CN104932579A - CO2 supercritical extraction temperature fraction order PID control method - Google Patents

Abstract

The invention discloses a CO2 supercritical extraction temperature fraction order PID control method. In the method, internal model control and fractional-order control are combined; a disadvantage that there are many controller setting parameters is overcome and performance of a control system is improved. Simultaneously, based on an OPC technology, a WinCC is used as a bridge so that MATLAB/Simulink and S7-200PLC can realize real-time communication. On the Simulink, real-time control can be performed on kettle temperature extraction through using a fraction order PID control algorithm. By using the method in the invention, accurate control of the temperature can be effectively realized so that application of intelligent control in an actual industrial control system is realized.

Description

A kind of CO 2supercritical extract temperature Fractional Order PID control method

Technical field

The present invention relates to a kind of production process of carbon dioxide supercritical extraction, particularly a kind of application of Fractional Order PID control method in carbon dioxide supercritical extraction process in temperature control of adjusting based on internal mold.

Background technology

Over nearly twenty or thirty year, along with scientific-technical progress and living standard improve, people have had new understanding, to food, medicine, cosmetics etc. about able-bodied product and related methods of production propose higher standard and requirement to healthy, environment.Although the in recent years representatively CO of one of " clean chemical industry " and " Green Chemistry " theory new technology ₂the practical application of supercritical extract has achieved larger progress, but balances each other and the basic data of hereditary property in extraction process owing to lacking supercritical fluid system, and can not set up satisfied correlation and prediction model; In the supercritical state, change, nonlinear feature when the state modulator such as temperature have, normal feedback control device is difficult to the accurate control ensureing extraction temperature, brings difficulty thus to suitability for industrialized production.

Affect supercritical fluid extraction because have crushing material granularity, extracting pressure, temperature, the character of extract itself, CO ₂flow, extraction time, entrainer, separating pressure and separation temperature etc.Supercritical extract process extraction temperature affects supercritical CO ₂the principal element of effect of extracting is also very significant on the impact of supercritical fluid solubility property.But this impact shows as double action, under the condition that pressure ratio is lower, raised temperature can improve volatile grade and the diffusivity of component to be separated, but this raising is not enough to make up because temperature rising causes supercritical CO ₂the fluid solvent power that density declines and brings weakens, and therefore shows as the rising of the solubility with temperature of solute and declines; Under the condition of relatively high pressure, supercritical CO ₂density ratio larger, compressibility is little, now make because temperature raises the increase of component vapour pressure to be separated and coefficient of diffusion greatly exceed the reduction of the dissolving power caused because supercritical fluid densities reduces, thus the solubility property of supercritical fluid is strengthened with the rising of temperature.At Near The Critical Point, the subtle change of temperature will cause fluid density great changes, and correspondingly shows as the change of solubleness.Therefore, the change of temperature can be utilized to realize the process of extraction and fractionation.

CO ₂in supercritical extract process, temperature and pressure is interactional, but in the production application of reality often pressure can be relatively easy to reach ideal value, but temperature is difficult to reach optimal value due to the impact of other factors and the reason of control method.So realize CO in actual applications ₂the control of supercritical extract process temperature becomes a great problem that supercritical extraction process is applied.STATE FEEDBACK CONTROL based on state observer, the PREDICTIVE CONTROL based on multi-model, be applied to Complex Temperature based on advanced control method Zeng Jun such as fuzzy PID Self tuning control and self-adaptation Smith Prediction Control control by trial.These methods are all theoretical based on integer rank transport function.Integer rank PID method because control algolithm is simple, strong robustness, the parameter feature such as be easy to adjust is widely used in the every field of Industry Control.But due to the integer rank system that research object or controlled device are not generally desirable, but be made up of the differential equation of arbitrary order and integral equation, therefore the limitation of integer rank PID can not meet the performance requirement of controlled device.This method adopts fractional model to describe the attributive character of dynamic system, can continuously change systematic parameter attribute.The Fractional Order PID control algolithm that the present invention adopts internal mold to adjust is to realize CO ₂the control of supercritical extract process temperature all has more advantages than general control method in control accuracy, robustness, parameter tuning etc.

Summary of the invention

The object of the invention is to solve due to change, nonlinear feature when the state modulator such as temperature have, normal feedback control device is difficult to the problem of the accurate control ensureing extraction temperature, and provides a kind of CO ₂supercritical extract temperature Fractional Order PID control method, the present invention effectively can realize the accurate control of temperature, thus realizes the utilization of Based Intelligent Control in actual industrial control system.

The method of the present invention comprises the following steps:

1, the temperature control system adopted includes: analog quantity acquisition circuit, Fractional Order PID Controller, PWM drive circuit.The present invention represents transport function with new fractional-order system, and the responding ability of Fractional Order PID control method and antijamming capability and regulating power are all better than integer rank PID control method, internal model control is combined with fractional order control, the shortcoming that controller tuning parameter is more can be overcome, and the performance of control system can be improved; Utilize WinCC for bridge based on OPC technology simultaneously, make MATLAB/Simulink and S7-200PLC realize real-time Communication for Power, Simulink realizes Fractional Order PID control algolithm extraction kettle temperature is controlled in real time.

2, supercritical extract process temperature fractional model is set up.

Supercritical extract process temperature model is fractional model,

The expression formula of fractional model is $G\left(s\right)=\frac{b_m{s}^{{\mathrm{\β}}_m}+...+b_1{s}^{{\mathrm{\β}}_1}+b_0{s}^{{\mathrm{\β}}_0}}{a_n{s}^{{\mathrm{\α}}_n}+...+a_1{s}^{{\mathrm{\α}}_1}+a_0{s}^{{\mathrm{\α}}_0}}---\left(1\right)$

In formula, α _k, β _k(k=0,1,2 ...) be any real number, β _m> ... β ₁> β ₀, α _n> ... α ₁> α ₀, a _k, b _k(k=0,1.2 ...) be constant;

Direct is difficult to modelling controller shown in (1) formula, and often can not get desirable control effects, is therefore necessary the fractional model of complexity to carry out simplify processes, adopts simplified model:

$M\left(s\right)=\frac{k}{{\mathrm{as}}^{1+\mathrm{\β}}+bs+1}{e}^{-Ls}---\left(2\right)$

In formula, k is open-loop gain, β be greater than 0 any real number, a, b and L are constant.

Basic Matlab adopts the simplification of least square method implementation model, and concrete steps are:

Call step (G, t) function, carry out step analysis to the master mould of formula (1) and the simplified model of formula (2) respectively, obtain corresponding response vector y and h, wherein h is the function about c, c=[k, a, α, β, b, L]

The lsqcurvefit function called based on least square curve fit method solve objective function J optimum time c value, and substituted into formula (2) equivalent simplified model can be obtained.

3, according to the transport function of Fractional Order PID control method, the fractional order PI with internal model control structure is drawn ^λd ^μcontroller.

Internal model control basic structure as shown in Figure 1.

In figure: G _iMCs () is internal mode controller; G _ps () is process object; G _ms () is fractional order process model.By asking for reference input R and the transport function between disturbance input D and the output of process Y, easily show that the closed loop response of system is:

$Y\left(s\right)=\frac{G_{IMC}\left(s\right)G_p\left(s\right)}{1+G_{IMC}\left(s\right)\[G_p\left(s\right)-G_m\left(s\right)\]}R\left(s\right)+\frac{\[1-G_{IMC}\left(s\right)G_m\left(s\right)\]}{1+G_{IMC}\left(s\right)\[G_p\left(s\right)-G_m\left(s\right)\]}D\left(s\right)---\left(3\right)$

Can obtain feedback signal by Fig. 1 is

D _e(s)＝[G _p(s)-G _m(s)]U(s)+D(s) (4)

If model is accurate, i.e. G _p(s)=G _m(s), and there is no external disturbance, then controller has desirable controller characteristic, namely free in and under any interference effect, system exports and all equals input setting value, ensures to follow the tracks of the bias free of reference input.

Idealized score rank PI ^λd ^μcontroller transfer function is for being shown below:

G _IMC(s)＝K _p+K _is ^-λ+K _ds ^μ(5)

In formula: K _pfor proportional gain; K _ifor storage gain; K _dfor the differential gain; λ is integration order; μ is differential order.λ, μ >0 and be real number.When λ and μ gets different values, fractional order control device PI ^λd ^μthere is different structures.

In order to obtain the control structure corresponding to (5) formula, Fig. 1 is transformed to the equivalent construction of the IMC shown in Fig. 2.

Inner loop feedback controlling unit in Fig. 2 is had:

$G_c\left(s\right)=\frac{G_{IMC}\left(s\right)}{1-G_{IMC}\left(s\right)G_m\left(s\right)}---\left(6\right)$

Now by fractional order control device G _cthe PI that s () changes into (5) corresponding to formula ^λd ^μversion.Process is as follows:

1), factorization process model

By G _ms () resolves into G _m+(s) and G _m-(s) two parts.

I.e. G _m(s)=G _m+(s) G _m-(s) (7)

In formula: G _m-s () represents the minimum phase part of model; G _m+s () represents the non-minimum phase bit position of model.

2), IMC controller is designed.

G _IMC(s)＝G ^-1 _m-(s)F(s) (8)

$F\left(s\right)=\frac{1}{{(fs+1)}^n}---\left(9\right)$

In formula: F (s) is low-pass filter, its objective is to reduce the susceptibility of internal model control system to Unmarried pregnancy and model adaptation, improving the robustness of control system, ensure controller G simultaneously _iMCs () physics can realize; F is filter coefficient; The value of n depends on G _m-s the order of (), target makes the transport function of internal mode controller become fraction, thus can physics realization.

3), PI is obtained ^λd ^μcontroller G _c(s)

$G_c\left(s\right)=\frac{{G^{-1}}_{m-}\left(s\right)}{{(fs+1)}^n-G_{m+}\left(s\right)}---\left(10\right)$

When fractional model is known, according to formula (10) and PI ^λd ^μcontrol formula, by the principle of s polynomial expression every power coefficient correspondent equal, solving can based on the PI of internal model control principle ^λd ^μeach parameter value of controller.In formula, filter parameter f is unique setting parameter of controller, and the control performance of f and system is closely related: when f reduces, the dynamic property of system improves, but robustness is deteriorated; Just in time contrary when f increases, the robustness of system improves, but bad dynamic performance.Select the performance of suitable f Guarantee control system.

4, fractional order PI ^λd ^μcontrol System Design realizes.

Utilize Al-Alaoui+CFE impulse response not political reform to G _cs () carries out discretize realization, and then obtain the fractional order PI of fractional order object in Matlab ^λd ^μcontroller closed module.S7-200 Real-time Collection scene temperature value, set up OPC by CP243-1 ethernet module with WinCC to communicate, utilize WinCC for bridge based on OPC technology simultaneously, Simulink realizes Fractional Order PID control algolithm, make MATLAB/Simulink and S7-200PLC realize real-time Communication for Power, extraction kettle temperature is controlled in real time.

Beneficial effect of the present invention:

The present invention is according to supercritical CO ₂the temperature object of extraction, fractional model is adopted to describe the attributive character of dynamic system, transport function is represented with new fractional-order system, and the responding ability of Fractional Order PID control method and antijamming capability and regulating power are all better than integer rank PID control method, internal model control is combined with fractional order control, the shortcoming that controller tuning parameter is more can be overcome, and the performance of control system can be improved, solve the problem of Fractional-order Control Systems parameter tuning difficulty preferably.Utilize WinCC for bridge based on OPC technology simultaneously, make MATLAB/Simulink and S7-200PLC realize real-time Communication for Power, Simulink realizes Fractional Order PID control algolithm extraction kettle temperature is controlled in real time.Achieve the engineer applied that Fractional Order PID realizes complicated algorithm on comparatively conventional controller.Compared with the PID control method of integer rank, it is short that the present invention has the rise time, and steady-state error is little, the advantage of strong robustness, applied range.

Accompanying drawing explanation

Fig. 1 is internal model control system structural drawing of the present invention.

Fig. 2 is IMC equivalent construction of the present invention.

Embodiment

The method of the present invention comprises the following steps:

1, the temperature control system adopted mainly comprises: analog quantity acquisition circuit, Fractional Order PID Controller, PWM drive circuit.The present invention represents transport function with new fractional-order system, and the responding ability of Fractional Order PID control method and antijamming capability and regulating power are all better than integer rank PID control method, internal model control is combined with fractional order control, the shortcoming that controller tuning parameter is more can be overcome, and the performance of control system can be improved; Utilize WinCC for bridge based on OPC technology simultaneously, make MATLAB/Simulink and S7-200PLC realize real-time Communication for Power, Simulink realizes Fractional Order PID control algolithm extraction kettle temperature is controlled in real time.

2, supercritical extract process temperature fractional model is set up.

Supercritical extract process temperature model is fractional model,

The expression formula of fractional model is $G\left(s\right)=\frac{b_m{s}^{{\mathrm{\β}}_m}+...+b_1{s}^{{\mathrm{\β}}_1}+b_0{s}^{{\mathrm{\β}}_0}}{a_n{s}^{{\mathrm{\α}}_n}+...+a_1{s}^{{\mathrm{\α}}_1}+a_0{s}^{{\mathrm{\α}}_0}}---\left(1\right)$

In formula, α _k, β _k(k=0,1,2 ...) be any real number, β _m> ... > β ₁> β ₀, α _n> ... > α ₁> α ₀, a _k, b _k(k=0,1.2 ...) be constant;

Direct is difficult to modelling controller shown in (1) formula, and often can not get desirable control effects, is therefore necessary the fractional model of complexity to carry out simplify processes, adopts simplified model:

$M\left(s\right)=\frac{k}{{\mathrm{as}}^{1+\mathrm{\β}}+bs+1}{e}^{-Ls}---\left(2\right)$

In formula, k is open-loop gain, β be greater than 0 any real number, a, b and L are constant.

Basic Matlab adopts the simplification of least square method implementation model, and concrete steps are:

Call step (G, t) function, carry out step analysis to the master mould of formula (1) and the simplified model of formula (2) respectively, obtain corresponding response vector y and h, wherein h is the function about c, c=[k, a, α, β, b, L]

The lsqcurvefit function called based on least square curve fit method solve objective function J optimum time c value, and substituted into formula (2) equivalent simplified model can be obtained.

3, according to the transport function of Fractional Order PID control method, the fractional order PI with internal model control structure is drawn ^λd ^μcontroller.

Internal model control basic structure as shown in Figure 1.

In figure: G _iMCs () is internal mode controller; G _ps () is process object; G _ms () is fractional order process model.By asking for reference input R and the transport function between disturbance input D and the output of process Y, easily show that the closed loop response of system is:

$Y\left(s\right)=\frac{G_{IMC}\left(s\right)G_p\left(s\right)}{1+G_{IMC}\left(s\right)\[G_p\left(s\right)-G_m\left(s\right)\]}R\left(s\right)+\frac{\[1-G_{IMC}\left(s\right)G_m\left(s\right)\]}{1+G_{IMC}\left(s\right)\[G_p\left(s\right)-G_m\left(s\right)\]}D\left(s\right)---\left(3\right)$

Can obtain feedback signal by Fig. 1 is

D _e(s)＝[G _p(s)-G _m(s)]U(s)+D(s) (4)

If model is accurate, i.e. G _p(s)=G _m(s), and there is no external disturbance, then controller has desirable controller characteristic, namely free in and under any interference effect, system exports and all equals input setting value, ensures to follow the tracks of the bias free of reference input.

Idealized score rank PI ^λd ^μcontroller transfer function is for being shown below:

G _IMC(s)＝K _p+K _is ^-λ+K _ds ^μ(5)

In formula: K _pfor proportional gain; K _ifor storage gain; K _dfor the differential gain; λ is integration order; μ is differential order.λ, μ >0 and be real number.When λ and μ gets different values, fractional order control device PI ^λd ^μthere is different structures.

In order to obtain the control structure corresponding to (5) formula, Fig. 1 is transformed to the equivalent construction of the IMC shown in Fig. 2.

Inner loop feedback controlling unit in Fig. 2 is had:

$G_c\left(s\right)=\frac{G_{IMC}\left(s\right)}{1-G_{IMC}\left(s\right)G_m\left(s\right)}---\left(6\right)$

Now by fractional order control device G _cthe PI that s () changes into (5) corresponding to formula ^λd ^μversion.Process is as follows:

1), factorization process model

By G _ms () resolves into G _m+(s) and G _m-(s) two parts.

I.e. G _m(s)=G _m+(s) G _m-(s) (7)

In formula: G _m-s () represents the minimum phase part of model; G _m+s () represents the non-minimum phase bit position of model.

2), IMC controller is designed.

G _IMC(s)＝G ^-1 _m-(s)F(s) (8)

$F\left(s\right)=\frac{1}{{(fs+1)}^n}---\left(9\right)$

In formula: F (s) is low-pass filter, its objective is to reduce the susceptibility of internal model control system to Unmarried pregnancy and model adaptation, improving the robustness of control system, ensure controller G simultaneously _iMCs () physics can realize; F is filter coefficient; The value of n depends on G _m-s the order of (), target makes the transport function of internal mode controller become fraction, thus can physics realization.

3), PI is obtained ^λd ^μcontroller G _c(s)

$G_c\left(s\right)=\frac{{G^{-1}}_{m-}\left(s\right)}{{(fs+1)}^n-G_{m+}\left(s\right)}---\left(10\right)$

When fractional model is known, according to formula (10) and PI ^λd ^μcontrol formula, by the principle of s polynomial expression every power coefficient correspondent equal, solving can based on the PI of internal model control principle ^λd ^μeach parameter value of controller.In formula, filter parameter f is unique setting parameter of controller, and the control performance of f and system is closely related: when f reduces, the dynamic property of system improves, but robustness is deteriorated; Just in time contrary when f increases, the robustness of system improves, but bad dynamic performance.Select the performance of suitable f Guarantee control system.

4, fractional order PI ^λd ^μcontrol System Design realizes.

Utilize Al-Alaoui+CFE impulse response not political reform to G _cs () carries out discretize realization, and then obtain the fractional order PI of fractional order object in Matlab ^λd ^μcontroller closed module.S7-200 Real-time Collection scene temperature value, set up OPC by CP243-1 ethernet module with WinCC to communicate, utilize WinCC for bridge based on OPC technology simultaneously, Simulink realizes Fractional Order PID control algolithm, make MATLAB/Simulink and S7-200PLC realize real-time Communication for Power, extraction kettle temperature is controlled in real time.

Claims (1)

1. a CO ₂supercritical extract temperature Fractional Order PID control method, the method comprises the following steps:

One, supercritical extract process temperature fractional model is set up;

Supercritical extract process temperature model is fractional model,

The expression formula of fractional model is $G\left(s\right)=\frac{b_m{s}^{{\mathrm{\β}}_m}+...+b_1{s}^{{\mathrm{\β}}_1}+b_0{s}^{{\mathrm{\β}}_0}}{a_n{s}^{{\mathrm{\α}}_n}+\mathrm{...}+a_1{s}^{{\mathrm{\α}}_1}+a_0{s}^{{\mathrm{\α}}_0}}---\left(1\right)$

In formula, α _k, β _k(k=0,1,2 ...) be any real number, β _m> ... > β ₁> β ₀, α _n> ... > α ₁> α ₀, a _k, b _k(k=0,1.2 ...) be constant;

Direct is difficult to modelling controller shown in (1) formula, and often can not get desirable control effects, is therefore necessary the fractional model of complexity to carry out simplify processes, adopts simplified model:

$M\left(s\right)=\frac{k}{{\mathrm{as}}^{1+\mathrm{\β}}+bs+1}{e}^{-Ls}---\left(2\right)$

In formula, k is open-loop gain, β be greater than 0 any real number, a, b and L are constant.

Basic Matlab adopts the simplification of least square method implementation model, and concrete steps are:

Call step (G, t) function, carry out step analysis to the master mould of formula (1) and the simplified model of formula (2) respectively, obtain corresponding response vector y and h, wherein h is the function about c, c=[k, a, α, β, b, L]

The lsqcurvefit function called based on least square curve fit method solve objective function J optimum time c value, and substituted into formula (2) equivalent simplified model can be obtained;

Two, according to the transport function of Fractional Order PID control method, the fractional order PI with internal model control structure is drawn ^λd ^μcontroller;

Internal model control system structure as shown in Figure 1; Wherein: G _iMCs () is internal mode controller; G _ps () is process object; G _ms () is fractional order process model; By asking for reference input R and the transport function between disturbance input D and the output of process Y, easily show that the closed loop response of system is:

$Y\left(s\right)=\frac{G_{IMC}\left(s\right)G_p\left(s\right)}{1+G_{IMC}\left(s\right)\[G_p\left(s\right)-G_m\left(s\right)\]}R\left(s\right)+\frac{\[1-G_{IMC}\left(s\right)G_m\left(s\right)\]}{1+G_{IMC}\left(s\right)\[G_p\left(s\right)-G_m\left(s\right)\]}D\left(s\right)---\left(3\right)$

Can obtain feedback signal by Fig. 1 is

D _e(s)＝[G _p(s)-G _m(s)]U(s)+D(s) (4)

If model is accurate, i.e. G _p(s)=G _m(s), and there is no external disturbance, then controller has desirable controller characteristic, namely free in and under any interference effect, system exports and all equals input setting value, ensures to follow the tracks of the bias free of reference input;

Idealized score rank PI ^λd ^μcontroller transfer function is for being shown below:

G _IMC(s)＝K _p+K _is ^-λ+K _ds ^μ(5)

In formula: K _pfor proportional gain; K _ifor storage gain; K _dfor the differential gain; λ is integration order; μ is differential order; λ, μ >0 and be real number; When λ and μ gets different values, fractional order control device PI ^λd ^μthere is different structures;

In order to obtain the control structure corresponding to (5) formula, by the equivalent construction that the internal model control system Structural Transformation in Fig. 1 is the IMC shown in Fig. 2;

Inner loop feedback controlling unit in Fig. 2 is had:

$G_c\left(s\right)=\frac{G_{IMC}\left(s\right)}{1-G_{IMC}\left(s\right)G_m\left(s\right)}---\left(6\right)$

Now by fractional order control device G _cthe PI that s () changes into (5) corresponding to formula ^λd ^μversion; Process is as follows:

1), factorization process model

By G _ms () resolves into G _m+(s) and G _m-(s) two parts;

I.e. G _m(s)=G _m+(s) G _m-(s) (7)

In formula: G _m-s () represents the minimum phase part of model; G _m+s () represents the non-minimum phase bit position of model.

2), IMC controller is designed;

G _IMC(s)＝G ^-1 _m-(s)F(s) (8)

$F\left(s\right)=\frac{1}{{(fs+1)}^n}---\left(9\right)$

In formula: F (s) is low-pass filter, its objective is to reduce the susceptibility of internal model control system to Unmarried pregnancy and model adaptation, improving the robustness of control system, ensure controller G simultaneously _iMCs () physics can realize; F is filter coefficient; The value of n depends on G _m-s the order of (), target makes the transport function of internal mode controller become fraction, thus can physics realization.

3), PI is obtained ^λd ^μcontroller G _c(s)

$G_c\left(s\right)=\frac{{G^{-1}}_{m-}\left(s\right)}{{(fs+1)}^n-G_{m+}\left(s\right)}---\left(10\right)$

When fractional model is known, according to formula (10) and PI ^λd ^μcontrol formula, by the principle of s polynomial expression every power coefficient correspondent equal, solving can based on the PI of internal model control principle ^λd ^μeach parameter value of controller; In formula, filter parameter f is unique setting parameter of controller, and the control performance of f and system is closely related: when f reduces, the dynamic property of system improves, but robustness is deteriorated; Just in time contrary when f increases, the robustness of system improves, but bad dynamic performance; Select the performance of suitable f Guarantee control system.

Three, fractional order PI ^λd ^μcontrol System Design realizes

Utilize Al-Alaoui+CFE impulse response not political reform to G _cs () carries out discretize realization, and then obtain the fractional order PI of fractional order object in Matlab ^λd ^μcontroller closed module; S7-200 Real-time Collection scene temperature value, set up OPC by CP243-1 ethernet module with WinCC to communicate, utilize WinCC for bridge based on OPC technology simultaneously, Simulink realizes Fractional Order PID control algolithm, make MATLAB/Simulink and S7-200PLC realize real-time Communication for Power, extraction kettle temperature is controlled in real time.