CN1333487A - Method and device for implementing optimized self anti-interference feedback control - Google Patents

Abstract

The present invention relates to a method for implementing optimization self-antijamming feedback control and its equipment. Said invention is applicable to the feedback control which can calculate the control quantity of controlled object by means of controlling error of state constructive value and target value of the object, and is a transient process control method for controlling transient process of target value. It is a transient process control method which can utilize the varied type of displacement acceleration of the above-mentioned transient process to define the type of the above-mentioned transient process, and can utilize the above-mentioned defined type of transient process to control the transient process of target value, and is characterized by said transient process.

Description

Realize the method and apparatus of optimized self anti-interference FEEDBACK CONTROL

The present invention is relevant, in more detail, relevant with the controller of the state that can infer its controlling object according to the input signal and the output signal of controlling object and unknown disturbances with the controller of suitable transient process control.

At present, most controllers of using in the process control are PID regulator and the mutation thereof that form the forties.After the sixties, obtained very great development based on the modern control theory of controlled device mathematical model.But a large amount of practical objects can not given appropriate mathematic model, and the modern control theory achievement is difficult in the working control engineering.So begin to have occurred various " advanced control " method the eighties, but all do not break away from the Shu Bo of mathematical model, all to adopt complicated formalities such as " build and touch ", " System Discrimination ", " adaptation ", make the control algolithm complexity, its application is very limited.

The PID technology that in embryo produces of kybernetics and analogue technique finished various controlled target with flying colors in a large amount of working control engineerings, thereby PID becomes a kind of almost ideal control technology.Yet further developing of science and technology makes the controlled target variation, and the requirement of control accuracy and speed is more and more higher, and original PID can not adapt to this new variation fully.People suspect PID " not all right ", think that PID is its disadvantage to the mathematical description out of true of object, set up new object factory method and inquire into new control mechanism.So, obtained very great development for the modern control theory of basic Chu with the mathematical models (state-space model) of object since the sixties.Yet this new theory fails to provide the method for designing of practical control device, is difficult to be applied in its achievement engineering practice.So at the end of the eighties, occurred the new ideological trend of " re-recognizing PID " again.

Seek practicality and controller efficiently, need correctly be familiar with the relative merits of PID and modern control theory.

PID can access extensive application in process control basic reason is, it is not to determine control strategy by mathematics model, but determine to eliminate this error Control strategy by " error between controlled target and the controlled device agenda ", its control mechanism is totally independent of mathematics model.Yet, it generates the method for controlled quentity controlled variable, since be subjected at that time the level of understanding and the restriction of technical conditions, fairly simple: " weighted sum " form of the past (I) of " error ε between target and the behavior ", present (P) and variation tendency (D) is directly to remove to handle " error ε between target and the agenda " to come controlled amount.The limitation of PID is caused by " simple process " of this " echo signal " and " agenda signal ".Briefly: " not pattern type " is advantage, and " handling simple " is its shortcoming.Though modern control theory has been made very big contribution to the systematic analysis understanding of control system fundamental mechanism (promptly to), because a large amount of engineering objects is given to go out appropriate mathematic model, the control method of its proposition is difficult to obtain practical application.Briefly: " pattern type " is its advantage, also is can't practical maximum " shortcoming ".

If modern control theory combines to the understanding and the modern signal processing technology of control system, develop the strong point of PID " not pattern type ", improve its " simple process " way, we can construct the better novel practical controller than PID so.

Above-mentioned past PID technology has following four aspects to need to improve:

1. controlled target can saltus step, but as the output of inertial element, the agenda of object can only be gradual, and it is irrational requiring " gradual behavior " tracking " target of sudden change ".

2. lack the suitable way of obtaining the error differential signal.

3. error ε " past " ( , i.e. I), " now " (P) and " variation tendency " " weighted sum " not necessarily best array configuration (D).

4. the introducing of I to eliminating the outer influence of disturbing of unknown normal value, has certain effect, and in addition has little significance.

To this, the inventor of the application's patent, invented the control technology of these four weakness that can solve PID:

1. invented ability, arranged the technology of the differential signal of suitable " transient process " and this process earlier according to desired value and object.

2. invented Nonlinear Dynamic link-" Nonlinear Tracking differentiator " technology (Tracking-Differentiator-TD) that rationally to extract differential signal of developing; The detailed description of this technology please refer to the Chinese document [1,2] of following document A and table 1.

Document A:Han Jing-Qing.Nonliner Design Methods For Control Systems.

IFAC?World?Congress?1999，Beijing，P.R.China，C-2a-15-4，521-526，(5th-9th?July?1999)．

(annotate: IFAC:The International Federation of AutomaticControl)

3. invented the technology that adopts the suitable nonlinear combination strategy of error between the transient process of arranging and the system's virtual condition; The detailed description of this technology please refer to the Chinese document [3] of table 1.

4. invent Nonlinear Dynamic link-" extended state observer " (Extended State Observer-ESO) that to estimate Obj State and uncertain disturbance by the input/output signal of object, be used to estimate Obj State and unknown disturbance (list of references [4]).This " extended state observer " be independent of object concrete mathematical model technology; The detailed description of this technology please refer to above-mentioned document A, the Chinese document [4] of following document B and table 1.

Document B: バ ゲ ス マ Ha ワ Application, Luo Zhenghua, Han Jingqing (inventor of present patent application), in

New one: " high speed of the robot by extended state observer and high-precision motion control ", association of Japanese robot will, Vol.18, No.2, pp.244～251,2000.

This " extended state observer " is and the irrelevant independently existence of the concrete mathematical model of controlling object.

This patent inventor according to above 4 aspect technology, has invented novel nonlinear pid controller.This controller, at first, the 1st " tracking differentiator " sets transient process, and extracts its differential signal out, and secondly, the 2nd " tracking differentiator " follows the trail of the actual movement of controlled device, and extracts its differential signal out.Then, calculate the differential signal of the above-mentioned transient process of sum of errors of the actual movement that transient process that the 1st " tracking differentiator " set and the 2nd " tracking differentiator " follow the trail of controlled device and the differential error of above-mentioned actual movement differential signal.And the above-mentioned error of integration.At last, the nonlinear combination of integration output valve and above-mentioned error and differential error, the controlled quentity controlled variable of generation controlled device please refer to the Fig. 1 of preceding note document A and the Chinese document [4] of table 1 to this technology detailed description.Above-mentioned novel non-linearity PID controller is compared with PID controller in the past, and its control effect is very good, need not to measure outer disturbing and can eliminate its influence, and parameter adjustment is also very simple.

In addition, the this patent inventor, be the adaptive faculty of the uncertain factor of strengthening controller and the unknown corresponding ability of interference, utilize state observer thought and nonlinear feedback special-effect, " extended state observer " of developing the brute force that to infer controlled device and uncertain factor and interference according to the input signal and the output signal of controlled device, and utilize it to invent " getting rid of interference suppressor automatically " (Auto-Disturbances-Rejection Controller:ADRC), because " extended state observer " can infer uncertain interference, to ADRC, the above-mentioned the 1st error intergal feedback just there is no need.The detailed description of this technology please refer to 4.2 joints (Fig. 2) of above-mentioned document A and the Chinese document [5] of table 1, [6].

" automatic disturbance rejection controller " (ADRC) is made up of following three parts: arrange transient process and extract its differential signal with a tracking differentiator (TD); Estimate the state variable of object and the real-time action of unknown disturbance with extended state observer (ESO); The suitable nonlinear combination of error and the compensation of unknown disturbance estimator generate control signal between transient process of arranging and the Obj State estimator.

All used suitable nonlinear characteristic in this three part.This is not obstacle concerning digital controller, because digitial controller is only recognized program, can not distinguish linear and non-linear.

Automatic disturbance rejection controller has adapted to the requirement in digital control epoch fully, and the time lag system control that the also complete Mi deficiency of having mended conventional PID, and PID is difficult for realizing, multi-variable system decoupling zero control etc. are all accomplished than being easier to.In automatic disturbance rejection controller, deterministic system control can be united fully with the control of uncertain system.

Yet from engineering practical angle, automatic disturbance rejection controller also has some to need the part of further improving.

Need improved part to mainly contain following three aspects in the automatic disturbance rejection controller:

1. " with following the tracks of differentiator (TD) " transient process of arranging has the jump of acceleration, causes the jump of controlled quentity controlled variable in the transient process easily, sometimes Project Realization is brought certain difficulty;

2. used nonlinear function calculation amount is more in " extended state observer (ESO) ";

3. the nonlinear feedback form of sum of errors error differential need be carried out optimization.

Improving " automatic disturbance rejection controller " these three not enough points, proposed new more practical controller scheme-" optimum automatic disturbance rejection controller " (Optimal Auto-Disturbances-Rejection Controller), is the main contents of asking patent in this.

[table 1]

List of references

(1) Han Jingqing, Wang Wei, Nonlinear Tracking-differentiator,＜system science and mathematics 〉, 1994 (2), 177-183; (2) Han Jingqing, Yuan Lulin, the discrete form of tracking-differentiator,＜system science and mathematics 〉, 1999 (3), 268-273; (3) Han Jingqing, nonlinear pid controller,＜robotization journal 〉, 1994 (4), 487-490; (4) Han Jingqing, " extended state observer " of the uncertain object of a class,＜empty system and decision-making 〉, 1995 (1), 85-88; (5) Han Jingqing, nonlinear state Error Feedback rule NLSEF,＜control and decision-making 〉, 1995 (3), 221-225; (6) Han Jingqing, automatic disturbance rejection controller and application thereof,＜control and decision-making 〉, 1998 (1), 18-23;

The 1st kind of form of the present invention be exactly, and is applicable to according to by the error of empty Obj State estimated value and setting value, calculates the FEEDBACK CONTROL of its controlling object controlled quentity controlled variable, with the transient process control method of the transient process of control setting value as prerequisite.At first, according to the acceleration change form of transient process change amount, the form of decision transient process.Again, according to the form of its transient process, the transient process of control setting value.

In more detail, acceleration change form according to transient process change amount, the change amount differential form of the differential form of decision transient process change amount, determine the multi-form change amount form of transient process change amount again according to above-mentioned form, according to change amount form that is determined and change amount differential form, control the change amount and the change amount differential of the transient process of setting value again.

The 2nd kind of form of the present invention is, calculate the error of the actual change amount of the estimated value change amount of controlled device state and controlled device state with the transforming function transformation function that comprises nonlinear function, comprise the uncertain effect of dynamic characteristic of the unknown of unknown interference and controlling object system between variable of state with the possible observer observation of observation.

At first, carry out the calculation of using the transforming function transformation function mapping fault, then,, calculate a multivariate estimated value of controlled device state and the estimated value of uncertain effect with observer according to the output valve of its calculation with the calculation of polygronal function mapping fault.

The 3rd kind of form of the present invention is, calculate the change amount sum of errors of error of the transient process change amount of the change amount of so-called controlled device state estimation value and setting value, the change amount differential error of the error of the change amount differential of so-called controlled device state estimation value and the transient process change amount differential of setting value, import its change amount error and change amount differential error, calculation comprises that its error of energy narrows down to the transforming function transformation function of zero nonlinear function jointly, controls controlled device by the Error Feedback controlled quentity controlled variable of calculating its controlled device controlled quentity controlled variable.And the feedback of compensation controlled device state change amount is as prerequisite.

And, as transforming function transformation function, when its change amount and change amount differential narrow down to zero, having the characteristic that suppresses its error amount in zero vibrations that nearby taken place, further detailed saying calculated above-mentioned transforming function transformation function according to several 1 formulas.

[several 1]

d＝rh ₁

d ₀＝dh ₁

y＝ε ₁(t)＋h ₁ε ₂(t) $a_0=\sqrt{d^2+8r\left|y\right|}$ $a={\{}_{s_2\left(t\right)+\frac{\mathrm{sign}\left(y\right)(a_0-d)}{2},\left|y\right|>{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}_0}^{{\mathrm{\&epsiv;}}_2\left(t\right)+\frac{y}{h_1},\left|y\right|\&le;{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}_0}$ $\mathrm{fst}({\mathrm{\&epsiv;}}_1\left(t\right),{\mathrm{\&epsiv;}}_2\left(t\right),r,h_1)={\{}_{\mathrm{rsign}\left(a\right),\left|a\right|>d}^{\frac{\mathrm{ra}}{d},\left|a\right|\&le;d}$ u ₀₀(t)＝fst(ε ₁(t)，ε ₂(t)，r，h ₁)

The 4th kind of form of the present invention is according to each inscape of above-described the present invention's the 1st to the 3rd form of suitable combination, to realize the feedback of optimized self anti-interference.

Below, explain example of the present invention with reference to figure.

Fig. 1 is an example pie graph of the present invention.

Fig. 2 is the 1st specific character figure of transient process form.

Fig. 3 is the 2nd specific character figure of transient process form.

Fig. 4 is the 3rd specific character figure of transient process form.

Fig. 5 is the 4th specific character figure of transient process form.

Fig. 6 is the polygronal function performance plot of ESO.

Fig. 7 is the optimization nonlinear function performance plot of O.S.E.F.

Fig. 8 is the initial setting action flow chart.

Fig. 9 is the main body action flow chart.

Figure 10 is the A.T.P action flow chart.

Figure 11 is the O.S.E.F action flow chart.

Figure 12 is the ESO action flow chart.

Figure 13 is experimental result performance plot (γ=1).

Figure 14 is experimental result performance plot (γ=10).

Fig. 1 is as example of the present invention, to realize the pie graph of optimized self anti-interference controller (optimization ADRC) 101.

Optimization ADRC101 was by what following function constituted.

At first, transient process setting apparatus (A.T.P:Arrangement of TransientProcess) 102 is given the transient process change amount v1 and the transient process change amount differential v2 that generate setting value v0.

Extended state observer (ESO:Extended State Observer) 103 is estimated controlled device state and uncertain interference effect, and the state estimation value change amount z of so-called controlled device state is estimated in output ₁And state estimation change amount differential z ₂Estimate the uncertain effect estimated value z of all ambiguous models and uncertain interference with what is called ₃The input value of ESO103 is exactly, the known action amount f that will take advantage of out the value bu that obtains behind the controlled quentity controlled variable u of controlled device and the known coefficient b and known action amount exerciser 105 to be exported with multiplier 104 with addometer 106 ₀The value that obtains after adding and the output valve y of controlled device.

Error exerciser 107, the calculation transient process change amount v that A.T.P102 generated ₁The controlled device state estimation change amount z that is exported with ESO103 ₁Error change amount just error ε ₁

Differential error exerciser 108, the calculation transient process change amount differential v that A.T.P102 generated ₂The controlled device state estimation change amount differential z that is exported with ESO103 ₂Error change amount just differential error ε ₂

Optimal state Error Feedback device (O.S.E.F) 109 is according to change amount error ε ₂With change amount differential error ε ₂, output optimally compensates the FEEDBACK CONTROL amount u of its error ₀₀

Simultaneously, with addometer 110 with uncertain effect estimated value z that ESO103 exported ₃The known action amount f that is exported with known action amount exerciser 105 ₀The value that the value that obtains after adding and known coefficient-1/b obtain after being multiplied by with multiplier 111 again is imported into 112 li of addometers as the interference compensation controlled quentity controlled variable.

Addometer 112, the value that obtains after the interference compensation controlled quentity controlled variable that Error Feedback controlled quentity controlled variable that O.S.E.F109 exported and multiplier 111 are exported adds is as the controlled quentity controlled variable output of controlled device.

To above-mentioned formation, known action amount exerciser 105 is according to the state estimation change amount z that ESO103 exported ₁And state estimation change amount differential z ₂With known interference effect amount w ₀By carrying out known function f ₀(z ₁, z ₂, w ₀) come, calculate known action amount f ₀But known action amount exerciser 105 is not necessary, when known action is failed to understand, can ignore.

Again, the multi-form selection portion 113 of transient process, as the feature of most critical of the present invention, A.T.P102 is to setting value v ₀Generate transient process change amount v ₁And transition transition change amount differential v ₂The time employed transient process form function, according to user's indication, select a kind ofly in the middle of the pre-set multiple transient process form, offer A.T.P102.

Equally, nonlinear function selection portion 114 is as the feature of most critical of the present invention, when ESO103 calculates state estimation change amount z ₁, state estimation change amount differential z ₂, and uncertain effect estimator z ₃The time nonlinear function g that uses ₁, g ₂, g ₃, according to user's indication, select a kind ofly in the middle of the pre-set multiple kind, offer ESO103.

Also have, O.S.E.F109 as the feature of most critical of the present invention, though do not illustrate, for calculating the Error Feedback controlled quentity controlled variable, is suitable for the optimization nonlinear function.

To the action of the invention process form, make the following description with above-mentioned formation.

The operating principle of＜A.T.P102 〉

1. illustrated the same of the problem of " problem that invention will solve ", controlled target can saltus steps, but as the output of inertial element, the agenda of object can only be gradual, and it is irrational requiring " gradual behavior " tracking " target of sudden change ".Therefore, when A.T.P102 implements the FEEDBACK CONTROL of controlled device, not directly to use setting value, but generate transient process change amount and transient process change amount differential, then, this generation value is used for the FEEDBACK CONTROL of controlled device setting value.

The arrangement of transient process is by setting value (desired value) v ₀T settling time that can allow with object decides, and its general principle is: earlier the time interval of transient process [0T] separated into two parts: [0T ₁] and [T ₁T], a preceding part is a boost phase, a back part is the decelerating phase;

1. give a kind of acceleration a (t) of form

(1) definition of acceleration a (t)

[several 2]

(2) integration of a (t) on interval [0T] is 0.Be that the positive field of a (t) and the area in negative field are identical.

2. (the integrating acceleration a (t) of 0≤t≤T), the differential signal v of the transient process that obtains arranging from 0 to t ₂(t), i.e. the speed of transient process;

3. again from 0 to t integrating rate v ₂(t), obtain the transient process v that arranges ₁(t);

4. in order to simplify the calculation amount, the most handy polynomial form of acceleration a (t).

Condition enactment according to above 1～4, this patent inventor, definition " τ=t/T ", following several 3 formulas of decision and Fig. 2, several 4 formulas and Fig. 3, several 5 formulas and Fig. 4, several 6 formulas and Fig. 5, each shown transient process acceleration a (t), transient process change amount v ₁, and transient process differential signal v ₂Combination.

[several 3] $a\left(t\right)={\{}_{0,r>1}^{6v_0(1-2r)/{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">T</figure-callout>}}^2,r\&le;1}$ $v_1\left(t\right)={\{}_{{\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">v</figure-callout>}}_0,r>1}^{v_0{r}^3(3-2r),r\&le;1}$ $v_2\left(t\right)={\{}_{0,r>1}^{6v_{0}r(1-r)/T,r\&le;1}$

[several 4] $a\left(t\right)={\{}_{0,r>1}^{12v_0(2-3r)/T^2,r\&le;1}$ $v_1\left(t\right)={\{}_{v_0,r>1}^{v_0{r}^3(4-3r),r\&le;1}$ $v_2\left(t\right)={\{}_{0,r>1}^{12v_0{r}^2(1-r)/T,r\&le;1}$ [several 5] $a\left(t\right)={\{}_{0,r>1}^{12v_0(1-4r+3r^2)/T^2,r\&le;1}$ $v_1\left(t\right)={\{}_{v_0,r>1}^{v_0{T}^2(6-8r+3r^2),t\&le;1}$ $v_2\left(t\right)={\{}_{0,r>1}^{12v_{0}r{(1-r)}^2/T,r\&le;1}$ [several 6] $a\left(t\right)={\{}_{0,r>1}^{6o{v}_{0}r(1-3r+2r^2)/T^2,r\&le;1}$ $v_1\left(t\right)={\{}_{v_0,r>1}^{v_0{r}^3(10-15r+6r^2),r\&le;1}$ $v_2\left(t\right)={\{}_{0,r>1}^{3o{v}_0{r}^2{(1-r)}^2/T,r\&le;1}$

Here, several 3 formulas and Fig. 2 illustrate the transient process feature of controlled device form that the jump of acceleration is arranged when the initial moment and transient process finish corresponding to transient process; Several 4 formulas and Fig. 3 illustrate the transient process feature that the controlled device form of jump is arranged when finishing corresponding to transient process; Several 5 formulas and Fig. 4 illustrate the transient process feature that the controlled device form of jump is arranged when initial corresponding to transient process; Several 6 formulas and Fig. 5 illustrate corresponding to transient process equal transient process feature of the controlled device form of nonaccelerated jump when the starting and ending.In example of the present invention, when the user arranges transient process to controlled device, according to the various features of controlled device input value, to the transient process form selection portion 113 of Fig. 1, choose one of the 4 kinds of transient process forms shown in several 3～several 6 of stating, will be about transient process change amount v ₁And transient process differential signal v ₂The calculation formula be set in the A.T.P102, but, do not use the calculation formula of acceleration a (t).

The operating principle of＜ESO103 〉

ESO103 can estimate controlled device state and unknown interference.

At first, set the variable of state x of controlled device system, input value u, output valve y considers that then 1 output of the following stated goes into 2 nonlinear system of value.

[several 7] ${\{}_{y=x}^{\frac{d^2\mathrm{<figure-callout\; id="2"\; label="x\; d\; t"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">x</figure-callout>}}{d{t}^{}}=f_0(x,\frac{\mathrm{dx}}{\mathrm{dt}},w_0)+f_1(x,\frac{\mathrm{dx}}{\mathrm{dt}},w)+\mathrm{bu}}$

Here, w ₀Be known limited interference, w is unknown limited interference, f ₀(x, dx/dT, w ₀) be the known dynamic characteristic of system that comprises known disturbances.f ₁(x, dx/dT, w) (simple in order to illustrate, be designated hereinafter simply as f ₁()) be the dynamic characteristic that comprises system's the unknown of unknown disturbances.Suppose f ₁() is uncertain or can not measure exactly, and f ₀(x, dx/dT, w ₀) when failing to understand, can ignore.B is relevant with input value u, and its value is known.That can measure from several 7 formulas is exactly x and u.The ESO103 most important function is exactly to measure the dynamic characteristic f of the unknown of several 7 formulas ₁() is as long as f is estimated in design ₁The observer of () feeds back to controlled device controlled quentity controlled variable u (Fig. 1) by its estimated value and can compensate unknown dynamic characteristic f ₁().

For this reason, the following parameter of definition.

[several 8] $a\left(t\right):=f_1(x,\frac{\mathrm{dx}}{\mathrm{dt}},w)$ With above-mentioned several 8 formulas, the 1st row of several 7 formulas can be changed into as follows: [several 9] $\frac{d^2\mathrm{<figure-callout\; id="2"\; label="x\; d\; t"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">x</figure-callout>}}{d{t}^{}}=a+f_0(x,\frac{\mathrm{dx}}{\mathrm{dt}},w_0)+\mathrm{bu}$

Above-mentioned several 9 formulas are for constituting the mathematic(al) mode of ESO103.Here, importantly, the dynamic characteristic f of controlled device system ₁() regards simple function of time a (a (t)) as, and a is irrelevant in the acceleration from several 1 formulas to several 6 formulas, only is used in the parameter of the inside of formula.

Below, define following new state parameter.

[several 10]

From several 10 formulas, the nonlinear system of several 9 formulas is made into following equation of state.

[several 11]

The x of above-mentioned several 11 formulas ₃Can be described as " expansion state parameter ".For estimated state parameter x ₁, x ₂, x ₃, the nonlinear observer that is constructed as follows.To this theory, please refer to the Chinese literature [4] of above-mentioned table 1.

[several 12]

The β that above-mentioned several 12 formulas comprise ₀₁, β ₀₂, β ₀₃(＞0) is adjustable parameter, and g ₁(ε), g ₂(ε), g ₃(ε) be the suitable nonlinear function of error ε.z ₁And z ₂Be the estimation of variable He its differential of controlled device state, and z ₃(t) the real-time summation effect that provides all ambiguous models of object and disturb outward.

The Nonlinear System of Equations of above-mentioned several 12 formulas with the simplest Euler (Euler) approximate solution shown in following several 13 formulas, is found the solution several 14 formulas.

[several 13]

By inciting somebody to action $\frac{\mathrm{dx}}{\mathrm{dt}}=f(t,x)$ Be approximately $\frac{x(t+h)-x\left(t\right)}{h}=f(t,x)$

As with the calculating of getting off

x(t＋h)＝x(t)＋hf(t，x)

[several 14]

In several 14 formulas, t is a discrete time, and h is the sampling step length of discrete time.Like this, decision adjustable parameter β ₀₁, β ₀₂, β ₀₃And nonlinear function g ₁, g ₂, g ₃After, to each discrete time t, as state estimation value z ₁(t) and the error ε (t) that calculates of the error of controlled device output valve y (t) and, from according to state estimation value z ₁(t) and state estimation value differential z ₂(t) and uncertain effect estimated value z ₃(t) and, the control of controlled device import the input value bu (t) that obtains after the known parameters on duty and, z ₁(t), z ₂(t) and known interference effect amount w ₀(t), the known action amount f that calculates ₀(z ₁(t), z ₂(t), w ₀(t)), calculate state estimation value z1 and state estimation value differential z to following discrete time t+h ₂And uncertain effect estimated value z ₃And, when above-mentioned known action amount is failed to understand, can ignore f ₀(z ₁(t), z ₂(t), w ₀(t)).

In several 14 formulas, nonlinear function g ₁(ε), g ₂(ε) and g ₃Selection (ε) (below, " (t) " omitted explanation), the key factor of differentiation ESO103 performance.In the middle of the document in the past, this patent inventor, employing be the nonlinear function shown in several 15 formulas.

[several 15]

g _i(ε)＝|ε| ^αsign(ε)

Here, Sign (ε) is the function of the value of symbol (+1 or-1) of calculation error ε.

But this calculates more complicated, and the calculation amount is also very big, and control performance is impacted.Therefore, the present inventor, invention substitutes the nonlinear function g of power time function with simple polygronal function ₁(ε), g ₂(ε) and g ₃(ε).These polygronal functions are input as x (corresponding above-mentioned ε) to function, with any function representation of following several 16 formulas and Fig. 5 (a) or several 17 formulas and Fig. 5 (b).

[several 16] $\mathrm{fp}{l}_2(x,{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A0112943300371.png,A0112943300381.png"\; state="\{\{state\}\}">d</figure-callout>}}_1,k_1)={\{}_{((k_1-k_2){\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A0112943300371.png,A0112943300381.png"\; state="\{\{state\}\}">d</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">k</figure-callout>}}_2|x\left|\right)\mathrm{sign}\left(x\right),\left|x\right|>d_1}^{k_{1}x,\left|x\right|\&le;{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A0112943300371.png,A0112943300381.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}$ 0＜d ₁＜1，0＜k ₁，k ₁d ₁≤1， ${\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">k</figure-callout>}}_2=\frac{1-k_1{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="A0112943300371.png,A0112943300381.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}{1-d_1}$ [several 17] fpl ₃(x, d ₁, d ₂, k ₁, k ₂) 0＜d ₁＜d ₂＜1,0＜k ₂＜k ₁, (k ₁-k ₂) d ₁+ k ₂d ₂＜1, $k_3=\frac{1-(k_1-k_2)d_1-k_2{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}{1-{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}$

The calculation of these polygronal functions is fairly simple, as long as suitably select parameter d ₁, d ₂, k ₁, k ₂Just can reduce the calculation amount of ESO103, and provide the estimation effect of feeling quite pleased.

By with several 16 formula fpl ₂(x, d ₁, k ₁) or several 17 formula fpl ₃(x, d ₁, d ₂, k ₁, k ₂) the nonlinear function g that calculates several 14 formulas ₁(ε), g ₂(ε) and g ₃(ε) come,, calculate state estimation value z with few calculation amount ₁, state estimation value differential z ₂, and uncertain effect estimated value z ₃

The user selects part 114 by the nonlinear function of Fig. 1, carries out each g ₁(ε), g ₂(ε) and g ₃(ε), fpl ₂(x, d ₁, k ₁) or fpl ₃(x, d ₁, d ₂, k ₁, k ₂) correspondence.

The operating principle of＜O.S.E.F109 〉

As controlled device, the same when investigating ESO103, consider 2 nonlinear system that the output of 1 shown in several 7 formulas is gone into.

As mentioned above, because the observer of the unknown dynamic characteristic f () of ESO103 explanation design energy estimative figure 7 formulas.So, O.S.E.F109, the controlled quentity controlled variable u (Fig. 1) according to controlled device feeds back its estimated value, thus compensating non-linear characteristic f ₁().

Existing, controlled quentity controlled variable u (or u (t)) is resolved into 2 parts.

[several 18]

u＝u ₀₀＋u ₁

u(t)＝u ₀₀(t)＋u ₁(t)

Here, we with uncertain effects such as uncertain mathematical model or uncertain interference and, known action such as known models or known disturbances are broadly defined as " interference effect ", controlled quentity controlled variable u ₀₀(or u ₀₀(t)) for not relying on the pure Error Feedback item of controlled device of interference effect.Below, we are referred to as the Error Feedback controlled quentity controlled variable.Conversely, controlled quentity controlled variable u ₁(or u ₁(t)), for the compensate for disturbances effect the item.Below, we are referred to as the interference compensation controlled quentity controlled variable.

If interference compensation controlled quentity controlled variable u ₁Can compensate uncertain effect and known action such as known models or known disturbances such as ambiguous model or uncertain interference exactly, can eliminate the 1st and the 2nd on the right of several 7 formulas, as a result, controlling object system and system shown below become much at one, and realize the active disturbance rejection function.

[several 19] $\frac{d^2\mathrm{<figure-callout\; id="2"\; label="x\; dt"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">x</figure-callout>}}{{\mathrm{dt}}^{}}=b{u}_{00}$ --simple integrator continuous type object

According to several 14 formulas, the estimated value z of ESO103 output ₃(t) be the estimated value of all ambiguous models and uncertain interference.Again, the state estimation value z that exports according to ESO103 ₁(t) and output state estimation value differential z ₂(t) and known interference effect amount w ₀(t), can calculate known action amount f ₀(z ₁(t), z ₂(t), w ₀(t)).Then, calculate interference compensation operational ton u with several 20 formulas ₁(t), can compensate uncertain effect and known action such as known models or known disturbances such as ambiguous model or uncertain interference exactly, can make the system objective system become the state shown in several 19 formulas, can realize the active disturbance rejection function.

[several 20] $u_1\left(t\right)=-\frac{z_3\left(t\right)+f_0(z_1\left(t\right),z_2\left(t\right),w_0\left(t\right)))}{b}$

Example of the present invention shown in Figure 1, at first, known action amount exerciser 105 is according to the state estimation value z of ESO103 output ₁(t) and state estimation value differential z ₂(t) and known interference effect amount w ₀(t), calculate known action amount f ₀(z1 (t), z ₂(t), w ₀(t)), then, addometer 110 above-mentioned the resulting in and the uncertain effect estimated value exported of ESO103 that add also has, multiplier 111, according to its result that adds take advantage of-1/b calculates the interference compensation controlled quentity controlled variable u shown in several 20 formulas ₁(t).

The PID in past control does not have the interference compensation controlled quentity controlled variable, its usefulness be from setting value v ₀Directly generate its differential signal and integrated signal with the output error ε of controlling object, again, " weighted sum " form shown below generates controlled quentity controlled variable u.

[several 21] $u={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">k</figure-callout>}}_0{\&Integral;}_0^1\mathrm{\&epsiv;dt}+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="A0112943300371.png,A0112943300381.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\mathrm{\&epsiv;}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\frac{\mathrm{d\&epsiv;}}{\mathrm{dt}}$

On the function gimmick of this compensation unknown disturbances, the present invention, above-mentioned head and shoulders above gimmick in the past.

One side, Error Feedback controlled quentity controlled variable u ₀₀, be interference-free of acting on and compensating controlling object change amount purely.As mentioned above, the estimated value z of ESO103 output ₁(t) and z ₂(t) the change amount and the differential signal thereof of the estimated value of charge system Obj State.Again, the v that A.T.P102 exported ₁(t) and v ₂(t) refer to that setting refers to v ₀Transient process change amount and differential signal thereof, like this, we can be according to several 22 formulas, can calculate the error ε that transient process that this change amount and the pairing setting of differential signal thereof are planted and state estimation refer to ₁(t) and ε ₂And realize calculating Error Feedback controlled quentity controlled variable u (t), with these margins of error ₀₀(t) possibility.

[several 22]

ε ₁(t)＝v ₁(t)－z ₁(t)

ε ₂(t)＝v ₂(t)－z ₂(t)

The present inventor is as according to change amount error ε ₁(t) and change amount differential error ε ₂(t), calculate Error Feedback controlled quentity controlled variable u ₀₀(t) gimmick has been invented and has been used suitable nonlinear function g (ε ₁(t), ε ₂(t)) gimmick, in other words, Error Feedback controlled quentity controlled variable u ₀₀(t), can calculate with following several 23 formulas.

[several 23]

u ₀₀(t)＝g(ε ₁(t)，ε ₂(t))

The present inventor, Fa Ming " automatic disturbance rejection controller (ADRC) " lining in the past, its Error Feedback controlled quentity controlled variable u ₀₀, be (discrete time index " (t) " will be omitted) of calculating with the nonlinear function shown in following several 24.

[several 24]

u ₀₀＝β ₁|ε ₁| ^α1sign(ε ₁)＋β ₂|ε ₂| ^α2sign(ε ₂)

Though this formula is to play the effect of accelerating target following, does not consider the optimality of error combination, for a long time, what mode a lot of people discussed with and come controlling object to make it reach the problem of controlled target by the optimum way of certain meaning.To pure integrator series connection shape object, obtained the ideal formula of error combination.

[several 25] $u_{00}=\mathrm{rsign}({\mathrm{\&epsiv;}}_1+\frac{\left|{\mathrm{\&epsiv;}}_2\right|{\mathrm{\&epsiv;}}_2}{2r})$

But, this be only get two value+r and-function of r.If when directly controlling with this formula, Error Feedback controlled quentity controlled variable u ₀₀On desired value, stop incessantly to be easy to generate high frequency oscillation at target proximity.What Fig. 6 (a) illustrated is for making change amount error ε with several 25 formulas ₁And change amount differential error ε ₂Each value (Error Feedback controlled quentity controlled variable u soon that becomes 0 ₀₀Consistent with desired value) and ε when carrying out compensating movement ₁And ε ₂The variation of value.

Can learn near ε initial point from this chart ₁And ε ₂Value produce concussion.Therefore, the nonlinear function of several 25 formulas still is difficult to the problem that is used to the working control process.For example, use in simple modification, its effect still is not ideal, so this theoretical being difficult to is popularized.

For solving the calculation shakedown problems of following the tracks of differentiator, the present inventor has provided the quick optimum control comprehensive function of the discrete form that depends on sampling step length h formula in the Chinese literature [2] of above-mentioned table 1: (The synthesis function of time-optimal control ofthe discrete system with the sampling steph).

[several 26]

d＝rh

d ₀＝dh

y＝x ₁－v＋hx ₂ $a_0=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}^2+8r\left|y\right|}$ $={\{}_{x_2+\frac{\mathrm{sign}\left(y\right)(a_0-d)}{2},\left|y\right|>d_0}^{x_2+\frac{y}{h},\left|y\right|\&le;{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}_0}$ $\mathrm{fs}{t}_2(x_1,x_2,v,r,h)={\{}_{-\mathrm{rsign}\left(a\right),\left|a\right|>d}^{-\frac{\mathrm{ra}}{d},\left|a\right|\&le;d}$

This formula can not directly be used and Error Feedback controlled quentity controlled variable u ₀₀Calculation, still, just can use as long as change this formula 27 formulas are the same in full as can be seen.(below, consider discrete time index " (t) ".)

[several 27]

d＝rh ₁

d ₀＝dh ₁

y＝ε ₁(t)＋h ₁ε ₂(t) $a_0=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}^2+8r\left|y\right|}$ $a={\{}_{{\mathrm{\&epsiv;}}_2\left(t\right)+\frac{\mathrm{sign}\left(y\right)(a_0-d)}{2},\left|y\right|>{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}_0}^{{\mathrm{\&epsiv;}}_2\left(t\right)+\frac{\mathrm{<figure-callout\; id="1"\; label="y\; h"\; filenames="A0112943300371.png,A0112943300381.png"\; state="\{\{state\}\}">y</figure-callout>}}{h_{}},\left|y\right|\&le;{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">d</figure-callout>}}_0}$ $\mathrm{fst}({\mathrm{\&epsiv;}}_1\left(t\right),{\mathrm{\&epsiv;}}_2\left(t\right),r,h_1)={\{}_{\mathrm{rsign}\left(a\right),\left|a\right|>d}^{\frac{\mathrm{ra}}{d},\left|a\right|\&le;d}$

u ₀₀(t)＝fst(ε ₁(t)，ε ₂(t)，r，h ₁)

Here, r refers to parameter.

The O.S.E.F109 of Fig. 1 is with above-mentioned several 27 formulas, to every discrete time t, according to change amount ε ₁(t) and change amount differential error ε ₂(t) and, parameter r and h ₁, output error FEEDBACK CONTROL amount u ₀₀(t).

And y in several 26 formulas and several 27 formulas and the controlled device output valve y of Fig. 1 are irrelevant.Again, the function a (t) of the acceleration a (t) of a and several 1 formula～several 6 formulas or several 9 formulas is irrelevant.This variable all only is used in these formula inside.

What Fig. 6 (b) illustrated is, with several 27 formulas for making change amount error ε ₁(t) and change amount differential error ε ₂(t) each value becomes 0 and ε during the execution compensating movement ₁(t) and ε ₂(t) variation.Compare with Fig. 6 (b), can learn ε according to several 25 formulas ₁(t) and ε ₂(t) value can not produce concussion near initial point, carry out extraordinary compensating movement.

Below, describe the concrete motion flow of example in detail according to Fig. 1 of above-mentioned action specification.

The motion flow of＜initial setting 〉

At first, carry out the initial setting of the optimization ADRC101 of Fig. 1.Fig. 8 is the action flow chart of initial setting.This action flow chart, the central processing unit (CPU) of all actions of the optimum ADRC101 of realization control chart 1, there is the control program not have illustrated especially special reading memory storehouse (ROM) to wait in note, and use does not have the action of working memory storehouses such as (RAM), illustrated especially reading and writing memory storehouse execution.

At first, the parameter h that A.T.P102 and ESO103 use, be set in the illustrated especially variable management holder not (with reference to Fig. 8 801).Parameter h is the sampling step length of discrete time.

Then, the maximum calculation time T max when indication stops to control, be set in the illustrated especially variable management holder not (with reference to Fig. 8 802).

Then, the desired value v that A.T.P102 is used in calculation ₀, be set in the illustrated especially variable management holder not (with reference to Fig. 8 803).

Then, T settling time that A.T.P102 uses in calculation, be set in the illustrated especially variable management holder not (with reference to Fig. 8 804).

Then, by transient process form selection portion 113, indication according to the user, lining, illustrated never especially special reading memory storehouse (ROM) is pre-selects the function of the transient process form that A.T.P102 uses in calculation in the various ways that note keeps, and be set in the illustrated especially variable management holder not (with reference to Fig. 8 805).

Then, the initial stage output valve z in time T=0 o'clock of ESO103 ₁(0), z ₂(0), reaches z ₃(0) each value be set to 0 (with reference to Fig. 8 806).

Then, the adjustable parameter β that ESO103 is used in calculation ₀₁, β ₀₂, β ₀₃, be set in the illustrated especially variable management holder not (with reference to Fig. 8 807).

Then, the nonlinear function g that uses in the ESO103 calculation ₁, g ₂And g ₃, by nonlinear function selection portion 114, according to user's indication, the function f pl that lining, illustrated never especially special reading memory storehouse (ROM) keeps in note in advance ₂Or fpl ₃In select one, and set in does not wait in illustrated especially reading and writing memory storehouse (RAM), simultaneously, the parameter combinations { d of these functions uses ₁, k ₁(work as fpl ₂When selected) or { d ₁, d ₂, k ₁, k ₂(work as fpl ₃When selected) also be set in the illustrated especially variable management holder not (with reference to Fig. 8 808).

Then, input value adjustability coefficients b, be set in the illustrated especially variable management holder not (with reference to Fig. 8 809).

Then, the calculation program of decision known action flow function f0, be set to lining, illustrated especially reading and writing memory storehouse (RAM) not (with reference to Fig. 8 810).

Then, parameter r and the h that O.S.E.F109 is used in calculation ₁, be set in the illustrated especially variable management holder not (with reference to Fig. 8 811).And setup parameter h ₁Value greater than the h value of the sampling step length of 801 li settings of Fig. 8.

At last, the parameter h that set according to 801 of several 27 formulas and Fig. 8 ₁And r, parameter d and d that calculation O.S.E.F109 uses in calculation ₀, and be set in the illustrated especially variable management holder not (with reference to Fig. 8 812).

＜main body action flow chart 〉

After above-mentioned initial setting motion flow was performed, the main body motion flow began to carry out.Fig. 9 is the main body action flow chart.This action flow chart, the central processing unit (CPu) of all actions of the optimum ADRC101 of realization control chart 1, there is the control program not have illustrated especially special reading memory storehouse (ROM) to wait in note, and use does not have the action of working memory storehouses such as (RAM), illustrated especially reading and writing memory storehouse execution.

The main body motion flow, at first be set in after the time variable t that does not have in the illustrated especially variable management holder is set to 0, (901 among Fig. 9) according to fixed discrete time at interval, time variable t increases (905 among Fig. 9) with the unit of the step-length h that 801 of Fig. 8 sets, surpass the maximum calculation time T max that 802 of Fig. 8 sets up to judgement time variable t, (when 906 among Fig. 9 judges NO) with each discrete time t office, (902 among Fig. 9) handled in the action of A.T.P102, the action processing (904 among Fig. 9) that (903 among Fig. 9) and ESO10 3 are handled in the action of O.S.E.F109 is performed one by one.

When judgement time variable t surpassed maximum calculation time T max, (when 906 among Fig. 9 judges YES) just finished the optimum ADRC control action of an action potential.

The motion flow of＜A.T.P102 〉

Figure 10 is, as 902 processing of the main body motion flow of Fig. 9, the action flow chart of the expression A.T.P102 that is performed action.This action flow chart, handle the central processing unit (CPU) of the action of A.T.P102, there is the A.T.P operation control program not have illustrated especially special reading memory storehouse (ROM) to wait in note, and use does not have the action of working memory storehouses such as (RAM), illustrated especially reading and writing memory storehouse execution.

At first,, remove T settling time that 804 of Fig. 8 sets and come, calculate variable τ (records before reference number 3 formulas) above-mentioned time variable t, after be saved in illustrated especially variable manager not (with reference to Figure 10 1001).

Then,, use the function of the transient process form of selecting in the transient process form selection portion 113, use the calculation formula of choosing any one kind of them of above-mentioned several 3 formulas～several 6 formulas, calculate transient process change amount v discrete time t from 805 li of Fig. 8 ₁(t) and transient process change amount differential v ₂(t), be saved in not illustrated especially variable manager after.At this moment, 803 of Fig. 8 desired value v that set ₀With, 804 of Fig. 8 sets settling time t and, the variable τ that 1001 of Figure 10 calculates is used in the calculation (more than, Figure 10 1002 and 1003).

Like this, A.T.P102, just can generate Fig. 9 the main body motion flow according to successive transformation discrete time t produced to desired value v ₀Transient process change amount v ₁(t) and transient process change amount differential v ₂(t).

The motion flow of＜O.S.E.F109 〉

Figure 11 is, as 903 processing of the main body motion flow of Fig. 9, the action flow chart of the demonstration O.S.E.F109 that is performed action.This action flow chart, handle the central processing unit (CPU) of the action of O.S.E.F109, there is the O.S.E.F operation control program not have illustrated especially special reading memory storehouse (ROM) to wait in note, and use does not have the action of working memory storehouses such as (RAM), illustrated especially reading and writing memory storehouse execution.

At first, according to above-mentioned several 22 formulas, respectively calculate the transient process change amount v of the discrete time t that 1002 of Figure 10 is calculated ₁(t) and following Figure 12 that will illustrate 1206, to a discrete time (the state estimation value change amount z of=discrete time t that t-1) calculates ₁(t) change amount error ε ₁(t) and, the transient process change amount differential v of the discrete time t that 1003 of Figure 10 calculates ₂(t) and following Figure 12 that will illustrate 1207, to a discrete time (the state estimation value change amount differential z of=discrete time t that t-1) calculates ₂(t) change amount error differential ε ₂(t), be saved in after illustrated especially variable manager not (with reference to Figure 11 1101).

Then, according to several 27 formulas, calculate above-mentioned ε ₁(t) and ε ₂(t) and, use the 801 parameter h that set of Fig. 8 ₁, calculate variable y, after be saved in illustrated especially variable manager not (with reference to Figure 11 1102).

Then,, use 812 parameter d that calculate of the 811 parameter r that calculate and same Fig. 8 of above-mentioned variable y and Fig. 8, calculate variable a according to several 27 formulas ₀After be saved in illustrated especially variable manager not (with reference to Figure 11 1103).

Then, according to several 27 formulas, judgment variable y whether under the parameter d 0 that 812 of Fig. 8 calculates (with reference to Figure 11 1104).

If this judgement is YES,, use the change amount error differential ε that calculates at 1101 of Figure 11 according to the 1st kind (top) of the calculation formula of several 27 formula built-in variable a ₂(t) and, the parameter h that 801 of Fig. 8 sets ₁With, the variable y that 1102 of Figure 11 calculates calculates variable a, after be saved in illustrated especially variable manager not (with reference to Figure 11 1105).

One side, 1104 the judgement of Figure 11 is NO, according to the 2nd kind (below) of the calculation formula of several 27 formula built-in variable a, uses the change amount error differential ε that calculates at 1101 of Figure 11 ₂(t) and the 1102 variable y that calculate of 812 parameter d that set of Fig. 8 and Figure 11 and, the variable a that 1103 of Figure 11 calculates ₀Calculate variable a, after be saved in illustrated especially variable manager not (with reference to Figure 11 1106).

Then, according to several 27 formulas, judge variable a that 1105 or 1106 of above-mentioned Figure 11 calculates whether under the parameter d that 812 of Fig. 8 calculates (with reference to Figure 11 1107).

If, this judgement is YES, according to the 1st kind (top) of the calculation formula of several 27 formula intrinsic function fst, uses the parameter r that sets at 811 of Fig. 8 and the 1105 or 1106 variable a that calculated of Figure 11, enumeration function value fst, its value is as the Error Feedback controlled quentity controlled variable u to discrete time t ₀₀(t) be saved in illustrated especially variable manager not (with reference to Figure 11 1108).

One side, 1107 the judgement of Figure 11 is NO, the 2nd kind (below) according to the calculation formula of several 27 formula intrinsic function fst, the parameter r that use sets at 811 of Fig. 8 and, 1105 or the 1106 variable a that calculated of Figure 11, enumeration function value fst, its value is as the Error Feedback controlled quentity controlled variable u to discrete time t ₀₀(t) be saved in illustrated especially variable manager not (with reference to Figure 11 1109).

Then, use addometer 110 and multiplier 111,, calculate interference compensation controlled quentity controlled variable u according to several 20 formulas ₁(t), in this calculation, at first, according to 1206 and 1207 of following Figure 12 that will illustrate, to (the state estimation value change amount z of=discrete time t that t-1) calculates before 1 discrete time ₁(t) and state estimation value change amount differential z ₂(t) and, from the known disturbances action w of the discrete time t of outside input ₀(t), 810 of the execution graph 8 known function calculation f that set ₀(z ₁(t), z ₂(t), w ₀(t)), calculate known action amount f to discrete time t ₀, after be saved in not illustrated especially variable manager, then, by on the known action amount f that calculates to discrete time t ₀With, below 1208 of the Figure 12 that will illustrate, to (the uncertain effect estimated value z of=discrete time t that t-1) calculates before 1 discrete time ₃(t), add with addometer 110, its result that adds is again by (1/b) (input adjustability coefficients b sets for 809 of Fig. 8) takes advantage of calculation, and the back it take advantage of the calculation result as the interference compensation controlled quentity controlled variable u to discrete time t ₁(t) be saved in illustrated especially variable manager not (with reference to Figure 11 1110).

At last, 1108 of Figure 11 or the 1109 Error Feedback controlled quentity controlled variable u that calculate ₀₀(t) and above-mentioned interference compensation controlled quentity controlled variable u ₁(t) back (addometer 112) that adds as the controlled quentity controlled variable u (t) to discrete time t, is saved in not illustrated especially variable manager, simultaneously controlling object export its value (with reference to Figure 11 1111).

Like this, O.S.E.F109 can carry out the optimization compensating movement of controlled device.

The motion flow of＜ESO103 〉

Figure 12 is, as 904 processing of the main body motion flow of Fig. 9, the action flow chart of the demonstration ESO103 that is performed action.This action flow chart, handle the central processing unit (CPU) of the action of ESO103, there is the ESO operation control program not have illustrated especially special reading memory storehouse (ROM) to wait in note, and use does not have the action of working memory storehouses such as (RAM), illustrated especially reading and writing memory storehouse execution.

At first, from the input adjustability coefficients b that the controlled quentity controlled variable u to discrete time t (t) lining that 1111 of Figure 11 calculates takes advantage of 809 of nomogram 8 to set, it is taken advantage of and calculates on the result known action amount f to discrete time t that 1110 of the Figure 11 that adds calculates ₀, after calculate variable bu (t)+f for the moment ₀Be saved in not illustrated especially variable manager, simultaneously controlling object export its value (with reference to Figure 12 1201).

Then, according to several 14 formulas, with Figure 12 1206 to a discrete time (the state estimation value change amount z of=discrete time t that t-1) calculates ₁(t) and, be input to the controlling object output valve y (t) to discrete time t (now) of controlling object, calculate error ε (t) to discrete time t (with reference to Figure 12 1202).

Then, according to 808 the setting of Fig. 8, with several 16 formula (fpl ₂When being chosen) or several 17 formula (fpl ₃When being chosen), calculate out nonlinear function g to discrete time t ₁(ε (t))=fpl ₂(ε (t), d ₁, k ₁) or g ₁(ε (t))=fpl ₃(ε (t), d ₁, d ₂, k ₁, k ₂) (with reference to Figure 12 1203).

Equally, according to 808 the setting of Fig. 8,, calculate out nonlinear function g to discrete time t with several 16 formulas or several 17 formulas ₂(ε (t))=fpl ₂(ε (t), d ₁, k ₁) or g ₂(ε (t))=fpl ₃(ε (t), d ₁, d ₂, k ₁, k ₂) (with reference to Figure 12 1204).

Also have,, calculate out nonlinear function g discrete time t according to 808 the setting of Fig. 8 ₃(ε (t))=fpl ₂(ε (t), d ₁, k ₁) or g ₃(ε (t))=fpl ₃(ε (t), d ₁, d ₂, k ₁, k ₂) (with reference to Figure 12 1205).

Then, according to several 14 formulas, before per 1 discrete time of 1206 and 1207 to Figure 12 (=t-1), the state estimation value change amount z that is calculated to discrete time t ₁(t) and state estimation value change amount differential z ₂(t) and, the nonlinear function g that 1203 of above-mentioned Figure 12 calculates to discrete time t ₁(ε (t)) and, the parameter h that 801 of Fig. 8 sets and, the adjustable parameter β that 807 of Fig. 8 sets ₀₁As the basis, control is to next discrete time (=t+h) state estimation value change amount z ₁(t+h).This state estimation value change amount z ₁(t+h), as z to next discrete time ₁(t), the content of its variable is replaced.After be saved in not illustrated especially variable manager, (with reference to Figure 12 1206).

Then, according to several 14 formulas, before per 1 discrete time of 1207 and 1208 to Figure 12 (=t-1), the state estimation value change amount differential z that is calculated to discrete time t ₂(t) and uncertain effect estimated value z ₃(t) and, the nonlinear function g that 1204 of above-mentioned Figure 12 calculates to discrete time t ₂(ε (t)) and, the parameter h that 801 of Fig. 8 sets and, the adjustable parameter β that 807 of Fig. 8 sets ₀₂With, variations per hour bu (the t)+f that 1201 of Figure 12 calculates ₀As the basis, control is to next discrete time (=t+h) state estimation value change amount differential z ₂(t+h), this state estimation value change amount differential z ₂(t+h), as z to next discrete time ₂(t), the content of its variable is replaced.After be saved in not illustrated especially variable manager, (with reference to Figure 12 1207).

At last, according to several 14 formulas, before per 1 discrete time of 208 to Figure 12 (=t-1), the uncertain effect estimated value z that is calculated to discrete time t ₃(t) and, the nonlinear function g that 1205 of above-mentioned Figure 12 calculates to discrete time t ₃(ε (t)) and, the parameter h that 801 of Fig. 8 sets and, the adjustable parameter β that 807 of Fig. 8 sets ₀₃As the basis, control is to next discrete time (=t+h) uncertain effect estimated value z ₃(t+h), this uncertain effect estimated value z ₃(t+h) as z to next discrete time ₃(t), the content of its variable is replaced.After be saved in not illustrated especially variable manager, (with reference to Figure 12 1208).

Like this, with few calculation amount, can calculate state estimation value change amount z to discrete time t ₁(t), state estimation value change amount differential z ₂(t), reach uncertain effect estimated value z ₃(t).

Below, to the effect that the invention described above example is brought, lift the object lesson explanation.

At first, controlled device is assumed to be following several 28 formulas.For

[several 28] $\frac{d^2\mathrm{<figure-callout\; id="2"\; label="x\; d\; t"\; filenames="A0112943300381.png,A0112943300382.png"\; state="\{\{state\}\}">x</figure-callout>}}{d{t}^{}}=\mathrm{rsign}\left(\sin \left(\frac{t}{2}\right)\right)+u$

Here

[several 29] $\mathrm{rsign}\left(\sin \left(\frac{t}{2}\right)\right),0<r\&le;10$

Interference for the unknown.

If control target is v ₀=1, promptly setting value is 1.Get T=3 second settling time.Select in the form of transient process by above-mentioned several 6 formulas of arranging.Nonlinear function g among the ESO ₁(ε), g ₂(ε), g ₃(ε) and parameter beta ₀₁, β ₀₂, β ₀₃Be taken as follows respectively:

[several 30]

Controlled quentity controlled variable u ₀₀Calculate the sampling step length h=0.01 of discrete time with following formula.

[several 31]

u ₀₀(t)＝fst(ε ₁(t)，ε ₂(t)，10，0.05)

As follows according to the above experimental result that imposes a condition when controlling.Figure 13 and Figure 14 show the control effect of γ=1 o'clock and γ=10 o'clock and the ESO estimation condition to unknown disturbance respectively.

Find out that from experimental result " optimum automatic disturbance rejection controller " of the present invention can control very large-scale object.

More than, though a kind of example of the present invention has been made detailed explanation, the present invention also can bring into play its effect independently of one another with after other controlling factor combination such as A.T.P102, ESO103 and O.S.E.F109.

Also have, to ESO103, several 7 formulas of the invention process form, several 12 formulas in the explanation of several 14 formulas etc., as the controlled device system, suppose it is 2 nonlinear system, but the present invention is not limited thereto, also are easy to n time expansion.To n time gross morphology, such as (5) formula of document B, the nonlinear function gj (z here ₁(t)-x (t)) on, being suitable for several 16 formulas or several 17 formulas shown in the invention process form is without any circumscribed.

Also have, among the present invention, the various nonlinear functions shown in the invention described above example also can use suitable linear function as an alternative.

According to the present invention, " optimum automatic disturbance rejection controller " can detect automatically and " in disturb (model) " and " disturbing outward " of target compensation acts on, thereby also can guarantee very high control accuracy under various rugged surroundings.

Also have, realizes when of the present invention, because nonlinear algorithm is simple, design optimization Active Disturbance Rejection Control system easily, and its parameter adaptation scope is wide, so can realize a kind of desirable practical digital controller.

" optimum active disturbance rejection controller " that the present invention realizes mainly has following 9 characteristics:

1) is independent of the fixed structure of mathematical model of controlled plant;

2) can realize fast, non-overshoot, zero steady state error control;

3) controlled variable explicit physical meaning, easily setting parameter;

4) algorithm is simple, the ideal digital controller of can realize at a high speed, high accuracy being controlled;

5) need not to disturb outside the measurement and can eliminate its impact;

6) need not distinguish linearity, non-linear, the time become, the time constant object;

7) object model is known better, and the unknown is also harmless;

8) easily realize the control of large dead time object;

9) decoupling zero control is simple especially.

At present, most industrial control unit (ICU)s all occur with the digitial controller form, and old analog controller is also replaced by digital controller. Whole controller industry has entered digitlization, optimization, modularization, integrated epoch.

" optimum active disturbance rejection controller " that the present invention realizes is born for the requirement that adapts to this New Times, and it will remove extensive PID and the existing various forms " advanced controller " that adopts in the alternative Process control with higher efficient and precision.

Also have, the structure moulding of " optimum automatic disturbance rejection controller " of the present invention, to different object (object can belong to same class very on a large scale), the relevant parameter that only need adjust initial setting just can be practical.

Predecessor's " automatic disturbance rejection controller " of " optimum automatic disturbance rejection controller " of the present invention (ADRC), in the high speed of " robot ", High Accuracy Control; " the lasting group of planes control of mechanics "; " Control for Kiln Temperature "; " generator excitation control "; " magnetic levitation is floating apart from control "; " four hydraulic cylinders are coordinated control "; " motion control of gearing "; " variable frequency speed modulation of asynchronous motor control "; All obtained very ideal control effect in the full-scale investigation of different devices such as " controls of high-speed, high precision lathe for machining ".In " control of electric system controllable series compensation "; " control of electric system static reactive "; " earthquake-resistant architectural system control "; " control of space flight body attitude "; The simulation study that different field such as " controls of motion carrier platform " is carried out has also all obtained very ideal results.This shows the application that it is very big to us.

New " optimum automatic disturbance rejection controller " that the present invention realizes (OptimalARDC), compared with its predecessor " automatic disturbance rejection controller " (ADRC), algorithm is more simple, control efficiency is higher, has bigger application prospect.

Claims (8)

1. one kind is applicable to that the error of condition estimating value by controlling object and desired value calculates the FEEDBACK CONTROL of the controlled quentity controlled variable of controlled device, it is a kind of transient process control method of transient process of control target, it is the change type according to above-mentioned transient process displacement acceleration, determine the type of above-mentioned transient process, again, with the type of the transient process of above-mentioned decision control above-mentioned desired value transient process comprise the transient process control method of its transient process as feature.

2. control method as claimed in claim 1 is the same, it is the change type according to above-mentioned transient process displacement acceleration, determine the displacement differential-type of above-mentioned relevant transient process displacement differential, again, the displacement type that decides relevant transient process displacement according to this displacement differential-type comprises the transient process control method of its process as feature according to what this displacement type and displacement differential-type were controlled the transient process displacement of above-mentioned desired value and displacement differential again.

3. one kind is applicable to that the error of condition estimating value by controlling object and desired value calculates the feedback control system of controlled device controlled quentity controlled variable, it is a kind of transient process controller of transient process of control target, this is corresponding to the multiple change type of the displacement acceleration of above-mentioned transient process, it comprises the above-mentioned displacement differential-type and the memory storage of the displacement type of above-mentioned relevant transient process displacement and the multiple transient process type of memory and according to the state characteristic of controlled device about transient process displacement differential, from above-mentioned transient process type memory storage device, select a kind of displacement type and displacement differential-type, and according to selected type, generate the transient process displacement of above-mentioned desired value and the transient process generating apparatus of displacement differential and comprise foregoing, calculate the above-mentioned feedback control system of the controlled quentity controlled variable of above-mentioned controlling object according to the error of the displacement differential of the transient process displacement differential of the above-mentioned desired value of sum of errors of the transient process displacement of above-mentioned desired value and the displacement of above-mentioned controlled device condition estimating value and above-mentioned controlling object condition estimating value, as the transient process controller of feature.

4. one kind comprises with comprising that nonlinear function calculates the actual addendum modification of value displacement of controlling object condition estimating and above-mentioned controlling object state and the transforming function transformation function of error, and between state, utilize observer observation to comprise the expansion state observation procedure of uncertain effect of dynamic characteristic of the unknown of unknown interference and controlling object system, when calculating above-mentioned error with transforming function transformation function, calculate above-mentioned error with polygronal function, output valve according to this calculation, calculate each presumed value of repeatedly side of above-mentioned controlled device state and the presumed value of above-mentioned uncertain effect with above-mentioned observer, comprise the expansion observation procedure of above-mentioned each process as feature.

5. the error of the actual addendum modification of the presumed value displacement of a controlling object state and controlling object state usefulness comprises the transforming function transformation function mapping function of nonlinear function, comprise the extended state observer that utilizes observer that the uncertain effect of dynamic characteristic of the unknown of unknown interference and controlling object system can be observed by variable of state, by calculate above-mentioned error with polygronal function, realize conversion polygronal function calculation apparatus and according to the output valve of this polygronal function calculation apparatus with above-mentioned transforming function transformation function, the calculus of observation device that calculates the presumed value of each presumed value of repeatedly side of above-mentioned controlled device state and above-mentioned uncertain effect with above-mentioned observer comprises the extended state observer of above each device as feature.

The stand-off error of the error of the transient process displacement by calculating the presumed value displacement that refers to the controlled device state and desired value and, the displacement differential error of error that refers to the transient process displacement differential of the presumed value displacement differential of above-mentioned controlling object state and above-mentioned desired value, import this stand-off error and displacement differential error, calculating out this error is reduced to and levels off to zero the transforming function transformation function that can comprise nonlinear function jointly, calculate again above-mentioned controlling object controlled quentity controlled variable error just the feedback operation amount control the control of above-mentioned controlled device, compensate the feedback of above-mentioned controlling object state displacement, above-mentioned transforming function transformation function, when above-mentioned stand-off error and displacement differential error are reduced to zero, set the function that nearly zero circle that control makes this error amount encloses the vibrations that taken place and comprise the feedback of each process as feature.

7. control method as claimed in claim 6 is the same, with following formula the calculation of above-mentioned transforming function transformation function comprise the feedback of above-mentioned each process as feature,

[several 1]

d＝rh ₁

d ₀＝dh ₁

y＝ε ₁(t)＋h ₁ε ₂(t) $a_0=\sqrt{d^2+8r\left|y\right|}$ $a={\{}_{s_2\left(t\right)+\frac{\mathrm{sign}\left(y\right)(a_0-d)}{2},\left|y\right|>d_0}^{{\mathrm{\&epsiv;}}_2\left(t\right)+\frac{y}{h_1},\left|y\right|\&le;d_0}$ $\mathrm{fst}({\mathrm{\&epsiv;}}_1\left(t\right),{\mathrm{\&epsiv;}}_2\left(t\right),r,h_1)={\{}_{\mathrm{rsign}\left(a\right),\left|a\right|>d}^{\frac{\mathrm{ra}}{d},\left|a\right|\&le;d}$

u ₀₀(t)＝fst(ε ₁(t)，ε ₂(t)，r，h ₁)

Here, t: discrete time, ε ₁(t): to the stand-off error input value of discrete time t, ε ₂(t): to the displacement differential error input value of discrete time t, r: the setup parameter relevant, h with the transient process acceleration ₁: parameter, y: inner parameter, a ₀: inner parameter, sign (y) and sign (a): function, a of the value of symbol (+1 or-1) of calculation input value y or a: inner parameter, fst (ε ₁(t), ε ₂(t), r, h): nonlinear function value, u ₀₀(t): to the Error Feedback controlled quentity controlled variable of discrete time t.

8. feedback of calculating the controlled device controlled quentity controlled variable according to the error of the presumed value of controlling object state and desired value, change type according to the transient process displacement acceleration of desired value, determine the displacement differential-type of above-mentioned transient process, according to this displacement differential-type, determine the displacement type of above-mentioned transient process, again, according to the displacement type and the displacement differential-type that are determined, generate the process transition displacement of above-mentioned desired value and become slightly and divide, calculate and comprise the error of calculating the actual addendum modification of the presumed value displacement of above-mentioned controlled device state and above-mentioned controlled device state with polygronal function, between variable of state with have the observer of observing function to calculate to comprise presumed value and the condition estimating value displacement of above-mentioned controlled device and a displacement differential of above-mentioned controlled device condition estimating value of uncertain effect of dynamic characteristic of the unknown of unknown interference and controlled device system, calculate the just above-mentioned controlled device condition estimating of the sum of errors displacement differential error value displacement differential of process transition displacement of value displacement of the just above-mentioned controlled device condition estimating of stand-off error and above-mentioned desired value and the transient process displacement differential of above-mentioned desired value, if this stand-off error and displacement differential error are as input value, calculation comprises that its error narrows down to the transforming function transformation function of zero nonlinear function jointly, calculate the Error Feedback controlled quentity controlled variable of the controlled quentity controlled variable of above-mentioned controlled device, presumed value according to above-mentioned uncertain effect, the interference compensation controlled quentity controlled variable of the controlled quentity controlled variable of the above-mentioned controlled device of this uncertain effect of calculation compensation, control above-mentioned controlled device with above-mentioned Error Feedback controlled quentity controlled variable and above-mentioned interference compensation controlled quentity controlled variable, compensate the state of above-mentioned controlled device, comprise that process is as the certainly anti-random feedback of the optimization of feature.

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