CN111522224A - Parameter self-tuning PLC control method based on prediction PI and bias relay feedback - Google Patents
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Abstract
The invention discloses a prediction PI parameter self-tuning control system based on bias relay feedback and PLC, relating to the technical field of industrial process control. When the system output has a large error with the expected output, the system automatically enters an identification state, and returns to a control state again after the identification is finished, so that the aim of predicting the parameter self-tuning of the PI controller is fulfilled. The method combines and encapsulates two algorithms in the PLC, replaces the original PID control module in the PLC, and has better control performance and robustness.
Description
Technical Field
The invention relates to a parameter self-tuning PLC control method based on a prediction PI and a bias relay feedback, and belongs to the technical field of industrial process control.
Background
In actual industrial production, due to the reasons of overlong transport pipelines, delayed control action and the like, various large-time-lag and large-inertia control objects exist, and the objects cannot achieve satisfactory effects by using a traditional PID control method. In 1959, Smith proposed an estimation control method, which utilized a compensation link to feed the controlled quantity back to the input end of the controller in advance, so that the controller acts in advance. In 1992, Hagglund firstly provides the idea of a predictive PI control method, the method can effectively overcome the problem of time lag caused by large lag and large inertia objects, and then through continuous improvement of experts, the predictive PI control method becomes more and more mature and perfect, and is applied to a plurality of industrial production processes nowadays.
The control effect of the control method depends on whether the value of the controller parameter is proper or not, and the controller parameter is calculated by analyzing the control object model. Often, the aging of industrial production equipment or the change of operating environment can cause the drift of system parameters, and finally the mismatch of models causes the rapid deterioration of control effect. Therefore, in order to ensure the best control effect, the control object model needs to be identified again and the controller parameters need to be modified every time the control object model changes, which is a time-consuming and labor-consuming work and greatly increases the labor cost. In order to solve the problem, in the 90 s of the 20 th century, Astrom et al proposed a method for obtaining system critical information and realizing PID parameter self-tuning by using relay feedback, and the method was completed in a closed-loop state, and critical oscillation information of the system can be rapidly obtained without additional input signals. In 1987, Luyben proposed an ATV (auto tuning differentiation) method on the basis of the method, which is a standard relay identification method in industrial application because the method is simple and easy to implement, but the ATV method needs to identify a time constant under the condition that the gain and the time lag of a control object are known. In 1997, Wang, Q and G applied the bias relay feedback model identification method with hysteresis to engineering for the first time, and for the first-order plus hysteresis model, a more accurate object model could be obtained by using the identification method.
The identification method based on the bias relay feedback calculates a control object model by obtaining system critical oscillation information, then sets PID parameters through an empirical formula, and applies a PID method to a control system. Compared with a PID method, the PI prediction method has better control performance, high response speed, no overshoot and few control parameters. Moreover, the identification method based on the bias relay feedback needs to manually calculate the parameters of the controller after each identification is finished, so that the labor cost is greatly increased. Therefore, the parameter self-tuning controller based on the PI prediction method and the bias relay feedback has a large practical application value.
Disclosure of Invention
The invention aims to solve the technical problems that object models in industrial control are various and easy to change, a traditional PID control method cannot effectively control a large-lag object, and parameters of a controller need to be manually adjusted.
In order to solve the technical problems, the technical scheme of the invention is to provide a parameter self-tuning PLC control method based on a prediction PI and a bias relay feedback, which is characterized in that for a relay system with an asymmetric hysteresis loop, the first order of the relay system is added with a pure hysteresis model transfer function of
Wherein, KpT and tau respectively represent object gain, time constant and time lag, and s represents a state quantity; the hysteresis loop has the size that the output is u0+ u1 or u0-u1, wherein u1 is the output of a conventional relay link, u0 is the offset, the output of the system generates oscillation near a set value sp, and the trough part of the oscillation period obtained according to the oscillation waveform of the limit loop is Tu1The peak part is Tu2Amplitude of oscillation peak is AuAmplitude of oscillation trough is Ad(ii) a Model identification is carried out according to the following formula to calculate the parameters of the first-order plus pure hysteresis model as follows:
the control object model is:
the desired closed loop transfer function is:
wherein λ is an adjustable parameter for adjusting response speed, and can be obtained by closed-loop transfer function calculation:
wherein G isp(s) is the temperature object transfer function, Go(s) is the desired closed loop transfer function, Gc(s) is a predicted PI controller transfer function, and a specific expression of the controller transfer function is as follows:
obtaining the input-output relational expression of the controller from the above expression
Wherein, u(s) is the output of the controller, e(s) is the error input of the controller, i.e. the difference between the set value and the measured value, and the above formula is discretized to obtain:
wherein k is a discretization variable, e (k) and u (k) are respectively a discretized error value and a controller output value, and the two formulas are subtracted to obtain an incremental formula:
in the formula TsRepresents a sampling time;
according to the above formula, the control method specifically comprises the following steps:
the method comprises the following steps: setting a timer module;
step two: judging the model identification part or the prediction PI control part according to a flag variable flag; judging whether the current system is in a manual state before the execution of the model identification part, and assigning a valve position value manually input on a human-computer interface to an actual valve position value if the current system is in the manual state; if the current system is in an automatic state, simulating a relay link to output a waveform with hysteresis;
step three: after the oscillation output waveform of the system is obtained, the trough part T of the oscillation period is obtained through analysisu1Peak portion Tu2Amplitude of oscillation peak AuAmplitude of oscillation trough AdAnd storing the data into the corresponding register;
step four: when the flag variable flag judges that the program needs to execute the code of the predictive PI control part, whether the error between the system output value and the set value of the previous times meets the condition of executing the identification part is judged, if the error between the system output value and the set value exceeds the set error value and the errors of the previous five times are all within the set error value, the program in the next sampling period needs to execute the model identification code, and therefore the value of the flag is changed;
step five: the method comprises the steps that a program of a prediction PI control part also judges whether a current system is in a manual state before being executed, and if the current system is in the manual state, a valve position value manually input on a human-computer interface is assigned to an actual valve position value; if the current system is in an automatic state, calculating according to the data in the register in the step three and an incremental form formula;
step six: calculating the increment of the valve position value according to an increment form formula, limiting the increment between the maximum value and the minimum value of the set valve position value, adding the increment of the valve position value and the last valve position value to form a new valve position value, simultaneously establishing an array, storing valve position value data of each time, updating the array after each calculation is finished, and keeping the valve position value in the array to be the valve position value between (t-tau, t), wherein t is the current moment; and finally, establishing an array for recording the system output value.
Drawings
FIG. 1 is a schematic diagram of a relay feedback with an asymmetric hysteresis loop;
wherein SP is a set value, Y is an output value, ERROR is an ERROR between the set value and a measured value, u1For conventional relay link output, u0Is the offset and the hysteresis loop size;
FIG. 2 is a waveform of a relay link oscillation;
wherein u is the output waveform of the relay, y is the system response curve, AuAnd AdRespectively, oscillation peak amplitude and oscillation valley amplitude, Tu1And Tu2Respectively a wave trough part and a wave crest part of the oscillation period;
FIG. 3 is a schematic diagram of a predictive PI controller;
wherein, KpT and tau represent object gain, time constant and time lag respectively;
FIG. 4 is a flow chart of a control method of the present invention;
FIG. 5 is a Matlab Simulink simulation model;
the method comprises the following steps that A, a Uniform Random Number is a Random interference signal, simout and simout1 are modules for inputting data into a Matlab working space, OPCConfig is an OPC tool configuration module, OPC Read and OPCwrite are OPC data Read-write modules respectively, TransferFun is a control object transfer function (without delay), TransportDelay is a delay module, and Scope is an oscilloscope;
fig. 6 is a graph of the feedback oscillation and control.
Detailed Description
The invention will be further explained with reference to the drawings and simulation software:
the invention relates to a parameter self-tuning PLC control method based on a prediction PI and a bias relay feedback, the system combines the prediction PI control method and the bias relay feedback technology, can perform online tracking identification on an industrial control object, and the system oscillates near a set value during identification, thereby not causing great influence on production; and the method has a better control effect on a large-lag object, can realize the self-tuning of the parameters of the controller, and reduces the labor cost.
The technical scheme adopted by the invention is to package the discrete PI prediction method and the bias relay feedback technology into independent modules. Compared with a self-contained PID control module in the PLC, the module based on the prediction PI and the bias relay feedback has stronger control performance, is additionally provided with a model identification and controller parameter self-tuning function, and has higher practical application value.
The specific information is as follows:
the system principle is as shown in fig. 1, a traditional relay feedback link is replaced by a biased relay feedback link with hysteresis loops, and because the output of the relay is not a waveform symmetrical about a time axis any more, the output of the system presents more information under the action of the relay, the wave crests and the wave troughs of the limit loops are not symmetrical about the time axis any more, and the level widths of the positive value and the negative value of the output of the relay are not the same. The method expands the relation between the limit cycle information and each parameter, and makes it possible to identify all the control object model parameters in one experiment.
The relay outputs with asymmetric hysteresis are u0+ u1 and u0-u1 respectively, wherein u1 is the output of a conventional relay link, u0 is an offset, and | u0| < u1 is generally taken as the size of the hysteresis. When the relay input e (t) is greater, the relay output is u0+ u1, with the decrease in e (t), the delay in relay output will remain, i.e., the output will switch to u0-u1 when e (t) is less than-. Similarly, when e (t) is less than-the relay output is u0-u1, and due to hysteresis, the relay output switches to u0+ u1 when e (t) increases. And u0 is equal to 0, and when it is equal to 0, the relay becomes a conventional relay. The overall feedback process is the same as that of the traditional relay feedback, the system output generates oscillation near a set value sp, and the model parameters of the controlled object are calculated according to the generated limit ring image information.
Consider a FOPDT (first order plus pure hysteresis) model:
wherein KpT and τ represent object gain, time constant and time lag, respectively.
The limit cycle oscillation waveform is shown in FIG. 2, from which it can be read that the oscillation period is Tu1+Tu2Oscillatory wavePeak amplitude of AuAmplitude of oscillation trough is Ad. The link between this information and the control object model can be derived from the following formula.
The detailed derivation process is given below:
when t is not 0, the system output y (t)>sp, and y (t) is increasing, the relay output is u0-u1. Let t be t1The time relay output is u0+u1，t＝t2When the relay jumps again to u0-u1And so on, the output values are changed in turn at the time of t3, t4, t5 and the like. Then after a delay τ the system output is
When t is equal to t1Then the relay output becomes u0+u1When e (t) is equal, the system output is therefore
Can be derived from the above formula
At t1+ τ ≦ t<In the time interval of t1+ t2+ tau, the output of the relay can be regarded as u0+u1Thus, at this time, the system output can be expressed as:
when t is t1+ t2, the relay output jump becomes u0-u1When e (t) ═ is present, so the system outputs at this time
From the above formula can be derived
The combination of formula (8) gives:
an expression can thus be obtained for τ:
similarly, in the time interval t1+ t2+ τ ≦ t < t1+ t2+ t3+ τ, the system output may be expressed as
When t is t1+ t2+ t3, the relay output jumps again, and the slave u jumps again0-u1Jump to u0+u1At this time, e (t) is equal, so the system output can be expressed as:
from equation (15) again one can obtain:
thus again, another expression for τ is obtained:
because the system output is in a periodic oscillation state, the system output is in a periodic oscillation state
t2＝t4＝t6＝...＝Tu1(18)
t3＝t5＝t7＝...＝Tu2(19)
The time lag of the control object model can be calculated by the limit cycle oscillation period. Similarly, the limit cycle oscillation amplitude may be obtained from the system output values at times t-t 1+ τ and t-t 1+ t2+ τ:
finally, the model parameter formula can be derived from the formulas (2) to (5):
the predictive PI control algorithm is also a PID controller in nature, except that the controller incorporates some advanced control mechanisms, such as internal model control, genetic algorithm, artificial intelligence, etc. The prediction PI algorithm combined with the prediction algorithm and the PID algorithm has the prediction function of the prediction algorithm and the robustness and the practicability of the PID algorithm.
Also set the control object model as
And the desired closed loop transfer function is
Wherein lambda is an adjustable parameter, and the response speed can be adjusted. Then the closed loop transfer function calculation can be used to obtain
Wherein G isp(s) is the temperature object transfer function, Go(s) is the desired closed loop transfer function, Gc(s) is the predicted PI controller transfer function. Substituting (25) and (26) into (27) can obtain the controller transfer function
The input-output relation of the controller can be obtained from (28)
Fig. 3, where u(s) is the output of the controller, and e(s) is the error input of the controller, i.e. the difference between the set value and the measured value. The part within the dashed box is the predictive PI controller.
Because the parameters of the predictive PI control algorithm are less, the algorithm is only related to lambda and the model parameters of the control object, and the lambda is usually determined by the expected time constant and the actual time constant, the model parameters of the control object only need to be identified, and a better control effect can be realized.
In order to use the predictive PI algorithm in the PLC, equation (29) is discretized to obtain equations (30) and (31):
where k is the discretization variable, e (k) and u (k) are the discretized error value and the controller output value, respectively.
The incremental form is obtained by subtracting equation (30) from equation (31):
in the formula TsRepresenting the sampling time.
1. Firstly, the implementation of the method steps and the encapsulation of the module. The method is realized by two parts: the flow chart of the method of the identification part and the control part is shown in figure 4.
The two different states are controlled by a flag variable flag, and when the flag is 1, the program is in an identification state; when flag is 0, the routine is in a control state. The routine will determine if flag is 1 each time before executing the identification code. The output value of the system is obtained by continuously sampling Matlab simulation output data, and the data required to be used are as follows: the system output peak value during periodic oscillation, the system output valley value during periodic oscillation and the oscillation period when the relay outputs a positive value and a negative value respectively. And immediately after the required data is recorded, calculating the static gain, the time constant and the time lag of the object model according to a derivation formula, changing the value of a flag variable flag to be 0, and entering a control state.
Before each execution of the control state program segment, the following decisions are made: whether flag is 0; whether the output value of the current system output for the first 5 times is within the set error range or not. When the conditions are met, the program starts to execute the control code, namely calculation is carried out according to the deduced discretization prediction PI formula and the model parameter of the control object to obtain the output value of the controller, and the output value of the system is recorded into the array every time to judge whether the identification needs to be carried out again. When the system in the array outputs a value exceeding the error, namely the value of the flag is changed, the process of the next sampling cycle enters the identification state.
The module uses encryption package to perform encryption work such as key generation through an encryption function of the PLC, wherein the sampling time of the PLC is set to 10 ms. The specific programming steps are as follows:
the method comprises the following steps: a timer module is set.
Step two: and judging the model identification part or the prediction PI control part according to a flag variable flag. And the model identification part judges whether the current system is in a manual state before execution, and assigns the valve position value manually input on the human-computer interface to the actual valve position value if the current system is in the manual state. And if the current system is in an automatic state, simulating a waveform with a hysteresis loop output by a relay link.
Step three: after the system oscillation output waveform is obtained, the peak valley value and the period value of the system oscillation are obtained through analysis, and data are stored in corresponding registers.
Step four: when the flag variable flag judges that the program needs to execute the code of the predictive PI control part, whether the condition of executing the code of the identification part is met or not is judged according to the errors of the system output and the system set value of the previous times. If the error between the system output value and the set value exceeds the set error value and the errors of the previous five times are within the set error value, the program in the next sampling period is judged to need to execute the model identification code, and therefore the value of the flag is changed.
Step five: and the predictive PI control part program also judges whether the current system is in a manual state before being executed, and assigns the valve position value manually input on the human-computer interface to the actual valve position value if the current system is in the manual state. If the current system is in the automatic state, the calculation is performed according to the data in the register in step three and the formula (32).
Step six: calculating the increment of the valve position value according to the formula (32), limiting the increment between the maximum value and the minimum value of the set valve position value, adding the increment of the valve position value and the last valve position value to form a new valve position value, simultaneously establishing an array, storing the valve position value data of each time, updating the array after the calculation is finished each time, and keeping the valve position value in the array to be the valve position value between (t-tau, t), wherein t is the current moment. And finally establishing an array for storing the system output value.
2. And then the building communication of the simulation system and the application process of the combined example.
The Studio5000logixEmula is simulation software matched with the programming software Studio5000, and is connected with the Studio5000 program in a mode of inserting a controller into the slot, and the virtual PLC controller is inserted into the slot 2.
RslinxClassic is a server suitable for OPC, and can receive data from a plurality of OPC clients as a data sharing platform, and the setting steps are as follows:
1) select ConfigureDrivers in the RslinxClassic toolbar, select ethernet devices and click AddNew.
2) The corresponding Topic is established for the simulation controller, and DDE/OPC- > TopicConfiguration (Topic setting) is selected and clicked. And entering a data source page of the Topic, clicking the bottom NEW to newly establish the Topic, and naming the Topic as the PPI. Each Topic corresponds to a corresponding hardware device, and can be selectively configured according to needs.
3) Select the newly created virtual controller in Studio5000logixEmula and click on Apappliance.
After the setting of the RslinxClassic is finished, data needs to be communicated with Matlab, and since MatlabSimulink cannot be directly connected with the RslinxOPC server, Kepserver is selected as a data relay platform. Kepserver is also an OPC software, realizes an OPC standard interface, and an application program can be connected with the Kepserver through an OPC protocol. The setting mode is as follows:
1) and (4) creating a channel, and selecting an OPCDACLIENTDriver (OPC DA client driver) as a DeviceDriver (device driver).
2) The OPC server is selected to be rslinxpopcserver (rslinxpopc server).
3) Selecting a new Device and importing a controller output variable MV and a measured value variable PV from RSLinx to Kepserver.
At this time, the Kepserver completes the establishment of communication with the RslinxOPC server, and the current variable value can be read by an OPC test client in the Kepserver.
Matlab Simulink is used as a building platform of a simulation model, an OPC tool box is integrated in a version above 7.0, two using modes of a command line and a GUI (graphical user interface) are provided, and the setting steps are as follows:
1) an OPCConfigral-Time (OPC real-Time communication setting module) module in an OPCToolbox (OPC tool box) is selected as an OPC client, and KEPware, namely a Kepserver server, is selected from OPC servers.
2) And respectively selecting a controller output variable MV and a measured value variable PV in an OPC read-write module as data items, adding a random noise signal into the output in order to simulate a real industrial environment, and finally obtaining a Matlab simulation model as shown in FIG. 5.
Let the control object model be
Parameters are input in the PLC, the Matlab simulation object model is changed into a formula (33), a system response curve graph is obtained after downloading operation, the Matlab simulation object model is changed again after the first object identification is finished, the system automatically identifies the control object again after detecting that the output is changed, and therefore the function of self-tuning of the parameters of the controller is achieved.
Claims (1)
1. A parameter self-tuning PLC control method based on prediction PI and bias relay feedback is characterized in that for a relay system with an asymmetric hysteresis loop, the transfer function of an order plus a pure hysteresis model is
Wherein, KpT and tau respectively represent object gain, time constant and time lag, and s represents a state quantity; hysteresis magnitude is, its outputIs u0+ u1 or u0-u1, wherein u1 is output of a conventional relay link, u0 is offset, system output generates oscillation around a set value sp, and a trough part of an oscillation period is T according to limit ring oscillation waveformu1The peak part is Tu2Amplitude of oscillation peak is AuAmplitude of oscillation trough is Ad(ii) a Model identification is carried out according to the following formula to calculate the parameters of the first-order plus pure hysteresis model as follows:
the control object model is:
the desired closed loop transfer function is:
wherein λ is an adjustable parameter for adjusting response speed, and can be obtained by closed-loop transfer function calculation:
wherein G isp(s) is the temperature object transfer function, Go(s) is the desired closed loop transfer function, Gc(s) is a predicted PI controller transfer function, and a specific expression of the controller transfer function is as follows:
obtaining the input-output relational expression of the controller from the above expression
Wherein, u(s) is the output of the controller, e(s) is the error input of the controller, i.e. the difference between the set value and the measured value, and the above formula is discretized to obtain:
wherein k is a discretization variable, e (k) and u (k) are respectively a discretized error value and a controller output value, and the two formulas are subtracted to obtain an incremental formula:
in the formula TsRepresents a sampling time;
according to the above formula, the control method specifically comprises the following steps:
the method comprises the following steps: setting a timer module;
step two: judging the model identification part or the prediction PI control part according to a flag variable flag; judging whether the current system is in a manual state before the execution of the model identification part, and assigning a valve position value manually input on a human-computer interface to an actual valve position value if the current system is in the manual state; if the current system is in an automatic state, simulating a relay link to output a waveform with hysteresis;
step three: after the oscillation output waveform of the system is obtained, the trough part T of the oscillation period is obtained through analysisu1Peak portion Tu2Amplitude of oscillation peak AuAmplitude of oscillating troughValue AdAnd storing the data into the corresponding register;
step four: when the flag variable flag judges that the program needs to execute the code of the predictive PI control part, whether the error between the system output value and the set value of the previous times meets the condition of executing the identification part is judged, if the error between the system output value and the set value exceeds the set error value and the errors of the previous five times are all within the set error value, the program in the next sampling period needs to execute the model identification code, and therefore the value of the flag is changed;
step five: the method comprises the steps that a program of a prediction PI control part also judges whether a current system is in a manual state before being executed, and if the current system is in the manual state, a valve position value manually input on a human-computer interface is assigned to an actual valve position value; if the current system is in an automatic state, calculating according to the data in the register in the step three and an incremental form formula;
step six: calculating the increment of the valve position value according to an increment form formula, limiting the increment between the maximum value and the minimum value of the set valve position value, adding the increment of the valve position value and the last valve position value to form a new valve position value, simultaneously establishing an array, storing valve position value data of each time, updating the array after each calculation is finished, and keeping the valve position value in the array to be the valve position value between (t-tau, t), wherein t is the current moment; and finally, establishing an array for recording the system output value.
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