CN103336539B - A kind of control method for pressure balance of cracking waste plastics reactor - Google Patents

Abstract

The invention discloses a kind of control method for pressure balance of cracking waste plastics reactor.The pressure equilibrium of current cracking waste plastics reactor controls substantially to adopt the better simply modes such as standard P ID control, and control effects is not ideal enough.The present invention adopt PREDICTIVE CONTROL and dynamic Feedforward compensate the composite control method combined carry out cracking waste plastics reactor pressure equilibrium control, first at system cloud gray model steadily and design predictive controller when not having measurable disturbance to input, then the dynamic Feedforward controller of the strict canonical of method design of series connection low-pass filter is passed through when system has measurable disturbance, finally above-mentioned two quasi-controllers are combined, obtain feed-forward and feedback complex controll rule, thus improve control accuracy and the interference free performance of the control of cracking waste plastics reaction pressure, contribute to the efficient of cracking reaction and safe operation.

Description

A kind of control method for pressure balance of cracking waste plastics reactor

Technical field

The invention belongs to technical field of automation, the pressure equilibrium relating to one way of life rubbish cracking waste plastics reactor controls, utilize the composite control method that PREDICTIVE CONTROL-dynamic Feedforward compensates, realize controlling the pressure equilibrium of cracking waste plastics reactor, may be used for the Stress control of chemical industry reactor.

Background technology

Along with the development that modern urbanization is gone down town, in daily life, create a large amount of house refuses.In these house refuses, packing plastics bag, plastic ware, medical waste plastics etc. are all regenerated resources.If do not carry out Appropriate application to these renewable resources in house refuse, not only can cause serious environmental pollution, and make serious waste of resources.Waste plastics in house refuse not only can reduce the pollution to environment by cracking liquefaction, can alleviate day by day serious energy shortage problem to a certain extent simultaneously.

Reactor is the nucleus equipment of cracking waste plastics liquefaction, and the pressure equilibrium of reactor controls extremely important, and control effects requires also comparatively strict, is the core technology ensureing reactor continuous charging and discharging and safety in production.In cracking waste plastics process, need to ensure that reactor is in pressure-fired all the time, otherwise will lysis efficiency be affected and very easily cause safety problem.In current commercial production, the pressure equilibrium of cracking waste plastics reactor controls, and the general PID mode adopting routine, control effects is undesirable.For this present situation, the present invention proposes one way of life rubbish cracking waste plastics reactor control method for pressure balance, by the composite control method that PREDICTIVE CONTROL-dynamic Feedforward compensates, the deficiency of the traditional control methods such as PID in control accuracy and interference free performance can be made up, ensure that reactor Stress control has higher precision and anti-interference, meet industrial demand.

Summary of the invention

Object of the present invention is exactly for utilizing the methods such as existing PID to control the deficiency of house refuse cracking waste plastics reactor pressure, providing the new method that a kind of reactor pressure equilibrium controls.First, when there is not disturbance input, forecast Control Algorithm design of feedback control law is utilized in system even running; Then, when consideration system exists the input of all kinds of measurable disturbance, utilize the dynamic Feedforward control law of the strict canonical of method design of series connection low-pass filter, improve the interference free performance of system; Finally, by both combinations above-mentioned, design PREDICTIVE CONTROL-dynamic Feedforward compensates the complex controll rule combined.The composite control method of the PREDICTIVE CONTROL-dynamic Feedforward proposed by the present invention, can realize the pressure balanced effective control of counterincision solution reaction kettle, ensures the carrying out that cracking reaction is efficient, safe.

The concrete steps of house refuse cracking reaction still control method for pressure balance of the present invention are:

Step one: even running, the Predictive control design do not existed in disturbance input situation

A. systematic steady state model is set up.First, with house refuse cracking waste plastics reactor rotating speed, excess air coefficient, flue gas efflux velocity, charging rate, discharging speed and catalyzer supply for control inputs amount, force value in the cracking reaction still collected with pressure-measuring device is output quantity, when controlled system even running, there is not disturbance input, by system identifying method, set up the discrete time transfer function model that reactor pressure equilibrium controls

Wherein for kmoment measures the force value in the cracking reaction still of gained by pressure transducer; for kthe control inputs vector in moment, 6 control inputs components represent successively kthe reactor rotating speed in moment, excess air coefficient, flue gas efflux velocity, charging rate, discharging speed and catalyzer supply; with represent and obtain systematic parameter by identification

，

Wherein , represent the model parameter needing identification, irepresent the unit matrix with suitable dimension, , represent number of samples.

Then, can be following state-space model by previous reaction still control pressurer system model representation

Wherein for state vector, for kthe increment of moment control inputs, matrix of coefficients a, bwith cbe respectively

B. output valve is predicted.Walked the cracking reaction still control pressurer system model set up by a, by iterative computation, can obtain k+ jthe output valve in moment is

Wherein for vector estimated value, jfor positive integer.

Further, prediction output can be expressed as following form

Wherein

Wherein nwith n _u represent prediction time domain respectively and control time domain, for k+ sthe predicted value of moment output quantity, and .

From above formula, the prediction of output quantity depends on state vector estimated value .By designing an asymptotic astimation device, for the estimation of state vector.Utilize standard pole-assignment, design the observer gain matrix that a dimension is suitable l, make matrix ( a- lC) all eigenwerts be all less than 1, then this observer is asymptotic convergence.Now, estimated value can be calculated as follows

C. optimizing control rule solves.Set up quadratic form optimization object function

Wherein with for scalar factor.

When getting with time ( scalar for permanent), optimization object function can be written as

Utilize the method for solving of quadratic programming (QP) problem can obtain optimum control to be input as

Wherein ithe unit matrix that representation dimension is suitable.

In control implementation process, only has control sequence one-component, namely , be sent to actual cracking waste plastics reactor, make it produce corresponding control effects, and repeat the calculating of above-mentioned Optimization Solution in next sampling instant.

Step 2: existence can survey the dynamic Feedforward Compensation Design under input disturbance situation

In cracking reaction process; especially start and stop, operational mode change, waste plastics quality and many reasons such as composition transfer, Changes in weather, the input quantity disturbance all making system there is excess air coefficient, heat supply flue-gas temperature, flue gas efflux velocity, charging rate, discharging speed etc. can to survey.In this case, by design dynamic Feedforward controller, dynamic compensation can be carried out to corresponding measurable disturbance, improve the interference free performance of system.

First, when system exist can disturbance input, by system identifying method, set up following reactor pressure equilibrium control transfer function model

Wherein , respectively kthe pressure measuring value in moment and control inputs vector, provide before concrete form; for kthe noise vector surveyed in moment; , , represent the systematic parameter obtained by identification

， ，

Wherein , , represent the model parameter needing identification, irepresent the unit matrix with suitable dimension, , , represent number of samples.

Then, transport function when controlled device does not have a disturbance is introduced with the transport function of controlled device disturbance passage , can obtain

Wherein , .

Be expressed as needing the feedforward control gain of design , then after adding feedforward compensation link, the output of system can be expressed as

Obviously, when time, have .If make again , then can design corresponding feedforward controller gain, concrete form is

Therefore, the output of dynamic Feedforward controller is

Finally, canonical, attainable Feedforward Controller Design is carried out.For the control object of much reality, due to transport function when above-mentioned controlled device does not have a disturbance be strict canonical, cause it inverse non-regular and not attainable, and irregularity feedforward controller when control inputs will be caused to be high frequency amplitude too large.

In order to design the dynamic Feedforward controller of strict canonical, the method by the following low-pass filter of series connection is eliminated by the present invention high fdrequency component

Wherein tfor the sampling period, , 100,120,140,160 can be taken as successively ... equivalent.

Step 3: the complex controll design that PREDICTIVE CONTROL-dynamic Feedforward compensates

The predictive controller of combining step one and step 2 design and dynamic Feedforward controller, adopt feed-forward and feedback composite control method to correct system, realize the pressure balanced effective control of cracking waste plastics reactor.

According to step one and step 2, the PREDICTIVE CONTROL-dynamic Feedforward complex controll rule that finally can obtain system is

Wherein .

PREDICTIVE CONTROL and dynamic Feedforward method organically combine by the inventive method, control effectively to the pressure equilibrium of house refuse cracking waste plastics reactor.For modes such as general accepted standard PID controls at present, make the shortcomings such as control accuracy is low, Ability of Resisting Disturbance is poor, the present invention proposes and compensate based on PREDICTIVE CONTROL-dynamic Feedforward the composite control method combined.First, by forecast Control Algorithm, inertia and the delay character of cracking reaction still pressure equilibrium control can be overcome; Then, by the dynamic Feedforward controller of the strict canonical of series connection low pass filter design, the antijamming capability of system to measurable disturbance can be improved; Finally, PREDICTIVE CONTROL and dynamic Feedforward are compensated the formation complex controll that combines, cracking waste plastics reaction pressure control balancing is all significantly improved in control accuracy and interference free performance, for the efficient of cracking reaction and safe operation, there is vital role.

Embodiment

Specific embodiment of the invention step is as follows:

Step one: even running, the Predictive control design do not existed in disturbance input situation

A. systematic steady state model is set up.First, when system even running, there is not disturbance input, by system identifying method, set up reactor pressure equilibrium control discrete time transfer function model

Wherein for kmoment measures the force value in the cracking reaction still of gained by pressure transducer; for kthe control inputs vector in moment, 6 control inputs components represent successively kthe reactor rotating speed in moment, excess air coefficient, flue gas efflux velocity, charging rate, discharging speed and catalyzer supply; with represent and obtain systematic parameter by identification

，

Wherein , represent the model parameter needing identification, irepresent the unit matrix with suitable dimension, , represent number of samples.

Then, define kthe increment of moment control inputs , and selection mode vector is , then the discrete time transfer function model of previous reaction still control pressurer system can be expressed as following state-space model

Wherein matrix of coefficients a, bwith cbe respectively

B. output valve is predicted.Walked the cracking reaction still control pressurer system model set up by a, by iterative computation, can output valve be obtained

Wherein for vector estimated value, y( k+ j) be k+ jthe output valve in moment, jfor positive integer.

Further, make nwith n _u represent prediction time domain respectively and control time domain, prediction output can be expressed as following form

Wherein

In formula for k+ sthe predicted value of moment output quantity, and .

From above formula, the prediction of output quantity depends on state vector estimated value .By designing an asymptotic astimation device, for the estimation of state vector.Utilize standard pole-assignment, design the observer gain matrix that a dimension is suitable l, make matrix ( a- lC) all eigenwerts be all less than 1, then this observer is asymptotic convergence.Now, estimated value can be calculated as follows

C. optimizing control rule solves.Set up quadratic form optimization object function

Wherein with for scalar factor.

When getting with time ( scalar for permanent), optimization object function can be written as

Utilize the method for solving of quadratic programming (QP) problem can obtain optimum control to be input as

Wherein ithe unit matrix that representation dimension is suitable.

In control implementation process, by control sequence one-component deliver to actual cracking waste plastics reactor after being transformed by digital-to-analogue, produce corresponding control effects, and repeat the calculating of above-mentioned Optimization Solution in next sampling instant.

Step 2: existence can survey the dynamic Feedforward Compensation Design under input disturbance situation

In cracking reaction process; especially start and stop, operational mode change, waste plastics quality and many reasons such as composition transfer, Changes in weather, the input quantity disturbance all making system there is excess air coefficient, heat supply flue-gas temperature, flue gas efflux velocity, charging rate, discharging speed etc. can to survey.In this case, by design dynamic Feedforward controller, dynamic compensation can be carried out to corresponding measurable disturbance, improve the interference free performance of system.

The design of dynamic Feedforward controller can be carried out as follows:

A. when system exist can disturbance input, by system identifying method, set up following reactor pressure equilibrium control transfer function model

Wherein , respectively kthe pressure measuring value in moment and control inputs vector, provide before concrete form; for kthe noise vector surveyed in moment; , , represent the systematic parameter obtained by identification

， ，

Wherein , , represent the model parameter needing identification, irepresent the unit matrix with suitable dimension, , , represent number of samples.

B. the transfer function model in aforementioned a. is converted, can obtain

Transport function when wherein controlled device does not have a disturbance with the transport function of controlled device disturbance passage be respectively with .

After adding feedforward control link, the output of system can be expressed as

Wherein represent for needing the feedforward control gain of design.

Obviously, when time, have .Make again , can design corresponding feedforward controller gain, concrete form is

Therefore, the output of dynamic Feedforward controller is

C. canonical, attainable feedforward controller is designed.For the control object of much reality, due to transport function when above-mentioned controlled device does not have a disturbance be strict canonical, cause it inverse non-regular and not attainable, and irregularity feedforward controller when control inputs will be caused to be high frequency amplitude too large.

In order to design the dynamic Feedforward controller of strict canonical, the method by the following low-pass filtering link of series connection is eliminated by the present invention high fdrequency component

Wherein tfor the sampling period, , 100,120,140,160 can be taken as successively ... equivalent.

Step 3: the complex controll design that PREDICTIVE CONTROL-dynamic Feedforward compensates

The predictive controller of combining step one and step 2 design and dynamic Feedforward controller, adopt feed-forward and feedback composite control method to correct system, realize the pressure balanced effective control of cracking waste plastics reactor.

According to step one and step 2, the complex controll rule that finally can obtain PREDICTIVE CONTROL-dynamic Feedforward compensation is

。

Claims (1)

1. a control method for pressure balance for cracking waste plastics reactor, is characterized in that the concrete steps of the method are:

Step one: even running, the Predictive control design do not existed in disturbance input situation

A. systematic steady state model is set up; First, with house refuse cracking waste plastics reactor rotating speed, excess air coefficient, flue gas efflux velocity, charging rate, discharging speed and catalyzer supply for control inputs amount, force value in the cracking reaction still collected with pressure-measuring device is output quantity, when controlled system even running, there is not disturbance input, by system identifying method, set up the discrete time transfer function model that reactor pressure equilibrium controls

A(z ^-1)y(k)＝B(z ^-1)u(k)

Wherein y (k) is for the k moment is by the force value in the cracking reaction still of pressure-measuring device measurement gained; U (k)=[u ₁(k), u ₂(k), u ₃(k), u ₄(k), u ₅(k), u ₆(k)] ^tfor the control inputs vector in k moment, 6 control inputs components represent the reactor rotating speed in k moment, excess air coefficient, flue gas efflux velocity, charging rate, discharging speed and catalyzer supply successively; A (z ^-1) and B (z ^-1) represent obtain systematic parameter by identification

$A\left(z^{-1}\right)=I+\underset{i=1}{\overset{n_a}{\mathrm{\Σ}}}{A}_i{z}^{-i},B\left(z^{-1}\right)=\underset{i=0}{\overset{n_b}{\mathrm{\Σ}}}{B}_i{z}^{-i}$

Wherein A _i, B _irepresent the model parameter needing identification, I represents the unit matrix with suitable dimension, n _a, n _brepresent number of samples;

Then, can be following state-space model by previous reaction still control pressurer system model representation

x(k+1)＝Ax(k)+BΔu(k)

y(k)＝Cx(k)

Wherein x (k)=[y (k) ... y (k-n _a) Δ u (k-1) ... Δ u (k-n _b)] ^tfor state vector, the increment that Δ u (k)=u (k)-u (k-1) is k moment control inputs, coefficient matrices A, B and C are respectively

$B={\left[\begin{array}{ccccccccc}{B}_0^T& 0& ...& 0& |& I& 0& ...& 0\end{array}\right]}^T$

C＝[I 0 … 0 |0 0 … 0]

B. output valve is predicted; Walked the cracking reaction still control pressurer system model set up by a, by iterative computation, the output valve that can obtain the k+j moment is

$y(k+j)={\mathrm{CA}}^j\hat{x}\left(k\right)+\underset{i=0}{\overset{j-1}{\mathrm{\Σ}}}{\mathrm{CA}}^{j-i-1}\mathrm{B\Δu}(k+i)$

Wherein for the estimated value of vector x (k), j is positive integer;

Further, prediction output can be expressed as following form

$Y\left(k\right)=F\hat{x}\left(k\right)+\mathrm{HU}\left(k\right)$

Wherein

$Y\left(k\right)=\left[\begin{array}{c}\hat{y}(k+1|k)\\ \hat{y}(k+2|k)\\ .\\ .\\ .\\ \hat{y}(k+N|k)\end{array}\right],U\left(k\right)=\left[\begin{array}{c}\mathrm{\Δu}\left(k\right)\\ \mathrm{\Δu}(k+1)\\ .\\ .\\ .\\ \mathrm{\Δu}(k+N_u-1)\end{array}\right],$

Wherein N and N _urepresent prediction time domain respectively and control time domain, for the predicted value of k+s moment output quantity, and s=1,2 ..., N;

From above formula, the prediction of output quantity depends on the estimated value of state vector x (k) by designing an asymptotic astimation device, for the estimation of state vector; Utilize standard pole-assignment, design the observer gain matrix L that a dimension is suitable, make all eigenwerts of matrix (A-LC) all be less than 1, then this observer is asymptotic convergence; Now, the estimated value of x (k) can be calculated as follows

$\hat{x}(k+1)=(A-\mathrm{LC})\hat{x}\left(k\right)+\mathrm{B\Δu}\left(k\right)+\mathrm{Ly}\left(k\right)$

C. optimizing control rule solves; Set up quadratic form optimization object function

$J=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\α}\left(j\right){\hat{y}}^2(k+j|k)+\underset{j=1}{\overset{N_u}{\mathrm{\Σ}}}\mathrm{\β}\left(j\right){\mathrm{\Δu}}^2(k+j-1)$

Wherein α (j) and β (j) is scalar factor;

When getting α (j)=1 and β (j)=β, β is permanent scalar, and optimization object function can be written as

$J={[\mathrm{HU}\left(k\right)-F\hat{x}\left(k\right)]}^T[\mathrm{HU}\left(k\right)-F\hat{x}\left(k\right)]+{\mathrm{\βU}}^T\left(k\right)U\left(k\right)$

Utilize the method for solving of quadratic programming problem can obtain optimum control to be input as

$U\left(k\right)=-{(H^{T}H+\mathrm{\βI})}^{-1}{H}^{T}F\hat{x}\left(k\right)$

The unit matrix that wherein I representation dimension is suitable;

In control implementation process, only have the one-component of control sequence U (k), i.e. Δ u (k), be sent to actual cracking waste plastics reactor, make it produce corresponding control effects, and repeat the calculating of above-mentioned Optimization Solution in next sampling instant;

Step 2: existence can survey the dynamic Feedforward Compensation Design under input disturbance situation

In cracking reaction process, due to start and stop, operational mode change, waste plastics quality and composition transfer, Changes in weather reason, system is all made to there is the input quantity disturbance of surveying of excess air coefficient, heat supply flue-gas temperature, flue gas efflux velocity, charging rate, discharging speed; In this case, by design dynamic Feedforward controller, dynamic compensation is carried out to corresponding measurable disturbance, improves the interference free performance of system;

First, when system exist can disturbance input, by system identifying method, set up following reactor pressure equilibrium control transfer function model

A(z ^-1)y(k)＝B(z ^-1)u(k)+C(z ^-1)ω(k)

Wherein y (k), u (k) distinguish pressure measuring value and the control inputs vector in k moment, provide before concrete form; ω (k) is the noise vector surveyed in k moment; A (z ^-1), B (z ^-1), C (z ^-1) represent the systematic parameter obtained by identification

$A\left(z^{-1}\right)=I+\underset{i=1}{\overset{n_a}{\mathrm{\Σ}}}{A}_i{z}^{-i},B\left(z^{-1}\right)=\underset{i=0}{\overset{n_b}{\mathrm{\Σ}}}{B}_i{z}^{-i},\left(z^{-1}\right)=I+\underset{i=1}{\overset{n_c}{\mathrm{\Σ}}}{C}_i{z}^{-i}$

Wherein A _i, B _i, C _irepresent the model parameter needing identification, I represents the unit matrix with suitable dimension, n _a, n _b, n _crepresent number of samples;

Then, transport function G (z when controlled device does not have a disturbance is introduced ^-1) and the transport function G of controlled device disturbance passage _ω(z ^-1), can obtain

y(k)＝G(z ^-1)u(k)+G _ω(z ^-1)ω(k)

Wherein G (z ^-1)=A (z ^-1) ^-1b (z ^-1), G _ω(z ^-1)=A (z ^-1) ^-1c (z ^-1);

K is expressed as by needing the feedforward control gain of design _ω(z ^-1), then after adding feedforward compensation link, output y (k) of system can be expressed as

y(k)＝G(z ^-1)[u(k)+K _ω(z ^-1)ω(k)]+G _ω(z ^-1)ω(k)

＝G(z ^-1)u(k)+[G(z ^-1)K _ω(z ^-1)+G _ω(z ^-1)]ω(k)

Obviously, when u (k)=0, there is y (k)=[G (z ^-1) K _ω(z ^-1)+G _ω(z ^-1)] ω (k); If make G (z again ^-1) K _ω(z ^-1)+G _ω(z ^-1)=0, then can design corresponding feedforward controller gain, concrete form is

K _ω(z ^-1)＝-G(z ^-1) ^-1G _ω(z ^-1)

Therefore, the output of dynamic Feedforward controller is

u _ω(k)＝K _ω(z ^-1)ω(k)＝-G(z ^-1) ^-1G _ω(z ^-1)ω(k)

Finally, canonical, attainable Feedforward Controller Design is carried out; For the control object of much reality, due to transport function G (z when above-mentioned controlled device does not have a disturbance ^-1) be strict canonical, cause it against G (z ^-1) ^-1non-regular and not attainable, and G (z ^-1) ^-1irregularity feedforward controller K when control inputs will be caused to be high frequency _ω(z ^-1) amplitude too large;

In order to design the dynamic Feedforward controller of strict canonical, the method by series connection low-pass filter is eliminated K _ω(z ^-1) high fdrequency component

$K_{\mathrm{\ω}}\left(z^{-1}\right)=-(\frac{{\mathrm{\λ}}_{1}z}{z-e^{-{\mathrm{\λ}}_{1}T}}\frac{{\mathrm{\λ}}_{2}z}{z-e^{-{\mathrm{\λ}}_{2}T}}...\frac{{\mathrm{\λ}}_{v}z}{z-e^{-{\mathrm{\λ}}_{v}T}})G{\left(z^{-1}\right)}^{-1}{G}_{\mathrm{\ω}}\left(z^{-1}\right)$

Wherein T is the sampling period, ν=n _a-n _b+ 1, λ ₁, λ ₂..., λ _νbe taken as 100,120,140,160 successively

Step 3: the complex controll design that PREDICTIVE CONTROL-dynamic Feedforward compensates

The predictive controller of combining step one and step 2 design and dynamic Feedforward controller, adopt feed-forward and feedback composite control method to correct system, realize the pressure balanced effective control of cracking waste plastics reactor;

According to step one and step 2, the PREDICTIVE CONTROL-dynamic Feedforward complex controll rule that finally can obtain system is

$u\left(k\right)=-\mathrm{\Φ}{(H^{T}H+\mathrm{\βI})}^{-1}{H}^{T}F\hat{x}\left(k\right)-(\frac{{\mathrm{\λ}}_{1}z}{z-e^{-{\mathrm{\λ}}_{1}T}}\frac{{\mathrm{\λ}}_{2}z}{z-e^{-{\mathrm{\λ}}_{2}T}}...\frac{{\mathrm{\λ}}_{v}z}{z-e^{-{\mathrm{\λ}}_{v}T}})G{\left(z^{-1}\right)}^{-1}{G}_{\mathrm{\ω}}\left(z^{-1}\right)\mathrm{\ω}\left(k\right)$

Wherein Φ=[1 0 ... 0].