of PCI1720U and PCI1710HG; a normal distribution noise module is used to represent the quantization noise in the conversion process of the two; a transfer function including a pole and a zero point is used to represent the conversion delay model; The analog signal input range of PCI1710HG is [-10V, 10V], and the output range of PCI1720U is [-10V, 10V], so it is necessary to add a saturation link at the input and output ends of the identification model. In the semi-physical simulation control system design, control engineers can use equivalent models to replace the digital-to-analog conversion card and the analog-to-digital conversion card to establish a simulation model of the control system. Furthermore, various optimization algorithms can be used to redesign the controller to improve the performance of the control system. .

9). Verify the equivalent model

Under Simulink, an equivalent model is used to replace PCI1720U and PCI1710HG to build a new test model. Use Real Time Workshop to generate real-time code, and download it to the target machine to run in real time, and upload the test results to the host machine after the run is completed. Compare the test results obtained under the new test model with the test results obtained by the actual test model, as shown in Figure 6. It can be seen that the mean value of the difference between the two is approximately zero, indicating that the equivalent model can accurately simulate the constant value drift of the digital-to-analog conversion card and the analog-to-digital conversion card; there is no obvious trend item in the difference between the two, indicating that the equivalent model can accurately Simulate the conversion delay characteristics of digital-to-analog conversion cards and analog-to-digital conversion cards. The reason for the difference between the two: Since the two test models do not belong to the same test process, the error in the new test model has no correlation with the quantization error of the actual test model. According to the formula for calculating the variance of two uncorrelated signals:

D(X-Y)＝D(X)+D(Y) (10)

X and Y respectively represent the data sequences obtained in the two test processes, and when the two are subtracted, their noise variances will overlap each other.

It can be seen from this embodiment that the identification accuracy rate of the four channels reaches 99.88% by adopting the simplified conversion delay equivalent model structure, and the final identification result hardly has any errors caused by constant value drift and conversion delay. This shows that the equivalent models of PCI1720U and PCI1710HG are accurately identified by using the digital-to-analog and analog-to-digital conversion identification method based on equivalent model transformation.

Claims (6)

1. A/D and D/A conversion card identification method based on the equivalent model conversion is characterized in that may further comprise the steps:

The first step, adopt Simulink and xPCTarget to set up the test platform of a digital-to-analogue transition card and analog-to-digital conversion card, be used for the series connection test of semi-physical simulation digital-to-analog conversion card and analog-to-digital conversion card, signal input and storage by the pure digi-tal formula obtain input/output test data accurately;

Second step, based on equivalent model conversion principle, set up the equivalent model after digital-to-analog conversion card and analog-to-digital conversion card are connected, this model has comprised constant value drift, quantization error and transfer delay, utilize the input/output test data of under test platform, gathering that equivalent model is carried out identification then, comprise the constant value drift identification, quantization error identification and transfer delay identification, wherein adopt curve fitting and normal distribution proof method to obtain the constant value drift and the quantization error of digital-to-analog conversion card and analog-to-digital conversion card, and based on the minimized method acquisition of predicated error transfer delay model, carry out the equivalent model checking at last, finish whole identification process;

Described constant value drift identification is meant: deduct reference-input signal with analog-to-digital conversion card in the test data and digital-to-analog conversion card output result under Matlab, obtain the residual values of the two, utilize Fourier progression that the residual error curve is carried out match:

$f\left(x\right)=\frac{a_0}{2}+\underset{n=1}{\overset{8}{\mathrm{\&Sigma;}}}[a_n\cos \left(\mathrm{n\&omega;x}\right)+b_n\sin \left(\mathrm{n\&omega;x}\right)]---\left(1\right)$

Wherein: a ₀, a _n, b _nBe Fourier leaf-size class coefficient, ω is a fundamental frequency, utilizes Data Statistics instrument among the Matlab can obtain the average of matched curve, and this average is the constant value drift of digital-to-analog conversion card and analog-to-digital conversion card;

Described quantization error identification is meant: on constant value drift identification basis, utilize residual values to deduct matched curve, the difference table registration mould transition card of the two and the quantization error of analog-to-digital conversion card;

Described transfer lag identification is meant: the transfer delay model of digital-to-analog conversion card and analog-to-digital conversion card is:

$G_{\mathrm{delay}}\left(s\right)=\frac{K(1+\mathrm{as})}{1+\mathrm{bs}}---\left(2\right)$

Wherein: K, a, the parameter to be identified in the b difference representation model, K ∈ (0, inf); A ∈ (0, inf); B ∈ (0, inf);

Described equivalent model checking, be meant: the equivalent model that under Simulink, constant value drift, quantization error and transfer lag model group is constituted altogether digital-to-analog conversion card and analog-to-digital conversion card, and equivalent model put into the authentic testing model, the digital-to-analog conversion card that substitutes and the interface module of analog-to-digital conversion card promptly do not have actual digital-to-analog conversion card and analog-to-digital conversion card in the test model.

2. the A/D and D/A conversion card identification method based on the equivalent model conversion according to claim 1 is characterized in that, the described test platform of setting up digital-to-analog conversion card and analog-to-digital conversion card, and step is as follows:

1. test platform is based on main frame-target machine pattern foundation, adopt two PCs, a main frame is used for modelling, code generation and data analysis, another target machine machine is used for test model real time execution and data acquisition, the Matlab development environment is installed on main frame, comprise Simulink, xPCTarget, Real TimeWorkshop, Curve Fitting and System Identification, utilize the xPCTarget tool box to generate a real time operating system, be installed on the target machine;

2. based on ICP/IP protocol, in LAN (Local Area Network) main frame and target machine are coupled together, realize the communication of the two, the code of main frame can download to target machine like this, and the test data of target machine can upload to main frame;

3. according to the interface shape of transition card, transition card and target machine are coupled together,, couple together with the simulation output and the analog input channel of lead with the two for model after logarithmic mode transition card and the analog-to-digital conversion card series connection carries out identification;

4. set up digital-to-analog conversion card and analog-to-digital test model under Simulink, this model comprises a standardized digital signal source, digital-to-analog conversion card interface module, analog to digital conversion card interface module and data acquisition module;

5. on main frame, utilize Real Time Workshop tool box that test model is compiled, generate real-time code, then real-time code is downloaded on the target machine, the user defines working time, sampling period according to demand, carry out real-time simulation then, data exist in the internal memory of target machine in the simulation process, and emulation must upload on the main frame after finishing.

3. the A/D and D/A conversion card identification method based on the equivalent model conversion according to claim 1, it is characterized in that, described constant value drift identification, be meant: under Matlab, deduct reference-input signal with analog-to-digital conversion card in the test data and digital-to-analog conversion card output result, obtain the residual values of the two, utilize Fourier progression that the residual error curve is carried out match and obtain smooth curve, adopt eight rank fourier series to improve the accuracy of match:

$f\left(x\right)=\frac{a_0}{2}+\underset{n=1}{\overset{8}{\mathrm{\&Sigma;}}}[a_n\cos \left(\mathrm{n\&omega;x}\right)+b_n\sin \left(\mathrm{n\&omega;x}\right)]$

Here a ₀, a _n, b _nBe Fourier leaf-size class coefficient, ω is a fundamental frequency, utilizes the average of Data Statistics instrument acquisition matched curve among the Matlab, and this average is the constant value drift of digital-to-analog conversion card and analog-to-digital conversion card.

4. the A/D and D/A conversion card identification method based on the equivalent model conversion according to claim 1, it is characterized in that, described quantization error identification, be meant: on constant value drift identification basis, utilize residual values to deduct matched curve, the difference table registration mould transition card of the two and the quantization error of analog-to-digital conversion card, may comprise a part of circuit noise in this error, adopt normal distribution method that this part difference distribution character is verified, in the proof procedure, adopt normplot (X) the order picture data profile among the Matlab, wherein X represents the difference data set, if the data Normal Distribution, the figure that obtains is approximately straight line, (X, alpha) order acquisition difference data is integrated into average and the variance under (1-alpha) % confidence level to utilize normfit then.

5. the A/D and D/A conversion card identification method based on the equivalent model conversion according to claim 1, it is characterized in that, described transfer lag identification is meant: digital-to-analog conversion card and analog-to-digital conversion card have time-delay and zeroth order retention performance, handle the transfer delay model that obtains the two by simplification to be:

$G_{\mathrm{delay}}\left(s\right)=\frac{K(1+\mathrm{as})}{1+\mathrm{bs}}$

K wherein, a, parameter to be identified in the b difference representation model, utilize the SystemIdentification tool box among the Matlab to carry out identification: at first to adopt process model discrimination method based on the predicated error minimum, then according to the transfer lag model structure, select only to comprise the model of a pole and zero, the interval of parameter to be identified in the model then is set: K ∈ (0, inf); A ∈ (0, inf); B ∈ (0, inf), the times N of selecting the identification process recurrence to carry out, N is a natural number.

6. the A/D and D/A conversion card identification method based on the equivalent model conversion according to claim 1, it is characterized in that, described equivalent model checking, be meant: under Simulink with constant value drift, quantization error and transfer lag model group constitute the equivalent model of digital-to-analog conversion card and analog-to-digital conversion card altogether, and equivalent model put into the authentic testing model, the digital-to-analog conversion card that substitutes and the interface module of analog-to-digital conversion card, be not have actual digital-to-analog conversion card and analog-to-digital conversion card in the test model, utilize Real Time Workshop to generate the code of new test model, and download to real time execution on the target machine, after operation is finished new test result is uploaded to main frame, the test result that comprises analog-to-digital conversion card and digital-to-analog conversion card in acquisition test result and the authentic testing model under the new test model is compared, if the mean approximation of the two difference is zero, illustrate that equivalent model can accurately simulate the constant value drift of digital-to-analog conversion card and analog-to-digital conversion card; If the two difference does not have the visible trend item, illustrate that equivalent model can accurately simulate the transfer delay characteristic of digital-to-analog conversion card and analog-to-digital conversion card.

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