CN1049051C - Model-less control technology and controller for industrial control - Google Patents

Abstract

The present invention relates to an industrial automatic control technique and a hardware structure of a controller developed by the industrial automatic control technique. The industrial automatic control technique is composed of a model-less control rule, a time varying parameter estimation algorithm and a controlled system. The present invention provides a self-control technique which directly uses the controlled system to input and output data without needing to establish a controlled system digital model, and a model-less controller which is made by the self-control technique. The present invention aims to meet requirements for the control technique having low cost and high quality and a controller in industrial process control.

Description

The Model free control technology

The present invention relates to a kind of industry automatic control technology and constitute with the hardware of the controller of this technology development.

At present, domestic and external modern control technology can be divided into two classes basically, one just is based on the control technology that must set up the controlled system mathematical model of modern control theory and method, the technical know-how achievement in research of this part is very abundant, obtaining brilliant success aspect national defence and the space flight, and in Industry Control, also obtaining using widely.The main present situation that it is used in Industry Control is: at some concrete controll plants, set up scientific research project, set up scientific research group, by to controll plant system deep understanding and grasp, set up the off-line of controlled system or online mathematical model (may be unknown parameters), based on this mathematical model, use modern control theory and method design control system (or adaptive control system) thereby realization control (or adaptive control) automatically then.This kind technology major defect deficiency is:

1. must set up the mathematical model of controlled system, this thing is not an easy thing, time-consuming, costly, effort, sometimes or even impossible (such as chemical reaction process, converter temperature etc.); 2. even the mathematical model of controlled system can be set up, because the complicacy of industrial process, also can only be that some of real system is approximate, also having many system dynamics not to be established in the system model goes, so just many problems have been brought in actual applications based on the mathematical model of controlled system designed control system or controller, even by theoretical proof have good control performance (such as having stability, convergence and strong robustness) technology and method also will go wrong in actual applications (as instability, to environment or some parameter problem such as sensitivity too); 3. range of application is narrow.The mature achievement of existing majority only can be applicable to linear, the single output of single input, the time constant system control, and the many industrial systems in the reality all are non-linear, many inputs, many outputs, coupling, the time-varying system that band disturbs.Though some is about the report of Control of Nonlinear Systems success on document, but the result of these reports, because the diversity of nonlinear system, only can be applied to the controlled system be concerned about again, being difficult to be generalized to other system gets on, even same controll plant, because the different electricity of environment may go wrong.4. expense costliness, the control system complexity.

Therefore, how to set up the control technology and the method that do not rely on the controlled system mathematical model, overcome above-mentioned shortcoming and deficiency, and make it easier in industrial practical application, be the problem that domestic and international control theory circle and control engineering Shi Yizhi are concerned about, pay close attention to and try hard to solve, this type of control technology also is development trend (12th IFAC World Congress, the Preprints of Papers of present control technology, Sydey, 1993).This type of control problem also is the control problem of model-free "black box" system.This type of control technology is at present representational to mainly contain two kinds, it is a kind of to be PID control technology and PID modification technology with classics, be commonly referred to as the PID class, as intelligent PID, POLE PLACEMENT USING PID, from the PID etc. that adjusts, this type of technology is not only ripe, and commercially produced product arranged, the Kang Changjie people such as (C.C.Hang) of the more representational K.J.Astr  m that Sweden arranged and former Czechoslovakian J.Marsik and Singapore and under company, as long as this type of does not all overcome the major defect of PID class: 1. only can handle linear, the single output of single input, time-invariant system; 2. the control effect is undesirable; 3. require the user to grasp special knowledge and to the abundant understanding of controlled system.Its two kinds is exactly the application of artificial neural network technology in control that grew up in recent years, and attempts to solve the Model free control problem of nonlinear system, yet the shortcoming of this technology is: 1. the arithmetic speed height that requires computing machine; System can not the time become, the exponent number of system must be known; 3. and to network node, hidden layer have dependence: 4. can not carry out theoretical analysis, hardware is realized difficulty etc., does not up to the present also see the possibility that is applied in the industrial reality.

The purpose of this invention is, provide a kind of and need not set up the controlled system mathematical model, export and directly use the automatic control technology of controlled system inputoutput data and can use a series of list input lists that comprise of this technology development, the single output of many inputs, the Non-Model Controller of multiple-input and multiple-output is intended to satisfy in the industrial process control requirement to low-cost, high-quality control technology and controller.

The objective of the invention is to realize by following technical measures:

It is made up of model free control law, time-varying parameter algorithm for estimating and controlled system, it is characterized in that:

A. the single output of the many inputs nonlinear system situation of described model free control law is realized by following formula:

Wherein, u (k), y (k) represent control input vector and the system output of controlled system in the k sampling instant, ρ respectively _kBe 0＜ρ _k≤ 2, λ is 0≤λ≤10, and ‖ ‖ is certain norm, y ^※(k+1) be the desired output signal of controll plant in the k+1 sampling instant,

Be pseudo-gradient vector φ (k) estimated value;

B. the single output of the many inputs nonlinear system situation of the multistep time lag of described model free control law is realized by following formula:

$-\underset{i=0}{\overset{d-2}{\mathrm{\Σ}}}\widehat{\mathrm{\φ}}(k-i)\mathrm{\Δu}(k-1-i)]$ Wherein other symbol as hereinbefore, d represents system's time lag, d 〉=2, ∑ is represented Lian Jiahe, Δ u (i-1)=u (i-1)-u (i-2);

C. the multiple-input and multiple-output nonlinear system situation of described model free control law is realized by following formula:

U (k) wherein, Y (k) represents input vector and the output vector of controlled system in the k sampling instant respectively, The estimated value of the expression pseudo-Jacobi matrix Φ of controlled system (k), the transposition of T representing matrix, Y ^※(k+1) the expression controlled system is at k+1 system's desired output signal constantly, I representation unit matrix.

Described many input lists are exported nonlinear system, also comprise the single nonlinear system of exporting of single input of special case; The model free control law of its multiple-input and multiple-output nonlinear system also can be realized by following formula:

Advantage of the present invention and good effect are:

1. the problem to be solved of application in control is the same with PID type control technology and artificial neural network technology for this invention problem to be solved, yet technical do not have any relation with it.Technical related with it be adaptive control technology, yet the prerequisite of adaptive control technology is at first to know the structure of the mathematical model of controlled system, and being input and output (I/O) data according to controlled system, its model parameter estimates online by parameter estimation algorithm, thereby obtain the mathematical model of controlled system online, online thus mathematical model is the design control law algorithm constantly, the control law algorithm is calculated the control input thus, and controlled system is controlled in the control input thus, realizes adaptive control.And technology path of the present invention and adaptive control technology route are similar, different principal character parts is that condition precedent of the present invention is to know the structure of the mathematical model of controlled system in advance, and it two is that time-varying parameter algorithm for estimating in this invention is to be used for estimating online the so-called pseudo-gradient vector (pseudo-gradient vector) or the pseudo-Jacobi matrix (pseudo-Jacobi matrix) of nonlinear system.But not the model parameter of controlled system.

2. can handle single single output of input (SISO), many single outputs of input (MISO), the adaptive control for nonlinear systems problem that becomes during multiple-input and multiple-output (MIMO).

Need adjust 3 parameters (scale factor, integrating factor, differential divisor) 3.PID the controller of type is handled the control problem (SISO situation) of a system, and the controller of developing with the technology of the present invention only must 1 parameter of online adjustment.Number that only must online adjustment parameter to this controller of multiple-input and multiple-output situation is (input * output).

4. control law algorithm (controller) is irrelevant with mathematical model, the controlled system exponent number of controlled system, only utilizes the I/O data of controlled system.

5. the method for operation is iterative learning (comprising the control law algorithm), adaptive mode operation.

6. the control effect all is better than the control effect of existing control technology, and can handle the problem that prior art can't be handled.

7. because the technology of this invention does not rely on the mathematical model and the exponent number of certain concrete controll plant, so its dynamic property (stability, robustness) all is better than prior art.

8. controller principle is simple, is easy to hardware and realizes that expense is low, applied range.

Description of drawings is as follows:

Fig. 1 is a control technology basic functional principle block scheme of the present invention;

Fig. 2 forms block scheme for controller hardware implementation structure of the present invention;

Fig. 3 is a controller operational scheme block scheme of the present invention.

To further specify know-why of the present invention below, will do a detailed description with embodiment in conjunction with the accompanying drawings simultaneously:

The present invention can solve the very big class control problem of nonlinear system very widely, wherein:

Technical key of the present invention is:

1. the single output of many inputs nonlinear system (special case is the single output of a single input nonlinear system)

Technical foundation: the single output of general discrete many inputs nonlinear system

y(k+1)＝f[Y(k)，u(k)，U(k-1)]+e(k+1)

U (k) wherein, y (k), e (k) represents the input vector of controlled system in the k sampling instant respectively, output, and the output white noise disturbs Y (k), U (k-1) represents k and the system's output till the k-1 moment and the set of input vector respectively, f (...) represent unknown nonlinear function.Under certain assumed condition, necessarily there is a vectorial φ (k), the pseudo-gradient vector of being known as when Δ u (k) ≠ 0, makes

Δ y (k+1)=φ ^T(k) Δ u (k)+Δ e (k+1) ... (1) and φ (k) bounded

Δ u (k)=u (k)-u (k-1) wherein, Δ e (k+1)-e (k), Δ y (k+1)=y (k+1)-y (k)

The model free control law algorithm:

Suppose the estimated value of φ (k)

Known, promptly the pseudo-gradient vector of system can be estimated by some time-varying parameter algorithm for estimating, then according to above-mentioned technical foundation process mathematical derivation, just can obtain following model free control law algorithm

ρ wherein _kBe to become the constant row for the moment, can be set at normal value 0＜ρ _k≤ 2, λ is a certain constant, 0≤λ≤10, certain norm of ‖ ‖, y ^※(k+1) the expression system is at the desired output signal of k+1 sampling instant.

The pseudo-gradient vector algorithm for estimating of the single output of many inputs nonlinear system (special case is the single output of a single input nonlinear system).

The algorithm for estimating of (k) in the aforementioned major part formula (2)

Pseudo-gradient vector (k) is a time-varying parameter, and from the form of (1) formula, our any as can be seen time-varying parameter algorithm for estimating all can be used to ask for the valuation of (k) As with the time become the least-squares algorithm of forgetting factor; The least-squares algorithm that variance resets; The least-squares algorithm of variance correction; Time-varying parameter algorithm for estimating based on Kalman filtering; And the nonlinear system gradient project algorithms that provide of the inventor based on (1) formula $\widehat{\mathrm{\φ}}\left(k\right)=\widehat{\mathrm{\φ}}(k-1)+\frac{{\mathrm{\η}}_k\mathrm{\Δu}(k-1)}{\mathrm{\μ}+\left|\right|\mathrm{\Δu}(k-1){\left|\right|}^2}[\mathrm{\Δy}\left(k\right)-\mathrm{\Δ}{u}^T(k-1)\widehat{\mathrm{\φ}}(k-1)]$

η wherein _k∈ (0,2), μ ∈ (0,10)

Or the like.

2. the single output of many inputs of multistep time lag nonlinear system (being without loss of generality, is 2 to be example with time lag).

Through similarly deriving, just can obtain the model free control law algorithm

$-\widehat{{\mathrm{\φ}}^T}\left(k\right)\mathrm{\Δu}(k-1)\·\·\·\·\·\·\·\·\·\left(3\right)$

Wherein symbolic significance is identical with front formula (1) situation.

The pseudo-gradient vector algorithm for estimating of the single output of the many inputs nonlinear system of multistep time lag.

(k+1) in the aforementioned formula (3), the algorithm for estimating of (k).

Can use in 1 all time-varying parameter algorithm for estimating fully and estimate pseudo-gradient vector (k).

3. multiple-input and multiple-output nonlinear system

Technical foundation: general discrete multiple-input and multiple-output nonlinear system

Y (k+1)=F[Y (k), U (k), U (k-1)]+E (k+1) U (k) wherein, Y (k), E (k) represents the input vector of controlled system in the k sampling instant respectively, output vector and output white noise disturb vector, F (...) be unknown nonlinear function, meeting some requirements down, there is the matrix Φ (k) of the pseudo-acobi matrix of being known as, make when ‖ Δ U (k) ‖ ≠ 0, have

Δ Y (k+1)=Φ (k) Δ U (k)+Δ E (k+1) ... (4) and ‖ Φ (k) ‖ bounded.Δ Y (k+1)=Y (k+1)-Y (k) wherein, Δ U (k)=U (k)-U (k-1), Δ E (k+1)=E (k+1)-E (k)

The model free control law algorithm:

According to above-mentioned technical foundation,, just can obtain following model free control law algorithm through a series of mathematical derivation: $1)U\left(k\right)=U(k-1)+{\mathrm{\ρ}}_k{(\widehat{{\mathrm{\φ}}^T}\left(k\right)\widehat{\mathrm{\φ}}\left(k\right)+\mathrm{\λI})}^{-1}\widehat{{\mathrm{\φ}}^T}\left(k\right)$

[Y ^※(K+1)-Y(k)]……………………………(5)

Wherein Be the estimated value of Φ (k), Y ^※(k+1) the expression system is at system's desired output signal of k+1 sampling instant, and other symbol as hereinbefore.

The pseudo-Jacobi Matrix Estimation algorithm of multiple-input and multiple-output nonlinear system.

In aforementioned formula (5), (6)

Algorithm for estimating.

Algorithm for estimating with the pseudo-gradient vector of many inputs single output nonlinear system is the same, and the time-varying parameter algorithm for estimating of any multiple-input and multiple-output form all can be used for estimating the value of pseudo-Jacobi matrix, becomes the forgetting factor least-squares algorithm during as band; Variance resets least-squares algorithm; The least-squares algorithm of variance correction, and two kinds of new algorithms of providing of the inventor based on (4) formula: $1)\widehat{{\mathrm{\φ}}^T}\left(k\right)=\widehat{{\mathrm{\φ}}^T}(k-1)+{\mathrm{\η}}_k{(\mathrm{\ΔU}(K-1)\mathrm{\Δ}{U}^T(k-1)+\mathrm{\μI})}^{-1}$ $\mathrm{\ΔU}(k-1)\·[\mathrm{\Δ}{Y}^T\left(k\right)-\mathrm{\Δ}{U}^T(k-1)\widehat{{\mathrm{\φ}}^T}(k-1)]$ $2)\widehat{{\mathrm{\φ}}^T}\left(k\right)=\widehat{{\mathrm{\φ}}^T}(k-1)+\frac{{\mathrm{\η}}_k\mathrm{\Δ}(k-1)}{\mathrm{\μ}+\left|\right|{\mathrm{\ΔU}(k-1)\left|\right|}^2}[\mathrm{\Δ}{Y}^T\left(k\right)-$ $\mathrm{\Δ}{U}^T(k-1)\widehat{{\mathrm{\φ}}^T}(k-1)]$

η wherein _k∈ (0,2), μ ∈ (0,10) or the like.

4. the technical key of Non-Model Controller:

Resetting of pseudo-gradient vector or pseudo-Jacobi matrix.

In order to improve the ability of time-varying parameter algorithm keeps track time-varying parameter, and prevent that controller from losing normal control action in operation work, should adopt the form of resetting of pseudo-gradient vector or pseudo-Jacobi matrix, promptly after pseudo-gradient vector or pseudo-Jacobi matrix have been estimated, add following discriminating program.

If

Not $\widehat{\mathrm{\φ}}\left(k\right)=\widehat{\mathrm{\φ}}\left(k\right)$

Perhaps if

Not $\widehat{\mathrm{\φ}}\left(k\right)=\widehat{\mathrm{\φ}}\left(k\right)$

Wherein, ε is given in advance, generally should get ε ∈ (0,0.5)

Manually with automatic switchover

This controller is in actual industrial process control is used, because the working point of actual controlled system and original state are difficult for being provided with, so should at first adopt the manual mode operation, its objective is in order to find reasonable duty, the original state that is beneficial to this controller is set, and manual mode comprises manual or uses the PID control technology.

Alarm indication

The input and output of many systems do not allow to surpass certain boundary in the actual industrial process control, differentiate y (k+1) 〉=Y, the program of u (k) 〉=U so should add in this controller.If there is one to surpass its set-point Y among them, U, then this controller is reported to the police at once and is quit work, so that engineer inspection's fault.

Controller can form: 1) the single output of single input nonlinear system Non-Model Controller; 2) the single output of many inputs nonlinear system Non-Model Controller; 3) the single output of many inputs multistep time lag Non-Model Controller; 4) 4 big serial controllers such as multiple-input and multiple-output nonlinear system Non-Model Controller.

As shown in Figure 1, y among the figure ^※(k+1) the desired output signal of expression controlled system, the model free control law algorithm can be with any substitution of the formula in the technical key (2), (3), (5), (6), the time-varying parameter algorithm for estimating then can substitute with any time-varying parameter algorithm for estimating in the technical key, uses this technology and just can develop multiple Non-Model Controller and realize that controlled system output y (k+1) follows the tracks of y ^※(k+1) signal.

Input is exactly the inputoutput data of controlled system among Fig. 2, transmitter is exactly the simulating signal that realizes the standard that converts to of controlled system inputoutput data, A/D is firm and hard now to become digital signal so that arithmetical unit is realized computing from analog quantity, it can be with 8,12, decide according to different control of quality, the computing of arithmetical unit implementation algorithm defined, available single card microcomputer, display can be used forms such as number or light beam, to be easy to watch is purpose, alarm indication can be with pilot lamp and audible alarm, and change-over switch should realize not having disturbance to be switched, and output is exactly this control input analog amount constantly of controlled system.

The mid-manual mode purpose of Fig. 3 is in order to start controlled system, and can seek the working point of system and near state thereof roughly, near the memory work point system initial state, finger system inputoutput pair, it is the value that pseudo-gradient vector or pseudo-Jacobi matrix are set that initial parameter value is set, reset the lower bound ε of constant, it is the ρ that is provided with in the control law algorithm that adjustable constant value is set _k, λ, and the constant value in the time-varying parameter algorithm for estimating switch on the automated manner, the desired output signal y of input controlled system ^※(k+1), available keyboard input, read sampled data y (k) and be meant the controlled system output signal that records with measurement instrument or sensor, memory previous moment u (k-1), and this pseudo-gradient vector value constantly, calculation control input signal u (k) is meant the model free control law algorithmic formula (2) in the application technology key, or (3), or (5), or (6) calculate u (k), whether differentiate needs to report to the police, if not, then read detection signal y (k+1) be meant with measurement instrument or sensor measurement controlled system accept control input signals u (k) later through the system output signal after the sampling period, whether differentiate needs to report to the police, if not, estimate pseudo-gradient vector (k+1), be meant with (k) y (k+1), u (k) sends into pseudo-gradient vector algorithm for estimating given in the technical key and calculates (k+1), whether need reset, not, change next control cycle if differentiating; Be, put again, change next control cycle.

Industrial furnace control:

Background: under the certain situation of voltage (220V), convert 12V voltage to through transformer, then with this 12V power supply as controller power source, control furnace temperature by size of current.

Implementation step:

Step 1: initial mode adopts manually, through after the certain hour, switches on the automatic control mode again and (tentatively determines the working point, obtain the system initial state data).Initial pseudo-gradient vector value (a certain value between desirable-1 to 1) is set, parameter reformation lower limit circle is set) ε=0.001, get λ, μ is the some values between 0 and 5, gets ρ _kIt is a certain value (above these constants are imported by keyboard) between 0.5 to 2.

Step 2: the control input current digital signal value of the last sampling instant of storer memory, pseudo-gradient vector value and detect this furnace temperature constantly and convert digital signal to through the modulus plate, keyboard is imported electric furnace desired output signal y ^※

Step 3: pseudo-gradient vector value and furnace temperature digital signal are sent into the control law arithmetical unit, and the electric current after its output is come out by the digital-to-analogue plate is exactly that next moment furnace temperature reaches desired output y ^※Current Control input.

Step 4: electric furnace is sent in above-mentioned Current Control input of trying to achieve, detected through the furnace temperature after the sampling period with temperature sensor.

Step 5: will give pseudo-gradient through the furnace temperature digital signal of modulus plate and estimate arithmetical unit, its output is this pseudo-gradient vector value constantly, in the backspace step 2, repeats above each step till quitting work.

Claims (2)

1. the Model free control technology is made up of model free control law, time-varying parameter algorithm for estimating and controlled system, it is characterized in that:

A. the single output of the many inputs nonlinear system situation of described model free control law is realized by following formula:

Wherein, u (k), y (k) represent control input vector and the system output of controlled system in the k sampling instant, ρ respectively _kBe 0＜ρ _k≤ 2, λ is 0≤λ≤10, and ‖ ‖ is certain norm, y ^※(k+1) be the desired output signal of controll plant in the k+1 sampling instant,

Be pseudo-gradient vector φ (k) estimated value:

B. the single output of the many inputs nonlinear system situation of the multistep time lag of described model free control law is realized by following formula:

$-\underset{i=0}{\overset{d-2}{\mathrm{\Σ}}}\widehat{\mathrm{\φ}}(k-i)\mathrm{\Δu}(k-1-i)]$

Wherein other symbol as hereinbefore, d represents system's time lag, d 〉=2, ∑ is represented Lian Jiahe, Δ u (i-1)=u (i-1)-u (i-2);

C. the multiple-input and multiple-output nonlinear system situation of described model free control law is realized by following formula:

U (k) wherein, Y (k) represents input vector and the output vector of controlled system in the K sampling instant respectively,

The estimated value of the expression pseudo-Jacobi matrix Φ of controlled system (k), the transposition of T representing matrix, Y ^※(k+1) the expression controlled system is at k+1 system's desired output signal constantly, I representation unit matrix.

2. Model free control technology as claimed in claim 1 is characterized in that the single output of described many inputs nonlinear system, also comprises the single output of the single input nonlinear system of special case; The model free control law of its multiple-input and multiple-output nonlinear system also can be realized by following formula:

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