CN113050604B - Data drive controller correction method based on comprehensive performance indexes - Google Patents

Data drive controller correction method based on comprehensive performance indexes Download PDF

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CN113050604B
CN113050604B CN202110332116.5A CN202110332116A CN113050604B CN 113050604 B CN113050604 B CN 113050604B CN 202110332116 A CN202110332116 A CN 202110332116A CN 113050604 B CN113050604 B CN 113050604B
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王志国
陈军军
赵顺毅
栾小丽
刘飞
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Jiangnan University
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Abstract

The invention discloses a data driving controller correction method based on comprehensive performance indexes, and belongs to the field of industrial process control. The method constructs a new comprehensive performance index by fusing the IAE index and the MV standard, and selects the optimal reference model of the controlled system according to the new comprehensive performance index, thereby solving the problem that the existing controller correction method needs to rely on the experience of engineering personnel when selecting the reference model; and the corresponding reference model is selected according to the performance index of the controlled system fused with the IAE index and the MV benchmark, so that the selected reference model is ensured to be the optimal reference model of the controlled system, and the control performance of the corrected controller is better; meanwhile, the method can correct the parameters of the controller only by using a group of measured closed-loop input and output data, does not need to carry out model identification on the controlled object, and is simpler to realize; and the method reduces the error generated by the approximate processing of the delay link, so the control performance is relatively better.

Description

Data drive controller correction method based on comprehensive performance indexes
Technical Field
The invention relates to a data driving controller correction method based on comprehensive performance indexes, and belongs to the field of industrial process control.
Background
In the industrial processes of petroleum, chemical industry, light industry and the like, a plurality of control loops of various types are operated, and the performance of the control loops directly influences the precision of the whole control system. The control parameters of these circuits are typically carefully adjusted during the initial stages of system commissioning. However, as time goes on, each link itself, the operating environment, the operating point, etc. constituting the control system may change, which requires real-time monitoring of the control performance and correction of the controller when the performance is poor. In recent years, Data-driven (Data-drive) based controller calibration and design methods have attracted considerable attention because they do not require a system identification process.
The controller correction method based on data driving is a model parameter-free method, namely, the parameters of the controller are directly adjusted by directly utilizing the working data of the system without establishing a model for a controlled system. In 1994, Hjalmarson et al proposed an Iterative feedback correction method (IFT) that utilized response data from multiple closed-loop experiments and based on gradient iterations to achieve controller parameter tuning (see Hjalmarson H, Gunnasson S, Gevers M.A transformed Iterative compensated control design [ C ]. Proceedings of the 33rd IEEE reference on Decision and control. Pitcataway: IEEE,1994: 1735-. Subsequently, Campi et al introduces a Virtual Reference signal, obtains controller parameters through Direct identification of actual data and Virtual input data at the input end of the system, and proposes a Virtual Reference Feedback correction Method (VRFT) (see Campi M C, Lecchini A. savari S M. Virtual Reference Feedback Tuning-A Direct Method for the Design of Feedback Controllers [ J ] Automatics, 2002,38(8): 1337-. The method is a disposable data driving method, and avoids the waste of cost and time caused by multiple experiments of IFT. In 2016, Campesrini et al extended VRFT into multiple-input multiple-output (MIMO) systems, achieving unbiased estimation of optimal MIMO controllers (see Campesrini L, Eckhard D, Choi ia L A, et al. Unbiaded MIMO VRFT with application to Process Control [ J ]. Journal of Process Control,2016,39: 35-49.). The method is then used to control the multivariable water tank system and the chamber tuner in the particle accelerator. Eckhard et al improve the suppression of the VRFT against disturbance by introducing a virtual disturbance signal for frequent load disturbance (see Eckhard D, Cammestrini, L, Christ Boeira E. virtual disturbance feedback [ J ]. IFAC Journal of Systems and Control,2018,3: 23-29.). In 2019, Ikezaki et al provided a Virtual internal model Tuning method (VIMT) by virtualizing an internal model structure and directly identifying controller parameters by Using Closed-Loop Output Data (see Ikezaki T, Kaneko O.A New Approach to Parameter Tuning of Controllers by Using Output Data of Closed Loop systems [ J ]. IEEJ transformations on Electronics, Information systems and s.2019,139(7): 780-) -785.). The method can be realized only by one group of closed-loop output data, and inverse and input power spectrums of expected transfer functions solved by VRFT are avoided.
In the data-driven controller correction method, experienced engineers are required to manually determine an expected transfer function, namely, a reference model of a controlled system is determined, and then the controller is corrected according to the determined reference model; the selection of the reference model directly affects the performance of the actual control system, but the desired transfer function determined by the engineer is usually not the best desired performance of the controlled system, that is, the method depends on the experience of the engineer when correcting the controller. To try to make The artificial determination of The desired transfer function match The desired best performance of The controlled system, Bazanella et al propose guidelines for choosing reference models, i.e., reference models that need to contain system non-minimum phase zeros and whose relativity cannot be smaller than that of The controlled object (causal relationships), and choose reference models according to these constraints (Bazanella a S, campestini L, and Eckhard D, Data-drive Controller Design: The h2approach. dordredcright, The Netherlands: Springer, 2011.). Later, the method is popularized to the MIMO system, but the method is difficult to implement, because the determination process of the non-minimum phase zero point of the system is very complicated, the requirement on the experience of engineering personnel is high, and at the same time, the Control performance of the system cannot be comprehensively reflected only by considering the constraint of the non-minimum phase zero point, so that the selected Reference Model still cannot ensure that the system obtains the optimal Control performance (Goncaves Da Silva G R.Bazanella A S, Campesrini, L.on the Choice of an application Reference Model for Control of multiple substrates [ J ] IEEE Transactions on Control Systems technologies.2019, 27 (1937) -.
Disclosure of Invention
In order to solve the problem that the existing controller correction method excessively depends on the experience of engineering personnel, the invention provides a data drive controller correction method based on comprehensive performance indexes, which comprises the following steps:
step 1: acquiring N groups of input and output data { u (t), y (t) }, t is 1, …, N, u (t) represents the input data of the controlled system acquired at the t-th moment, y (t) represents the output data of the controlled system at the t-th moment, and N represents the number of the groups of the acquired input and output data;
step 2: according to the N groups of collected input and output data, evaluating the current control performance of the controlled system through an MV reference;
step 3: judging whether the controller parameters need to be set according to the current control performance of the controlled system obtained by Step2 and the priori knowledge; if the new comprehensive performance index is needed, a weight coefficient lambda is given, an IAE index and an MV standard are fused to construct a new comprehensive performance index, and an optimal reference model of the controlled system under the new comprehensive performance index is obtained;
step 4: calculating the controller parameters after the controlled system is set according to the optimal reference model obtained by Step 3;
step 5: inputting the set controller parameters calculated at Step4, continuously acquiring input and output data of the controlled system under the set controller parameters, and monitoring the control performance of the controlled system after the controller is corrected through MV reference according to Step 2;
step 6: and repeating the steps from Step2 to Step5 during the operation of the controlled system to realize the correction of the controller of the controlled system.
Optionally, Step2 includes:
step2.1 utilizes a cross-correlation method to estimate an estimated value of a delay coefficient theta of a controlled system
Figure GDA0003456087640000031
Figure GDA0003456087640000032
y (t) represents output data of the controlled system at the t moment, and u (t-theta) represents input data of the controlled system collected at the t-theta moment; e represents expectation;
step2.2, carrying out time sequence analysis on the N groups of collected input and output data { u (t), y (t) }, and obtaining the minimum variance estimation value of the controlled system
Figure GDA0003456087640000033
And actual output variance
Figure GDA0003456087640000034
Step2.3 defines the MV benchmark-based control performance evaluation index η as:
Figure GDA0003456087640000035
optionally, the time sequence analysis is performed on the N sets of collected input and output data { u (t), y (t) }, so as to obtain the minimum variance of the controlled system
Figure GDA0003456087640000036
And actual output variance
Figure GDA0003456087640000037
The method comprises the following steps:
step2.2.1 the minimum variance of the controlled system is calculated according to the following formula:
Figure GDA0003456087640000038
wherein f isiFor the impulse response coefficient of the transfer function from noise to output,
Figure GDA0003456087640000039
Figure GDA00034560876400000310
is an estimate of the variance of the random noise;
step2.2.2 due to fiAnd
Figure GDA00034560876400000311
unknown, so time series analysis is performed on the acquired N sets of input and output data { u (t), y (t) }, and fitting an ARMAX model of the controlled system by MATLAB is as follows:
Figure GDA00034560876400000312
where ξ (t) is a random noise sequence of the controlled system;
Figure GDA00034560876400000313
wherein the content of the first and second substances,
Figure GDA00034560876400000314
denotes a back shift of naThe post-shift operator for each time instant,
Figure GDA00034560876400000315
is the corresponding coefficient; thereby obtaining an estimated value of the disturbance model
Figure GDA00034560876400000316
Estimation value of controlled system model
Figure GDA00034560876400000317
And an estimate of the random noise sequence
Figure GDA00034560876400000318
And variance of random noise sequence
Figure GDA00034560876400000319
Step2.2.3 from Step2.2.2
Figure GDA00034560876400000320
Solving f by performing a de-mapping decompositioni(ii) a Will f isiVariance with random noise sequence
Figure GDA0003456087640000041
Substituted into the formula in Step2.2.1
Figure GDA0003456087640000042
Obtaining the minimum variance of the controlled system
Figure GDA0003456087640000043
Optionally, the optimal reference model T of the controlled system in Step3des(s) in the basic form:
Figure GDA0003456087640000044
wherein, Tdes(s) is the expression form of the optimal reference model in the complex frequency domain, s is a complex variable factor, and epsilon is a filter parameter in the reference model;
optionally, the Step3 gives a weight coefficient λ, integrates the IAE index and the MV standard to construct a new comprehensive performance index, and obtains an optimal reference model of the controlled system under the new comprehensive performance index, including:
determining the relationship between the IAE index and the filter parameter epsilon in the reference model as follows:
Figure GDA0003456087640000045
determining the relation between the system performance index eta in the MV standard and the filter parameter epsilon in the reference model as follows:
Figure GDA0003456087640000046
wherein the content of the first and second substances,
Figure GDA0003456087640000047
is the estimated value of the minimum variance of the controlled system,
Figure GDA0003456087640000048
outputting variance for actual output of the controlled system:
Figure GDA0003456087640000049
Figure GDA00034560876400000410
defining comprehensive performance indexes, and determining the relation between the comprehensive performance indexes and the filter parameters epsilon as follows:
Figure GDA00034560876400000411
wherein the content of the first and second substances,
Figure GDA00034560876400000412
Figure GDA00034560876400000413
wherein the content of the first and second substances,
Figure GDA00034560876400000414
is the lower value of IAE, eta, which varies with the value of epsiloniControlling the performance index value for the corresponding MV which changes along with the epsilon value;
to pair
Figure GDA00034560876400000415
And ηiNormalizing to eliminate dimension by
Figure GDA00034560876400000416
And
Figure GDA00034560876400000417
represents;
lambda is a weight coefficient, and the value of lambda is more than or equal to 0 and less than or equal to 1;
to obtain the filter parameter epsilon under the comprehensive performance index*The following objective function is defined:
Figure GDA0003456087640000051
ε*representing filter parameters under the comprehensive performance index;
will obtain epsilon*Substituting the best reference model T of the controlled systemdes(s) in basic form, the final desired reference model T is determineddes(s)。
Optionally, Step4 includes:
step4.1 filtering the acquired input and output data;
step4.2 utilizes the collected input and output data to determine virtual error data and virtual input signals
Figure GDA0003456087640000052
Comparison in Step4.3
Figure GDA0003456087640000053
The loss function is defined as:
Figure GDA0003456087640000054
step4.4 by least squares identification method, as J1And (ρ) → 0, a PID controller parameter vector ρ is obtained.
Optionally, the step4.1 filters the acquired input and output data, and the filter is in the form of:
L(q-1)＝Tdes(q-1)(1-Tdes(q-1))
wherein, Tdes(q-1) As a reference model Tdes(s) representation in the frequency domain; t isdes(q-1) And Tdes(s) interconversion by Z transformation:
Tdes(q-1)＝Z[Tdes(s)]。
optionally, the step4.2 determines a virtual error signal and a virtual input signal
Figure GDA0003456087640000055
The method comprises the following steps:
step4.2.1 the equation for determining the virtual error signal is:
Figure GDA0003456087640000056
wherein the content of the first and second substances,
Figure GDA0003456087640000057
representing a virtual reference signal, determining
Figure GDA0003456087640000058
The formula of (1) is:
Figure GDA0003456087640000059
step4.2.2 the formula for determining the virtual input signal is:
Figure GDA00034560876400000510
wherein, C (rho, q)-1) Representing a discrete form of PID controller.
Optionally, the step4.4 determines the estimated value of the parameter vector of the PID controller by a least square identification method
Figure GDA00034560876400000511
The method comprises the following steps:
Figure GDA0003456087640000061
wherein the content of the first and second substances,
Figure GDA0003456087640000062
Figure GDA0003456087640000063
Figure GDA0003456087640000064
Figure GDA0003456087640000065
representing filtered output data yL(t) the constructed measurable information vector; beta (q)-1) A known vector representing the discrete-time transfer function of the PID controller; estimation value of current PID controller parameter vector
Figure GDA0003456087640000066
Proportional gain k with conventional PID controllerpIntegral time constant TiDifferential time constant TdThe conversion formula is:
Figure GDA0003456087640000067
Figure GDA0003456087640000068
Figure GDA0003456087640000069
wherein, TsRepresenting the sampling time.
The application also provides a temperature control system, and the temperature control system corrects the parameters of the controller by adopting the method.
The invention has the beneficial effects that:
a new comprehensive performance index is constructed by fusing the IAE index and the MV standard, and the constructed new comprehensive performance index is used for selecting the optimal reference model of the controlled system, so that the problem that the conventional controller correction method needs to rely on the experience of engineering personnel when selecting the reference model is solved; in addition, the corresponding reference model is selected according to the performance index of the controlled system fused with the IAE index and the MV benchmark, so that the selected reference model is ensured to be the optimal reference model of the controlled system, and the control performance of the corrected controller is better; compared to IMC-PID corrections. The invention can correct the controller parameter only by using a group of measured closed-loop input and output data without carrying out model identification on the controlled object, thereby being simpler and more accurate to realize; furthermore, the invention reduces the error generated by the approximate processing of the delay link in the internal model control design process, so the control performance of the corrected controller is relatively better; compared with other data driving methods, the method is a one-time data driving controller correction method, additional experiments are not needed, time is saved, and unnecessary resource waste is avoided; meanwhile, the problem of controller adjustment is expressed as the problem of controller parameter identification, the least square algorithm is adopted, gradient iteration is not needed, and the calculated amount is reduced.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flowchart illustrating implementation steps of a method for driving a calibration based on comprehensive performance index data according to an embodiment of the present invention.
FIG. 2 is a flow chart of a process for controlling the temperature of a beer fermentation process according to an embodiment of the present invention.
FIG. 3 is a graph of a composite performance indicator as a function of filter parameters in an embodiment of the present invention.
FIG. 4 is a graph of the output response of the system before and after adjustment of the controller parameters in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Introduction of basic theory:
the PID controller consists of a proportional unit P, an integral unit I and a differential unit D. By adjusting the controller parameter kp，TiAnd TdA desired control result is achieved. The PID control structure is as follows:
Figure GDA0003456087640000071
wherein, Delta: ═ 1-q-1For the difference operator, kpTo proportional gain, TiTo integrate the time constant, TdIs a differential time constant, TsRepresenting the sampling time.
Order:
Figure GDA0003456087640000072
Figure GDA0003456087640000073
Figure GDA0003456087640000074
is expressed as containing the controller parameter p1,ρ2,ρ3The general structure controller expression of (1) is:
Figure GDA0003456087640000075
the first embodiment is as follows:
the present embodiment provides a method for correcting a data driving controller based on comprehensive performance indexes, please refer to fig. 1, where the method includes:
step 1: acquiring N groups of input and output data { u (t), y (t) }, t is 1, …, N, u (t) represents the input data of the controlled system acquired at the t-th moment, y (t) represents the output data of the controlled system at the t-th moment, and N represents the number of the groups of the acquired input and output data;
step 2: according to the N groups of collected input and output data, evaluating the current control performance of the controlled system through an MV reference;
step 3: judging whether the controller parameters need to be set according to the current control performance of the controlled system obtained by Step2 and the priori knowledge; if the new comprehensive performance index is needed, a weight coefficient lambda is given, an IAE index and an MV standard are fused to construct a new comprehensive performance index, and an optimal reference model of the controlled system under the new comprehensive performance index is obtained;
step 4: calculating the controller parameters after the controlled system is set according to the optimal reference model obtained by Step 3;
step 5: inputting the set controller parameters calculated at Step4, continuously acquiring input and output data of the controlled system under the set controller parameters, and monitoring the control performance of the controlled system after the controller is corrected through MV reference according to Step 2;
step 6: and repeating the steps from Step2 to Step5 during the operation of the controlled system to realize the correction of the controller of the controlled system.
Example two:
the embodiment provides a temperature control system, which takes a temperature control system of a beer fermentation process as an example for explanation, and the temperature control system adopts the data drive controller correction method based on the comprehensive performance index described in the embodiment one to correct a controller adopted in the beer fermentation process.
Refer to the schematic diagram of the beer fermentation temperature control structure shown in FIG. 2. The principle of the temperature control process is as follows: the temperature in the beer fermentation tank is detected and transmitted to the PLC controller, and the valve opening of the refrigerant regulating valve is controlled by performing logic operation on the difference value between the acquired temperature and the set value temperature through the PLC, so that the refrigerant flow is controlled, and the temperature is regulated.
The steps of the method shown with reference to fig. 1 include:
the method comprises the following steps: collecting data
The input and output data (namely the internal temperature of the fermentation tank and the flow of the refrigerant flowing through the tank jacket) of the beer fermentation system are collected. Wherein the content of the first and second substances,
1 the embodiment of the present application selects an initial controller parameter as kp＝0.2,Ti＝17.857,Td＝36.1；
2, appointing the sampling time to be 10 s;
3, determining the name description standard and the storage path of the data sample of the beer fermentation process;
and 4, determining the number N of the collected samples to be 20000.
It should be noted that the data drive controller correction method based on the comprehensive performance index provided by the invention can also be applied to a robot joint control system, an inverted pendulum control system, a direct current servo system, a pH neutralization control system and a temperature control system in the thermal engineering industry. The input and output data collected correspond to different systems:
for example, in a Continuous Stirred Tank Heater (CSTH), temperature regulation is generally performed by collecting input steam flow in a CSTH device to regulate temperature data in a water outlet pipe, so that when the temperature regulation is performed in the CSTH device, the input data is a steam valve opening signal, and the output data is the temperature in the water outlet pipe.
For another example, the pH neutralization reaction control process is widely applied in the aspects of drug development, chemical production, ecological environment protection (wastewater treatment) and the like. In general, an aqueous solution is neutralized by hydrochloric acid (HCl) in a PH neutralization reaction apparatus, and a flow rate of the hydrochloric acid input to the PH neutralization reaction apparatus and PH data after the PH neutralization reaction are collected, so that when the PH neutralization reaction control apparatus is applied to the PH neutralization reaction control, input data is the input flow rate of the hydrochloric acid, and output data is the PH data after the PH neutralization reaction.
Step two: evaluating control performance of a current system
And judging the temperature control performance of the current fermentation process by utilizing the collected internal temperature of the fermentation tank and the flow of the refrigerant flowing through the tank jacket. If the effect is good, the parameters of the controller do not need to be corrected; otherwise, the controller parameters need to be re-tuned.
The value range of a control performance evaluation index eta of the controlled system based on the MV reference is between 0 and 1, and when the eta is closer to 1, the control of the controlled system is closer to the control of the minimum variance, and the control performance is better; when η approaches 0, it means that the control performance of the system is poor and the controller parameters need to be recalibrated. The threshold value of the control performance evaluation index eta of the controller parameter needing to be re-corrected by the specific controlled system can be judged according to the priori knowledge of the controlled system in the industry.
1, preprocessing collected internal temperature of a fermentation tank and flow data of a refrigerant flowing through a tank jacket, and rejecting abnormal or damaged data, filling missing data and correcting error data;
2 estimating the estimated value of the delay coefficient theta of the system by using the cross-correlation method
Figure GDA0003456087640000091
Based on the following formula:
Figure GDA0003456087640000092
wherein E represents expectation; y (t) represents the output data of the temperature control system in the beer fermentation process at the t-th moment, namely the flow rate of the refrigerant flowing through the tank jacket, u (t-theta) represents the flow rate of the refrigerant flowing through the tank jacket collected at the t-theta moment, and the estimated value of the delay coefficient is obtained according to the formula and is 87.
3 to the N that gathers 20000 group fermentation cylinder internal temperature and the coolant flow data of flowing through the jar body jacket carry out time series analysis, and the ARMAX model of fitting beer fermentation temperature control system is:
A(q-1)y(t)＝B(q-1)ξ(t)
wherein the content of the first and second substances,
A(q-1)＝1-0.2774q-1-1.043q-2-0.05486q-3+0.3678q-4+0.01149q-5
B(q-1)＝1+0.3444q-1-0.601q-2-0.2454q-3+0.1584q-4
q-1the fitting degree of the ARMAX model and the beer fermentation system reaches 86.93 percent by representing a backward shift operator at the backward shift moment, and an estimated value of the minimum variance of the beer fermentation temperature control system is obtained based on the following formula
Figure GDA0003456087640000101
Figure GDA0003456087640000102
Determining the actual output variance of the beer fermentation temperature control system based on the output data, i.e. the internal temperature of the beer fermentation tank
Figure GDA0003456087640000103
Based on the following formula:
Figure GDA0003456087640000104
the current performance of the beer fermentation temperature control system under the MV reference is obtained as follows: and eta is 0.4974, the control performance of the temperature control system in the beer fermentation process is only 0.5, and according to the prior knowledge of the industry, the performance of the temperature control system in the beer fermentation process is poor, and the controller parameters need to be corrected again to improve the system performance.
Step three: optimal reference model for determining beer fermentation temperature control system based on comprehensive performance indexes
According to the calculation result of the second step, the temperature control effect of the current fermentation process is found to be poor, the method provided by the invention needs to be used for correcting the parameters of the controller again, and the control performance of the beer fermentation temperature control system is improved. When the method is used for correction, an optimal reference model of the beer fermentation temperature control system needs to be determined firstly:
1 the best reference model of the beer fermentation temperature control system is given by the connection of the method and the ideal Internal Model Control (IMC)Tdes(s) in the basic form:
Figure GDA0003456087640000105
wherein, TdesAnd(s) is the expression form of the optimal reference model in a complex frequency domain, s is a complex variable factor, and epsilon is a filter parameter in the reference model. All expressions referring to the complex variable s are expressions in the complex frequency domain, and can be converted into expressions in the time domain or the frequency domain through inverse Laplace transformation and Z transformation.
2 determining the best reference model of the beer fermentation temperature control system based on the following objective function.
Figure GDA0003456087640000106
ε*Representing filter parameters under the comprehensive performance index; delta is a new comprehensive performance index of the fusion IAE index and MV reference structure;
the determination process of δ includes:
determining the relationship between the IAE index and the filter parameter epsilon in the reference model as follows:
Figure GDA0003456087640000107
determining the relation between the system performance index eta in the MV standard and the filter parameter epsilon in the reference model as follows:
Figure GDA0003456087640000111
wherein the content of the first and second substances,
Figure GDA0003456087640000112
for the minimum variance of the system to be controlled,
Figure GDA0003456087640000113
outputting variance for actual output of a controlled system;
Figure GDA0003456087640000114
Figure GDA0003456087640000115
defining comprehensive performance indexes, and determining the relation between the comprehensive performance indexes and the optimal filter parameter epsilon as follows:
Figure GDA0003456087640000116
wherein the content of the first and second substances,
Figure GDA0003456087640000117
Figure GDA0003456087640000118
wherein the content of the first and second substances,
Figure GDA0003456087640000119
is the lower value of IAE, eta, which varies with the value of epsiloniControlling the performance index value for the corresponding MV which changes along with the epsilon value;
to pair
Figure GDA00034560876400001110
And ηiNormalizing to eliminate dimension by
Figure GDA00034560876400001111
And
Figure GDA00034560876400001112
represents;
lambda is a weight coefficient, and the value of lambda is more than or equal to 0 and less than or equal to 1;
in this embodiment, the weighting factor λ is selected to be 0.9, and referring to the schematic diagram of the performance index varying with the filter parameter shown in fig. 3, when ∈ is 53, the performance index takes a minimum value. The best reference model of the beer fermentation temperature control system at this time is as follows:
Figure GDA00034560876400001113
Tdesand(s) is the expression form of the reference model in a complex frequency domain, and s is a complex variable factor.
Step four: and correcting the optimal controller parameters of the beer fermentation temperature control system.
According to the third step, with the best reference model of the beer fermentation temperature control system, the PID controller parameters of the temperature control system of the beer fermentation process can be corrected based on the principle of the method.
1 the required filter L (q) of the method of the present application is determined using the optimal reference model of the beer fermentation temperature control system based on the following formula-1)；
L(q-1)＝Tdes(q-1)(1-Tdes(q-1))
Wherein, Tdes(q-1) For the reference model T obtained in step threedes(s) representation in the frequency domain. The conversion may be achieved by a Z-transform.
Tdes(q-1)＝Z[Tdes(s)]
2 determining the virtual error data and the virtual input signal based on the following formula according to the observed input and output data
Figure GDA0003456087640000121
Figure GDA0003456087640000122
Figure GDA0003456087640000123
Wherein, C (rho, q)-1) A PID controller representing a discrete form;
Figure GDA0003456087640000124
representing a virtual reference signal, determining
Figure GDA0003456087640000125
The formula of (1) is:
Figure GDA0003456087640000126
2 comparison
Figure GDA0003456087640000127
The loss function is defined as:
Figure GDA0003456087640000128
3 determining the parameters of the PID controller by a least square identification method based on the following formula.
Figure GDA0003456087640000129
Wherein the content of the first and second substances,
Figure GDA00034560876400001210
Figure GDA00034560876400001211
Figure GDA00034560876400001212
when J is1When (rho) is approximately equal to 0, the parameter vector is obtained
Figure GDA00034560876400001213
Comprises the following steps:
ρ1＝17.7380,ρ2＝-34.7995,ρ3＝17.0705
according to the following conversion formula:
Figure GDA00034560876400001214
Figure GDA00034560876400001215
Figure GDA00034560876400001216
the obtained PID controller parameters are:
kp＝0.6586,Ti＝73.9169,Td＝25.9193
step five: and repeating the second step and the third step, and comparing the performances before and after the parameter adjustment of the controller.
See the response curve of the system output before and after the controller parameter adjustment shown in fig. 4. Before the controller is corrected, the system response is slow, and overshoot exists, and it is known that if the system overshoot phenomenon is serious and difficult to stabilize, the system overshoot phenomenon can cause great abrasion to an execution element, and the system overshoot phenomenon can affect the quality of beer fermentation. The system output set value adjusted by the invention has strong tracking capability, quick response, no overshoot and good damping property.
Referring to the system performance indicators before and after the controller parameter adjustment shown in Table 1, the rise time t of the system before correctionrRegulating time t as 651ss913s, and the present invention increases the rise time to tr438s, the adjustment time is increased to tr443s, a large increase in the dynamic performance of the system is also reflected.
The IAE indexes before and after correction of the controller are compared, the actual IAE value of the system is reduced to 1449 corrected by the invention from 2322 under the control of the initial PID, and the result shows that the accumulated error after correction is small and the transient response characteristic is good. The temperature of beer fermentation process is adjusted fast effectual, can promote beer taste and quality.
For the random performance index MV, eta of the system under the control of the initial PID is 49.15 percent and is increased to the eta of 77.33 percent after the correction of the invention, which shows that the random performance of the current beer fermentation temperature control system is good, the external interference inhibition capability is strong, the output variance of the system is reduced, and the efficiency and the yield of the beer fermentation are improved.
TABLE 1 Performance of the controller before and after tuning
Figure GDA0003456087640000131
Some steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A data driving controller correction method based on comprehensive performance indexes is characterized by comprising the following steps:
step 1: acquiring N groups of input and output data { u (t), y (t) }, t is 1, …, N, u (t) represents the input data of the controlled system acquired at the t-th moment, y (t) represents the output data of the controlled system at the t-th moment, and N represents the number of the groups of the acquired input and output data;
step 2: according to the N groups of collected input and output data, evaluating the current control performance of the controlled system through an MV reference;
step 3: judging whether the controller parameters need to be set according to the current control performance of the controlled system obtained by Step2 and the priori knowledge; if the new comprehensive performance index is needed, a weight coefficient lambda is given, an IAE index and an MV standard are fused to construct a new comprehensive performance index, and an optimal reference model of the controlled system under the new comprehensive performance index is obtained;
step 4: calculating the controller parameters after the controlled system is set according to the optimal reference model obtained by Step 3;
step 5: inputting the set controller parameters calculated at Step4, continuously acquiring input and output data of the controlled system under the set controller parameters, and monitoring the control performance of the controlled system after the controller is corrected through MV reference according to Step 2;
step 6: and repeating the steps from Step2 to Step5 during the operation of the controlled system to realize the correction of the controller of the controlled system.
2. The method of claim 1, wherein Step2 comprises:
step2.1 utilizes a cross-correlation method to estimate an estimated value of a delay coefficient theta of a controlled system
Figure FDA0003393744660000011
Figure FDA0003393744660000012
y (t) represents output data of the controlled system at the t moment, and u (t-theta) represents input data of the controlled system collected at the t-theta moment; e represents expectation;
step2.2, carrying out time sequence analysis on the N groups of collected input and output data { u (t), y (t) }, and obtaining the minimum variance estimation value of the controlled system
Figure FDA0003393744660000013
And actual output variance
Figure FDA0003393744660000014
Step2.3 defines the MV benchmark-based control performance evaluation index η as:
Figure FDA0003393744660000015
3. the method according to claim 2, wherein the time-series analysis is performed on the N collected sets of input/output data { u (t), y (t) } to obtain the minimum variance of the controlled system
Figure FDA0003393744660000016
And actual output variance
Figure FDA0003393744660000017
The method comprises the following steps:
step2.2.1 the minimum variance of the controlled system is calculated according to the following formula:
Figure FDA0003393744660000021
wherein f isiFor the impulse response coefficient of the transfer function from noise to output,
Figure FDA0003393744660000022
Figure FDA0003393744660000023
is an estimate of the variance of the random noise;
step2.2.2 due to fiAnd
Figure FDA0003393744660000024
unknown, so time series analysis is performed on the acquired N sets of input and output data { u (t), y (t) }, and fitting an ARMAX model of the controlled system by MATLAB is as follows:
Figure FDA0003393744660000025
where ξ (t) is a random noise sequence of the controlled system;
Figure FDA0003393744660000026
wherein the content of the first and second substances,
Figure FDA0003393744660000027
denotes a back shift of naThe post-shift operator for each time instant,
Figure FDA0003393744660000028
is the corresponding coefficient; thereby obtaining an estimated value of the disturbance model
Figure FDA0003393744660000029
Estimation value of controlled system model
Figure FDA00033937446600000210
And an estimate of the random noise sequence
Figure FDA00033937446600000211
And variance of random noise sequence
Figure FDA00033937446600000212
Step2.2.3 from Step2.2.2
Figure FDA00033937446600000213
Solving f by performing a de-mapping decompositioni(ii) a Will f isiVariance with random noise sequence
Figure FDA00033937446600000214
Substituted into the formula in Step2.2.1
Figure FDA00033937446600000215
Obtaining the minimum variance of the controlled system
Figure FDA00033937446600000216
4. The method of claim 3, wherein said Step3 is characterized by the optimal reference model T of the controlled systemdes(s) in the basic form:
Figure FDA00033937446600000217
wherein, TdesAnd(s) is the expression form of the optimal reference model in a complex frequency domain, s is a complex variable factor, and epsilon is a filter parameter in the reference model.
5. The method according to claim 4, wherein the Step3, given the weight coefficient λ, combines the IAE index and the MV reference to construct a new comprehensive performance index, and obtains the optimal reference model of the controlled system under the new comprehensive performance index, comprising:
determining the relationship between the IAE index and the filter parameter epsilon in the reference model as follows:
Figure FDA0003393744660000031
determining the relation between the system performance index eta in the MV standard and the filter parameter epsilon in the reference model as follows:
Figure FDA0003393744660000032
wherein the content of the first and second substances,
Figure FDA0003393744660000033
is the estimated value of the minimum variance of the controlled system,
Figure FDA0003393744660000034
outputting variance for actual output of the controlled system:
Figure FDA0003393744660000035
Figure FDA0003393744660000036
defining comprehensive performance indexes, and determining the relation between the comprehensive performance indexes and the filter parameters epsilon as follows:
Figure FDA0003393744660000037
wherein the content of the first and second substances,
Figure FDA0003393744660000038
Figure FDA0003393744660000039
wherein the content of the first and second substances,
Figure FDA00033937446600000310
is the lower value of IAE, eta, which varies with the value of epsiloniControlling the performance index value for the corresponding MV which changes along with the epsilon value;
to pair
Figure FDA00033937446600000311
And ηiNormalizing to eliminate dimension by
Figure FDA00033937446600000312
And
Figure FDA00033937446600000313
represents;
lambda is a weight coefficient, and the value of lambda is more than or equal to 0 and less than or equal to 1;
to obtain the filter parameter epsilon under the comprehensive performance index*The following objective function is defined:
Figure FDA00033937446600000314
ε*representing filter parameters under the comprehensive performance index;
will obtain epsilon*Substituting the best reference model T of the controlled systemdes(s) in basic form, the final desired reference model T is determineddes(s)。
6. The method of claim 5, wherein Step4 comprises:
step4.1 filtering the acquired input and output data;
step4.2 utilizes the collected input and output data to determine virtual error data and virtual input signals
Figure FDA0003393744660000041
Comparison in Step4.3
Figure FDA0003393744660000042
The loss function is defined as:
Figure FDA0003393744660000043
step4.4 by least squares identification method, as J1And (ρ) → 0, a PID controller parameter vector ρ is obtained.
7. The method of claim 6, wherein Step4.1 filters the collected input and output data, and wherein the filter is of the form:
L(q-1)＝Tdes(q-1)(1-Tdes(q-1))
wherein, Tdes(q-1) As a reference model Tdes(s) representation in the frequency domain; t isdes(q-1) And Tdes(s) interconversion by Z transformation:
Tdes(q-1)＝Z[Tdes(s)]。
8. the method of claim 7, wherein Step4.2 determines the virtual error signal and the virtual input signal
Figure FDA0003393744660000044
The method comprises the following steps:
step4.2.1 the equation for determining the virtual error signal is:
Figure FDA0003393744660000045
wherein the content of the first and second substances,
Figure FDA0003393744660000046
representing a virtual reference signal, determining
Figure FDA0003393744660000047
The formula of (1) is:
Figure FDA0003393744660000048
step4.2.2 the formula for determining the virtual input signal is:
Figure FDA0003393744660000049
wherein, C (rho, q)-1) Representing discrete shapesA PID controller of formula (i).
9. The method of claim 8 wherein said step4.4 determines an estimate of a PID controller parameter vector by least squares identification
Figure FDA0003393744660000051
The method comprises the following steps:
Figure FDA0003393744660000052
wherein the content of the first and second substances,
Figure FDA0003393744660000053
Figure FDA0003393744660000054
Figure FDA0003393744660000055
Figure FDA0003393744660000056
representing filtered output data yL(t) the constructed measurable information vector; beta (q)-1) A known vector representing the discrete-time transfer function of the PID controller; estimation value of current PID controller parameter vector
Figure FDA0003393744660000057
Proportional gain k with conventional PID controllerpIntegral time constant TiDifferential time constant TdThe conversion formula is:
Figure FDA0003393744660000058
Figure FDA0003393744660000059
Figure FDA00033937446600000510
wherein, TsRepresenting the sampling time.
10. A temperature control system, wherein the temperature control system uses the method of any of claims 1-9 to correct a controller parameter.
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