CN109884884A - A kind of method of adjustment and relevant apparatus of system Control platform - Google Patents

A kind of method of adjustment and relevant apparatus of system Control platform Download PDF

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CN109884884A
CN109884884A CN201910243328.9A CN201910243328A CN109884884A CN 109884884 A CN109884884 A CN 109884884A CN 201910243328 A CN201910243328 A CN 201910243328A CN 109884884 A CN109884884 A CN 109884884A
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parameter
control
transfer function
optimizing
index
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李炳楠
朱峰
燕志伟
梁正玉
闫乃明
白小虎
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Rundian Energy Science and Technology Co Ltd
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Rundian Energy Science and Technology Co Ltd
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Abstract

A kind of method of adjustment of system Control platform provided herein, by the transfer function model and controller transfer function of establishing controlled device respectively, establish system closed loop transfer function, and residual, pole and constant term of the computing system closed loop transfer function, under default pumping signal, further obtain practical Control platform index, and continuous optimizing, until practical Control platform index meets the requirement of the default control index of quality.Using classical control theory as foundation, utilize the zero of system closed loop transfer function, pole and residue theory, the influence of system parameter and control parameter to system response curve can be gone out with quantitative analysis, it recycles optimizing algorithm to find suitable control parameter, solves the mismatch problems of control parameter and system model.The application also provides a kind of Feature Analyzes and parameter optimization system, a kind of computer readable storage medium and a kind of process control terminal, has above-mentioned beneficial effect.

Description

A kind of method of adjustment and relevant apparatus of system Control platform
Technical field
This application involves process control field, in particular to a kind of the method for adjustment and relevant apparatus of system Control platform.
Background technique
Process control technology has a wide range of applications in industrial circle, and in the industry of the Large processes such as petrochemical industry, power generation, chemical industry In, have the characteristics that the largely procedures system with non-linear, big inertia, parameter time varying.Along with wherein there are many variables The factors such as coupling, speed system cooperation operation, external variable random perturbation, cause process industrial control system more complicated.This Huge challenge is brought to traditional Industry Control mode.
Debugging of most of control systems at the beginning of operation Jing Guo system, system parameter and control parameter cooperation are run, Required Control platform can be reached.However, the longtime running and external disturbance with system are examined beyond initial debugging Consider range, will lead to control parameter and system parameter mismatch, and then lead to the Control platform of system worse and worse, or even threatens and be The normal operation of system.Wherein, system parameter is generally changed slowly by equipment influence on system operation, is not necessarily to real-time identification.And control parameter It in addition to being influenced by system parameter, is also influenced by inside and outside disturbance, mission nonlinear etc., this just needs to carry out control parameter real When recognize.
Summary of the invention
The method of adjustment, adjustment system, one kind that the purpose of the application is to provide a kind of system Control platform are computer-readable Storage medium and a kind of process control terminal rely only on people for control parameter in the process control for solving existing industry The problem of work experiential operating.
In order to solve the above technical problems, the application provides a kind of method of adjustment of system Control platform, specific technical solution It is as follows:
S1: the history data in acquisition controlled device preset time, according to history data foundation The transfer function model of controlled device;
S2: controller initial parameter, the optimizing step-length of each controller parameter and corresponding optimizing step-length, default control are determined The index of quality processed;
S3: system closed loop transfer function, is established according to the controller initial parameter and the transfer function model;
S4: residual, pole and constant term of the system closed loop transfer function, under default pumping signal are calculated;
S5: practical Control platform index is obtained according to the residual, pole and constant term of system;
S6: judge whether the practical Control platform index meets the default control index of quality requirement;If it is not, into S7;
S7: it is newly controlled in each corresponding optimizing section by optimizing algorithm according to the optimizing step-length of each control parameter Parameter processed, and S3 is returned, using the new control parameter as the controller initial parameter, until the practical Control platform refers to Mark meets the default control index of quality requirement.
Wherein, the transfer function model is specially using transmission function as the engineering universal model of the form of expression.
Wherein, it is established according to the history data after the transfer function model of the controlled device further include:
Model parameter is recognized according to field data, and the transfer function model is verified using new field data, To guarantee the precision of the transfer function model.
Wherein, recognizing model parameter according to field data includes:
Model parameter is recognized using least square method or gunz method according to field data.
Wherein it is determined that controller initial parameter includes:
Rule of thumb formula computing controller parameter, the controller initial parameter as optimizing algorithm;
Wherein, the corresponding control strategy of the controller parameter is pid algorithm.
The application also provides the system of a kind of Feature Analyzes and parameter optimization, and specific technical solution is as follows:
Model building module is transported for acquiring the history data in controlled device preset time according to the history Row data establish the transfer function model of the controlled device;
Parameter setting module, for determining the optimizing step-length of controller initial parameter, each controller parameter and corresponding Optimizing step-length, the default control index of quality;
Function establishes module, for establishing system closed loop according to the controller initial parameter and the transfer function model Transmission function;
Data computation module, for calculating residual, pole of the system closed loop transfer function, under default pumping signal With constant term;
As a result output module obtains practical Control platform index for the residual, pole and constant term according to system;
Quality comparison module, for judging whether the practical Control platform index meets the default control index of quality It is required that;If it is not, entering circulation optimizing module;
Optimizing module is recycled, for the optimizing step-length according to each control parameter by seeking in each corresponding optimizing section Excellent algorithm obtains new control parameter, and establishes module into the function, using the new control parameter as at the beginning of the controller Beginning parameter, until the practical Control platform index meets the default control index of quality requirement.
The application also provides a kind of computer readable storage medium, is stored thereon with computer program, the computer journey The step of method as described above is realized when sequence is executed by processor.
The application also provides a kind of process control terminal, including memory and processor, has calculating in the memory The step of machine program, the processor realizes method as described above when calling the computer program in the memory.
A kind of method of adjustment of system Control platform provided herein, comprising: S1: acquisition controlled device preset time Interior history data establishes the transfer function model of the controlled device according to the history data;S2: control is determined Device initial parameter processed, the optimizing step-length of each controller parameter and corresponding optimizing step-length, the default control index of quality;S3: root System closed loop transfer function, is established according to the controller initial parameter and the transfer function model;S4: it calculates the system and closes Residual, pole and constant term of the ring transmission function under default pumping signal;S5: according to the residual, pole and constant term of system Obtain practical Control platform index;S6: judge whether the practical Control platform index meets the default control index of quality It is required that;If it is not, into S7;S7: it is calculated in each corresponding optimizing section by optimizing according to the optimizing step-length of each control parameter Method obtains new control parameter, and returns to S3, wants until the practical Control platform index meets the default control index of quality It asks.
The application, can using the zero of system closed loop transfer function, pole and residue theory using classical control theory as foundation Go out the influence of system parameter and control parameter to system response curve with quantitative analysis, optimizing algorithm is recycled to find suitable control Parameter processed solves the mismatch problems of control parameter and system model.The application also provides a kind of Feature Analyzes and seeks with parameter Major clique system, a kind of computer readable storage medium and a kind of process control terminal, have above-mentioned beneficial effect, no longer superfluous herein It states.
Detailed description of the invention
In order to illustrate the technical solutions in the embodiments of the present application or in the prior art more clearly, to embodiment or will show below There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this The embodiment of application for those of ordinary skill in the art without creative efforts, can also basis The attached drawing of offer obtains other attached drawings.
Fig. 1 is a kind of flow chart of the method for adjustment of system Control platform provided by the embodiment of the present application;
Fig. 2 is system control block frame figure provided by the present application;
Fig. 3 is a kind of adjustment system structure diagram of system Control platform provided by the embodiment of the present application.
Specific embodiment
To keep the purposes, technical schemes and advantages of the embodiment of the present application clearer, below in conjunction with the embodiment of the present application In attached drawing, the technical scheme in the embodiment of the application is clearly and completely described, it is clear that described embodiment is Some embodiments of the present application, instead of all the embodiments.Based on the embodiment in the application, those of ordinary skill in the art Every other embodiment obtained without making creative work, shall fall in the protection scope of this application.
Referring to FIG. 1, Fig. 1 is a kind of process of the method for adjustment of system Control platform provided by the embodiment of the present application Figure, this method comprises:
S1: the history data in acquisition controlled device preset time is established described controlled according to history data The transfer function model of object;
This step is intended to first obtain the history data in controlled device preset time.It should be noted that here Controlled device is that general name, such as temperature, water level, pressure, load and flow of a class object etc. need in Process Control System Care and the parameter of manipulation etc., can also be other parameters certainly.And the targeted controlled device of the application can be this kind One in object or any several combination.Then natural preset time refers to certain past a period of time, herein for The length and preset time range of preset time are not construed as limiting.It such as can be some period of system operation, or Several days can also be several days etc. that some time point starts in the past.It is, of course, preferable to, selected controlled device is gone through History data answer representative and real-time, and the history data closer apart from current point in time can more reflect controlled device Current state, and representative history data is then easy to reflect system operation characteristic.
After collecting history data again, need to establish model according to history data.Control theory is in practical work Mathematical model of the application dependent on production equipment or process in journey, the method for mathematical modeling have very much, including modelling by mechanism, distinguish Know modeling, statistics modeling, machine learning modeling etc..On the one hand, control theory pass through many years development, formd with Control system's reform method based on transfer function model;On the other hand, it is contemplated that the rapidity of mathematical modeling and It is effective, it is not necessary that estimation model to be selected too complicated, as long as the needs for being suitble to engineering are selected, specifically, building Vertical transfer function model allows large error relative to laboratory standard, is also required to control certainly in error range.Change sentence It talks about, which is specifically as follows the engineering universal model using transmission function as the form of expression.Here, the application mentions For a kind of model structure being suitable for for general procedures system, it is shown below:
Wherein, K is system gain, and τ is pure delay time constant, and T is system inertia time constant, and m is integral part Order, n are the order of inertia portion, and β is derivative time constant.And history data is system input and output parameter in frequency Then the expression formula in domain can be found out above-mentioned based on history data and using the methods of least square method or gunz method Parameter in expression formula.
Further, it is established according to history data after the transfer function model of controlled device further include:
Model parameter is recognized according to field data, and transfer function model is verified using new field data, to protect Demonstrate,prove the precision of transfer function model.Specifically, model can be recognized using least square method or gunz method according to field data Parameter.
After determining model structure, model parameter can be recognized according to the history data of controlled device collected. There are many method of parameter identification, including least square method, gunz method, linear regression, sliding average etc..It is also contemplated that ginseng Number identification rapidities and actual effect, can also using based on random search gunz method (e.g., genetic algorithm, ant group algorithm, Particle swarm algorithm etc.), such method only needs to provide the substantially section of parameter according to the historical trend of controlled device, can be fast Speed finds globe optimum.Period can constantly reduce the identification section of parameter according to identification effect, repeatedly be searched for, from And find the relatively figure of merit or optimal value of model parameter.
S2: controller initial parameter, the optimizing step-length of each controller parameter and corresponding optimizing step-length, default control are determined The index of quality processed;
This step it needs to be determined that controller initial parameter, the optimizing step-length of each controller parameter and optimizing section, and The default control index of quality for finally needing to compare.
For controller initial parameter, can rule of thumb formula computing controller parameter, the control as optimizing algorithm Device initial parameter.Specifically, empirical equation can be Z-N method, attenuation curve method, critical proportional band law etc., controller ginseng is obtained Several empirical values, the empirical value will be used for the initial value of optimizing algorithm.Specific optimizing algorithm is not construed as limiting herein.
Since control algolithm is numerous, and pid algorithm is most widely used in engineering, therefore the present invention is with pid algorithm Example is illustrated.It should be noted that control algolithm is also referred to as control strategy, it is different from optimizing algorithm above.Controller Rule of thumb formula obtains initial parameter, and optimizing algorithm is the optimized parameter in order to find controller, what control algolithm referred to It is the control strategy of controller.There are many method of pid parameter adjusting, can be according to Z-N after the model of controlled device determines Method, attenuation curve method, critical proportional band law etc. obtain the empirical value of pid parameter, and the empirical value will be as the first of optimizing algorithm Initial value.
In addition, it is necessary to the default control index of quality of the system of determination, such as overshoot, attenuation rate, rise time and transition Time etc., or one or any several combination among these can also be other index of quality certainly.These indexs Whether the configuration for being used to examine pid parameter is met the requirements.Meanwhile optimizing section and optimizing are provided according to pid parameter initial value Step-length is ready for subsequent optimizing algorithm.
Specifically, section is extended centered on initial value, and the range in section depends on after controller initial parameter determines Whether reach the boundary in section in final optimizing result, need to expand section if reaching, if optimizing result is from section side Boundary farther out, then needs to reduce section;The setting of optimizing step-length needs to be cooperated with section, when carrying out rough search for the first time, To save the time, if section is very big, general optimizing step-length also be will increase, when the region of search reduces, to improve optimizing result Precision, optimizing step-length are also required to accordingly reduce, and general optimizing step-length selects 2 orders of magnitude lower than optimizing section.
S3: system closed loop transfer function, is established according to controller initial parameter and transfer function model;
After obtaining the model of controlled device and PID controller, the closed loop transfer function, for system that you can get it.Such as Fig. 2 institute Show, for controlled device, u is input, and y is output, and x is state, and v is setting value, then error e=v-y=v-x;For control Device processed, error e are input, and u is output.It is possible thereby to the closed loop transfer function, of system and controller be obtained respectively, such as following formula institute Show:
By taking second-order inertia system as an example, it is corrected using PID controller.System passes through y (t)=x under the action of u (t) process is finally reached v, i.e. error e goes to zero, i.e., does not have static difference after system compensation, be shown below:
Wherein, k is proportional action, and g is integral action, and q is the differential action, and T is the time constant of controlled device.
S4: residual, pole and constant term of the computing system closed loop transfer function, under default pumping signal;
Under normal circumstances, the system closed loop transfer function, in S3 can be write as following formula:
Wherein, K is gain coefficient, and zi is residual, and si is pole.
In addition, for the unit-step response convenient for finding out high order system, it can be by polynomial molecule multinomial and denominator Multinomial carries out factorization.
After obtaining the closed loop transfer function, of system, default pumping signal response, the zero point of available system, pole are carried out Point, residual and constant term.It is not construed as limiting herein for presetting the type of pumping signal, such as can be step excitation, it can also be with For other kinds of pumping signal.Wherein, according to the poles and zeros assignment of system, the frequency characteristic of system and steady can be qualitatively judged Determine characteristic.
S5: practical Control platform index is obtained according to the residual, pole and constant term of system;
Since the zero point and pole of closed loop biography letter are only possible to be real number or conjugate complex number, spread out as partial fraction shape Formula is shown below:
It is available for the above-mentioned second-order inertia system for sealing in PID controller still by taking second-order inertia system as an example:
Counter pull type transformation is carried out to the formula, is obtained
Y (t)=r4+r3*exp[p3·t]
+2*real(r12)*exp[real(p12)·t]*cos[imag(p12)·t]
+2*imag(r12)*exp[real(p12)·t]*sin[imag(p12)·t]
Wherein, p3For real pole, p12WithFor complex-conjugate poles, r3With r4For real number residual, r12WithIt is total Yoke plural number residual, is analyzed as follows the formula:
1. in first item, the corresponding real number residual r of zero pole point4The as stable state extreme value of system;
2. in Section 2, pole p3With residual r3It is generally negative, therefore this curve is similar with inertial element curve. Residual r3Absolute value increases, and starting point absolute value increases;Pole p3Absolute value reduces, and rise time tr extends.And this will all cause be Uniting, " new line " is insufficient, i.e. system response is slack-off, can not be rapidly achieved stationary value.It is on the contrary then anti-.
3. in Section 3, EXP function is multiplied with triangle cosine function, the stable extremal of such type function is zero, starting Point is non-zero.It is conjugated residual real root real (r12) absolute value increase, the raising of starting point absolute value, overshoot MP increase;Conjugate pole Real root real (p12) absolute value reduction, then triangle cosine function weight increases, and overshoot MP increases, and rise time tr extends, mistake Time ts extension is crossed, system oscillation number increases;Conjugate pole imaginary root imag (p12) absolute value reduction, then EXP function weight increases Greatly, overshoot MP reduces, and rise time tr extends, and transit time ts reduces, and system oscillation number is reduced.It is on the contrary then anti-.
4. in Section 4, EXP function is multiplied with trigonometric sine function, the stable extremal of such type function is zero, starting Point is also zero.It is conjugated residual imaginary root imag (r12) absolute value increase, overshoot MP increase, attenuation rate FAI reduction;Conjugate pole is real Root real (p12) absolute value reduction, then trigonometric sine function weight increases, and overshoot MP increases, and transit time ts extends, system The number of oscillation increases;Conjugate pole imaginary root imag (p12) absolute value reduction, then EXP function weight increases, and overshoot MP reduces, mistake Time ts reduction is crossed, system oscillation number is reduced.It is on the contrary then anti-.
5. in general, | real (r) | > | imag (r) |, so, the specific gravity of Section 3 is larger, and Section 4 only plays phase shift Effect.
For example, letter is passed for any second orderPID controller passes letterUnit is pre- If the system closed loop under pumping signal passes letterThen the zero point of the biography letter is z=- 0.0333, pole isCorresponding to residual isIt is then corresponding anti- Formula after pull-type variation, it can be deduced that response curve of each time domain fraction under unit step.
It can thus be seen that pole and residual directly affect the tendency of response curve, and pole and residual are by being controlled What image parameter and controller parameter codetermined.Wherein, object parameters do not have as one under fixed operating condition and substantially become Change, thus can be by analyzing and changing the influence of controller parameter antipodal points and residual, and then influence becoming for response curve Gesture variation allows response curve according to anticipation Long-term change trend.
S6: judge whether practical Control platform index meets the requirement of the default control index of quality;If it is not, into S7;
Judge whether practical Control platform index obtained in S5 meets the requirements, i.e., whether meets the default control product in S2 Matter index request.
S7: it is newly controlled in each corresponding optimizing section by optimizing algorithm according to the optimizing step-length of each control parameter Parameter processed, and S3 is returned, using the new control parameter as the controller initial parameter, until the practical Control platform refers to Mark meets the default control index of quality requirement.
If S6 is judged as NO, optimizing algorithm is passed through in each corresponding optimizing section according to the optimizing step-length of each control parameter New control parameter is obtained, and is calculated since S3 again, until Control platform index is met the requirements.
The application, can using the zero of system closed loop transfer function, pole and residue theory using classical control theory as foundation Go out the influence of system parameter and control parameter to system response curve with quantitative analysis, optimizing algorithm is recycled to find suitable control Parameter processed solves the mismatch problems of control parameter and system model.
The system of a kind of Feature Analyzes provided by the embodiments of the present application and parameter optimization is introduced below, hereafter The system of description can correspond to each other reference with a kind of above-described method of adjustment of system Control platform.
The application also provides the system of a kind of Feature Analyzes and parameter optimization, and specific technical solution is as follows:
Model building module 100, for acquiring the history data in controlled device preset time, according to the history Operation data establishes the transfer function model of the controlled device;
Parameter setting module 200, for determining the optimizing step-length of controller initial parameter, each controller parameter and corresponding Optimizing step-length, the default control index of quality;
Function establishes module 300, for establishing system according to the controller initial parameter and the transfer function model Closed loop transfer function,;
Data computation module 400, for calculating residual of the system closed loop transfer function, under default pumping signal, pole Point and constant term;
As a result output module 500 obtain practical Control platform index for the residual, pole and constant term according to system;
Quality comparison module 600, for judging whether the practical Control platform index meets the default control quality Index request;If it is not, entering circulation optimizing module;
Optimizing module 700 is recycled, is led in each corresponding optimizing section for the optimizing step-length according to each control parameter It crosses optimizing algorithm and obtains new control parameter, and establish module into the function, using the new control parameter as the control Device initial parameter, until the practical Control platform index meets the default control index of quality requirement.
Present invention also provides a kind of computer readable storage mediums, have computer program thereon, the computer program The step of being performed the method for adjustment that a kind of system Control platform provided by above-described embodiment may be implemented.The storage medium It may include: USB flash disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), the various media that can store program code such as magnetic or disk.
Present invention also provides a kind of process control terminals, may include memory and processor, deposit in the memory There is computer program, when the processor calls the computer program in the memory, above-described embodiment may be implemented and mentioned A kind of the step of method of adjustment of the system Control platform supplied.Certain process control terminal can also include that various networks connect Mouthful, the components such as power supply.
Each embodiment is described in a progressive manner in specification, the highlights of each of the examples are with other realities The difference of example is applied, the same or similar parts in each embodiment may refer to each other.For embodiment provide system and Speech, since it is corresponding with the method that embodiment provides, so being described relatively simple, related place is referring to method part illustration ?.
Specific examples are used herein to illustrate the principle and implementation manner of the present application, and above embodiments are said It is bright to be merely used to help understand the present processes and its core concept.It should be pointed out that for the ordinary skill of the art For personnel, under the premise of not departing from the application principle, can also to the application, some improvement and modification can also be carried out, these improvement It is also fallen into the protection scope of the claim of this application with modification.
It should also be noted that, in the present specification, relational terms such as first and second and the like be used merely to by One entity or operation are distinguished with another entity or operation, without necessarily requiring or implying these entities or operation Between there are any actual relationship or orders.Moreover, the terms "include", "comprise" or its any other variant meaning Covering non-exclusive inclusion, so that the process, method, article or equipment for including a series of elements not only includes that A little elements, but also including other elements that are not explicitly listed, or further include for this process, method, article or The intrinsic element of equipment.In the absence of more restrictions, the element limited by sentence "including a ...", is not arranged Except there is also other identical elements in the process, method, article or apparatus that includes the element.

Claims (9)

1. a kind of method of adjustment of system Control platform characterized by comprising
S1: the history data in acquisition controlled device preset time is established described controlled according to the history data The transfer function model of object;
S2: controller initial parameter, the optimizing step-length of each controller parameter and corresponding optimizing step-length, default control product are determined Matter index;
S3: system closed loop transfer function, is established according to the controller initial parameter and the transfer function model;
S4: residual, pole and constant term of the system closed loop transfer function, under default pumping signal are calculated;
S5: practical Control platform index is obtained according to the residual, the pole and the constant term;
S6: judge whether the practical Control platform index meets the default control index of quality requirement;If it is not, into S7;
S7: it is obtained newly controlling ginseng by optimizing algorithm in each corresponding optimizing section according to the optimizing step-length of each control parameter Number, and S3 is returned, using the new control parameter as the controller initial parameter, until the practical Control platform index is full The foot default control index of quality requirement.
2. the method according to claim 1, wherein the transfer function model is specially using transmission function as table The engineering universal model of existing form.
3. according to the method described in claim 2, it is characterized in that, establishing the controlled device according to the history data Transfer function model after further include:
Model parameter is recognized according to field data, and the transfer function model is verified using new field data, to protect Demonstrate,prove the precision of the transfer function model.
4. according to the method described in claim 3, it is characterized in that, including: according to field data identification model parameter
Model parameter is recognized using least square method or gunz method according to field data.
5. the method according to claim 1, wherein determining that controller initial parameter includes:
Rule of thumb formula computing controller parameter, the controller initial parameter as optimizing algorithm.
6. according to the method described in claim 5, it is characterized in that, the corresponding control strategy of the controller parameter is PID calculation Method.
7. a kind of adjustment system of system Control platform characterized by comprising
Model building module, for acquiring the history data in controlled device preset time, according to the history run number According to the transfer function model for establishing the controlled device;
Parameter setting module, for determining the optimizing step-length and corresponding optimizing of controller initial parameter, each controller parameter Step-length, the default control index of quality;
Function establishes module, for establishing the transmitting of system closed loop according to the controller initial parameter and the transfer function model Function;
Data computation module, for calculating residual of the system closed loop transfer function, under default pumping signal, pole and often It is several;
As a result output module obtains practical Control platform index for the residual, pole and constant term according to system;
Quality comparison module is wanted for judging whether the practical Control platform index meets the default control index of quality It asks;If it is not, entering circulation optimizing module;
Optimizing module is recycled, is calculated in each corresponding optimizing section by optimizing for the optimizing step-length according to each control parameter Method obtains new control parameter, and establishes module into the function, initially joins using the new control parameter as the controller Number, until the practical Control platform index meets the default control index of quality requirement.
8. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that the computer program quilt The step of processor realizes method of adjustment as claimed in any one of claims 1 to 6 when executing.
9. a kind of process control terminal, which is characterized in that including memory and processor, have computer journey in the memory Sequence, the processor realize adjustment as claimed in any one of claims 1 to 6 when calling the computer program in the memory The step of method.
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CN112666821A (en) * 2020-11-25 2021-04-16 中国核电工程有限公司 Design method for optimal PID (proportion integration differentiation) parameter of closed-loop control system of nuclear power plant

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