CN100461036C - Resolution design method of decoupling controller of multivariable time delay system - Google Patents

Abstract

A method for designing decouple controller analysis of multivariable time lag system includes carrying on identification of transfer function matrix for chemical industrial multivariable time lag procedure, designing two regulation factors being able to be realized by controller and designing decouple controller, leading designed controller to be infinite high order if GO ( s ) still contains time lag item after object transfer function matrix is decomposed, applying controller order-decreasing technique to carry out order-decreasing on controller.

Description

Resolution design method of decoupling controller of multivariable time delay system

Technical field

What the present invention relates to is the method in a kind of industrial process control technology field, specifically is a kind of resolution design method of decoupling controller of multivariable time delay system.

Background technology

Ubiquity has the multiple-input and multiple-output process of transmission time lag in the Chemical Manufacture, and along with the fast development of various vanguard technologies, increasing production run is constructed to the higher-dimension multivariable control system, thereby realizes producing expeditiously high-quality product.Yet, make the single argument control method that great majority have developed be difficult to multivariable process owing to have crosslinked coupling between each output channel of multivariable process.Research method at multi-variable system mainly comprises linear quadratic optimum (LQG) method for designing, Quantitative Feedback method, Nyquist array method, sequence return difference method, the dyad method of development, forecast Control Algorithm, multivariate internal mold method for designing etc. at present.Wherein the internal mold method for designing at multi-variable system requires controlling object is carried out inside and outside decomposition.But up to now, inside and outside decomposition method all is based on state-space method and uses numerical operation, and decomposition method can only be applied to reasonable object, and to containing the multi-variable system of time lag, time-dependent system all can't be used.Other method then can not well solve multi-variable system Robustness Design problem.The most important thing is above-mentioned method for designing only at the multi-variable system that does not include time lag, then powerless to the multivariate object that comprises time lag.At present, the representative decoupling control method at the time lag multi-variable system mainly comprises the method for designing of static decoupling device, dynamic decoupling device, order decoupling zero and decoupling controller matrix, but the controller that these methods obtain mostly is not easy to online adjusting and setting, and used relevant speciality knowwhy is more, is not easy to be grasped and promote the use of by engineering technical personnel.

Find through literature search prior art, people such as Dong have delivered " Design of Robust Multivariable PID Controllers via IMC " (based on internal model control structure design robust multivariable PID controller) in " Proceedings of the AmericanControl Conference " (U.S.'s control meeting) (1997 the 5th volume 3380-3384 pages or leaves), a kind of decoupling controller method for designing is proposed in the literary composition, this method is the controlling object model and the general type of the optimum decoupling controller that decomposition obtains based on object model in theory all uses approximation method to be similar to, and equates to obtain the formula that embodies of decoupling controller then by corresponding element.Its deficiency is not provide optimum controlling object decomposition step, and this makes the practical application of this method be subjected to very big restriction.

Summary of the invention

The objective of the invention is to overcome deficiency of the prior art, provide a kind of at the resolution design method of decoupling controller of multivariable time delay system that comprises time lag.Make it adopt the input and output method for designing, method for designing is understood easily, and is easy to use, do not need status information.The controller of the present invention design can be realized system's output decoupling, and only need regulate limited Several Parameters, quantitative regulating system performance and robustness that just can be easily and effectively.

The present invention is achieved by the following technical solutions, and concrete steps of the present invention are as follows:

1) at first to the transfer function matrix identification model of chemical industry multivariable time-lag process

Wherein $g_{\mathrm{ij}}\left(s\right)=g_{\mathrm{oij}}\left(s\right)e^{-{\mathrm{\θ}}_{\mathrm{ij}}s},$ It is meant i transport function that is input to j output from controlled process, g _0ij(s) be the reasonable transport function part of its stable canonical, θ _IjBe its corresponding process transmission time lag, i, j=1 ... p decomposes, and decomposed form is as follows:

G(s)＝G _D(s)G _O(s)， (1)

Wherein,

$G_D\left(s\right)=\mathrm{diag}\{e^{{-\mathrm{\θ}}_{1}s},\·\·\·,e^{{-\mathrm{\θ}}_{p}s}\},---\left(2\right)$

$G_O\left(s\right)=G_D^{-1}\left(s\right)G\left(s\right),---\left(3\right)$

θ wherein _iBe taken as G ^-1(s) maximum discreet value in the i row.

2) be designed for attainable two regulatory factors of assurance controller:

$G_N\left(s\right)=\mathrm{diag}\{\underset{j=1}{\overset{r_z}{\mathrm{\Π}}}{\left(\frac{-s+z_j}{s+z_j^{*}}\right)}^{k_{1j}},\·\·\·,\underset{j=1}{\overset{r_z}{\mathrm{\Π}}}{\left(\frac{-s+z_j}{s+z_j^{*}}\right)}^{k_{\mathrm{pj}}}\},---\left(4\right)$

$J\left(s\right)=\mathrm{diag}\{\frac{1}{{({\mathrm{\&lambda;}}_{1}s+1)}^{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C200510112229E00162.png,C200510112229E00172.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{({\mathrm{\&lambda;}}_{n}s+1)}^{p_n}}\}---\left(5\right)$

Z wherein _jBe G ^-1(s) unsettled limit in the i row, k _IjBe z _jMaximum number.λ _iBe controller adjustable parameter, p _iThe maximal phase of getting i column element among the G (s) is to order.

3) the controller C of design decoupling zero is following form:

$C\left(s\right)=\frac{G^{-1}\left(s\right)G_D\left(s\right)G_N\left(s\right)J\left(s\right)}{I-G_D\left(s\right)G_N\left(s\right)J\left(s\right)}.---\left(6\right)$

Need explanation, in above-mentioned design process, if G after the target transfer function matrix decomposition _O(s) still contain the time lag item in, this controller that will cause designing is infinite high-order, at this moment uses the controller reducing technique that this controller is carried out depression of order.

The present invention can directly move enforcement on existing industrial computer, specific implementation process is as follows:

A) design slidably slide block on the configuration interface, coding is consistent the variation of adjustable parameter in moving of slide block and the decoupling controller.The initial value of elder generation's determining section parameter when adjusting comprises that mainly according to actual condition the model of controlling object being carried out identification obtains the object model parameter; According to the definite performance index parameter of expecting of the requirement of dynamic performance and robust stability, controller adjustable parameter initial value, common desirable 1.By industrial computer data are delivered among the storage unit RAM then; And system is set on the configuration interface is " off-line " adjustment state.Wherein multivariate object on-line identification method have a variety of, as relay feedback method etc.

B) click the " RUN " key on the configuration interface, the CPU that starts industrial computer thus carries out the program of the realization decoupling controller that weaves in advance.Innovation draws this programmed algorithm on the basis of the factorization rule of above-mentioned new proposition just.

C) the dull slide block of regulating on the configuration interface is regulated the adjustable parameter of decoupling controller, and the observing system closed-loop response curve, determines the optimizing controller parameter thus.Regulate parameter lambda _iThe rule of adjusting: turn λ down _iCan accelerate corresponding process output response speed, improve the nominal performance of control system, but the output energy of corresponding required i controller will increase, and its required output energy that provides of pairing topworks also will increase, can tend to exceed its range of capacity, in addition, when facing the not modeling dynamic perfromance of controlled process, be easy to show aggressive behavior, be unfavorable for the robust stability of control system; On the contrary, increase λ _lCorresponding process output response is slowed down, but the output energy of desired i controller reduces, and the needed output energy of its pairing topworks also can reduce, thereby help improving the robust stability of control system.So actual adjusting parameter lambda of adjusting _lThe time, should between the output capacity of the nominal performance of control system output response and each controller and topworks thereof, weigh.

D) system being set on the configuration interface is " online " adjustment state, and the CPU that starts industrial computer thus reads the optimizing controller parameter, calculates discrete domain decoupling zero control formula according to the discretize formula then, obtains controlled quentity controlled variable optimum under the current time off-line state.

E) to u _j(k) carry out amplitude limit, prevent that integration is saturated, by exporting actuator to after the D/A conversion, affact controlled device then, controlled device is operated in the given scope by actuator.Show on the configuration interface this moment is system's closed-loop response curve under the online situation, then with and the off-line regulative mode under identical method carry out on-line fine, so go round and begin again and realize controlling.

Described d) in, calculate discrete domain decoupling zero control formula, obtain controlled quentity controlled variable optimum under the current time off-line state according to the discretize formula, specific as follows:

At first each element in the controller is carried out discretize, and changes into the canonical form of shape suc as formula (7):

$C_{\mathrm{ij}}\left(z\right)=\frac{b_1+b_2{z}^{-1}+\&CenterDot;\&CenterDot;\&CenterDot;b_{m-1}{z}^{-(\mathrm{\&beta;}-1)}}{a_1+a_2{z}^{-1}+\&CenterDot;\&CenterDot;\&CenterDot;a_{n-1}{z}^{-(\mathrm{\&alpha;}-1)}}=\frac{u_{\mathrm{i\; j}}\left(z\right)}{e_{\mathrm{ij}}\left(z\right)}---\left(7\right)$

Get the weight expression of controller output controlled quentity controlled variable by expression formula (7):

a ₁u _ij(z)+a ₂u _ij(z-1)+…a _n-1u _ij(z-α+1) (8)

＝b ₁e _ij(z)+b ₂e _ij(z-1)+…b _m-1e _ij(z-β+1)

Being write following formula as the time recursive form is following form:

a ₁u _ij(k) ⁺a ₂u _ij(k-1)+…a _n-1u _ij(k-α+1) (9)

＝b ₁e _ij(k)+b ₂e _ij(k-1)+…b _m-1e _ij(k-β+1)

The expression formula of controlled thus device output controlled quentity controlled variable is as shown in the formula shown in (10):

$u_j\left(k\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{i\; j}}\left(k\right)---\left(10\right)$

α in the above-mentioned expression formula (8), β represents the order of each element molecule denominator of controller respectively.In expression formula (8-10) formula:

u _Ij(k)-current (k) C constantly _Ij(z) the output controlled quentity controlled variable of controller

e _Ij(k)-current (k) C constantly _Ij(z) the input deviation amount of controller

u _Ij(k-α+1)-current (k-α+1) is C constantly _Ij(z) the output controlled quentity controlled variable of controller

e _Ij(k-β+1)-current (k-β+1) is C constantly _Ij(z) the input deviation amount of controller

u _j(k)-current (k) j of controller exported controlled quentity controlled variable constantly.

The a complete set of adjustment process of the present invention can be finished on industrial computer configuration interface, compares with traditional multivariate method for designing, and the maximum characteristics at the controller design method of multivariable time delay system engineering model that the present invention provides are to have very strong practicality.The controller of design can be realized system's closed loop response decoupling zero, and design of Controller has optimum, the characteristics of parsing.When controlling, be difficult to the robustness of analytic system, use the present invention then can realize the quantitative adjusting of system performance and robustness with traditional decoupling control method.The present invention can also be used to contain the unstable non-minimum phase system of time lag and the multivariable process that contains states with time-delay except being used for the common multi-variable system that contains time lag.

Verified, the method for designing that the present invention provides is optimum, the present invention and Morari and Zafiriou, the difference of internal model control method is in 1989, internal model control be based on state space theory at the non-decoupling method for designing of stablizing reasonable object.

Description of drawings

The design proposal synoptic diagram of the decoupling controller that Fig. 1 provides for the present invention.

The structural representation that Fig. 2 adopts during for actual motion of the present invention.

The closed loop controlling structure figure that the decoupling controller method for designing that Fig. 3 provides for the present invention is adopted.

The configuration interface that Fig. 4 provides for the present invention.

Wherein, Fig. 4 (a) shows the configuration interface under the original state, and Fig. 4 (b) shows the configuration interface under the duty.

Fig. 5 is the output closed-loop response of rectification column object.

Wherein, Fig. 5 (a) shows the response curve of system's output under first step input action, Fig. 5 (b) shows the response curve of system's output under second step input action, represent with dotted line by system's output response curve that the present invention does not provide under the controller action that process is approximate, provide and export response curve through the system under the approximate controller action and represent with solid line by the present invention.

Fig. 6 is under the uncertain effect of the property taken advantage of, and the output closed-loop of rectification column object responds.

Wherein, Fig. 6 (a) shows the response curve of system's output under first step input action, Fig. 6 (b) shows the response curve of system's output under second step input action, dotted line represents that system is under the uncertain situation of the property taken advantage of, the output response curve that does not have the adjustment control parameter, solid line is represented system under the uncertain situation of the property taken advantage of, the output response curve after the adjustment control parameter.

Embodiment

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

As shown in Figure 1: the multivariate controlled device of band time lag link, the performance of expectation and robustness requirement, regulator and controller are the important module of forming the technical solution used in the present invention.Wherein with the time lag multivariate to as if controlled industrial object identification obtained, simultaneously, require multinomial control expectation such as controlled accuracy, rapidity and stability index according to field control.The parameter of these identification objects self and the requirement of performance and robustness are taken all factors into consideration in the regulator link.Each parameter of optimal controller is determined in the analysis emulation of process regulator, makes controller can effectively control on-the-spot object under the condition of output that meets the expectation.Most important link is a regulator in this process as can be seen, the present invention under this control idea key design the structure of new controller, and design the simple rule of regulating of a cover controller be set.

Embodiment:

Chemical industry hydrocarbonylation thing fractionator process for a broad research employing

The first step, design slidably slide block on the configuration interface, it is 1 that controller adjustable parameter initial value is set.By industrial computer data such as target model identification parameter are delivered among the storage unit RAM; And system is set on the configuration interface is " off-line " adjustment state.Set up a closed-loop control system according to the closed loop controlling structure figure shown in the accompanying drawing 3.The identification model of chemical industry hydrocarbonylation thing fractionator process is as follows:

$G\left(s\right)=\left[\begin{array}{cc}\frac{12.8e^{-s}}{16.7s+1}& \frac{-18.9e^{-3s}}{21s+1}\\ \frac{6.6e^{-7s}}{10.9s+1}& \frac{-19.4e^{-3s}}{14.4s+1}\end{array}\right],$

Second step: click the " RUN " key on the configuration interface, the CPU that starts industrial computer calls " off-line control program " parsing that weaves in advance and designs optimal controller.Concrete computation process is as follows:

(1) according to formula (1), (2) and (3) the process transfer function matrix is decomposed:

G(s)＝G _D(s)G _O(s)

Wherein

$G_D\left(s\right)=\left[\begin{array}{cc}{e}^{-\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="C200510112229E00152.png,C200510112229E00172.png"\; state="\{\{state\}\}">s</figure-callout>}}& 0\\ 0& e^{-3s}\end{array}\right]$

$G_O\left(s\right)=G_D^{-1}\left(s\right)G\left(s\right)=\left[\begin{array}{cc}\frac{12.8}{16.7s+1}& \frac{-18.9e^{-2s}}{21s+1}\\ \frac{6.6e^{-4s}}{10.9s+1}& \frac{-19.4}{14.4s+1}\end{array}\right]$

(2) be designed for attainable two regulatory factors of assurance controller according to formula (4) and (5):

G _N(s)＝I

$J\left(s\right)=\left[\begin{array}{cc}\frac{1}{{\mathrm{\&lambda;}}_{1}s+1}& 0\\ 0& \frac{1}{{\mathrm{\&lambda;}}_{2}s+1}\end{array}\right]$

(3) the controller C according to formula (6) design decoupling zero is following form:

$G\left(s\right)=\frac{\left[\begin{array}{cc}\frac{-19.4}{(14.4s+1)({\mathrm{\&lambda;}}_{1}s+1-e^{-s})}& \frac{18.9e^{-2s}}{(21s+1)({\mathrm{\&lambda;}}_{2}s+1-e^{-3s})}\\ \frac{-6.6e^{-4s}}{(10.9s+1)({\mathrm{\&lambda;}}_{1}s+1-e^{-s})}& \frac{12.8}{(16.7s+1)({\mathrm{\&lambda;}}_{2}s+1-e^{-3s})}\end{array}\right]}{\frac{124.7e^{-6s}}{228.9s^2+31.9s+1}-\frac{248.3}{240.5s^2+31.1s+1}}$

Will implement this controller as can be seen from above controller form, must adopt very complicated control structure, so use the controller reducing technique to simplify to calculate and keep designing requirement, it is as follows that controller is carried out depression of order:

$\frac{-248.32}{240.5s^2+31.1s+1}-\frac{-124.74e^{-6s}}{228.9s^2+31.9s+1}\&ap;\frac{-123.58}{134.63s^2+24.24s+1}$

$G\left(s\right)=\left[\begin{array}{cc}\frac{-19.4}{(14.4s+1)({\mathrm{\&lambda;}}_{1}s+1-e^{-s})}& \frac{18.9e^{-2s}}{(21s+1)({\mathrm{\&lambda;}}_{2}s+1-e^{-3s})}\\ \frac{-6.6e^{-4s}}{(10.9s+1)({\mathrm{\&lambda;}}_{1}s+1-e^{-s})}& \frac{12.8}{(16.7s+1)({\mathrm{\&lambda;}}_{2}s+1-e^{-3s})}\end{array}\right]\frac{134.63s^2+24.24s+1}{-123.58}$

Above process is not more than 2 according to the maximum order of each element in the controller and carries out depression of order, if order

Select greatly more, design accuracy is high more, but causes the controller complexity big more.

The 3rd step: dull adjusting slider 1 (λ ₁), slide block 2 (λ ₂), the observing system closed loop response is determined the optimizing controller parameter thus.Add input signal: r to system in two kinds of situation ₁=1, r ₂=0 and r ₁=0, r ₂=1, output overshoot is not more than under 5% situation in the assurance system, gets λ ₁=3.8, λ ₂=3.5, specifically see accompanying drawing 5.Observe the decoupling zero that the controller behind the depression of order still can the output of realization system from the system closed loop response.When investigating system robustness, suppose the uncertain Δ of the property taken advantage of input of physical presence controlled process G earlier _I=diag{ (s+0.3)/(s+1), (s+0.3)/(s+1) }, it approx physical interpretation be that two input control valves of controlled process have uncertainty up to 100% at high band, and have 30% uncertainty nearly in the low-frequency range working range.Carry out emulation experiment as mentioned above under this serious process input uncertainty, the computer artificial result of process output response as shown in Figure 6.As can be seen from the figure when there was uncertainty in system, big overshoot appearred in system responses, and by the adjusting parameter of dull adjustment control, system overshoot obviously reduces, and system obtains good robustness.

The 4th step: the system that is provided with on the configuration interface is " online " adjustment state, and the CPU that starts industrial computer reads the optimizing controller parameter, and carries out the controlled quentity controlled variable that " On-line Control program " obtains the current time optimum.

The 5th step: u (k) is carried out amplitude limit, prevent that integration is saturated, then by exporting actuator to after the D/A conversion, affact controlled device by actuator, controlled device is operated in the given scope. show on the configuration interface this moment is system's closed-loop response curve under the online situation, observe curve and carry out on-line fine, so go round and begin again and realize control.

What more than set forth is the good control effect that embodiment showed that the present invention provides.It may be noted that the present invention is not only limited to the foregoing description, for unstable multivariable time-lag process, use the double freedom structure, the method design perturbation control device and the setting value tracking controller that adopt the present invention to provide respectively also can be realized good control effect.Because the general multivariable time-lag process model that the present invention is directed in the chemical process provides the parsing controller design method, so be applicable to various chemical industry multivariable time-lag production run.The resolution design method of the multivariable time-lag process decoupling controller that the present invention provides can be widely used in the production run of industries such as petrochemical industry, metallurgy, medicine, building materials and weaving.

Claims (3)

1. resolution design method of decoupling controller of multivariable time delay system is characterized in that concrete steps are as follows:

1) at first to the transfer function matrix identification model of chemical industry multivariable time-lag process

Wherein $g_{\mathrm{ij}}\left(s\right)=g_{\mathrm{oij}}\left(s\right)e^{-{\mathrm{\&theta;}}_{\mathrm{ij}}s},$ It is meant i transport function that is input to j output from controlled process, g _Oij(s) be the reasonable transport function part of its stable canonical, θ _IjBe its corresponding process transmission time lag, i, j=1 ... p decomposes, and decomposed form is as follows:

G(s)＝G _D(s)G _O(s)，

Wherein, $G_D\left(s\right)=\mathrm{diag}\{e^{-{\mathrm{\&theta;}}_{1}s},\&CenterDot;\&CenterDot;\&CenterDot;.e^{-{\mathrm{\&theta;}}_{p}s}\},$

$G_O\left(s\right)=G_D^{-1}\left(s\right)G\left(s\right),$

θ wherein _iBe taken as G ^-1(s) maximum discreet value in the i row;

2) be designed for two regulatory factors that guarantee that controller can be realized:

$G_N\left(s\right)=\mathrm{diag}\{\underset{j=1}{\overset{r_z}{\mathrm{\&Pi;}}}{\left(\frac{-s+z_j}{s+z_j^{*}}\right)}^{k_{1j}},\&CenterDot;\&CenterDot;\&CenterDot;,\underset{j=1}{\overset{r_z}{\mathrm{\&Pi;}}}{\left(\frac{-s+z_j}{s+z_j^{*}}\right)}^{k_{\mathrm{pj}}}\}$

$J\left(s\right)=\mathrm{diag}\{\frac{1}{{({\mathrm{\&lambda;}}_{1}s+1)}^{p_1}},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{({\mathrm{\&lambda;}}_{n}s+1)}^{p_n}}\}$

Z wherein _jBe G ^-1(s) unsettled limit in the i row, k _IjBe z _jMaximum number, λ _iBe controller adjustable parameter, p _iThe maximal phase of getting i column element among the G (s) is to order;

3) the controller C of design decoupling zero is following form:

$C\left(s\right)=\frac{G^{-1}\left(s\right)G_D\left(s\right)G_N\left(s\right)J\left(s\right)}{I-G_D\left(s\right)G_N\left(s\right)J\left(s\right)},$

In said process, if G after the target transfer function matrix decomposition _O(s) still contain the time lag item in, the controller that will cause designing is infinite high-order, at this moment uses the controller reducing technique that this controller is carried out depression of order.

2. resolution design method of decoupling controller of multivariable time delay system as claimed in claim 1 is characterized in that, directly operation is implemented on existing industrial computer, and specific implementation process is as follows:

A) on the configuration interface, design slidably slide block, the initial value of elder generation's determining section parameter when adjusting, comprise that according to actual condition the model of controlling object being carried out identification obtains the object model parameter, according to the definite performance index parameter of expecting of the requirement of dynamic performance and robust stability, controller adjustable parameter initial value; By industrial computer data are delivered among the storage unit RAM then, and system is set on the configuration interface is " off-line " adjustment state;

B) click the " RUN " key on the configuration interface, the CPU that starts industrial computer thus carries out the program of the realization decoupling controller that weaves in advance;

C) the dull slide block of regulating on the configuration interface is regulated the adjustable parameter of decoupling controller, and the observing system closed-loop response curve, has determined the optimizing controller parameter thus;

D) system being set on the configuration interface is " online " adjustment state, and the CPU that starts industrial computer thus reads the optimizing controller parameter, calculates discrete domain decoupling zero control formula according to the discretize formula then, obtains controlled quentity controlled variable optimum under the current time off-line state;

E) to u _j(k) carry out amplitude limit, prevent that integration is saturated, then by exporting actuator to after the D/A conversion, affact controlled device by actuator, controlled device is operated in the given scope, show on the configuration interface this moment is system's closed-loop response curve under the online situation, then with and the off-line regulative mode under identical method carry out on-line fine, so go round and begin again and realize controlling;

Described d) in, the expression formula of controller output controlled quentity controlled variable is shown below:

$u_j\left(k\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}\left(k\right)$

u _Ij(k)-current (k) C constantly _Ij(z) the output controlled quentity controlled variable of controller, u _j(k)-current k j output of controller constantly controlled quentity controlled variable.

3. resolution design method of decoupling controller of multivariable time delay system as claimed in claim 2 is characterized in that, described a) in, controller adjustable parameter initial value gets 1.

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