CN107272404A - A kind of combined integral controller - Google Patents

A kind of combined integral controller Download PDF

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Publication number
CN107272404A
CN107272404A CN201710572404.1A CN201710572404A CN107272404A CN 107272404 A CN107272404 A CN 107272404A CN 201710572404 A CN201710572404 A CN 201710572404A CN 107272404 A CN107272404 A CN 107272404A
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mrow
controller
msub
combined integral
combined
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任正云
陈安钢
陈亮
文盼
闫子豪
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Donghua University
National Dong Hwa University
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Donghua University
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00Automatic controllers
    • G05B11/01Automatic controllers electric
    • G05B11/36Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.

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  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention provides a kind of combined integral controller, combined integral system transter is made up of two or more integration Object with Time Delay, for combined integral system, is controlled with following combination integral controller:Wherein, E (s) represents the input of controller, and U (s) represents the output of controller, kiFor target gain, τ1i、τ2iFor time delay constant.General principle of the invention based on internal model control and Model Predictive Control, proposing a class has good, the practical novel compositions integral controller of simple in construction, dynamic property, the controller itself is a positive feedback controller, and the average value that the current output of controller was only exported before controller is determined with current input.The controller has good response speed, antijamming capability and robustness.Under the controller action, controlled device with indifference without poor, the characteristics of controlling more than stable state.And the controller also has good control effect to non-combined integrating system.

Description

A kind of combined integral controller
Technical field
The present invention relates to technical field of industrial control, the first-order system commonly used more particularly in process control field, two A kind of novel compositions integral controller of the linear systems such as level system, high order system, integrating system.
Background technology
Integral process is frequently run onto in industrial process, while some time constants can be also seen as than larger first order process Integrating system.The control problem of integrating system is widely studied, and many advanced control algolithms are suggested. The systematic function and stability of this class process are easily influenceed by time-delay uncertainties, and the robust performance requirement to control algolithm is compared It is high.Many algorithms are in actual industrial process, it is difficult to obtain satisfied control effect.In recent years, many scholars are to practical application Research done substantial amounts of work, no doubt also achieve abundant achievement.
Although a large amount of new control theories are continued to bring out, conventional PID and improved PID controller still extensively should Used in industrial control field.Some new theory specificitys are strong, bad adaptability, robust performance is poor, algorithm is complicated, implements and safeguards into This height, these all limit their popularization and development.Therefore, how to make that controller architecture is simple, implement easily, robust performance Good, highly versatile, is the target that the technical staff of control field pursues always.
In process control field, what is often referred to is exactly the lines such as first-order system, second-order system, high order system, integrating system Sexual system, most of controller is also to be designed according to these systems.However, have many industrial process be represented by it is multiple not With the combination of time lag integral process, but few focus of attention this class processes.Such as the underlying process transmission function of destilling towerFor multiple time delay integral process, Morari proposes the control strategy based on internal model principle, and is tested by emulation Its control performance is demonstrate,proved.
There is a class to contain the object that multiple integral terms are formed by stacking referred to as combined integral process in addition.This class process is in steel It is widely present in the industry such as iron, petrochemical industry, cereal processing, tobacco.Combined integral process is inherently open loop stabilization, and can be led to Cross that time lag item is approximate and be approximately single order object with single order Pade.Current most of combined integral objects are considered single order Object with Time Delay uses common control strategy, such as:Pid control algorithm, Smith predictive algorithms or Internal Model Control Algorithm.These controls The need for device processed meets industrial production to a certain extent, this is also the reason for this class process gets the brush-off.But with the modern times The fast development of industry, product quality, energy resource consumption and environmental protection problem propose higher requirement to control accuracy.Tradition Control be not suitable for the control of combined integral object gradually, it is therefore desirable to new control strategy and method are to instruct control Design, regulation and the operation of system.
The content of the invention
The technical problem to be solved in the present invention is the first-order system for process industrial, second-order system, high order system, integration How the combined integral object of the linear systems such as system, carry out high-precision control, whole system is reached demand of industrial production.
In order to solve the above-mentioned technical problem, the technical scheme is that providing a kind of combined integral controller, its feature It is:In combined integral system, the transmission function of combined integral link is made up of two or more integration Object with Time Delay, is represented For:
Wherein, Gi(s) it is the Stable Polynomials for not including integral element;It is included in combined integral system Systems stabilisation in system;kiFor target gain, τ1i、τ2iFor time delay constant, equation is met:τ2i2(i-1)1(i-1);1 < I < knives, n is positive integer;
For combinations thereof integrating system, it is controlled with following combination integral controller:
Wherein, E (s) represents the input of controller, and U (s) represents the output of controller, and k represents target gain, τ1、τ2Represent Time delay constant.
Preferably, the output at the combined integral controller current time only has combined integral controller with for the previous period The average value of interior output and the input at current time are determined, therefore have anti-hysteresis, so as to overcome combined integral system The hysteresis quality of system.
In principle, combined integral controller has essence different with traditional controller, when going over one section according to controller Between the method that is controlled of average value, provide a kind of new thinking for Control System Design.While combined integral controller Different process objects are can adapt to, there is reference to one class general purpose controller of research.
General principle of the invention based on internal model control and Model Predictive Control a, it is proposed that class has simple in construction, dynamic Good, the practical novel compositions integral controller of state property energy.The controller itself is a positive feedback controller, controller The average value that current output was only exported before current input and controller is determined, overcomes traditional controller to combined integral system Control defect.The controller has good response speed, antijamming capability and robustness.Importantly, in the control Under device processed effect, controlled device with indifference without poor, the characteristics of controlling more than stable state.And the controller is to non-combined integrating system Also there is good control effect.
Brief description of the drawings
Fig. 1 is original controller structure;
Fig. 2 is improved controller architecture;
Fig. 3 is anti-hysteresis controller structure;
Fig. 4 is combined integral controller principle schematic diagram of the present invention;
Fig. 5 be embodiment in, the step response of control system and anti-interference response schematic diagram during model-free mismatch;
Fig. 6 be embodiment in, the step response of control system and anti-interference response schematic diagram when having model mismatch;
Fig. 7 be embodiment in, model structure change when control system step response and anti-interference response schematic diagram.
Embodiment
With reference to specific embodiment, the present invention is expanded on further.
Combined integral system transter model in industrial process typically has following five kinds:
The first:
Second:
The third:
4th kind:
5th kind:
To sum up, the transmission function of combined integral link is made up of two or more integration Object with Time Delay, is expressed as:Wherein, Gi(s) it is the Stable Polynomials for not including integral element,It is to include Systems stabilisation in combined integral system, kiFor target gain, τ1i、τ2iFor time delay constant.In order to ensure the process Continuity, time delay constant, τ1i、τ2iMeet equation:τ2i2(i-1)1(i-1), 1 < i < n, n is positive integer.
The present invention principle be:Combined integral controller is on the basis of original combined integral system, based on internal model A kind of new controller that principle and model prediction are proposed.It is specifically described as follows:
For the first combined integral system object:
Wherein, k is constant, and τ is time delay constant;
For the system, it is assumed that desired closed loop transfer function, is:
According to Design of Internal Model Controller principle, the transmission function for obtaining controller is:
The input E (s) of controller and the relation exported between U (s) are:
Above formula (2) is construed to:Current control action u (t) inputs e (t) by controller and is multiplied by proportionality coefficientDuring with t- τ The control action u's (t- τ) at quarter is cumulative, sees Fig. 1 original controller structures.U ' (s) is u (t- τ) pull-type conversion in Fig. 1.
The controller itself is a positive feedback controller, and structure is very simple, and realization is also very easy to, it is only necessary to current Input and former controller export.The controller has good response speed, antijamming capability and robustness. Importantly, under the controller action, controlled device with indifference without poor, the characteristics of controlling more than stable state.
However, the controller is found after commercial Application, controller output vibration is than larger, the abrasion to executing agency Than larger, its popularization in the industry is seriously limited.
In order to overcome the shortcoming of controller output vibration, it is necessary to the control action of smooth positive feedback part, it is contemplated that combination Integral elementThe essence of average value filtering, by the delay component e in Fig. 1-τsReplace withAnd will It is reduced toObtain improved controller architecture as shown in Figure 2.U ' (s) is the past period [t, t- τ] to export u in Fig. 2 (t) input of the controller in the pull-type conversion of average value, Fig. 2, output relation are:
The transmission function of controller is:
Closed loop transfer function, is:
The closed loop transfer function, is consistent with open-loop transfer function characteristic, the input of its discretization, output relation for (assuming that from 1) time of dissipating is:
In view of the convenience of implementation, by above formula proper transformation, approximate expression is obtained:
Above formula (7) is transformed to incremental form:
As can be seen from the above equation, input and past n- of the increment of controller output only with current time and previous moment 1 is relevant with the controller output at n- τ -1 moment.
For second of combined integral system object:
Wherein, k is constant, τ1、τ2For time delay constant;
System pure lag system more than the first system, according to the thinking of above controller design, it is contemplated that Current controlled variable and [t- τ2, t- τ12] period controller output it is relevant, by controller positive feedback link in Fig. 2WithReplace, obtain controller architecture as shown in Figure 3.It is the inputting of controller in Fig. 3, defeated Going out relation is:
The transmission function of the corresponding controller of above formula (9) is:
The corresponding closed loop transfer function, of above formula (9) is:
Equally, closed loop transfer function, is consistent with open-loop transfer function characteristic.The input of formula (11) discretization, output relation are (assuming that time discretization is 1):
Above formula is transformed to incremental form:
As can be seen from the above equation, formula (7) is using the approximate feasibility of formula (8).Inherently see, any process all has pure Hysteresis characteristic, the completely process without purely retarded are non-existent.Formula (13) controller is implemented very simple, it is only necessary to when current Carve the input with previous moment and past n- τ2With n- τ12The controller output at moment.
With reference to Fig. 4, according to derivation above, the definition of combined integral controller of the present invention is obtained:Combined integral controller It is to contain combined integral link in a class formationController, the output of controller is by currently inputting and passing by one The average value of section time controller output is constituted.Its formula can be expressed as:
Because formula (14) has anti-hysteresis, also referred to as resist delayed combined integral controller.Formula (3) is the one of above formula Individual special case, referred to as basic combined integral controller.
In practice, there is substantial amounts of combined integral system, petrochemical industry, grease, chemical fibre, papermaking, pharmacy, grain in industry The industrial process such as food processing all include combined integral system.The research of combined integral controller is to improving the control of the class object Precision and economic benefit, there is important more practical value.
The present invention is further illustrated with a specific embodiment below.
Cut-tobacco drier is that cut tobacco is dried as the key equipment in tobacco cutting production line, its maximum effect, it is ensured that Moisture content is to 11%~14%, and by moisture content precision controlling within 0.5%, to meet cigarette technological requirement.Dried in cut tobacco While dry, pipe tobacco is produced obvious expansion, improve the filling power of pipe tobacco, to weaken cigarette list case consumption silk amount have significantly into Effect.
The process object of pipe tobacco moisture content of outlet is second of combined integral system transter model, and parameter is τ1= 10, τ2=10, k=1.I.e.
This is a class Large Dead-time Process, is controlled using formula (14), its step response curve and noiseproof feature ( T=10s adds step, in the interference that T=45s is exported plus amplitude is 1) as shown in Figure 5.
Object parameters are changed to τ1=11, τ2=9, k=1.1, and controller parameter keeps constant, system still can With good control performance, as shown in Figure 6.
If controlled device is become and turns to single order process with long time delayIn T=10s plus step, in T =100s outputs plus the interference that amplitude is 1, equally, controller parameter keep constant.Although system response has slowed one A bit, flatness has been short of, but system still has good control performance:Non-overshoot, without poor, interference free performance more than stable state It is good, and controller output is more smooth, as shown in Figure 7.
It is described above, only presently preferred embodiments of the present invention, it is not any to the present invention in form and substantial limitation, It should be pointed out that for those skilled in the art, on the premise of the inventive method is not departed from, can also make Some improvement and supplement, these are improved and supplement also should be regarded as protection scope of the present invention.All those skilled in the art, Without departing from the spirit and scope of the present invention, when made using disclosed above technology contents it is a little more Dynamic, modification and the equivalent variations developed, are the equivalent embodiment of the present invention;Meanwhile, all substantial technologicals pair according to the present invention The variation, modification and evolution for any equivalent variations that above-described embodiment is made, still fall within the scope of technical scheme It is interior.

Claims (2)

1. a kind of combined integral controller, it is characterised in that:In combined integral system, the transmission function of combined integral link by Two or more integration Object with Time Delay are constituted, and are expressed as:
<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <msub> <mi>k</mi> <mi>i</mi> </msub> <mrow> <msub> <mi>sG</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mi>s</mi> </mrow> </msup> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mi>s</mi> </mrow> </msup> </mrow>
Wherein, Gi(s) it is the Stable Polynomials for not including integral element;It is included in combined integral system Systems stabilisation;kiFor target gain, τ1i、τ2iFor time delay constant, equation is met:τ2i2(i-1)1(i-1);1 < i < n, n For positive integer;
For combinations thereof integrating system, it is controlled with following combination integral controller:
<mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>k</mi> <mi>i</mi> </msub> </mfrac> <mi>E</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mi>s</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mi>s</mi> </mrow> </msup> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mi>s</mi> </mrow> </msup> <mi>U</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow>
Wherein, E (s) represents the input of controller, and U (s) represents the output of controller, kiFor target gain, τ1i、τ2iProlong for the time Slow constant.
2. a kind of combined integral controller as claimed in claim 1, it is characterised in that:When the combined integral controller is current The output at quarter is only had combined integral controller and determined with the input at the average value of interior output and current time for the previous period, therefore With anti-hysteresis, so as to overcome the hysteresis quality of combined integral system.
CN201710572404.1A 2017-07-13 2017-07-13 A kind of combined integral controller Pending CN107272404A (en)

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Cited By (2)

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Publication number Priority date Publication date Assignee Title
CN108021021A (en) * 2017-12-14 2018-05-11 东华大学 A kind of controller of double circle structure for integrator plus time delay object
CN109445275A (en) * 2018-11-08 2019-03-08 广东电网有限责任公司 A kind of ratio hysteretic control approach, device and equipment

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CN105334752A (en) * 2015-11-30 2016-02-17 东华大学 Control method with combined integrating link and predictive PI control algorithm combined
CN105337588A (en) * 2015-11-30 2016-02-17 东华大学 Combined integral filtering system
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CN101382773A (en) * 2008-10-17 2009-03-11 东华大学 Anti-time lag flase-proportional integral control system and method
CN105334752A (en) * 2015-11-30 2016-02-17 东华大学 Control method with combined integrating link and predictive PI control algorithm combined
CN105337588A (en) * 2015-11-30 2016-02-17 东华大学 Combined integral filtering system
CN105529022A (en) * 2015-12-18 2016-04-27 东华大学 Self-adaptive combined integration filtering apparatus and noise control system and method

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108021021A (en) * 2017-12-14 2018-05-11 东华大学 A kind of controller of double circle structure for integrator plus time delay object
CN109445275A (en) * 2018-11-08 2019-03-08 广东电网有限责任公司 A kind of ratio hysteretic control approach, device and equipment
CN109445275B (en) * 2018-11-08 2021-01-26 广东电网有限责任公司 Proportional hysteresis control method, device and equipment

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Application publication date: 20171020