CN108490767A - A kind of industrial unstable time lag process two-degree-freedom controller - Google Patents

A kind of industrial unstable time lag process two-degree-freedom controller Download PDF

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Publication number
CN108490767A
CN108490767A CN201810141465.7A CN201810141465A CN108490767A CN 108490767 A CN108490767 A CN 108490767A CN 201810141465 A CN201810141465 A CN 201810141465A CN 108490767 A CN108490767 A CN 108490767A
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controller
degree
freedom
time lag
unstable time
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Inventor
尹浩
邓刚毅
林淑怡
张卫东
罗均
韩华翔
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Shanghai Jiaotong University
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Shanghai Jiaotong University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G05B13/045—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance using a perturbation signal
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The present invention relates to a kind of industrial unstable time lag process two-degree-freedom controller, two-degree-freedom controller includes the stability controller G for calm erratic process and disturbance suppressiond, and the performance controller G for controlling input response performancecWith filter F.Compared with prior art, the present invention can be used for the control of unstable plant of the ratio less than 2 of lag time constant and crank-up time constant, have simple in structure, has a wide range of application, uses simple advantage.

Description

A kind of industrial unstable time lag process two-degree-freedom controller
Technical field
The present invention relates to a kind of industrial unstable time lag process controllers, more particularly, to a kind of industrial unstable time lag mistake Journey two-degree-freedom controller.
Background technology
The dynamic characteristic of many industrial processes shows unstable or critical unstable feature, for example paper production The liquid level of the pressurization head box of process or the boiler liquid level of thermal power generation unit, this class object are not easily controlled very much.Needle in the past The controller to be grown up to self regulating plant mostly cannot be used for the control of unstable plant, and difficulty is essentially from two sides Face：On the one hand, the presence of right half plane pole makes the calm extremely difficult of control system；On the other hand, purely retarded and right half In the presence of greatly constraining the system performance that can reach while plane zero.
Develop several classes based on the controller of PID in the past few decades to control single order added-time stagnant unstable plant, it is main Method has two classes.A kind of method is to design controller from phase margin condition, and the limitation of such methods is that lag time is normal The ratio of number and crank-up time constant is less than 1, therefore the ratio that can not be applied to lag time constant and crank-up time constant is more than 1 Object on.Another kind of method is to define optimal performance index, then obtains controller by solution.Such methods can be used for Object of the ratio less than 2 of lag time constant and crank-up time constant is controlled, but design process and result are all complex, It is difficult to apply in practice.
Invention content
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide when a kind of industrial unstable Stagnant process two-degree-freedom controller.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of industrial unstable time lag process two-degree-freedom controller, two-degree-freedom controller include unstable for calming The stability controller G of process and disturbance suppressiond, and the performance controller G for controlling input response performancecWith filter F, The transmission function of the two-degree-freedom controller is：
Y (s)=Yr(s)R(s)+Yd(s) D (s),
Wherein, Y (s) exports for two-degree-freedom controller, and R (s) inputs for two-degree-freedom controller, and D (s) is disturbance,For the transmission function of object model, Ge-LsFor the transmission function of practical object, GmFor in the transmission function of object model Transmission function in addition to delay component, G are the transmission function in the transmission function of practical object in addition to delay component, Lm、L For delay time, s is the complex variable in Laplace transform.
The stability controller GdFor PID controller：
kpFor stability controller scale parameter, kiFor stability controller integral parameter, kdFor stability controller differential parameter, s For complex variable.
Stability controller kp、kiAnd kdIt obtains in the following way：
(11) practical object is converted to single order unstable time lag object, i.e.,：
Then stability controller kpValue is：
Wherein α1It is solution of the following equation in (0, π) section：
K and T is the parameter of single order unstable time lag object；
(12) meet kpThe pole position so that the disturbance output response of two-degree-freedom controller is chosen under the conditions of value range K in reference axis left planeiAnd kd。
Performance controller GcFor PI controllers：
KcFor performance controller scale parameter, TiFor performance controller integral parameter, s is complex variable.
Performance controller GcParameter obtain in the following way：
Convert practical object to single order unstable time lag object, i.e.,：
Then：
Ti=γ,
λ is setting constant.
Filter F is：
λ1To set constant.
Compared with prior art, the invention has the advantages that：
(1) controller of two degrees of freedom of the invention has combined the calm and internal model control of unstable time lag object Come, and in the nominal case decouple input response with disturbance response, therefore unstable time lag object can be carried out effective Control, be significantly increased relative to existing method performance, can be small to the ratio of lag time constant and crank-up time constant Unstable plant in 2 can be controlled preferably.
(2) two-degree-freedom controller of the present invention is simple in structure, has a wide range of application, using simple.
Description of the drawings
Fig. 1 is the control block diagram of two-degree-freedom controller of the present invention；
K when Fig. 2 keeps system calm for stability controller of the present inventioniAnd kdStability range.
Specific implementation mode
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.Note that the following embodiments and the accompanying drawings is said Bright is substantial illustration, and the present invention is not intended to be applicable in it object or its purposes is defined, and the present invention does not limit In the following embodiments and the accompanying drawings.
Embodiment
As shown in Figure 1, a kind of industrial unstable time lag process two-degree-freedom controller, two-degree-freedom controller includes being used for The stability controller G of calm erratic process and disturbance suppressiond, and the performance controller G for controlling input response performancec With filter F.Estimation to input nonlinearities can be understood as by the signal that v is fed back.Work as F=0, GdWhen=0, the above control Device has just been degenerated to the Smith Predictor of standard.
The transmission function of two-degree-freedom controller is：
Y (s)=Yr(s)R(s)+Yd(s) D (s), (1)
Wherein, Y (s) exports for two-degree-freedom controller, and R (s) inputs for two-degree-freedom controller, and D (s) is disturbance,For the transmission function of object model, Ge-LsFor the transmission function of practical object, GmFor in the transmission function of object model Transmission function in addition to delay component, G are the transmission function in the transmission function of practical object in addition to delay component, Lm、L For delay time, s is the complex variable in Laplace transform.
In the nominal case：
At this point, (2) and (3) formula is reduced to：
It can be with it is clear to see that new controller be full decoupled by disturbance response and input response from (5), (6) formula.
Performance controller GcIt can be obtained by conventional internal model control method；Filter F can be taken as common second-order low-pass filter Device, but it is not limited to second order；Stability controller GdFixation is taken as PID controller, and parameter is determined by system stability.
The stability of system depends on characteristic equation：
(1+GmGc) can be individually designed so that it only has the pole of Left half-plane.Key is in formulaIt can To find out, the stability of characteristic equation (7) depends on the factor.The resolving ideas of the present invention is first to obtain to be used for quelling control Device scale parameter kpRange.For each scale parameter value in the range, integral and differential parameter are all fallen at one Inside convex polygon, and the range of the convex polygon can be obtained by directly calculating.The calculation of stability controller parameter is listed below Method.
Stability controller GdFor PID controller：
kpFor stability controller scale parameter, kiFor stability controller integral parameter, kdFor stability controller differential parameter, s For complex variable.
Stability controller kp、kiAnd kdIt obtains in the following way：
(11) practical object is converted to single order unstable time lag object, i.e.,：
If the order of control object is higher than single order, the parameter of single order object is obtained using order reducing method.
Then stability controller kpValue is：
Wherein α1It is solution of the following equation in (0, π) section：
K and T is the parameter of single order unstable time lag object；
(12) meet kpThe pole position so that the disturbance output response of two-degree-freedom controller is chosen under the conditions of value range K in reference axis left planeiAnd kd。
In T/L=-1, α1=pi/2.For the k outside this rangep, cannot just be used for quelling PID controller. For each k in range abovep, other two parameters are given by the square range of Fig. 2, under the parameters in figure pass through The mode of stating obtains：
(11) (11) are solved equation, the solution in section (0, π) is obtained.
(12) k is obtained by formula (10)pValue range select gain k in the case where process is uncertain unknownpSubstantially Value at the 1/5 close -1 of extent length.
(13) it solves equation：
By its positive real number solution, z is according to value arranged from small to largej, j=1,2.
(14) m in figure is obtained by following formulaj、bjAnd wj：
mj=m (zj),bj=b (zj), (13)
(15) k obtained by Fig. 2i,kdRange, ki,kdMedian in range of choice.
Performance controller GcFor PI controllers：
KcFor performance controller scale parameter, TiFor performance controller integral parameter, s is complex variable.
Performance controller GcParameter obtain in the following way：
Convert practical object to single order unstable time lag object, i.e.,：
Then：
Ti=γ,
λ is setting constant.
Filter F is：
λ1To set constant.
Parameter lambda1Have the function of adjusting robust performance, λ1Smaller input response is faster, but robustness is poorer.But it is opposite λ1For, Disturbance Rejection and robustness are more sensitive to three parameters for stability controller.So when practical application, λ1 Smaller can also be obtained, to accelerate the speed of input response, the robustness of loss is adjusted by the parameter of PID controller.
The above embodiment is only to enumerate, and does not indicate that limiting the scope of the invention.These embodiments can also be with other Various modes are implemented, and can make in the range of not departing from technical thought of the invention it is various omit, displacement, change.

Claims (6)

1. a kind of industrial unstable time lag process two-degree-freedom controller, which is characterized in that two-degree-freedom controller includes being used for The stability controller G of calm erratic process and disturbance suppressiond, and the performance controller G for controlling input response performancec Transmission function with filter F, the two-degree-freedom controller is：
Y (s)=Yr(s)R(s)+Yd(s) D (s),
Wherein, Y (s) exports for two-degree-freedom controller, and R (s) inputs for two-degree-freedom controller, and D (s) is disturbance,For The transmission function of object model, Ge-LsFor the transmission function of practical object, GmTo remove delay portion in the transmission function of object model Transmission function other than point, G are the transmission function in the transmission function of practical object in addition to delay component, Lm, L be delay when Between, s is the complex variable in Laplace transform.
2. a kind of industrial unstable time lag process two-degree-freedom controller according to claim 1, which is characterized in that described Stability controller GdFor PID controller：
kpFor stability controller scale parameter, kiFor stability controller integral parameter, kdFor stability controller differential parameter, s is multiple Variable.
3. a kind of industrial unstable time lag process two-degree-freedom controller according to claim 2, which is characterized in that calm Controller kp、kiAnd kdIt obtains in the following way：
(11) practical object is converted to single order unstable time lag object, i.e.,：
Then stability controller kpValue is：
Wherein α1It is solution of the following equation in (0, π) section：
K and T is the parameter of single order unstable time lag object；
(12) meet kpIt is chosen under the conditions of value range so that the pole of the disturbance output response of two-degree-freedom controller is located at coordinate K in axis left planeiAnd kd。
4. a kind of industrial unstable time lag process two-degree-freedom controller according to claim 1, which is characterized in that performance Controller GcFor PI controllers：
KcFor performance controller scale parameter, TiFor performance controller integral parameter, s is complex variable.
5. a kind of industrial unstable time lag process two-degree-freedom controller according to claim 4, which is characterized in that performance Controller GcParameter obtain in the following way：
Convert practical object to single order unstable time lag object, i.e.,：
Then：
Ti=γ,
λ is setting constant.
6. a kind of industrial unstable time lag process two-degree-freedom controller according to claim 5, which is characterized in that filtering Device F is：
λ1To set constant.
CN201810141465.7A 2018-02-11 2018-02-11 A kind of industrial unstable time lag process two-degree-freedom controller Pending CN108490767A (en)

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Cited By (1)

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Publication number Priority date Publication date Assignee Title
CN109557810A (en) * 2018-11-29 2019-04-02 杭州电子科技大学 A kind of temperature control method for heating furnace based on Novel two-freedom-degree Internal Model PID

Citations (4)

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Publication number Priority date Publication date Assignee Title
CN103631139A (en) * 2013-11-19 2014-03-12 聊城大学 Anti-interference PID (proportion integration differentiation) controller for unstable time-lag process and design method thereof
CN105068421A (en) * 2015-07-16 2015-11-18 浙江工业大学 Two-degree-of-freedom cooperative control method for multiple mobile robots
CN105607486A (en) * 2016-02-06 2016-05-25 北京化工大学 General control method for series chemical integration time lag process
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Publication number Priority date Publication date Assignee Title
CN103631139A (en) * 2013-11-19 2014-03-12 聊城大学 Anti-interference PID (proportion integration differentiation) controller for unstable time-lag process and design method thereof
CN105068421A (en) * 2015-07-16 2015-11-18 浙江工业大学 Two-degree-of-freedom cooperative control method for multiple mobile robots
CN105607486A (en) * 2016-02-06 2016-05-25 北京化工大学 General control method for series chemical integration time lag process
CN106802554A (en) * 2017-04-01 2017-06-06 中国船舶科学研究中心（中国船舶重工集团公司第七0二研究所） Two-Degree-of-Freedom Internal Model PID controller parameter setting method

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109557810A (en) * 2018-11-29 2019-04-02 杭州电子科技大学 A kind of temperature control method for heating furnace based on Novel two-freedom-degree Internal Model PID
CN109557810B (en) * 2018-11-29 2021-10-26 杭州电子科技大学 Heating furnace temperature control method based on novel two-degree-of-freedom internal model PID

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