CN1235104C - 3-freedom uncoupling control system for chemical ring-opening non-stable tandem course - Google Patents

Abstract

The present invention relates to a three-freedom degree decoupling control system of an open loop unstable cascade stage process of chemical industry, which is composed of a specified value response controller, a stabilization specified value response controller, disturbance observers, an identification model of a controlled intermediate stage unstable process, an identification model of a last stage stable process and a signal mixer. An open loop control mode is adopted by the specified value response of the system. A proportional controller is arranged on a forward passage to stabilize an unstable cascade stage process. The deviation value of the output of the identification model of the intermediate stage unstable process after stabilization and the output of an actual intermediate stage process, and the deviation value of the output of an identification model of a global cascade stage unstable process after stabilization and the output of an actual last stage process are respectively used as feedback information amount for inhibiting load disturbance signals of the intermediate stage process and the last stage process. A regulation function is executed by the disturbance observers arranged in an inner ring and an outer ring. The favorable robust stability of the control system of the present invention can be kept, and the control system can adapt the perturbation of model building errors and process parameters of a cascade stage process within a large range.

Description

The three freedom decoupling control system of chemical industry open-loop unstable tandem process

Technical field:

The present invention relates to a kind of three freedom decoupling control system of chemical industry open-loop unstable tandem process, be to export scalable open-loop unstable tandem process at intergrade erratic process in the Chemical Manufacture, based on the theory of optimal control and robust control theory, the decoupling and controlling system of a kind of novelty that proposes belongs to industrial process control technology field.

Background technology:

Instability in the chemical process is unmanageable to liking, especially for the erratic process with obvious time lag.It is responsive to the load interference ratio that outstanding problem is them, cause easily process output than great fluctuation process, as the thermal reactor of dum boiler, chemical continuous stirred tank reactor (CSTR) and energy industry.This situation is very unfavorable and harmful to actual production usually.So in the time might measuring the output of intergrade process, preferentially adopt the tandem control structure to suppress the load undesired signal.A common cascade control system comprises two FEEDBACK CONTROL closed loops, promptly with ring in the nested control of FEEDBACK CONTROL outer shroud.In this control in the ring to as if intergrade can measure the process of output.When this intergrade process was sneaked in the load interference, the interior ring of control adjustment process intake as early as possible made the output of intergrade process steadily, thereby guarantees the stability that main final stage process is exported to reduce and to suppress load's disturbance.On the world in control field and domestic important publication, published the Optimal Design Method and the rule of adjusting of the conventional tandem control structure control of the application open-loop unstable tandem process that some well-known scholars and engineering specialist propose in recent years, and flexible implementation structure.Being extruded with representationally has: Nagrath, D., Prasad, V. and Bequette, B.W. at document A model predictive formulation forcontrol of open-loop unstable cascade systems (Chemical Engineering Science, 2002,57,365-378.) in propose to adopt predictive control theory to design the method that conventional cascade control system realizes online adjusting open-loop unstable tandem process, system's set-point response performance and load interference rejection capability have been optimized significantly, but shortcoming is to optimize the performance index of the two independently simultaneously, and the operand of adjust controlled variable and controller architecture is bigger; Saraf, V.S. and Bequette, B.W. at document Auto-tuning of cascadecontrolled open-loop unstable reactors (Proceedings of the American ControlConference, 2001,2021-2026.) the middle interior ring of the conventional cascade control system of a kind of on-line tuning and the method for outer ring controller of proposing, simplify this two rules that controller is adjusted although provided, but there is serious coupling between ring and the control outer shroud in the control, can not distinguishes the performance index of optimizing them independently; Lee, Y.H., Oh, S.G and Park, S.W. is document Enhanced control with a general cascade control structure. (Ind.Eng.Chem.Res, 2002,41 (11), 2679-2688.) the middle proposition based on H ₂The conventional cascade control system of optimum index Design is controlled the method for open-loop unstable tandem process, although the control performance of ring and outer shroud reaches the optimization based on square-error index (ISE) in can realizing controlling, still fail to overcome the major defect of serious coupling between interior ring of control and the control outer shroud.The article that domestic scholars such as Liu Hongbo and Chai Tianyou deliver " a kind of new robust cascade control system and application thereof " (Chinese journal of scientific instrument .2000.21 (4), 384-387.) propose to design the method that conventional cascade control system is controlled open-loop unstable tandem process based on the infinite performance index of H, this method has improved the robust stability of control system, how to reach optimization control effect but can not prove, also solve the serious coupled problem between interior ring of control and the control outer shroud.

Generally speaking, the shortcoming that adopts conventional cascade control system is apparent in view, as has coupling between ring and the outer shroud in controlling, make to regulate and the control system of adjusting cumbersome.Ring controller and outer ring controller is changed to manual state in promptly at first will adjusting, ring controller was until reaching satisfied outer shroud control performance outside ring controller reached and adjusts behind the satisfied interior ring control performance again in adjusting.In case the The whole control system performance index that finally obtain can not reach the requirement of appointment, perhaps owing to causing the control system performance index to descend in system's generating process parameter perturbation in service, ring and outer ring controller in then must readjusting according to the above-mentioned step of adjusting, so be the conventional cascade control system or the conventional cascade control system of online adjusting all is more loaded down with trivial details of adjusting in advance, and the resulting control system performance of carefully not adjusting may not be certain better than the single loop control structure of classics.Especially for erratic process, when optimizing response of adjusting set-point and load disturbance response simultaneously very significantly water bed effect (Kemin Zhou, Doyle, J.C.and Glove can appear; K.Essentialsof Robust Control.Prentice hall, Upper Saddle River, 1998.), contradictions of these those length that disappear are much more sharp-pointed than open loop stabilization process cascade control system.

Thereby at present a lot of practical application in industry such as dum boiler, chemical continuous stirred tank reactor and pharmaceutical technology, slip-stick artist and actual user are after having weighed above-mentioned pros and cons even abandoned conventional tandem control structure and still adopt classical single loop control structure, make the superiority of tandem control structure not obtain due performance under adaptable occasion of reality and operating mode.

Summary of the invention:

The objective of the invention is to overcome the major defect of the conventional cascade control system structure of open-loop unstable process, fundamentally solve the adjusting of ring and outer shroud in the system set-point response that exists in the conventional cascade control system and coupled problem between the load disturbance response and the control and adjust between interrelated serious drawback, thereby reach better control effect, and the convenient and actual cascade control system that simplifies the operation.

For this reason, the present invention is directed in the Chemical Manufacture intergrade erratic process and export scalable open-loop unstable tandem process, provide a kind of decoupling zero cascade control system of novelty.Its basic controlling thought is that open loop control mode is adopted in system's set-point response, by on the forward direction input channel, adopting a proportional controller unstable tandem process of calming, thereby avoided and the back is used to suppress produce coupling between the control closed loop that load disturbs, promptly realized full decoupled between system's set-point response and the load disturbance response, the while is based on H ₂Optimum index Design set-point response controller can guarantee that the set-point response of control system reaches optimum.Be used to suppress that ring is arranged between the input end and output terminal of intergrade process in the control of intergrade process load undesired signal, utilize departure between the output of the output of intergrade erratic process identification model after calm and actual intergrade process as the feedback regulation quantity of information of inhibition intergrade process load undesired signal, send it to be arranged on the interior ring of the control feedback channel disturbance observer, export to the input end of actual intergrade process through the disturbance observer judgement with after handling with degenerative form, thereby the size of regulating its input quantity is sneaked into the purpose that the load undesired signal of intergrade process has a negative impact to reach elimination.In like manner, utilize departure between the output of the output of overall tandem erratic process identification model after calm and actual final stage process as the feedback regulation quantity of information of inhibition final stage process load undesired signal, send it to be arranged on the control outer shroud feedback channel disturbance observer, through disturbance observer judge and handle after with output quantity with the degenerative form input end of actual intergrade process that is added to, thereby the size of regulating its input quantity is sneaked into the purpose that the load undesired signal of final stage process has a negative impact to reach asymptotic elimination.

Decoupling zero cascade control system of the present invention consists of the following components: the disturbance observer of the disturbance observer of ring, control outer shroud in the controller of the calm set-point response of set-point response controller, two, the control, overall tandem process identification model and six signal mixers of being formed by intergrade erratic process identification model and final stage stabilization process identification model serial connection.Control system be input as outside set-point input signal, connect the input end of set-point response controller, control system is output as the output of second signal mixer.First signal mixer is arranged on the output of set-point response controller, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output divides two-way, one the tunnel connects the positive polarity input end of second signal mixer, and another road connects the positive polarity input end of the 3rd signal mixer; Second signal mixer is arranged on the input end of actual intergrade process, and it has one tunnel positive polarity input end and two-way negative polarity input end, and its output terminal connects the input end of actual intergrade process; The 3rd signal mixer is arranged on the input end of intergrade process identification model, and it has one tunnel positive polarity input end and one tunnel negative polarity input end, and its output terminal connects the input end of intergrade process identification model; The 4th signal mixer is arranged on the input end of overall tandem process identification model, and it has one tunnel positive polarity input end and one tunnel negative polarity input end, and its output terminal connects the input end of overall tandem process identification model; The 5th signal mixer is arranged on the output of actual intergrade process, and it has one tunnel positive polarity input end and one tunnel negative polarity input end, and its output terminal connects the input end of the disturbance observer of ring in the control; The 6th signal mixer is arranged on the output of actual final stage process, and it has one tunnel positive polarity input end and one tunnel negative polarity input end, and its output terminal connects the input end of the disturbance observer of control outer shroud; The output of set-point response controller divides two-way, and one the tunnel connects the positive polarity input end of first signal mixer, and another road connects the positive polarity input end of the 4th signal mixer; The no time lag that the input end of the controller of first calm set-point response connects intergrade process identification model partly is the output terminal of rational part, its output divides two-way, one the tunnel connects one tunnel negative polarity input end of second signal mixer, and another road connects the negative polarity input end of the 3rd signal mixer; The input end of the controller of second calm set-point response connects the output terminal of the intergrade process identification model rational part in the overall tandem process identification model, and its output terminal connects the negative polarity input end of the 4th signal mixer; The input end of the disturbance observer of ring connects the output terminal of the 5th signal mixer in the control, and its output terminal connects another road negative polarity input end of second signal mixer; The input end of the disturbance observer of control outer shroud connects the output terminal of the 6th signal mixer, and its output terminal connects the negative polarity input end of first signal mixer.

The set-point response controller is followed the tracks of and is amplified the set-point input signal, offers the needed intake of controlled open-loop unstable tandem process work, thereby makes the output of controlled tandem process reach the requirement of set-point signal.The controller of first calm set-point response is identical with the control structure of the controller of second calm set-point response, wherein the function of the controller of first calm set-point response is the stationarity that guarantees the set-point response of controlled unstable intergrade process, and the function of the controller of second calm set-point response is the stationarity that guarantees the set-point response of overall open-loop unstable tandem process identification model.The function of disturbance observer of ring is to sneak into the intergrade erratic process because of the load undesired signal and cause deviation takes place in its output signal to handle and amplify detected in the control, send into the input end of intergrade process then with degenerative form, thereby regulate the input quantity size of intergrade process, reach and eliminate the purpose that the load undesired signal influences the output of intergrade process.The disturbance observer of control outer shroud is sneaked into the final stage stabilization process because of the load undesired signal and is caused deviation takes place in its output signal to handle and amplify detected, send into the input end of intergrade process then with degenerative form, thereby regulate the input quantity size of intergrade process, reach the purpose that asymptotic elimination load undesired signal influences the output of final stage process.The function of intergrade process identification model, final stage process identification model and overall tandem process identification model is the output of simulating actual intergrade process and overall tandem process respectively, the reference process output signal is provided, and is the controller of the above-mentioned set-point response controller of design, calm set-point response and the foundation of controlling the disturbance observer of interior ring and outer shroud.The function of signal mixer is that the multichannel input signal is mixed into one tunnel output signal.

During actual motion decoupling zero cascade control system of the present invention, at first control system set-point input signal is sent into the set-point response controller, the set-point response controller amplifies and level and smooth set-point input signal, provide the work of controlled overall tandem process needed intake, thereby make the output of controlled tandem process reach the requirement of set-point signal.The output signal of set-point response controller is divided into two-way, and one the tunnel gives the input controlled quentity controlled variable of actual intergrade process, and the input end of overall tandem process identification model is sent on another road.Secondly, the controller of first calm set-point response will be amplified by the signal that the output of the rational part of intergrade process identification model is sent here, send into the input end of actual intergrade process and the input end of intergrade process identification model respectively with degenerative form, thereby play the effect of the set-point response of calm controlled intergrade erratic process, the set-point response of the intergrade erratic process identification model of also having calmed simultaneously; The controller of second calm set-point response will be amplified by the signal that the output of the intergrade process identification model rational part in the overall tandem process identification model is sent here, send into the input end of overall tandem process identification model with degenerative form, thus the set-point response of the overall tandem erratic process identification model of calming; Then, the detection signal of the output of actual intergrade stabilization process and the intergrade process identification model output signal after calm is sent into signal mixer ask difference operation, gained departure signal is sent into the disturbance observer of ring in the control, send into the input end of actual intergrade process after the disturbance observer of ring is handled and amplified in controlling with degenerative form, thereby regulate the size of the input controlled quentity controlled variable of actual intergrade process, reach and eliminate the purpose that the load undesired signal of sneaking into the intergrade process influences controlled intergrade erratic process output; At last, the detection signal of the output of actual final stage stabilization process and the overall tandem erratic process identification model output signal after calm is sent into signal mixer ask difference operation, gained departure signal is sent into the disturbance observer of control outer shroud, after handling amplification, the disturbance observer of control outer shroud sends into the input end of actual intergrade process with degenerative form, thereby regulate the size of the input controlled quentity controlled variable of controlled intergrade process, reach asymptotic elimination and sneak into the purpose that the load undesired signal of final stage process influences controlled final stage stabilization process output.

For single order intergrade erratic process identification model and single order final stage stabilization process identification model, according to the set-point response rise time t of system of common definition _rFor controlled process output reaches the required time of 90% final value, the set-point response rise time t of system _rControlled variable λ with system's set-point response controller _cBetween tuning formulae be t _r=3.8897 λ _c+ θ, wherein θ is pure retardation time of the summation of overall tandem erratic process identification model.Therefore, utilize above-mentioned tuning formulae, can regulate quantitatively and the time domain index of the set-point of the control system of adjusting response.

The outstanding advantage of the decoupling zero tandem control structure that the present invention proposes is: 1. response of the set-point of control system and load disturbance response are full decoupled, can distinguish independently and regulate, and be used for suppressing ring and outer shroud in the control of load undesired signal and also can be respectively optimize separately performance index, thereby the traditional tandem control structure adjusting and the shortcoming of the trouble of adjusting have been overcome by the disturbance observer of regulating each self-loop; 2. can eliminate the load undesired signal of sneaking into the intergrade erratic process fast, steadily system's final stage process output, thus can reach than the better control performance of single loop control structure; 3. system's set-point response controller and being used to interior ring and outer shroud disturbance observer of suppressing the load undesired signal all is based on H ₂Optimal performance index (ISE) design so the tandem control structure that the present invention provides can make the control system performance index reach the optimum limit.4. system's set-point response controller and being used to suppresses the interior ring of load undesired signal and outer shroud disturbance observer and is one-parameter and adjusts, and can quantitatively regulate monotonously, thereby the time domain response index of control system can quantitatively be estimated and adjust.Under nominal case, system's set-point response does not have overshoot.The present invention has provided the numerical value tuning formulae between rise time of the controller parameter of set-point response controller and the response of system set-point, thereby is very easy to practical operation and online adjusting cascade control system; 5. the decoupling zero tandem control structure that provides of the present invention is based on the robust internal model control principle, so control structure can guarantee good robust stability, it is insensitive to change for procedure parameter, can be in endoadaptation tandem process model building error and procedure parameter perturbation in a big way.

Therefore the decoupling zero cascade control system that provides of the present invention has significant superiority and practicality, can give play to the superiority of tandem control structure in practical application in industry forcefully.

Description of drawings:

Accompanying drawing 1 is a decoupling zero cascade control system schematic diagram of the present invention.

P among the figure _1mAnd P _2mBe respectively the unstable scalable process P of intergrade ₁With final stage stabilization process P ₂The identification mathematical model, promptly $P_{1m}={\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1\mathrm{mo}}{e}^{-{\mathrm{\&theta;}}_{1m}s},P_{2m}=P_{2\mathrm{mo}}{e}^{-{\mathrm{\&theta;}}_{2m}s},$ P wherein _1moBe intergrade process identification model P _1mRational part, P _2moBe final stage process identification model P _2mRational part.C is the set-point response controller, F ₁And F ₂Be respectively the disturbance observer of interior ring of control and outer shroud, P _cIt is the controller that is used for calm set-point response.y ₁And y ₂Be respectively output of intergrade process and the output of final stage process.R is system's set-point input signal, u ₁Be intergrade process P ₁The input controlled quentity controlled variable, u ₂Be the output of controller C, f ₁Be disturbance observer F ₁Output, f ₂Be disturbance observer F ₂Output, e ₁Be the output of actual intergrade process and the departure between the output of intergrade erratic process identification model after calming, e ₂Be the output of actual final stage process and the departure between the output of overall tandem erratic process identification model after calming, d1 and d2 are the load undesired signals of sneaking into the intergrade erratic process, and d3 is the load undesired signal of sneaking into the final stage stabilization process.

Fig. 2 is disturbance observer F ₂Implementation structure figure.

F among the figure ₂Be the disturbance observer of control outer shroud, F ₂₀Be disturbance observer F ₂In control execution unit, P _1mAnd P _2mBut be respectively intergrade instability measuring process P ₁With final stage stabilization process P ₂The identification mathematical model, P _1moBe intergrade process identification model P _1mRational part, F ₂Be disturbance observer F ₂Output, e ₂Be the output of actual final stage process and the departure between the output of overall tandem erratic process identification model after calming.

Fig. 3 is the final stage process output response curve in the embodiment of the invention.

Fig. 4 is the final stage process output response curve under the situation that procedure parameter takes place to perturb in the embodiment of the invention.

Embodiment:

Below in conjunction with drawings and Examples technical scheme of the present invention is described further.

Decoupling zero cascade control system of the present invention consists of the following components as shown in Figure 1: the controller P of set-point response controller C, two calm set-point responses _c, control in the ring disturbance observer F ₁, control outer shroud disturbance observer F ₂, by intergrade process identification model $P_{1m}={\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1\mathrm{mo}}{e}^{-{\mathrm{\&theta;}}_{1m}s}$ With final stage process identification model $P_{2m}=P_{2\mathrm{mo}}{e}^{-{\mathrm{\&theta;}}_{2m}s}$ The overall tandem process identification model P that serial connection forms _1mP _2mAnd six signal mixers (the circle node among the figure).Control system be input as outside set-point input signal r, connect the input end of set-point response controller C, control system is output as the output of second signal mixer.First signal mixer is arranged on the output of set-point response controller C, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output divides two-way, one the tunnel connects the positive polarity input end of second signal mixer, and another road connects the positive polarity input end of the 3rd signal mixer; Second signal mixer is arranged on actual intergrade process P ₁Input end, it has one tunnel positive polarity input end and two-way negative polarity input end, its output terminal connects actual intergrade process P ₁Input end; The 3rd signal mixer is arranged on intergrade process identification model P _1mInput end, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects intergrade process identification model P _1mInput end; The 4th signal mixer is arranged on overall tandem process identification model $P_{1m}{P}_{2m}={\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1\mathrm{mo}}{P}_{2\mathrm{mo}}{e}^{-({\mathrm{\&theta;}}_{1m}+{\mathrm{\&theta;}}_{2m})s}$ Input end, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects overall tandem process identification model P _1mP _2mInput end; The 5th signal mixer is arranged on actual intergrade process P ₁Output, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects the disturbance observer F of ring in the control ₁Input end; The 6th signal mixer is arranged on actual final stage process P ₂Output, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects the disturbance observer F of control outer shroud ₂Input end; The output of set-point response controller C divides two-way, and one the tunnel connects the positive polarity input end of first signal mixer, and another road connects the positive polarity input end of the 4th signal mixer; The controller P of first calm set-point response _cInput end connect intergrade process identification model P _1mRational part P _1moOutput terminal, its output divides two-way, the one tunnel connects one tunnel negative polarity input end of second signal mixer, another road connects the negative polarity input end of the 3rd signal mixer; The controller P of second calm set-point response _cInput end connect overall tandem process identification model P _1mP _2mIn intergrade process identification model rational part P _1moOutput terminal, its output terminal connects the negative polarity input end of the 4th signal mixer; The disturbance observer F of ring in the control ₁Input end connect the output terminal of the 5th signal mixer, its output terminal connects another road negative polarity input end of second signal mixer; The disturbance observer F of control outer shroud ₂Input end connect the output terminal of the 6th signal mixer, its output terminal connects the negative polarity input end of first signal mixer.

During this decoupling zero cascade control system of actual motion, at first control system set-point input signal r is sent into set-point response controller C, set-point response controller C amplifies and level and smooth set-point input signal r, and controlled tandem process P is provided ₁P ₂Needed intake u works ₂Thereby, make controlled tandem process P ₁P ₂Output reach the requirement of set-point signal r.The output signal u of set-point response controller C ₂Be divided into two-way, the one tunnel gives actual intergrade process P ₁Input controlled quentity controlled variable u ₁, overall tandem process identification model P is sent on another road _1mP _2mInput end.Secondly, the controller P of first calm set-point response _cWill be by intergrade process identification model P _1mRational part P _1moThe signal sent here of output amplify, send into actual intergrade process P respectively with degenerative form ₁Input end and intergrade process identification model P _1mInput end, thereby play calm controlled intergrade erratic process P ₁The effect of set-point response, intergrade erratic process identification model P has also calmed simultaneously _1mSet-point response; The controller P of second calm set-point response _cWill be by overall tandem process identification model P _1mP _2mIn intergrade process identification model rational part P _1moThe signal sent here of output amplify, send into overall tandem process identification model P with degenerative form _1mP _2mInput end, thereby calm overall tandem erratic process identification model P _1mP _2mSet-point response; Then, with actual intergrade stabilization process P ₁Output y ₁Detection signal and intergrade process identification model P _1mOutput signal after calming is sent into signal mixer and is asked difference operation, gained departure signal e ₁Send into the disturbance observer F of ring in the control ₁, the disturbance observer F of ring in controlling ₁Handle the amplification back and send into actual intergrade process P with degenerative form ₁Input end, thereby regulate actual intergrade process P ₁Input controlled quentity controlled variable u ₁Size, reach to eliminate and sneak into intergrade process P ₁Load undesired signal d1 and d2 influence controlled intergrade erratic process P ₁The purpose of output; At last, with actual final stage stabilization process P ₂Output y ₂Detection signal and overall tandem erratic process identification model P _1mP _2mOutput signal after calming is sent into signal mixer and is asked difference operation, gained departure signal e ₂Send into the disturbance observer F of control outer shroud ₂, through the disturbance observer F of control outer shroud ₂Handle the amplification back and send into actual intergrade process P with degenerative form ₁Input end, thereby regulate controlled intergrade process P ₁Input controlled quentity controlled variable u ₁Size, reach asymptotic elimination and sneak into final stage process P ₂Load undesired signal d3 influence controlled final stage stabilization process P ₂The purpose of output.

Usually with following single order frequency domain mathematical expression form above-mentioned instability and scalable intergrade process and stable final stage process are described in the reality

$P_1\left(s\right)=\frac{k_1{e}^{-{\mathrm{\&theta;}}_{1}s}}{{\mathrm{\&tau;}}_{1}s-1},P_2\left(s\right)=\frac{k_2{e}^{-{\mathrm{\&theta;}}_{2}s}}{{\mathrm{\&tau;}}_{2}s+1}$

K wherein ₁And k ₂Be respectively intergrade erratic process P ₁With final stage stabilization process P ₂Steady-state gain, τ ₁And τ ₂Be respectively intergrade process P ₁With final stage process P ₂Time constant, θ ₁And θ ₂For being respectively intergrade process P ₁With final stage process P ₂Pure retardation time.Provide set-point response controller C below, the controller P of calm set-point response _cAnd the disturbance observer F of interior ring of control and outer shroud ₁And F ₂Design formula:

1. at first be identified for the controller P of calm set-point response _c, get P _c=k _c, it is a proportional controller (P), k satisfies condition when requiring the setup parameter value _c＞1/k ₁Guarantee the stability of system's set-point response.Need explanation, satisfying under the situation of constraint condition controller P _cParameter value can set arbitrarily, it does not influence the performance index of response of system set-point and load disturbance response.

2. secondly determine set-point response controller C, its design formula is

$C\left(s\right)=\frac{({\mathrm{\&tau;}}_{1}s+k_1{k}_c-1)({\mathrm{\&tau;}}_{2}s+1)}{k_1{k}_2{({\mathrm{\&lambda;}}_{c}s+1)}^2}---\left(1\right)$

λ wherein _cBe controlled variable, its rule of adjusting is: less λ adjusts _cValue can obtain system's set-point response faster but require bigger controller output energy, and the robust stability variation of set-point response; Bigger λ adjusts _cValue can make controller output energy less but the set-point response is correspondingly slack-off, and the robust stability of set-point response simultaneously strengthens.Controlled variable λ generally can adjust _cAt overall tandem erratic process pure retardation time of summation θ ₁+ θ ₂Realize the optimal compromise between the above-mentioned requirements near the value.The set-point response rise time t of system according to common definition _rFor controlled process output reaches the required time of 90% final value, for single order intergrade erratic process identification model and single order final stage stabilization process identification model, the set-point response rise time t of system _rWith controlled variable λ _cBetween adjust that to close be t _r=3.8897 λ _c+ θ, wherein θ is pure retardation time of the summation θ of overall tandem process identification model ₁+ θ ₂So utilize controlled variable λ _cThe set-point response index of adjusting system is very easily.

Above-mentioned design of Controller formula can adopt conventional analog controller to realize in actual applications.Realize if need go up, then need to adopt corresponding discretize algorithm pattern at industrial computer, single-chip microcomputer or digitial controller (DDC).Here provide increment type discretize control algolithm formula commonly used in the industrial practice.Input quantity and the output quantity of note controller C are respectively r _cAnd u _c, the control sampling period is T _sThen the discretize way of realization by formula (1) The controller C is

$\mathrm{\&Delta;}{u}_c\left(k\right)=\frac{1}{k_1{k}_2{\mathrm{\&lambda;}}_c^2+2k_1{k}_2{\mathrm{\&lambda;}}_c{T}_s}[k_1{k}_2{\mathrm{\&lambda;}}_c^2\mathrm{\&Delta;}{u}_c(k-1)-k_1{k}_2{T}_s^2{u}_c\left(k\right)+$

$({\mathrm{\&tau;}}_1{\mathrm{\&tau;}}_2+{\mathrm{\&tau;}}_1{T}_s+k_1{k}_c{\mathrm{\&tau;}}_2{T}_s-{\mathrm{\&tau;}}_2{T}_s)\mathrm{\&Delta;}{r}_c\left(k\right)-{\mathrm{\&tau;}}_1{\mathrm{\&tau;}}_2\mathrm{\&Delta;}{r}_c(k-1)+(k_1{k}_c-1)T_s^2{r}_c\left(k\right)]---\left(2\right)$

R wherein _c(k) expression kT _sValue constantly, Δ r _c(k)=r _c(k)-r _c(k-1),

Δr _c(k-1)＝r _c(k-1)-r _c(k-2)；

u _c(k) expression kT _sValue constantly, Δ u _c(k)=u _c(k)-u _c(k-1),

Δu _c(k-1)＝u _c(k-1)-u _c(k-2)。

Control sampling period T _sShould be in 0.01-0.2 value between second.

3. determine the disturbance observer F of ring in the control ₁, based on H ₂The desirable disturbance observer F that optimal performance index (ISE) design obtains ₁Form be

$F_{1-\mathrm{ideal}}\left(s\right)=\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;\frac{({\mathrm{\&tau;}}_{1}s-1)(\mathrm{\&alpha;s}+1)}{{({\mathrm{\&lambda;}}_{f1}s+1)}^2-(\mathrm{\&alpha;s}+1)e^{-{\mathrm{\&theta;}}_{1}s}}---\left(3\right)$

Wherein $\mathrm{\&alpha;}={\mathrm{\&tau;}}_1[{(\frac{{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">f</figure-callout>}1}}{{\mathrm{\&tau;}}_1}+1)}^2{e}^{\frac{{\mathrm{\&theta;}}_1}{{\mathrm{\&tau;}}_1}}-1],$ The control setting parameter is λ _F1Be not difficult to find out that it is at the s=1/ of s RHP τ ₁There is pole zero cancellation in the place, can not steady operation.So adopt approximate formula to realize here:

The PID form that Taylor's formula is approximate: $F_1\left(s\right)=k_f+\frac{1}{T_{1}s}+\frac{T_{D}s}{0.1s+1}---\left(4\right)$

Wherein $K_f=\underset{s\&RightArrow;0}{\lim }\frac{d\left[s{F}_{1-\mathrm{ideal}}\left(s\right)\right]}{\mathrm{ds}},T_i=\underset{s\&RightArrow;0}{\lim }\frac{1}{s{F}_{1-\mathrm{ideal}}\left(s\right)},T_d=\frac{1}{2}\underset{s\&RightArrow;0}{\lim }\frac{d^2\left[s{F}_{1-\mathrm{ideal}}\left(s\right)\right]}{d{s}^2}$

Three rank Pade approximate formulas: $F_1\left(s\right)=\frac{d_3{s}^3+d_2{s}^2+d_{1}s+d_0}{s(c_2{s}^2+c_{1}s+1)}---\left(5\right)$

Wherein ${\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">c</figure-callout>}}_1=\frac{b_2{b}_5-b_3{b}_4}{b_3^2-b_2{b}_4},c_2=\frac{b_4^2-b_3{b}_5}{b_3^2-b_2{b}_4},$ d ₀＝b ₀，d ₁＝b ₁+b ₀c ₁，d ₂＝b ₂+b ₁c ₁+b ₀c ₂，d ₃＝b ₃+b ₂c ₁+b ₁c ₂， $b_i=\frac{1}{i!}\underset{s\&RightArrow;0}{\lim }\frac{d^i}{{\mathrm{ds}}^i}\left[s{F}_{1-\mathrm{ideal}}\left(s\right)\right],$ i＝0，1，...，5。

Need explanation, use F ₁The constraint condition of three rank Pade approximate formulas are c ₁＞0 and c ₂＞0, could guarantee its job stability like this.Therefore, for same controlled variable λ _F1Value if the disturbance observer that adopts three rank Pade approximate formulas to obtain can guarantee steady operation, then should preferentially adopt.Otherwise can only adopt the disturbance observer of PID form.

Controlled variable λ _F1The rule of adjusting be: increase λ _F1The robust stability that makes ring in the control strengthens but has weakened the load interference rejection capability simultaneously; Reduce λ on the contrary _F1Its load interference rejection capability is strengthened but reduce closed loop robust stability simultaneously.Simulation study shows, controlled variable λ _F1Should adjust at θ pure retardation time of intergrade erratic process ₁Come the robust stability and the nominal performance of ring in the optimal compromise control about value.When obvious pure retardation time of this erratic process not can be for reference, but initial setting up λ _F1=0.5, increase or reduce to regulate controlled variable λ gradually _F1Disturb rejection until reaching satisfied load.

Note disturbance observer F ₁Input quantity and output quantity be respectively r _F1And u _F1, the control sampling period is T _s, then corresponding discretize delta algorithm execute form is

The pid algorithm formula: $\mathrm{\&Delta;}{u}_{f1}\left(k\right)=\frac{1}{T_s{T}_l}[(T_D{T}_l+k_f{T}_l{T}_s)\mathrm{\&Delta;}{r}_{f1}\left(k\right)-T_D{T}_l\mathrm{\&Delta;}{r}_{f1}(k-1)+T_s^2{r}_{f1}\left(k\right)]---\left(6\right)$

Three rank Pade approximate data formula:

$\mathrm{\&Delta;}{u}_{f1}\left(k\right)=\frac{1}{c_2+c_1{T}_s+T_s^2}[(2c_2+c_1{T}_s)\mathrm{\&Delta;}{u}_{f1}(k-1)-c_2\mathrm{\&Delta;}{u}_{f1}(k-2)+(d_3+d_2{T}_s+d_1{T}_s^2)\mathrm{\&Delta;}{r}_{f1}\left(k\right)$

$-(2d_3+d_2{T}_s)\mathrm{\&Delta;}{r}_{f1}(k-1)+d_3\mathrm{\&Delta;}{r}_{f1}(k-2)+T_s^3{r}_{f1}\left(k\right)---\left(7\right)$

In the above-mentioned algorithmic formula:

r _F1(k) expression kT _sValue constantly, Δ r _F1(k)=r _F1(k)-r _F1(k-1);

Δr _f1(k-1)＝r _f1(k-1)-r _f1(k-2)，Δr _f1(k-2)＝r _f1(k-2)-r _f1(k-3)；

u _F1(k) expression kT _sValue constantly, Δ u _F1(k)=u _F1(k)-u _F1(k-1),

Δu _f1(k-1)＝u _f1(k-1)-u _f1(k-2)，Δu _f1(k-2)＝u _f1(k-2)-u _f1(k-3)。

4. determine the disturbance observer F of control outer shroud ₂, its design formula is

$F_2\left(s\right)=\frac{F_{20}\left(s\right)}{1-F_{20}\left(s\right)\frac{P_{1\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">m</figure-callout>}}}{1+{\mathrm{<figure-callout\; id="1"\; label="P\; c\; P"\; filenames="C20031010795800191.png"\; state="\{\{state\}\}">P</figure-callout>}}_c{P}_{}{}_{1\mathrm{mo}}}{P}_{2m}},F_{20}\left(s\right)=\frac{({\mathrm{\&tau;}}_{1}s+k_1{k}_c-1)({\mathrm{\&tau;}}_{2}s+1)}{k_1{k}_2{({\mathrm{\&lambda;}}_{f2}s+1)}^2}---\left(8\right)$

Therefore, disturbance observer F ₂Can adopt control structure as shown in Figure 2 to carry out in actual applications, wherein λ _F2Be controlled variable.Need explanation, according to robust control theory, controlled variable λ _F2Adjust and can only satisfy F ₂Compromise between the robust stability of residing control outer shroud and the nominal performance.That is to say, increase λ _F2The robust stability that makes this control closed loop strengthens but has weakened the load interference rejection capability simultaneously; Reduce λ on the contrary _F2Its load interference rejection capability is strengthened but reduce closed loop robust stability simultaneously.Simulation study shows, controlled variable λ _F2Should adjust at overall tandem erratic process P ₁P ₂Pure retardation time of summation θ ₁+ θ ₂Come the robust stability and the nominal performance of this control closed loop of optimal compromise about value.

The disturbance observer F of control outer shroud ₂Design formula (8) can adopt conventional analog controller to realize in actual applications.Note disturbance observer F ₂Input quantity and output quantity be respectively r _F2And u _F2, the control sampling period is T _s, corresponding discretize delta algorithm execute form is

$\mathrm{\&Delta;}{u}_{f2}\left(k\right)=\frac{1}{k_1{k}_2{\mathrm{\&lambda;}}_{f2}^2+2k_1{k}_2{\mathrm{\&lambda;}}_{f2}{T}_s}[k_1{k}_2{\mathrm{\&lambda;}}_{f2}^2\mathrm{\&Delta;}{u}_{f2}(k-1)-k_1{k}_2{T}_s^2{u}_{f2}\left(k\right)+k_1{k}_2{T}_s^2{u}_{f2}(k-\frac{{\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2}{T_s})$

$({\mathrm{\&tau;}}_1{\mathrm{\&tau;}}_2+k_1{k}_c{\mathrm{\&tau;}}_2{T}_s-{\mathrm{\&tau;}}_2{T}_s+{\mathrm{\&tau;}}_1{T}_s)\mathrm{\&Delta;}{r}_{f2}\left(k\right)-{\mathrm{\&tau;}}_1{\mathrm{\&tau;}}_2\mathrm{\&Delta;}{r}_{f2}(k-1)+(k_1{k}_c-1)T_s^2{r}_{f2}\left(k\right)]$

$u_{f2}\left(k\right)=\mathrm{\&Delta;}{u}_{f2}\left(k\right)=0,k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{{\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2}{T_s}---\left(9\right)$

In this algorithmic formula:

r _F2(k) expression kT _sValue constantly, Δ r _F2(k)=r _F2(k)-r _F2(k-1),

Δr _f2(k-1)＝r _f2(k-1)-r _f2(k-2)；

u _F2(k) expression kT _sValue constantly, Δ u _F2(k)=u _F2(k)-u _F2(k-1),

Δu _f2(k-1)＝u _f2(k-1)-u _f2(k-2)。

Need explanation, control sampling period T _sShould be in 0.01-0.2 value between second, and should make pure retardation time of the summation θ of overall tandem process ₁+ θ ₂Be its integral multiple.

Investigate Wen, T. is at document IMC design for unstable processes with time delays. (Journal of Process Control, 2003,13,203-213.) Yan Jiu a chemical reaction erratic process

$P\left(s\right)=\frac{e^{-0.939s}}{(5s-1)(2.07s+1)}$

Here as emulation embodiment decoupling zero tandem control structure of the present invention is described.Suppose that this erratic process is made of following intergrade process and final stage process

$P_1\left(s\right)=\frac{e^{-0.339s}}{5s-1},P_2\left(s\right)=\frac{e^{-0.6s}}{2.07s+1}$

Use decoupling zero tandem control structure of the present invention, at first according to the structure of the structured flowchart shown in the accompanying drawing 1 control system; Carry out the design of controller then and adjust: the first step, according to the aforesaid controller P that is used for the set-point response of calm system _cMethod for designing, get P _c=2, i.e. k _c=2, satisfy stable constraint condition k _c＞1/k ₁k ₂

In second step, the design formula (1) of applying mechanically the set-point response controller C of system obtains

$C\left(s\right)=\frac{(5s+1)(2.07s+1)}{{({\mathrm{\&lambda;}}_{c}s+1)}^2}$

Initial setting up λ _c=0.939.

In the 3rd step, apply mechanically the disturbance observer F that encircles in the control ₁Design formula (3-4), initial setting up λ _F1=0.339, obtain

The PID form: $F_1\left(s\right)=14.6948+\frac{1}{0.0839s}+\frac{1.7585s}{0.1s+1}$

In the 4th step, apply mechanically the disturbance observer F that controls outer shroud ₂Design formula (8), obtain

$F_2\left(s\right)=\frac{F_{20}\left(s\right)}{1-\frac{F_{20}\left(s\right)}{(5s+1)(2.07s+1)}{e}^{-0.939s}},F_{20}\left(s\right)=\frac{(5s+1)(2.07s+1)}{{({\mathrm{\&lambda;}}_{f2}s+1)}^2}$

Disturbance observer F ₂Initial setting up λ can be carried out with the control structure shown in the accompanying drawing 2 _F2=0.939.

During l-G simulation test, add set point unit step input r constantly second at t=0 respectively, add reverse unit step load disturbance signal d1 constantly in intergrade process P second at t=25 ₁Input end.Final stage process output simulation result as shown in Figure 3.

As seen from Figure 3, no matter the decoupling zero tandem control structure (solid line) that the present invention provides is in system's set-point response or all significantly is better than not adopting the Wen of tandem control structure, T. method (dotted line) on the load disturbance response.Show thus, under the situation of actual capabilities, adopt the tandem control structure can reach better control performance.

Suppose actual intergrade process P now ₁With final stage process P ₂Time constant than process identification model P _1mAnd P _2mLess than normal 10%, and their pure retardation time is than process identification model P _1mAnd P _2mBigger than normal 10%.Carry out emulation experiment as mentioned above in this case, final stage process output response as shown in Figure 4.

Simulation result shown in Figure 4 shows that the decoupling zero tandem control structure (solid line) that the present invention provides can make control system keep very good robust stability.By contrast, do not adopt the Wen of tandem control structure, T. method (dotted line) just makes control system produce apparent in view vibration.Verified the decoupling zero tandem control structure procedure of adaptation identification model sum of errors parameter perturbation well that the present invention provides thus, and the nominal performance loss that is occurred when at controlled tandem process perturbation taking place is very little.

What more than set forth is the good control effect that the preferred embodiment of the present invention shows.It may be noted that, the present invention is not only limited to the foregoing description, because decoupling zero tandem control structure of the present invention is at general open-loop unstable tandem production run in the chemical process, the controller that provides is resolved design formula and is gone for the unstable and scalable tandem production run of various intergrade processes, so the present invention can be widely used in the open-loop unstable tandem production run of production technologies such as dum boiler, chemical stirred autoclave, metallurgy, pharmacy and papermaking.

Claims (2)

1, a kind of three freedom decoupling control system of chemical industry open-loop unstable tandem process is characterized in that the controller (P by set-point response controller (C), two calm set-point responses _c), control in the ring disturbance observer (F ₁), control outer shroud disturbance observer (F ₂), by intergrade process identification model (P _1m) and final stage process identification model (P _2m) the overall tandem process identification model (P that forms of serial connection _1mP _2m) and six signal mixers form, this control system be input as outside set-point input signal (r), connect the input end of set-point response controller (C), this control system is output as the output of second signal mixer; First signal mixer is arranged on the output of set-point response controller (C), it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output divides two-way, one the tunnel connects the positive polarity input end of second signal mixer, and another road connects the positive polarity input end of the 3rd signal mixer; Second signal mixer is arranged on actual intergrade process (P ₁) input end, it has one tunnel positive polarity input end and two-way negative polarity input end, its output terminal connects actual intergrade process (P ₁) input end; The 3rd signal mixer is arranged on intergrade process identification model (P _1m) input end, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects intergrade process identification model (P _1m) input end; The 4th signal mixer is arranged on overall tandem process identification model (P _1mP _2m) input end, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects overall tandem process identification model (P _1mP _2m) input end; The 5th signal mixer is arranged on actual intergrade process (P ₁) output, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects the disturbance observer (F of ring in the control ₁) input end; The 6th signal mixer is arranged on actual final stage process (P ₂) output, it has one tunnel positive polarity input end and one tunnel negative polarity input end, its output terminal connects the disturbance observer (F of control outer shroud ₂) input end; The output of set-point response controller (C) divides two-way, and one the tunnel connects the positive polarity input end of first signal mixer, and another road connects the positive polarity input end of the 4th signal mixer; Controller (the P of first calm set-point response _c) input end connect intergrade process identification model (P _1m) rational part (P _1mo) output terminal, its output divides two-way, the one tunnel connects one tunnel negative polarity input end of second signal mixer, another road connects the negative polarity input end of the 3rd signal mixer; Controller (the P of second calm set-point response _c) input end connect intergrade process identification model rational part (P in the overall tandem process identification model _1mo) output terminal, its output terminal connects the negative polarity input end of the 4th signal mixer; Disturbance observer (the F of ring in the control ₁) input end connect the output terminal of the 5th signal mixer, its output terminal connects another road negative polarity input end of second signal mixer; Disturbance observer (the F of control outer shroud ₂) input end connect the output terminal of the 6th signal mixer, its output terminal connects the negative polarity input end of first signal mixer.

2, as the three freedom decoupling control system of the said chemical industry open-loop unstable of claim 1 tandem process, when it is characterized in that described intergrade process identification model and final stage process identification model are single order, the set-point response rise time t of system _rBe defined as controlled process output and reach the required time of 90% final value, the controlled variable λ of itself and system's set-point response controller (C) _cBetween adjust that to close be t _r=3.8897 λ _c+ θ, wherein θ is pure retardation time of the summation of overall tandem process identification model.

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