CN113625549A - PID parameter setting method and system based on optimized path - Google Patents
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Abstract
The invention discloses a PID parameter setting method and system based on an optimized path, which comprises the following steps: acquiring historical data of a control variable and a controlled object; fitting a characteristic model by using the historical data to obtain parameters of the characteristic model; calculating a controlled optimal path through parameters of the characteristic model obtained by fitting; substituting a PID control formula into the characteristic model to calculate a predicted value of the characteristic model under the controlled condition; and using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters. The method improves the thought of optimizing and setting under the condition of not changing the PID controller architecture, introduces the optimal control path to replace the traditional fitness function so as to obtain better control effect, can better reduce the overshoot of the controlled object, and enables the control curve to smoothly and quickly approach the set value.
Description
Technical Field
The invention relates to the technical field of automation control, in particular to a PID parameter setting method and system based on an optimized path.
Background
Proportional-Integral-Derivative (PID) controllers are control loop mechanisms that employ feedback and are widely used in industrial control systems and various other applications requiring continuous modulation control. The PID controller continuously calculates an error value e (t) as the difference between the desired Set Point (SP) and the measured Process Variable (PV) and adjusts the control variable according to proportional, integral and derivative operators (designated P, I and D, respectively), hence the name. Currently, there are many existing PID tuning methods, including ziegler-dow gauss (ZN) tuning method and internal model method (also called Lambda), which require a lot of perturbation experiments to provide better parameters as initial values and also require experienced engineers to perform trial and error for obtaining better control performance.
In addition to this, optimization algorithms are often used for PID parameter tuning. The method can reduce the requirement on a senior engineer and automatically find a proper PID parameter by using an optimization algorithm. Commonly used error expression functions (fitness functions) in this type of method include Integral of Squared Error (ISE), integral of absolute value of error (IAE), integral of time multiplied by squared error (ITSE), and integral of time multiplied by absolute value of error (ITAE). However, the method also has disadvantages, and the PID parameters obtained by the optimization algorithm are often aggressive, and overshoot occurs.
Disclosure of Invention
The embodiment of the invention provides a PID parameter setting method and system based on an optimized path. The following presents a simplified summary in order to provide a basic understanding of some aspects of the disclosed embodiments. This summary is not an extensive overview and is intended to neither identify key/critical elements nor delineate the scope of such embodiments. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is presented later.
According to an embodiment of the present invention, in a first aspect, a PID parameter setting method based on an optimized path is provided, including:
s1: acquiring historical data of a control variable and a controlled object;
s2: fitting a characteristic model by using the historical data to obtain parameters of the characteristic model;
s3: calculating a controlled optimal path through parameters of the characteristic model obtained by fitting;
s4: substituting a PID control formula into the characteristic model to calculate a predicted value of the characteristic model under the controlled condition;
s5: and using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters.
In some embodiments, the feature models include a first order time-lapse system model, i.e., FOPDT, and a second order time-lapse system model, i.e., SOPDT;
first-order time-lag system model:
second-order time-lag system model:
in some embodiments, the parameters of the feature model include: the sum of K, τ,
and theta.
In some embodiments, the optimal path for the parameter calculation control of the feature model obtained by fitting includes two calculation models: linear models and non-linear models.
In some embodiments, the linear model is of the specific form:
y1＝k1·t+b
wherein:
k1：
b：
t: a time variable;
t0: step reaction start time;
PV0: initial values of controlled variables;
Δ y: step increment of a controlled variable;
n: ideally n response cycles converge to 97% of the setpoint.
In some embodiments, the non-linear model is of the specific form:
y2＝k2(1-exp(-a(t-c)))+d
k2：Δy；
a：
c：t0+θ；
d：PV0。
in some embodiments, the value of n is set to 2 to 6.
In some embodiments, the PID control formula is:
wherein the content of the first and second substances,
KP: scale factor, optimization parameter;
Ti: integrating time constants and optimizing parameters;
Td: differentiating the time constant, optimizing the parameter;
t: a period;
ek: difference between the set value and the process variable of the current period;
ek-1: set valueDifference from the last cycle process variable.
In some embodiments, the optimization algorithm comprises: gradient descent algorithm, meta-heuristic algorithm and Bayesian optimization algorithm. In a second aspect, the present application provides an optimized path-based PID parameter setting system, comprising,
the system comprises a historical data acquisition module, a characteristic model optimization module, an optimal path calculation module, a model output prediction module, a PID parameter optimization module and a user visualization interaction module;
the historical data acquisition module: acquiring historical data of a control variable and a controlled object;
the feature model optimization module: fitting a characteristic model by using the historical data to obtain parameters of the characteristic model;
the optimal path calculation module: calculating a controlled optimal path through parameters of the characteristic model obtained by fitting;
the model output prediction module: substituting a PID control formula into the characteristic model to calculate a predicted value of the characteristic model under the controlled condition;
the PID parameter optimization module: using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters;
the user visualization interaction module: previewing to obtain an optimal PID parameter control result, providing a user fine adjustment interface, and confirming the optimal control parameter
The technical scheme provided by the embodiment of the invention has the following beneficial effects:
the method improves the thought of optimizing and setting under the condition of not changing the PID controller architecture, introduces the optimal control path to replace the traditional fitness function so as to obtain better control effect, can better reduce the overshoot of the controlled object, and enables the control curve to smoothly and quickly approach the set value.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a flow diagram illustrating an optimized path based PID parameter setting method in accordance with an exemplary embodiment;
FIG. 2 is a block diagram illustrating an architecture of an optimized path based PID parameter setting system in accordance with an exemplary embodiment;
FIG. 3 is a first order time lag system model (FOPDT) fit to a mixing and stirring system shown in accordance with an exemplary embodiment;
FIG. 4 illustrates PID controller control effects of the present method optimized control path design and comparison to an internal model approach in accordance with an exemplary embodiment;
FIG. 5 is an illustration of a preview and trim interface in accordance with an exemplary embodiment.
In the figure, 1 is a historical data acquisition module, 2 is a feature model optimization module, 3 is an optimal path calculation module, 4 is a model output prediction module, 5 is a PID parameter optimization module, and 6 is a user visualization interaction module.
Detailed Description
The following description and the drawings sufficiently illustrate specific embodiments of the invention to enable those skilled in the art to practice them. The examples merely typify possible variations. Individual components and functions are optional unless explicitly required, and the sequence of operations may vary. Portions and features of some embodiments may be included in or substituted for those of others. The scope of embodiments of the invention encompasses the full ambit of the claims, as well as all available equivalents of the claims. Embodiments may be referred to herein, individually or collectively, by the term "invention" merely for convenience and without intending to voluntarily limit the scope of this application to any single invention or inventive concept if more than one is in fact disclosed. Herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed. The embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the structures, products and the like disclosed by the embodiments, the description is relatively simple because the structures, the products and the like correspond to the parts disclosed by the embodiments, and the relevant parts can be just described by referring to the method part.
It should be noted that: the relative arrangement of the components and steps, the numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present disclosure unless specifically stated otherwise.
It should be noted that although the various steps of the methods of the present disclosure are depicted in the drawings in a particular order, this does not require or imply that these steps must be performed in this particular order, or that all of the depicted steps must be performed, to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions, etc.
The invention is further described with reference to the following figures and examples:
example 1:
as shown in fig. 1, a PID parameter setting method based on an optimized path includes,
s1: acquiring historical data of a control variable and a controlled object;
s2: fitting a characteristic model by using the historical data to obtain parameters of the characteristic model;
s3: calculating a controlled optimal path through parameters of the characteristic model obtained by fitting;
s4: substituting a PID control formula into the characteristic model to calculate a predicted value of the characteristic model under the controlled condition;
s5: and using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters.
In some embodiments, the feature models include a first order time-lapse system model, i.e., FOPDT, and a second order time-lapse system model, i.e., SOPDT;
first-order time-lag system model:
second-order time-lag system model:
in some embodiments, the parameters of the feature model include: the sum of K, τ,
and theta.
In some embodiments, the optimal path for the parameter calculation control of the feature model obtained by fitting includes two calculation models: linear models and non-linear models.
In some embodiments, the linear model is of the specific form:
y1＝k1·t+b
wherein:
k1：
b：
t: a time variable;
t0: step reaction start time;
PV0: initial values of controlled variables;
Δ y: step increment of a controlled variable;
n: ideally n response cycles converge to 97% of the setpoint.
In some embodiments, the non-linear model is of the specific form:
y2＝k2(1-exp(-a(t-c)))+d
k2：Δy；
a：
c：t0+θ；
d：PV0。
in some embodiments, the value of n is set to 2 to 6.
In some embodiments, the PID control formula is:
wherein the content of the first and second substances,
KP: scale factor, optimization parameter;
Ti: integrating time constants and optimizing parameters;
Td: differentiating the time constant, optimizing the parameter;
t: a period;
ek: difference between the set value and the process variable of the current period;
ek-1: the difference between the set point and the last cycle process variable.
Example 2:
as shown in fig. 1, a PID parameter setting method based on an optimized path includes:
s1: acquiring historical data of a control variable and a controlled object;
in some embodiments, historical data of the control variable u and the controlled object y is obtained, where the historical data includes several pieces of step response data, and the data obtaining manner is as follows: firstly, history data is directly obtained from an OPC server, and secondly, an excel table is uploaded to a server. The table contains sampling time, the value of the control variable u corresponding to each sampling time and the value of the controlled object y corresponding to each sampling time.
S2: fitting a characteristic model by using the historical data to obtain parameters of the characteristic model;
the feature models include a first-order time-lag system model, i.e., FOPDT, and a second-order time-lag system model, i.e., SOPDT;
the mathematical expression of the characteristic model is shown in the following table:
the parameters of the feature model include: the sum of K, τ,
and theta.
In some embodiments, the feature model fits the historical data by minimizing loss functions including Mean Square Error (MSE), Sum of Squared Error (SSE), Mean Absolute Error (MAE), Sum of Absolute Error (SAE), and Root Mean Square Error (RMSE).
S3: calculating an optimal path for control through parameters of the characteristic model obtained by fitting so as to reduce the conditions of oscillation, overshoot and non-convergence of the PID controller caused by overlarge initial error when the controller is adjusted;
in some embodiments, the optimal path calculation includes two calculation methods, a linear model and a nonlinear model, the optimal path design includes a variable n, and n is set to a value of 2 to 6, i.e., 2 to 6 response cycles converge to the new set point, where n is 97% (i.e., within ± 3%) of the new set point for the n response cycles under ideal conditions.
According to the optimal path hypothesis, the coordinates of the initial point and the end point of the optimal path can be obtained:
| starting point | [t0+θ，PV0] |
| End point | [t0+θ+n·τ，PV0+0.97·Δy] |
Wherein t is0For step reaction initiation time, PV0And the initial value of the controlled variable is delta y, and the step increment of the controlled variable is delta y.
Through the starting point and the end point, the invention provides two example optimal paths, and the example optimal paths correspond to a function y of timeOPF (t) is as follows:
t: a time variable;
in some embodiments, the optimal control path may be formed by other commonly used functions, such as trigonometric functions, exponential functions, logarithmic functions, and the like.
S4: substituting a PID control formula into the characteristic model to calculate the predicted value y under the controlled condition of the characteristic modelpred；
The PID control formula is as follows:
wherein the content of the first and second substances,
KP: scale factor, optimization parameter;
Ti: integrating time constants and optimizing parameters;
Td: differentiating the time constant, optimizing the parameter;
t: a period;
ek: difference between the set value and the process variable of the current period;
ek-1: the difference between the set point and the last cycle process variable.
S5: and using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters.
In some embodiments, by using the optimal control path yOPCalculating ypredAnd yOPThe error, may be calculated using Mean Square Error (MSE), Sum of Squared Error (SSE), Mean Absolute Error (MAE), Sum of Absolute Error (SAE), and Root Mean Square Error (RMSE).
In some embodiments, the optimization algorithm comprises: gradient descent algorithm, meta-heuristic algorithm and Bayesian optimization algorithm.
Example 3:
as shown in fig. 2, a PID parameter setting system based on an optimized path includes,
the system comprises a historical data acquisition module 1, a characteristic model optimization module 2, an optimal path calculation module 3, a model output prediction module 4, a PID parameter optimization module 5 and a user visualization interaction module 6;
the historical data acquisition module 1: acquiring historical data of a control variable and a controlled object;
the feature model optimization module 2: fitting a characteristic model by using the historical data to obtain parameters of the characteristic model;
the optimal path calculation module 3: calculating a controlled optimal path through parameters of the characteristic model obtained by fitting;
the model output prediction module 4: substituting a PID control formula into the characteristic model to calculate a predicted value of the characteristic model under the controlled condition;
the PID parameter optimizing module 5: using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters;
the user visualization interaction module 6: and previewing to obtain an optimal PID parameter control result, providing a user fine adjustment interface, and confirming the optimal control parameter.
In some embodiments, the feature system fitting result and the PID parameter optimization result are visualized and interacted with a user, and a control effect is previewed.
In some embodiments, the resulting K will be optimizedP，Ti，TdAnd returning a control result to a user by combining the fitted characteristic system, and simultaneously providing a plurality of groups of different PID parameters for the user to refer to, such as the internal model parameter, the results of the Ziegler-Douglas parameter and the method of the invention to be displayed and compared at the same time.
In some embodiments, the user is provided with a pair parameter KP，Ti，TdAnd (4) fine-tuning control right, displaying the fine-tuning control effect, and finally confirming the PID parameters.
Example 4:
the method provides a PID parameter setting method and a setting system based on an optimized path, and comprises the following steps:
1. acquiring historical data of the control variable u and the controlled object y, wherein the historical data needs to contain a plurality of stages of step response data. The embodiment provides the data as historical data of a mixing and stirring system, wherein the control variable is the opening of a diluent valve, and the controlled variable is the outlet concentration of the device.
2. The historical data is used for fitting the characteristic model to obtain the parameters of the characteristic model, and the embodiment uses a first-order time-lag system model (FOPDT) for fitting, and the ordinary differential equation of the model is
3. The Mean Absolute Error (MAE) is used in the fitting process as the error between the model prediction and the historical data is measured by a loss function, which can be written as:
wherein y ispAs model predicted value, yTIs historical data.
4. Selecting an initial value, setting limiting conditions { tau > 0 and theta > 0}, and solving model parameters { K, tau and theta } by using a random gradient descent method to minimize a loss function. In this step, other optimization solving algorithms besides the stochastic gradient descent algorithm can be used in this step.
5. The solution of this example is found to be K ═ 0.106, τ ═ 2.820, and θ ═ 0.025. FIG. 3 shows that the fit model compares with historical data, and there is a better fit between the selected feature model and the historical data.
6. Using the obtained model, a step test simulation is carried out on the controlled object set point SP, namely, the delta y is equal to 1, and the starting time point of the step test is t0＝10。
7. An optimal control path is calculated, here using a non-linear path calculation,
yCurk (1-exp (-a (t-c))) + d, and n is set to 4. Then k is 1, a is 0.311, c is 10.1, and d is 0.
The complete optimization path can be written as:
8. in subsequent optimization of PID parameters, the complete path y is usedOPInstead of the usual fitness function.
9. Modeling a controller using PID control equations
As known from the PID control model, the control output is related to the error ekWherein { K }P，Ti，TdIs a parameter. Using the model, substituting into formula (1), the controlled object controlled model can be written as ypred＝q(ek|{KP，Ti，Td}). q (#) instead of equation (1), its model inputDerived parameter { KP，Ti，TdAnd (4) determining.
10. Using MAE as output y of controlled objectpredAnd the complete optimization path yOPError index in between.
11. Select { KP，Ti，TdThe initial point of { K } and solving for { K } using a random gradient descent methodP，Ti，TdLeading the controlled object to output and complete the optimized path yOPWith the smallest error between. In this step, other optimization solving algorithms besides the stochastic gradient descent algorithm can be used in this step.
12. The parameter value obtained in this case is KP＝-4.74，Ti＝2.83，Td0.013. The resulting controller output, set point change, calculated optimal control path, and comparison to the inner model method are shown in fig. 4. As shown, the resulting PID
The control measurements closely follow the designed control curve, quickly approach the set point, and no overshoot occurs.
13. The method designs and uses the optimal control path to replace the traditional fitness function, and has obvious improvement on the aspects of reducing overshoot and increasing the stability of the controller.
14. The resulting control parameters are passed to the user for viewing and fine-tuning by the user, the interface being shown in FIG. 5.
It is to be understood that the present invention is not limited to the procedures and structures described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the invention is limited only by the appended claims.
Claims (10)
1. A PID parameter setting method based on an optimized path is characterized by comprising the following steps,
s1: acquiring historical data of a control variable and a controlled object;
s2: fitting a characteristic model by using the historical data to obtain parameters of the characteristic model;
s3: calculating a controlled optimal path through parameters of the characteristic model obtained by fitting;
s4: substituting a PID control formula into the characteristic model to calculate a predicted value of the characteristic model under the controlled condition;
s5: and using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters.
2. The optimized path-based PID parameter setting method as claimed in claim 1, wherein the feature model includes a first order time lag system model, FOPDT, and a second order time lag system model, SOPDT;
first-order time-lag system model:
second-order time-lag system model:
3. the optimized path-based PID parameter setting method according to claim 2, wherein the parameters of the feature model include: the sum of K, τ,
and theta.
4. The optimal path-based PID parameter setting method according to claim 3, wherein the optimal path controlled by the parameter calculation of the feature model obtained by fitting includes two calculation models: linear models and non-linear models.
5. The optimized path-based PID parameter setting method according to claim 4, wherein the linear model is in a specific form:
y1＝k1·t+b
wherein:
k1：
b：
t: a time variable;
t0: step reaction start time;
PV0: initial values of controlled variables;
Δ y: step increment of a controlled variable;
n: ideally n response cycles converge to 97% of the setpoint.
6. The optimized path-based PID parameter setting method according to claim 5, wherein the non-linear model is in a specific form:
y2＝k2(1-exp(-a(t-c)))+d
k2：Δy；
c：t0+θ；
d：PV0。
7. the optimized path-based PID parameter setting method according to claim 6, wherein the value of n is set to 2 to 6.
8. The optimized path-based PID parameter setting method according to claim 1, wherein the PID control formula is:
wherein the content of the first and second substances,
KP: scale factor, optimization parameter;
Ti: integrating time constants and optimizing parameters;
Td: differentiating the time constant, optimizing the parameter;
t: a period;
ek: difference between the set value and the process variable of the current period;
ek-1: the difference between the set point and the last cycle process variable.
9. The optimized path-based PID parameter setting method according to claim 1, wherein the optimization algorithm comprises: gradient descent algorithm, meta-heuristic algorithm and Bayesian optimization algorithm.
10. An optimized path-based PID parameter setting system is characterized by comprising,
the system comprises a historical data acquisition module, a characteristic model optimization module, an optimal path calculation module, a model output prediction module, a PID parameter optimization module and a user visualization interaction module;
the historical data acquisition module: acquiring historical data of a control variable and a controlled object;
the feature model optimization module: fitting a characteristic model by using the historical data to obtain parameters of the characteristic model;
the optimal path calculation module: calculating a controlled optimal path through parameters of the characteristic model obtained by fitting;
the model output prediction module: substituting a PID control formula into the characteristic model to calculate a predicted value of the characteristic model under the controlled condition;
the PID parameter optimization module: using an optimization algorithm to iteratively optimize the PID parameters to minimize the error between the predicted value and the optimal path, thereby obtaining the optimal PID parameters;
the user visualization interaction module: and previewing to obtain an optimal PID parameter control result, providing a user fine adjustment interface, and confirming the optimal control parameter.
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| CN114002946A (en) * | 2021-12-31 | 2022-02-01 | 浙江中控技术股份有限公司 | Self-adaptive PID parameter setting method, system, electronic equipment and storage medium |
| CN114137827A (en) * | 2021-12-01 | 2022-03-04 | 电子科技大学 | Automatic PID controller parameter setting method based on multi-point parallel random gradient descent |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114137827A (en) * | 2021-12-01 | 2022-03-04 | 电子科技大学 | Automatic PID controller parameter setting method based on multi-point parallel random gradient descent |
| CN114002946A (en) * | 2021-12-31 | 2022-02-01 | 浙江中控技术股份有限公司 | Self-adaptive PID parameter setting method, system, electronic equipment and storage medium |
| CN114002946B (en) * | 2021-12-31 | 2022-05-03 | 浙江中控技术股份有限公司 | Self-adaptive PID parameter setting method, system, electronic equipment and storage medium |
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