CN103995469A - Method for designing controller of non-minimum-phase constant-temperature continuous stirred tank reactor - Google Patents

Abstract

The invention discloses a method for designing a controller of a non-minimum-phase constant-temperature continuous stirred tank reactor. According to the method for designing the controller, the stability of the zero dynamic inside a system can be guaranteed while it is guaranteed that the external dynamic of the system meets the performance requirement. The method for designing the controller of the non-minimum-phase constant-temperature continuous stirred tank reactor comprises the steps that firstly, system modeling is conducted on the continuous stirred tank reactor (CSTR) according to the actual production process, so that a nonlinear mathematical model of a control system is obtained; secondly, accurate feedback linearization is conducted on an obtained nonlinear system according to the state feedback linearization theory, so that a linear standard form of the nonlinear system is obtained; finally, the nonlinear controller of the constant-temperature CSTR having the non-minimum-phase characteristic is obtained based on the linear standard form according to the quadric form optimal control theory and the Lyapunov stability theory. The controller can be finally obtained through a digital signal processor, namely a DSP controller, by means of software programming.

Description

The controller design method of non-minimum phase isothermal CSTR

Technical field

The present invention relates to controller design and the building method of a kind of non-minimum phase isothermal CSTR (CSTR), relate in particular to controller design and building method thereof that a kind of CSTR of utilization produces this actual chemical process of cyclopentene, belong to automatic control technology field.

Background technology

CSTR is widely used a kind of reactor in polymeric chemical reaction, is chemical reaction system typical in process industrial, nonlinearity, and this chemical process that utilizes CSTR to produce cyclopentene just has typically non-linear, non-minimum phase characteristic.To having the stable control of the system of non-linear non-minimum phase characteristic, be the emphasis that people study always, produced thus various control method and strategy, approximately linear method and infinitesimal geometry method are two kinds of wherein the most frequently used methods.

The approximately linear control method of nonlinear system has developed to obtain comparative maturity as a kind of comparatively effectively control method, by former nonlinear system, a certain equilibrium point place in its state space carries out approximately linear to the main thought of the method, and then linearizing model is carried out to controller design.Yet many chemical systems are all Complex Nonlinear System in essence, when the disturbance that is subject to when system is larger, will there is larger skew in the operating point of system, now adopt linear control method will be difficult to meet actual performance requirement, therefore objectively just need on the basis of nonlinear characteristic that takes explicitly into account real system, design gamma controller.

In the last thirty years, along with the development of nonlinear control theory, nonlinear control method has also obtained research widely, such as various feedback linearization method (as infinitesimal geometry method and method of inverse etc.), Lyapunov direct control method etc.In above-mentioned the whole bag of tricks, with infinitesimal geometry method, use the widest again, the basic thought of this method is to adopt a suitable coordinate transform and an appropriate feedback of status that former nonlinear system is carried out to exact feedback linearization, so just, can obtain former linearization of nonlinear system standard form, and then the linear subsystem in standard form is partly carried out to controller design.This is a kind ofly to make nonlinear system on its whole state space or one of state space enough theory and the method for exact linearization method in large territory, by the control system of this method design, can solve the drawback that traditional approximately linear method is brought.The method is being carried out in linearizing process nonlinear system, by differomorphism, is converted and former nonlinear system can be transformed to two parts: the external dynamic that linear subsystem is described and the internal dynamic of non-linear subsystem description (zero dynamically).For non-minimum phase system (i.e. the system of zero dynamic instability), only the designed controller that can make external dynamic meet certain performance requirement of linear subsystem is but difficult to guarantee that internal system zero is dynamic stable, so non-minimum phase characteristic makes to have run into very big challenge based on differential geometric exact feedback linearization method.

In order really to realize the high performance control to chemical process, just must solve harmful effect non-linear, that non-minimum phase characteristic causes when system is moved, seek a kind of effective control method.

Summary of the invention

1, technical matters

The object of the invention is to for the deficiencies in the prior art, a kind of controller design and construction method of non-minimum phase isothermal CSTR is provided.For CSTR, produce typical non linear, the non-minimum phase characteristic that the chemical process of cyclopentene has, it is a kind of to the effective Design of non-linear controllers of this production run and building method that the present invention will provide, the controller that method construct goes out accordingly can well overcome the adverse effect producing because of non-linear non-minimum phase characteristic in process of production, and can guarantee in the larger range of operation of system, there is good control effect.

2, technical scheme

A kind of Design of non-linear controllers and the building method of non-minimum phase isothermal CSTR of the present invention, the technical scheme of taking is: the nonlinear mathematical model of first setting up cyclopentene production system according to actual condition, use on this basis and take exact feedback linearization theory that infinitesimal geometry is mathematical tool by the state feedback linearization that will control, obtain the standard form system after linearization; Then theoretical based on linear-quadratic optimal control and Lyapunov stability, this chemical producing system of producing cyclopentene for the employing CSTR with non-linear non-minimum phase characteristic, has provided a kind of optimization control method; Finally utilize dsp controller programming to realize the structure of this controller.Specifically comprise following step:

(1) according to actual cyclopentene production run, set up the nonlinear mathematical model of CSTR;

(2) this mathematical model is carried out to exact state feedback linearization, obtain its linearization standard form;

(3) whether checking controlled system is non-minimum phase system;

(4) the non-linear subsystem of standard form system is made to resolution process;

(5) general type of establishing controlled system controller is v=-Gx+v _nLwherein, the state that x is system, G is row gain vector, v _nLit is the nonlinear compensation item for inner zero dynamic stability of controlled system is introduced;

(6) by the theoretical definite undetermined parameter G of Quadratic Optimal Control; By Lyapunov stability theory, determine undetermined parameter v _nL.

In described step (1), what actual production process was selected is to utilize CSTR to produce this chemical process of cyclopentene, sets up nonlinear mathematical model and is shown below:

$\left\{\begin{array}{c}\frac{d{C}_A}{\mathrm{dt}}=\frac{F}{V}(C_{A0}-C_A)-k_1{C}_A-k_3{C}_A^2\\ \frac{d{C}_B}{\mathrm{dt}}=-\frac{F}{V}{C}_B+k_1{C}_A-k_2{C}_B\end{array}\right.$

y＝C _B

Wherein, C _aand C _bbe respectively the input flow velocity of substance A ' and the concentration of B', F be substance A ', V is the Chang Rongji of CSTR; k ₁, k ₂, k ₃the reaction time constant of tri-courses of reaction of corresponding CSTR;

Control target is: by controlling dilution rate F/V output y=C _bbe stabilized in set point C _bS, now substance A ' the corresponding C that is designated as of concentration _aS, (C _aS, C _bS) equilibrium point while regarding system stability as.

In described step (2), choose a coordinate transform

$\left\{\begin{array}{c}z=C_B\\ \mathrm{\η}=\frac{10-C_A}{C_B}\end{array}\right.$

Nonlinear mathematical model is turned to following standard form:

$\left\{\begin{array}{c}\frac{\mathrm{dz}}{\mathrm{dt}}=50(10-\mathrm{z\η})-100z-z\frac{F}{V}=v\\ \frac{\mathrm{d\η}}{\mathrm{dt}}=q(z,\mathrm{\η})=\frac{1500}{z}-150\mathrm{\η}+10z{\mathrm{\η}}^2-\frac{500}{z}\mathrm{\η}+50{\mathrm{\η}}^2\end{array}\right.$

Under this coordinate transform, equilibrium point (C during stable state _aS, C _bS) with new coordinate z and η, represent to be designated as (z ₀, η ₀), wherein $(z_0,{\mathrm{\η}}_0)=(C_{\mathrm{BS}},\frac{10-C_{\mathrm{AS}}}{C_{\mathrm{BS}}}).$

In standard form system, definition for nonlinear system zero dynamically, formula be called as zero dynamic equation, by zero dynamic equation at its equilibrium point (z ₀, η ₀) by the second Taylor series, carry out deconsolidation process, obtain $\stackrel{\·}{\mathrm{\η}}=q(z,\mathrm{\η})=A_z(z-z_0)+A_{\mathrm{\η}}\left(\mathrm{\η}{-\mathrm{\η}}_0\right)+\mathrm{\ω}(z,\mathrm{\η}),$ Wherein $A_Z=\frac{\∂q(z,\mathrm{\η})}{\∂z}{|}_{(z,\mathrm{\η})=(z_0,{\mathrm{\η}}_0)},$ the second order of nonlinear terms ω (z, η) in Taylor expansion and above determine.

Controller is made as:

$v=-G\left(\begin{array}{c}z-z_0\\ \mathrm{\η}-{\mathrm{\η}}_0\end{array}\right)+v_{\mathrm{NL}}$

Undetermined parameter G=(g wherein ₁, g ₂) be row gain vector, undetermined parameter v _nLit is the nonlinear compensation item of introducing in order to make system stability;

In conjunction with the expression formula after the second Taylor series deconsolidation process, obtain state space equation below:

$\left(\begin{array}{c}\stackrel{\·}{z}\\ \stackrel{\·}{\mathrm{\η}}\end{array}\right)=[A-\mathrm{BG}]\left(\begin{array}{c}z-z_0\\ \mathrm{\η}-{\mathrm{\η}}_0\end{array}\right)+\left(\begin{array}{c}{v}_{\mathrm{NL}}\\ \mathrm{\ω}(z,\mathrm{\η})\end{array}\right)$

According to the theoretical definite undetermined parameter G of Quadratic Optimal Control;

Use Lyapunov stability theory to solve undetermined parameter v _nL.

According to Quadratic Optimal Control is theoretical, determine that the step of undetermined parameter G is:

Given quadratic optimal performance index

$J=\frac{1}{2}\underset{0}{\overset{\∞}{\∫}}({\left(\begin{array}{c}z-z_0\\ \mathrm{\η}-{\mathrm{\η}}_0\end{array}\right)}^{T}Q\left(\begin{array}{c}z-z_0\\ \mathrm{\η}-{\mathrm{\η}}_0\end{array}\right)+u^T\mathrm{Ru})\mathrm{dt}$

In formula: Q and R are normal value symmetric positive definite matrix; Feedback gain matrix is by G=R ^-1b ^tp ^*determine P in formula ^*be the symmetrical constant matrices of n * n dimension positive definite, meet following multitude's card and carry matrix algebra equation:

-P ^*A-A ^TP ^*+P ^*BR- ¹B ^TP ^*-Q＝0。

Use Lyapunov stability theory to solve undetermined parameter v _nLstep be:

Be constructed as follows Lyapunov function:

$L(z,\mathrm{\η})={\left(\begin{array}{c}z-z_0\\ \mathrm{\η}-{\mathrm{\η}}_0\end{array}\right)}^{T}P\left(\begin{array}{c}z-z_0\\ \mathrm{\η}-{\mathrm{\η}}_0\end{array}\right)$

Wherein P is the positive definite matrix that meets following Lyapunov Equation:

$A_s^{T}P+P{A}_S=-\stackrel{\‾}{Q}$

A in formula _s=[A-BG], and for any positive definite matrix;

To Lyapunov function, differentiate obtains and make can determine v thus _nL.

Controller is by realizing with DSP (digital signal processor), and the connected mode of DSP and CSTR is: the input substance A of CSTR system ' concentration and the concentration of exporting material B' through 2 concentration sensors, connect respectively the input end of dsp controller; After A/D conversion, computing, D/A conversion, export analog quantity control signal, then through 4-20mA current transducer, be converted to the input control signal of electric control valve, automatically regulate the aperture of electric control valve with the flow of control inputs material and output material.

3, technique effect

The invention provides a kind of Design of non-linear controllers and building method of non-minimum phase isothermal CSTR.The present invention is applicable to have arbitrarily the control of the Complex Nonlinear System of non-minimum phase characteristic, and the design concept of controller is simple, without advanced mathematical derivation, realizes simply, has very strong using value.

The invention has the advantages that:

A. the given controller design method of the present invention is based upon on the basis of infinitesimal geometry exact feedback linearization method, can not lose the original information of system in theory by the designed gamma controller of the given controller design method of the present invention.

B. in the given controller design method of the present invention, even the non-linear subsystem part in standard form is carried out to resolution process by the method for Taylor expansion, compare with the method for approximately linear, also there is the advantage that drop-out is few, this is mainly reflected in two aspects: first, the method is only launched the partial status of system, and the method for approximately linear is that whole system is carried out to approximately linear processing; Secondly, can reduce as much as possible by improving the exponent number of Taylor expansion the loss of system information.

C. the controller design method that the present invention proposes is applicable to any nonlinear system, especially has the nonlinear system of non-minimum phase characteristic, therefore can be applied in all kinds of Practical Project systems, has broad application prospects.

D. the given controller design method of the present invention is not only applicable to single-input single-output nonlinear system, and is easy to be generalized in multiple-input and multiple-output nonlinear system.

E. controller design method proposed by the invention, without advanced knowwhy and complicated mathematical derivation, is easy to Project Realization.

Accompanying drawing explanation

Fig. 1 utilizes CSTR to produce the application scenarios schematic diagram of this actual chemical process of cyclopentene.Electric control valve 5 is controlled the input flow rate of substance A (cyclopentadiene), and electric control valve 6 is controlled the delivery rate of substance B (cyclopentene).

Fig. 2 is the structural drawing of control system.Wherein u (F/V) is controlled input, y (C _b) for controlling output, x (C _a) be state variable.

Fig. 3 is the connection diagram of controller and actual control system.Wherein input signal is u, and state variable is x, and output is y.

Fig. 4 is that the given controller design method of the present invention is to inner zero dynamic C _acontrol effect emulation figure, can see that the method can effectively guarantee that internal system zero is dynamic stable.

Fig. 5 is that the given controller design method of the present invention is to external dynamic C _bthat is the control effect emulation figure of the controlled output of system, can see that the method well makes external dynamic meet control performance requirement.

Fig. 6 be according to the present invention to the analogous diagram of the controller F/V that designs of controller design method.

Fig. 7 adopts dsp controller as the connection diagram of control device of the present invention.Comprising CSTR system 1, dsp controller 2,4-20mA current transducer 3,4, electric control valve 5,6, concentration sensor 7, concentration sensor 8, protected location 9, man-machine interaction 10.

Fig. 8 adopts dsp controller 2 to realize software flow figure of the present invention for control core.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.Following examples are only for technical scheme of the present invention is more clearly described, and can not limit the scope of the invention with this.

A kind of Design of non-linear controllers and the building method of non-minimum phase isothermal CSTR of the present invention, its specific embodiments is: first according to the feedback linearization theory of nonlinear system, the system that will control is carried out to exact feedback linearization; Then based on linear-quadratic optimal control and Lyapunov stability theory, the actual chemical system that adopts CSTR production cyclopentene to have so non-linear non-minimum phase characteristic is optimized to controller design; With dsp controller, be finally that control core is programmed and realized the controller of the present invention design.During concrete enforcement, according to different requirements, adopt different hardware and softwares to realize.

Concrete enforcement is divided into following 8 steps:

1. set up the mathematical model of real system.

The present invention mainly considers to utilize CSTR to produce this actual chemical process of cyclopentene, the scene schematic diagram of this process as shown in Figure 1, in CSTR, electric control valve 5 is controlled the delivery rate of substance A ' the input flow rate of (cyclopentadiene), electric control valve 6 control substance Bs ' (cyclopentene).

As shown in Figure 2, wherein u (F/V) is controlled input to structural drawing, y (C _b) for controlling output, x (C _a) be state variable.

The chemical equation of this process can be expressed as:

Above-mentioned reaction generates major product cyclopentene (B') and secondary product bicyclopentadiene (D') by cyclopentadiene (A'), and continues these three courses of reaction formations of reaction generation secondary product cyclopentanone (C') by cyclopentene.The course of reaction of A' → B' can be designated as to process 1, the course of reaction of B' → C' is designated as process 2, and the course of reaction of 2A' → D' is designated as process 3, based on substance A ' and mol balance and the energy conservation of B', the mathematical model that can set up this chemical process is as follows:

$\left\{\begin{array}{c}\frac{d{C}_A}{\mathrm{dt}}=\frac{F}{V}(C_{A0}-C_A)-k_1{C}_A-k_3{C}_A^2\\ \frac{d{C}_B}{\mathrm{dt}}=-\frac{F}{V}{C}_B+k_1{C}_A-k_2{C}_B\end{array}\right.$

y＝C _B

Wherein, C _aand C _bbe respectively the input flow rate of substance A ' and the concentration of B', F be substance A ', V is the Chang Rongji of CSTR.Other constant is: substance A ' initial concentration be C _a0=10gmol/l, the reaction time constant of three courses of reaction is respectively k ₁=50h ^-1, k ₂=100h ^-1, k ₃=10l/gmol h.In the present embodiment, control target is: by controlling dilution rate F/V output y=C _bbe stabilized in set point 1.05gmol/l, i.e. C _bS=1.05gmol/l, now easily calculates, and the corresponding steady-state value of its dependent variable is: dilution rate during final stable state is (F/V) _s=28.428h ^-1, substance A ' Css be C _as=2.697gmol/l.

2. theoretical by infinitesimal geometry exact feedback linearization, can choose a coordinate transform

$\left\{\begin{array}{c}z=C_B\\ \mathrm{\η}=\frac{10-C_A}{C_B}\end{array}\right.$

Nonlinear control system in the 1st step is turned to following standard form:

$\left\{\begin{array}{c}\frac{\mathrm{dz}}{\mathrm{dt}}=50(10-\mathrm{z\η})-100z-z\frac{F}{V}=v\\ \frac{\mathrm{d\η}}{\mathrm{dt}}=q(z,\mathrm{\η})=\frac{1500}{z}-150\mathrm{\η}+10z{\mathrm{\η}}^2-\frac{500}{z}\mathrm{\η}+50{\mathrm{\η}}^2\end{array}\right.$

Under this coordinate transform, equilibrium point (C during stable state _aS, C _bS) with new coordinate z and η, represent to be designated as (z ₀, η ₀), wherein $(z_0,{\mathrm{\η}}_0)=(C_{\mathrm{BS}},\frac{10-C_{\mathrm{AS}}}{C_{\mathrm{BS}}})=\left(\mathrm{1.05,6.9552}\right).$

3. in the standard form system of the 2nd step, define for nonlinear system zero dynamically, formula be called as zero dynamic equation, this is in second state equation and makes z=0 gained.If the zero dynamic instability of system, claims that nonlinear system is non-minimum phase.Making z=0 is generalized case, and the practical significance of its representative is the equilibrium point of system, for this practical problems, should get z=1.05.Be not difficult to verify the zero dynamic instability of this system, this has just illustrated that using CSTR to generate the so actual chemical producing system of cyclopentene is the system with typical non linear, non-minimum phase characteristic.

By zero dynamic equation above by the second Taylor series (ignoring other higher order term), do as lower linear deconsolidation process:

$\stackrel{\·}{\mathrm{\η}}=q(z,\mathrm{\η})=2209.5(z-1.05)+215.3887\left(\mathrm{\η}-6.9552\right)+\mathrm{\ω}(z,\mathrm{\η})$

Wherein

ω(z,η)＝-1708.3(z-1.05) ²+296.3093(z-1.05)(η-6.9552)+60.5(η-6.9552) ²

The system of linearization standard form so is just equivalent to following matrix form:

$\left(\begin{array}{c}\stackrel{\·}{z}\\ \stackrel{\·}{\mathrm{\η}}\end{array}\right)=A\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)+\mathrm{Bv}+\left(\begin{array}{c}0\\ \mathrm{\ω}(z,\mathrm{\η})\end{array}\right)=\left(\begin{array}{cc}0& 0\\ 2209.5& 215.3887\end{array}\right)\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)+\left(\begin{array}{c}1\\ 0\end{array}\right)v+\left(\begin{array}{c}0\\ \mathrm{\ω}(z,\mathrm{\η})\end{array}\right)$

Wherein:

$v=a(z,\mathrm{\η})+b(z,\mathrm{\η})u=50(10-\mathrm{z\η})-100z-z\frac{F}{V}$

5. the controller of uniting of setting up departments is:

$v=-G\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right){+v}_{\mathrm{NL}}=-g_1(z-1.05)-g_2(\mathrm{\η}-6.9552)+v_{\mathrm{NL}}$

Undetermined parameter G=(g wherein ₁, g ₂) be row gain vector, undetermined parameter v _nLit is the nonlinear compensation item of introducing in order to make system stability.The state equation that this controller associating the 4th step is obtained just has:

$\left(\begin{array}{c}\stackrel{\·}{z}\\ \stackrel{\·}{\mathrm{\η}}\end{array}\right)=[A-\mathrm{BG}]\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)+\left(\begin{array}{c}{v}_{\mathrm{NL}}\\ \mathrm{\ω}(z,\mathrm{\η})\end{array}\right)=\left(\begin{array}{cc}-g_1& -g_2\\ 2209.5& 215.3887\end{array}\right)\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)+\left(\begin{array}{c}{v}_{\mathrm{NL}}\\ \mathrm{\ω}(z,\mathrm{\η})\end{array}\right)$

6. according to the theoretical definite feedback gain matrix G of Quadratic Optimal Control.Can verify that this system is can control completely, given quadratic optimal performance index

$J=\frac{1}{2}\underset{0}{\overset{\∞}{\∫}}({\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)}^{T}Q\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)+u^T\mathrm{Ru})\mathrm{dt}$

In formula: Q and R are normal value symmetric positive definite matrix (conventionally Q is elected as to diagonal matrix, R elects unit matrix as).By the theoretical known system of Quadratic Optimal Control, have unique optimal control law, feedback gain matrix is by G=R ^-1b ^tp ^*determine P in formula ^*be the symmetrical constant matrices of n * n dimension positive definite, meet following multitude's card and carry matrix algebra equation:

-P ^*A-A ^TP ^*+P ^*BR ^-1B ^TP ^*-Q＝0

7. use Lyapunov stability theory to solve v _nL.Be constructed as follows Lyapunov function:

$L(z,\mathrm{\η})={\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)}^{T}P\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)$

Wherein P is the positive definite matrix that meets following Lyapunov Equation:

$A_s^{T}P+P{A}_S=-\stackrel{\‾}{Q}$

A in formula _s=[A-BG], and for any positive definite matrix, generalized case can be selected for unit matrix I.

To Lyapunov function, differentiate obtains:

$\stackrel{\·}{L}(z,\mathrm{\η})=-(z-1.05,\mathrm{\η}-6.9552)\stackrel{\‾}{Q}\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)+2\left(\begin{array}{cc}{v}_{\mathrm{NL}}& \mathrm{\ω}(z,\mathrm{\η})\end{array}\right)P\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)$

According to Lyapunov theorem of stability, make

$v=-G\left(\begin{array}{c}z-1.05\\ \mathrm{\η}-6.9552\end{array}\right)+v_{\mathrm{NL}}=-g_1(z-1.05)-g_2(\mathrm{\η}-6.9552)+v_{\mathrm{NL}}$

Closed-loop system under control action is stable, as long as .Due to be positive definite, must have $-(z-1.05,\mathrm{\&eta;}-6.9552)\stackrel{\&OverBar;}{Q}\left(\begin{array}{c}z-1.05\\ \mathrm{\&eta;}-6.9552\end{array}\right)<0,$ Therefore to make closed-loop system stable, only need

$c=\left(\begin{array}{cc}{v}_{\mathrm{NL}}& \mathrm{\&omega;}(z,\mathrm{\&eta;})\end{array}\right)P\left(\begin{array}{c}z-1.05\\ \mathrm{\&eta;}-6.9552\end{array}\right)\&le;0$

Above formula c=0 might as well be made, therefrom just v can be solved _nL.

So just, can controlled rule v.Recycling v=a (z, η)+b (z, η) u, counter solving

$u=\frac{v-a(z,\mathrm{\&eta;})}{b(z,\mathrm{\&eta;})}$

Above formula is exactly the final control law of the given non-linear non-minimum phase system of the present invention, and under the control action of this closed loop controller, as shown in Figure 3, wherein u (F/V) is controlled input to the structural drawing of system, y (C _b) for controlling output, x (C _a) be state variable.The analogous diagram of control effect is the (Q=diag (10 in emulation as Figure 4-Figure 6 ⁵, 1), R=1).

8. adopting dsp controller is that control core coding is realized above-mentioned controller design method.The connection diagram of dsp controller and CSTR as shown in Figure 7.Sample the respectively concentration C of the interior substance A of continues stirred-tank reactor 1 ' (cyclopentadiene) and substance B ' (cyclopentene) of concentration sensor 7, concentration sensor 8 _a, C _bthe A/D modular converter, the dsp controller 2 that as the feedback quantity of controller, send in dsp controller 2 are exported 2 tunnel analog quantity control signals after changing through computing and by D/A, again through 2 4-20mA current transducers 3,4 are converted to respectively electric control valve 5,6 input control signal, realize and automatically regulate the aperture of electric control valve 5,6 with the input flow rate of control loop pentadiene and the delivery rate of cyclopentene.And keep the aperture of electric control valve 8 identical with the aperture of electric control valve 7, to guarantee that in reactor, liquid volume is constant.Dsp controller 2 is also connected with CSTR by protected location 9, for the protection to CSTR system.Man-machine interaction 10 is responsible for realizing to the real-time demonstration of CSTR system and is controlled.

The program of DSP comprises a master routine and two interrupt service routines (abnormal interrupt service routine, Interruption service routine), and program flow diagram as shown in Figure 8.The operation of DSP program, from master routine, is first carried out initialization, then enters data and shows and the circulation of fault diagnosis, if receive master routine the finish command, finishes master routine.Master routine data show with fault diagnosis during, by certain hour interval run timing interrupt service routine, if there is fault, operation exception interrupt service routine.The treatment scheme of Interruption service routine is: first master routine is carried out to scene protection; next by various sensors and A/D conversion image data; again data are carried out to filtering processing; then filtered data are carried out to computing; afterwards the result obtaining is outputed in the storer of display unit, last restoring scene also returns to master routine.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, do not departing under the prerequisite of the technology of the present invention principle; can also make some improvement and distortion, these improvement and distortion also should be considered as protection scope of the present invention.

Claims (8)

1. the controller design method of non-minimum phase isothermal CSTR, is characterized in that:

(1) according to actual cyclopentene production run, set up the nonlinear mathematical model of CSTR;

(2) this mathematical model is carried out to exact state feedback linearization, obtain its linearization standard form;

(3) whether checking controlled system is non-minimum phase system;

(4) the non-linear subsystem of standard form system is made to resolution process;

(5) general type of establishing controlled system controller is v=-Gx+v _nLwherein, the state that x is system, G is row gain vector, v _nLit is the nonlinear compensation item for inner zero dynamic stability of controlled system is introduced;

(6) by the theoretical definite undetermined parameter G of Quadratic Optimal Control; By Lyapunov stability theory, determine undetermined parameter v _nL.

2. the controller design method of non-minimum phase isothermal CSTR according to claim 1, it is characterized in that, in described step (1), what actual production process was selected is to utilize CSTR to produce this chemical process of cyclopentene, sets up nonlinear mathematical model and is shown below:

$\left\{\begin{array}{c}\frac{d{C}_A}{\mathrm{dt}}=\frac{F}{V}(C_{A0}-C_A)-k_1{C}_A-k_3{C}_A^2\\ \frac{d{C}_B}{\mathrm{dt}}=-\frac{F}{V}{C}_B+k_1{C}_A-k_2{C}_B\end{array}\right.$

y＝C _B

Wherein, C _aand C _bbe respectively the input flow velocity of substance A ' and the concentration of B', F be substance A ', V is the Chang Rongji of CSTR;

Control target is: by controlling dilution rate F/V output y=C _bbe stabilized in set point C _bS, now substance A ' the corresponding C that is designated as of concentration _aS, (C _aS, C _bS) equilibrium point while regarding system stability as.

3. the controller design method of non-minimum phase isothermal CSTR according to claim 2, is characterized in that, in described step (2), chooses a coordinate transform

$\left\{\begin{array}{c}z=C_B\\ \mathrm{\&eta;}=\frac{10-C_A}{C_B}\end{array}\right.$

Nonlinear mathematical model is turned to following standard form:

$\left\{\begin{array}{c}\frac{\mathrm{dz}}{\mathrm{dt}}=50(10-\mathrm{z\&eta;})-100z-z\frac{F}{V}=v\\ \frac{\mathrm{d\&eta;}}{\mathrm{dt}}=q(z,\mathrm{\&eta;})=\frac{1500}{z}-150\mathrm{\&eta;}+10z{\mathrm{\&eta;}}^2-\frac{500}{z}\mathrm{\&eta;}+50{\mathrm{\&eta;}}^2\end{array}\right.$

Under this coordinate transform, equilibrium point (C during stable state _aS, C _bS) with new coordinate z and η, represent to be designated as (z ₀, η ₀), wherein $(z_0,{\mathrm{\&eta;}}_0)=(C_{\mathrm{BS}},\frac{10-C_{\mathrm{AS}}}{C_{\mathrm{BS}}}).$

4. the controller design method of non-minimum phase isothermal CSTR according to claim 3, is characterized in that, in standard form system, and definition for nonlinear system zero dynamically, formula be called as zero dynamic equation, by zero dynamic equation at its equilibrium point (z ₀, η ₀) by the second Taylor series, carry out deconsolidation process, obtain $\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=q(z,\mathrm{\&eta;})=A_z(z-z_0)+A_{\mathrm{\&eta;}}\left(\mathrm{\&eta;}{-\mathrm{\&eta;}}_0\right)+\mathrm{\&omega;}(z,\mathrm{\&eta;}),$ Wherein the second order of nonlinear terms ω (z, η) in Taylor expansion and above determine.

5. the controller design method of non-minimum phase isothermal CSTR according to claim 3, is characterized in that, controller is made as:

$v=-G\left(\begin{array}{c}z-z_0\\ \mathrm{\&eta;}-{\mathrm{\&eta;}}_0\end{array}\right)+v_{\mathrm{NL}}$

Undetermined parameter G=(g wherein ₁, g ₂) be row gain vector, undetermined parameter v _nLit is the nonlinear compensation item of introducing in order to make system stability;

In conjunction with the expression formula after the second Taylor series deconsolidation process, obtain state space equation below:

$\left(\begin{array}{c}\stackrel{\&CenterDot;}{z}\\ \stackrel{\&CenterDot;}{\mathrm{\&eta;}}\end{array}\right)=[A-\mathrm{BG}]\left(\begin{array}{c}z-z_0\\ \mathrm{\&eta;}-{\mathrm{\&eta;}}_0\end{array}\right)+\left(\begin{array}{c}{v}_{\mathrm{NL}}\\ \mathrm{\&omega;}(z,\mathrm{\&eta;})\end{array}\right)$

According to the theoretical definite undetermined parameter G of Quadratic Optimal Control;

Use Lyapunov stability theory to solve undetermined parameter v _nL.

6. the controller design method of non-minimum phase isothermal CSTR according to claim 5, is characterized in that, according to Quadratic Optimal Control is theoretical, determines that the step of undetermined parameter G is:

Given quadratic optimal performance index

$J=\frac{1}{2}\underset{0}{\overset{\&infin;}{\&Integral;}}({\left(\begin{array}{c}z-z_0\\ \mathrm{\&eta;}-{\mathrm{\&eta;}}_0\end{array}\right)}^{T}Q\left(\begin{array}{c}z-z_0\\ \mathrm{\&eta;}-{\mathrm{\&eta;}}_0\end{array}\right)+u^T\mathrm{Ru})\mathrm{dt}$

In formula: Q and R are normal value symmetric positive definite matrix; Feedback gain matrix is by G=R ^-1b ^tp ^*determine P in formula ^*be the symmetrical constant matrices of n * n dimension positive definite, meet following multitude's card and carry matrix algebra equation:

-P ^*A-A ^TP ^*+P ^*BR- ¹B ^TP ^*-Q＝0。

7. the controller design method of non-minimum phase isothermal CSTR according to claim 5, is characterized in that, uses Lyapunov stability theory to solve undetermined parameter v _nLstep be:

Be constructed as follows Lyapunov function:

$L(z,\mathrm{\&eta;})={\left(\begin{array}{c}z-z_0\\ \mathrm{\&eta;}-{\mathrm{\&eta;}}_0\end{array}\right)}^{T}P\left(\begin{array}{c}z-z_0\\ \mathrm{\&eta;}-{\mathrm{\&eta;}}_0\end{array}\right)$

Wherein P is the positive definite matrix that meets following Lyapunov Equation:

$A_s^{T}P+P{A}_S=-\stackrel{\&OverBar;}{Q}$

A in formula _s=[A-BG], and for any positive definite matrix;

To Lyapunov function, differentiate obtains and make can determine v thus _nL.

8. according to the controller design method of the non-minimum phase isothermal CSTR described in any one in claim 1-7, it is characterized in that, controller is by realizing with DSP, and the connected mode of DSP and CSTR is: the input substance A of CSTR system ' concentration and the concentration of output material B' through 2 concentration sensors, connect respectively the input end of dsp controller; After A/D conversion, computing, D/A conversion, export analog quantity control signal, then through 4-20mA current transducer, be converted to the input control signal of electric control valve, automatically regulate the aperture of electric control valve with the flow of control inputs material and output material.