CN111679578A - Novel active disturbance rejection control method for temperature system of ethylene cracking furnace - Google Patents

Novel active disturbance rejection control method for temperature system of ethylene cracking furnace Download PDF

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CN111679578A
CN111679578A CN202010511736.0A CN202010511736A CN111679578A CN 111679578 A CN111679578 A CN 111679578A CN 202010511736 A CN202010511736 A CN 202010511736A CN 111679578 A CN111679578 A CN 111679578A
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cracking furnace
ethylene cracking
temperature system
mouth temperature
furnace mouth
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刘晓伟
张日东
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Hangzhou Dianzi University
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    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

The invention relates to a design method of novel active disturbance rejection control of an ethylene cracking furnace temperature system. The invention aims to provide an ADRC controller of an ethylene cracking furnace temperature system with the capability of adjusting parameters in real time on line, so that the system has better control performance in each state, and the ADRC controller introduces a fuzzy PID algorithm, adjusts the parameters of an active disturbance rejection controller in real time on line through a fuzzy control rule, and meets the requirements of the active disturbance rejection controller under the conditions of different errors and error change rates. The technical scheme of the invention is that a differential tracker, an extended state observer and a nonlinear feedback link improved by a fuzzy controller are respectively constructed through a separation theorem of active disturbance rejection control, and a novel active disturbance rejection control method of an ethylene cracking furnace temperature system is provided.

Description

Novel active disturbance rejection control method for temperature system of ethylene cracking furnace
Technical Field
The invention mainly relates to the field of automatic control, in particular to a novel active disturbance rejection control method for a temperature system of an ethylene cracking furnace.
Background
Active Disturbance Rejection Control (ADRC) is a non-linear robust control technique that has developed since the nineties of the last century. Nowadays, the control objects and the control systems are increasingly complex, the traditional ADRC controller can not meet the control requirements gradually, which is mainly reflected in that the parameters of the traditional ADRC controller are fixed and the traditional ADRC controller can not adapt to various control occasions. Therefore, a technical problem to be solved by those skilled in the art is to design an algorithm capable of adjusting the ADRC parameters in real time on-line to ensure that the corresponding controller has the optimal parameters in various states of the system.
Disclosure of Invention
The invention aims to provide an ADRC controller of an ethylene cracking furnace temperature system with the capability of adjusting parameters in real time on line, so that the system has better control performance in each state, and the ADRC controller introduces a fuzzy PID algorithm, adjusts the parameters of an active disturbance rejection controller in real time on line through a fuzzy control rule, and meets the requirements of the active disturbance rejection controller under the conditions of different errors and error change rates.
The technical scheme of the invention is that a differential tracker, an extended state observer and a nonlinear feedback link improved by a fuzzy controller are respectively constructed through a separation theorem of active disturbance rejection control, and a novel active disturbance rejection control method of an ethylene cracking furnace temperature system is provided.
The method comprises the following specific steps:
step 1, designing a tracking differentiator
For a common second-order system, the specific design is as follows:
Figure BDA0002528623270000021
in the formula: r is the tracking speed factor of the system, the larger the value of r is, the faster the tracking speed is, x1(k)、x2(k) Is a discrete state variable of the system, h is an integration step length, h0For the filter factor, v (k) gives the input to the system, and the specific algorithm for fh is as follows:
Figure BDA0002528623270000022
the parameter to be adjusted is the filter factor h0And a speed factor r. The integration step is generally taken as large as possible, but h is generally taken as h to ensure that the system signal is not distorted00.01. The speed factor is also typically made as large as possible.
Step 2, designing an extended state observer
The form of the nonlinear extended state observer for a second order system is given as follows:
Figure BDA0002528623270000031
in the formula e1As an observation error of the system, β01To observe the error gain, β02To observe the error rate of change gain, β03To observe error acceleration gain, Z21For output estimation of the system, Z22Is to Z21Estimate of rate of change, Z23Is to Z22An estimate of the rate of change. b0To compensate for the factor, u is the system input and y is the system output.
The discrete extended state observer is likely to generate a certain high-frequency tremor phenomenon, and in order to eliminate the tremor, the above formula can be rewritten as follows:
Figure BDA0002528623270000032
wherein:
Figure BDA0002528623270000033
where e is the error signal, i is 1 or 2, αiRegarding the system order, sign () is a sign function for a segmentation point. fe is a non-linear function of the error velocity signal, fe1Is a non-linear function of the error acceleration signal.
Step 3, designing a nonlinear error feedback rate
In the auto-disturbance-rejection controller, in order to realize dynamic compensation linearization, both the model error of the controlled object and the external disturbance can be used
Figure BDA0002528623270000041
To express, a general second-order system model that is not accurate can be expressed by the following differential equation:
Figure BDA0002528623270000042
wherein
Figure BDA0002528623270000043
In order to output the rate of change,
Figure BDA0002528623270000044
is composed of
Figure BDA0002528623270000045
The rate of change of (a) is,
Figure BDA0002528623270000046
is the total perturbation.
The control law of the second-order ADRC is as follows:
u＝(u0-Z23)/b0(7)
wherein u is0The control rate obtained for the nonlinear feedback can be obtained from equation (10). The compound represented by formula (7) may be substituted for formula (6):
Figure BDA0002528623270000047
structural form ESO in ADRC:
Figure BDA0002528623270000048
definition of Z by ESO23I.e. the total estimate of the external interference and modeling error of the system, so let Z23F in formula (8)
Figure BDA0002528623270000049
In the dynamic compensation process, the compensation disturbance is estimated in real time by using ESO, the original system compensation is called a linear integral series system, and the system is further controlled. And u in FADRC0Can be expressed as follows:
u0＝kpfal(e1,α1,)+kdfal(e2,α2,),0<α1<α2(10)
k herepProportional system for fuzzy controller output in FADRC controllerNumber, kdThe input of the fuzzy controller is the difference between a TD link and an ESO link in the ADRC controller.
kp、kdThe running time value can be obtained by the following formula, wherein delta kpIncrement of the scaling factor, Δ k, for the output of the fuzzy controllerdIncrement of differential coefficient, k, for output of fuzzy controllerp0、kd0Is the initial value of the parameter of the fuzzy controller PD.
kp＝kp0+Δkp
kd＝kd0+Δkd(11)
For the designed second-order extended state observer in step 2, the corresponding final error feedback rate can be expressed as:
Figure BDA0002528623270000051
wherein: e1The difference between the tracking quantity of the differential tracker on the system input and the estimation quantity of the extended state observer on the system output, E2Is E1Rate of change of, Z11For differentiating the tracking quantity, Z, of the tracker to the system input12Is Z11An estimate of the rate of change.
And 4, integrating the steps, and combining the tracking differentiator in the step 1, the extended state observer in the step 2 and the improved nonlinear error feedback rate of the fuzzy controller in the step 3 into an active disturbance rejection controller according to the separation theorem of active disturbance rejection control to control the system.
The invention has the beneficial effects that: the invention provides an active disturbance rejection control method for a chemical industrial process, which improves an active disturbance rejection controller aiming at the condition that a control object model is not completely known, so that the active disturbance rejection controller has the function of adjusting parameters on line in real time, and further finds out the control parameters most suitable for the current system state.
Detailed Description
Taking the furnace mouth temperature system of the ethylene cracking furnace in the actual process as an example:
the controlled object of the ethylene cracking furnace is the outlet temperature of the furnace tube of the ethylene cracking furnace, and the outlet temperature balance of the furnace tube is controlled by adjusting the fuel flow of the cracking furnace.
Step 1, designing a tracking differentiator of an ethylene cracking furnace mouth temperature system
The furnace mouth temperature system of the second-order ethylene cracking furnace is specifically designed as follows:
Figure BDA0002528623270000061
in the formula: r is a tracking speed factor of an ethylene cracking furnace mouth temperature system, the larger the value of r is, the faster the tracking speed is, and x1(k)、x2(k) Is a discrete state variable of a furnace mouth temperature system of the ethylene cracking furnace, h is an integral step length, h0For the filter factor, v (k) gives the input to the system, and the specific algorithm for fh is as follows:
Figure BDA0002528623270000062
step 2, designing an extended state observer of an ethylene cracking furnace mouth temperature system
The form of the nonlinear extended state observer of the second-order ethylene cracking furnace mouth temperature system is given as follows:
Figure BDA0002528623270000071
in the formula e1Observed error of ethylene cracking furnace mouth temperature system, β01To observe the error gain, β02To observe the error rate of change gain, β03To observe error acceleration gain, Z21For output estimation of the furnace mouth temperature system of the ethylene cracking furnace, Z22Is to Z21Estimate of rate of change, Z23Is to Z22An estimate of the rate of change. b0For compensation factors, u is the input of the furnace mouth temperature system of the ethylene cracking furnace, and y is the output of the furnace mouth temperature system of the ethylene cracking furnace.
The discrete extended state observer is likely to generate a certain high-frequency tremor phenomenon, and in order to eliminate the tremor, the formula (3) can be rewritten as follows:
Figure BDA0002528623270000072
wherein:
Figure BDA0002528623270000073
where e is the error signal, i is 1 or 2, αiRegarding the system order, sign () is a sign function for a segmentation point. fe is a non-linear function of the error velocity signal, fe1Is a non-linear function of the error acceleration signal.
Step 3, designing the nonlinear error feedback rate of the ethylene cracking furnace mouth temperature system
In the auto-disturbance-rejection controller, in order to realize dynamic compensation linearization, both the model error of the controlled object and the external disturbance can be used
Figure BDA0002528623270000081
Therefore, the model of the inaccurate second-order ethylene cracking furnace mouth temperature system can be represented by the following differential equation:
Figure BDA0002528623270000082
wherein
Figure BDA0002528623270000083
In order to output the rate of change,
Figure BDA0002528623270000084
is composed of
Figure BDA0002528623270000085
The rate of change of (c).
The control law of the second-order ADRC is as follows:
u＝(u0-Z23)/b0(7)
wherein u is0The control rate obtained for the nonlinear feedback can be obtained from equation (10).
The compound represented by formula (7) may be substituted for formula (6):
Figure BDA0002528623270000086
structural form ESO in ADRC:
Figure BDA0002528623270000087
definition of Z by ESO23Namely the total estimation quantity of external interference and modeling error of the furnace mouth temperature system of the ethylene cracking furnace, so that Z is23F in formula (8)
Figure BDA0002528623270000091
The dynamic compensation process utilizes ESO to estimate compensation disturbance in real time, and the compensation of the original ethylene cracking furnace mouth temperature system is called as a linear integral series type ethylene cracking furnace mouth temperature system for further control. And u in FADRC0Can be expressed as follows:
u0＝kpfal(e1,α1,)+kdfal(e2,α2,),0<α1<α2(10)
k herepIs the proportional coefficient, k, of the fuzzy controller output in the FADRC controllerdThe input of the fuzzy controller is the difference between a TD link and an ESO link in the ADRC controller.
kp、kdThe running time value can be obtained by the following formula, wherein delta kpIncrement of the scaling factor, Δ k, for the output of the fuzzy controllerdIncrement of differential coefficient, k, for output of fuzzy controllerp0、kd0Is the initial value of the parameter of the fuzzy controller PD.
kp＝kp0+Δkp
kd＝kd0+Δkd(11)
For the designed second-order extended state observer in step 2, the corresponding final error feedback rate can be expressed as:
Figure BDA0002528623270000092
wherein: e1The difference between the tracking quantity input by the differential tracker to the furnace mouth temperature system of the ethylene cracking furnace and the estimation quantity output by the extended state observer to the furnace mouth temperature system of the ethylene cracking furnace, E2Is E1Rate of change of, Z11The tracking quantity, Z, input into a furnace mouth temperature system of the ethylene cracking furnace by a differential tracker12Is Z11An estimate of the rate of change.
And 4, integrating the steps, combining the tracking differentiator in the step 1, the extended state observer in the step 2 and the improved nonlinear error feedback rate of the fuzzy controller in the step 3 into an active disturbance rejection controller according to the separation theorem of active disturbance rejection control, and controlling a furnace mouth temperature system of the ethylene cracking furnace.
In summary, the invention provides an active disturbance rejection control method for an ethylene cracking furnace mouth temperature system. Aiming at the condition that the control object model is not completely known, the active disturbance rejection controller is improved to have the function of adjusting parameters on line in real time, and then the control parameters most suitable for the current system state are found.

Claims (3)

1. A novel active disturbance rejection control method for a temperature system of an ethylene cracking furnace is characterized in that a controlled object in the method is the outlet temperature of a furnace tube of the ethylene cracking furnace, and the outlet temperature balance of the furnace tube is controlled by adjusting the fuel flow of the cracking furnace, and the method comprises the following steps:
step 1, designing a tracking differentiator of an ethylene cracking furnace mouth temperature system
The furnace mouth temperature system of the second-order ethylene cracking furnace is specifically designed as follows:
Figure FDA0002528623260000011
in the formula: r is the tracking speed factor of the ethylene cracking furnace mouth temperature system, x1(k)、x2(k) Is a discrete state variable of a furnace mouth temperature system of the ethylene cracking furnace, h is an integral step length, h0V (k) is a filter factor, given input to the system, and fh is a set algorithm expression;
step 2, designing an extended state observer of an ethylene cracking furnace mouth temperature system
The form of the nonlinear extended state observer of the second-order ethylene cracking furnace mouth temperature system is given as follows:
Figure FDA0002528623260000012
in the formula e1Observed error of ethylene cracking furnace mouth temperature system, β01To observe the error gain, β02To observe the error rate of change gain, β03To observe error acceleration gain, Z21For output estimation of the furnace mouth temperature system of the ethylene cracking furnace, Z22Is to Z21Estimate of rate of change, Z23Is to Z22An estimate of the rate of change; b0For compensation factors, u is the input of an ethylene cracking furnace mouth temperature system, and y is the output of the ethylene cracking furnace mouth temperature system;
step 3, designing the nonlinear error feedback rate of the ethylene cracking furnace mouth temperature system
Using both model error and external disturbance of the controlled object
Figure FDA0002528623260000021
Therefore, the model of the inaccurate second-order ethylene cracking furnace mouth temperature system can be represented by the following differential equation:
Figure FDA0002528623260000022
wherein
Figure FDA0002528623260000023
In order to output the rate of change,
Figure FDA0002528623260000024
is composed of
Figure FDA0002528623260000025
The rate of change of (c);
the control law of the second-order active disturbance rejection control is as follows:
u＝(u0-Z23)/b0
wherein u is0A control rate obtained for nonlinear feedback;
the following can be obtained:
Figure FDA0002528623260000026
the structural form of ESO in the active disturbance rejection control is as follows:
Figure FDA0002528623260000027
definition of Z by ESO23Namely the total estimation quantity of external interference and modeling error of the furnace mouth temperature system of the ethylene cracking furnace, so that Z is23F, available as
Figure FDA0002528623260000028
In the dynamic compensation process, the compensation disturbance is estimated in real time by using ESO, and the compensation of the original ethylene cracking furnace mouth temperature system is called as a linear integral series type ethylene cracking furnace mouth temperature system for further control; wherein u is0Is represented as follows:
u0＝kpfal(e1,α1,)+kdfal(e2,α2,),0<α1<α2
k herepIs the proportional coefficient, k, of the fuzzy controller output in the FADRC controllerdThe input of the fuzzy controller is the difference between a TD link and an ESO link in the ADRC controller;
for the nonlinear extended state observer in step 2, the corresponding final error feedback rate is expressed as:
Figure FDA0002528623260000031
wherein: e1The difference between the tracking quantity input by the differential tracker to the furnace mouth temperature system of the ethylene cracking furnace and the estimation quantity output by the extended state observer to the furnace mouth temperature system of the ethylene cracking furnace, E2Is E1Rate of change of, Z11The tracking quantity, Z, input into a furnace mouth temperature system of the ethylene cracking furnace by a differential tracker12Is Z11An estimate of the rate of change;
and 4, integrating the steps, combining the tracking differentiator in the step 1, the extended state observer in the step 2 and the improved nonlinear error feedback rate of the fuzzy controller in the step 3 into an active disturbance rejection controller according to the separation theorem of active disturbance rejection control, and controlling a furnace mouth temperature system of the ethylene cracking furnace.
2. The novel active disturbance rejection control method of the temperature system of the ethylene cracking furnace according to claim 1, characterized in that: in order to eliminate the high-frequency trembling phenomenon of the nonlinear extended state observer in the step 2, the nonlinear extended state observer expression is rewritten into the following form:
Figure FDA0002528623260000041
wherein:
Figure FDA0002528623260000042
where e is the error signal and i is 1 or 2, αiRegarding the system order, sign () is a sign function for a segmentation point; fe is an errorNon-linear function of the velocity signal, fe1Is a non-linear function of the error acceleration signal.
3. The novel active disturbance rejection control method of the temperature system of the ethylene cracking furnace according to claim 1, characterized in that: k in step 3p、kdThe running time value can be obtained by the following formula, wherein delta kpIncrement of the scaling factor, Δ k, for the output of the fuzzy controllerdIncrement of differential coefficient, k, for output of fuzzy controllerp0、kd0The initial value of the parameter of the fuzzy controller PD;
kp＝kp0+Δkp
kd＝kd0+Δkd。
CN202010511736.0A 2020-06-08 2020-06-08 Novel active disturbance rejection control method for temperature system of ethylene cracking furnace Pending CN111679578A (en)

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