CN109634123A - Active Disturbance Rejection Control parameter tuning method for pH N-process - Google Patents

Abstract

The present invention provides the Active Disturbance Rejection Control parameter tuning methods for pH N-process, including establishing initial automatic disturbance rejection controller structure, obtain closed loop transfer function, expression formula corresponding with initial automatic disturbance rejection controller structure, formal argument is carried out to closed loop transfer function, expression formula based on closed-loop system fast convergence condition, is determined to setting parameter；Setting parameter is treated one by one and carries out adjusting processing, is determined each to the calculation of setting parameter；Based on charge and carbide ionic equilibrium principle is established in pH and model, realizes pH N-process Active Disturbance Rejection Control, and combine to be each adjusted to the calculation of setting parameter to pH N-process automatic disturbance rejection controller parameter in determining automatic disturbance rejection controller；The control that pH N-process is realized by using improved automatic disturbance rejection controller, can have stronger robustness and anti-interference ability while guaranteeing system tracking performance；Compared to other automatic disturbance rejection controllers, it is possible to reduce to setting parameters, optimize adjusting efficiency.

Description

Active Disturbance Rejection Control parameter tuning method for pH N-process

Technical field

The invention belongs to process control fields, in particular to are used for the Active Disturbance Rejection Control parameter tuning side of pH N-processMethod.

Background technique

The control of pH N-process is widely present in the every field of human lives and production, is carried out to pH N-processQuickly it has been accurately controlled extremely important real value and economic benefit.The control of medicine and hygiene fields, pH value will be straightThe content for influencing virus and bacteria in water quality is connect, once there is control error, gently then leads to drug failure, it is heavy then generate poisonous and harmfulSubstance.And in the industrial production, such as sewage treatment link, the pH value control that water is discharged improper will cause serious water body dirtyDye, endangers ecological environment.In such as pickling, the chemical-process such as electrolysis, the pH value of reaction process will directly affect the matter of productAmount and yield, are related to the productivity effect of enterprise.

But due to itself strong nonlinearity of pH N-process, high-gain near the point of neutralization and it is difficult to modelReason.Control to pH N-process is always the problem of industrial process control field.It is transported in pH N-process control at presentWith traditional PID approach is most widely still, although pid algorithm has design simple, it is easy to accomplish the advantages of, due to pHThe characteristics of N-process strong nonlinearity and variable-gain, common pid algorithm can not obtain preferable control effect.Variable-gain orNon-linearity PID method is equally used in the control of pH N-process, although these methods optimize the control of pH N-processRapidity and accuracy, but the robustness of controller and anti-interference ability are still to be improved.As pH N-process modelsThe development of technology, self adaptive control, the advanced control methods such as Model Predictive Control by Successful utilization pH N-process differenceModel it is upper, and achieve excellent control effect.But these advanced control methods generally require biggish operand andComplicated control structure, it is difficult to be widely popularized in industrial processes.

Automatic disturbance rejection controller has controller algorithm structure simple, independent of accurate mathematical model, it is easy to accomplish, ShandongThe advantages of stick and strong antijamming capability, has been widely used in the control of process industry.Currently, active disturbance rejection method is in pHIt is applied seldom in the control of N-process, and the parameter that conventional Application of Auto-Disturbance Rejection needs to adjust is more, the shape observedThere is still a need for carry out just can be carried out feedback after nonlinear combination for state.Moreover, the implementation of automatic disturbance rejection controller lacks specific parameterAdjusting strategy, parameter tuning process is complex, this makes the Auto-disturbance-rejection Control of pH N-process in actual production processIn application with promote there are still many inconveniences.

Summary of the invention

In order to solve shortcoming and defect existing in the prior art, the present invention provides the active disturbance rejections for pH N-processControl parameter setting method is reduced to setting parameters by using improved automatic disturbance rejection controller model, is optimizedAdjust efficiency.

In order to reach above-mentioned technical purpose, the present invention provides the Active Disturbance Rejection Control parameter tuning sides for pH N-processMethod, the parameter tuning method, comprising:

Initial automatic disturbance rejection controller structure is established, closed loop transfer function, corresponding with initial automatic disturbance rejection controller structure is obtainedExpression formula carries out formal argument to closed loop transfer function, expression formula based on closed-loop system fast convergence condition, determines wait adjust ginsengNumber；

On the basis of ensuring that automatic disturbance rejection controller corresponds to the response speed and stability of control system, adjusting is treated one by oneParameter carries out adjusting processing, determines in automatic disturbance rejection controller each to the calculation of setting parameter；

Based on charge and carbide ionic equilibrium principle is established in pH and model, in conjunction in determining automatic disturbance rejection controllerEach pH N-process Active Disturbance Rejection Control parameter is adjusted to the calculation of setting parameter；

Wherein, described to setting parameter includes yield value, control bandwidth and observation bandwidth.

Optionally, described to establish initial automatic disturbance rejection controller structure, it obtains corresponding with initial automatic disturbance rejection controller structureClosed loop transfer function, expression formula carries out formal argument to closed loop transfer function, expression formula based on closed-loop system fast convergence condition,It determines to setting parameter and includes:

The automatic disturbance rejection controller structural model including Nonlinear Tracking Differentiator and extended state observer is established, active disturbance rejection control is based onControl amount and output quantity in device structure processed determine the initial function expression of extended mode observer；

It is derived, is obtained based on initial function expression of the working principle of automatic disturbance rejection controller to extended state observerTo extended state observer more new-standard cement；

According to automatic disturbance rejection controller structure determination closed function expression formula, to closed loop under the conditions of closed-loop system fast convergenceAfter function expression is rewritten, obtain to setting parameter.

Optionally, described to establish the automatic disturbance rejection controller structure including Nonlinear Tracking Differentiator and extended state observer, it is based onControl amount and output quantity in automatic disturbance rejection controller structural model determine the function expression of extended state observer, comprising:

Shown in the function expression of extended state observer such as formula (1.1)

In formula, β₁、β₂And β₃Indicate the observer parameter in extended state observer, z₁,z₂,z₃For extended state observerQuantity of state, u be system control signal and system output y, b₀For yield value.

Optionally, it is described based on the working principle of automatic disturbance rejection controller to the initial function expression of extended state observerIt is derived, obtains extended state observer more new-standard cement, comprising:

Based on the corresponding expansion state detector of formula (1.1), when the corresponding control system of automatic disturbance rejection controller structural modelWhen controlled device is single order purely retarded model in system, total disturbance f, yield value b that the system of being defined as is subject to₀Expression formula be respectivelyShown in formula (1.2), formula (1.3)

It is obtained according to formula (1.2) and (1.3)

Formula (1.4) is rewritten as state-space expression form shown in formula (1.5)

U is introduced on the basis of formula (1.5)₀=f+b₀U obtains the extended mode equation as shown in formula (1.6)

Determine the control rate expression formula of automatic disturbance rejection controller

u₀=k_p(r-z₁)-k_dz₂Formula (1.7)

U=(u₀-z₃)/b₀Formula (1.8)

When extended mode observer is correctly adjusted, formula (1.7) and (1.8) are substituted into formula (1.4), obtained

It can be in the hope of the expectation closed-loop dynamic characteristic equation of system, to closed-loop dynamic feature by formula (1.9) substitution (1.7)Equation carries out the transmission function expression formula that Laplace converts the expected equation of available system

Based on initial automatic disturbance rejection controller structural model, be expanded state observer equation

It enables formula (1.6) and formula (1.11) to make poor, obtains error equation expression formula

Wherein, L is the gain vector of observer,

Obtain the characteristic equation of system:

Three parameters of observer are adjusted according to characteristic equation, so that it may design corresponding automatic disturbance rejection controller extensionState observer.

Optionally, described according to automatic disturbance rejection controller structure determination closed function expression formula, in closed-loop system fast convergenceUnder the conditions of closed function expression formula is rewritten after, obtain to setting parameter, including

The expression of the closed function as shown in formula (2.1) is determined based on the hierarchical structure in automatic disturbance rejection controller structural modelFormula

In formula, A₁(s)=s³+(β₁+k_d)s²+(β₁k_d+β₂) s,

A₂(s)=k_ps³+(β₃+β₂k_d+β₁k_p)s²+(β₃k_d+β₂k_p)s+β₃k_p；

It can analyze the stability of system, the necessary condition of closed-loop system fast convergence according to the closed loop transfer function, of systemBe this system features equation characteristic root all in negative half-plane, therefore formula (1.13) is rewritten are as follows:

s³+β₁s²+β₂s+β₃=(s+ ω_o)³Formula (2.3)

Equally, formula (1.10) is rewritten into following form:

Therefore there is s²+k_ds+k_p=(s+ ω_c)²Formula (2.5)

Formula (2.1) is only left 3 independent parameters, yield value b at this time₀, control bandwidth ω_cWith observation bandwidth ω_o。

Optionally, described that parameter tuning is carried out to controller gain parameter, control bandwidth and observation bandwidth respectively, it determines certainlyThe yield value of resistance controller and extended state observer, comprising:

During parameter tuning, b₀It can be according to the K, T of the approximate first-order lag model parameter of controlled device_p, T_dComeAdjusting.Because automatic disturbance rejection controller is stronger to the tolerance of time lag, generally for the response speed for guaranteeing adjusting system, b₀Value can be taken as

b₀=K/ (T_p×T_d') formula (2.6)

T in formula_d'=0.1 × T_d；

By formula (2.4) it is found that k_pAnd k_dDetermine the expection dynamical equation of Active Disturbance Rejection Control system；

Substituting into formula (2.5) can obtain: k_p=ω_c², k_d=2 ω_c。

Optionally, described that parameter tuning is carried out to controller gain parameter, control bandwidth and observation bandwidth respectively, it determines certainlyThe yield value of resistance controller and extended state observer, comprising:

Under unit step input, it is contemplated that the pull-type transformation of dynamical equation output are as follows:

The unit-step response of system can be obtained are as follows:

It is defined according to regulating time:

|y(t_s)-y (∞) |=△ formula (2.9)

As y (∞)=1,When,It solves:

t_s=5.85/ ω_cFormula (2.10)

As the regulating time t of system requirements it can be seen from above-mentioned derivation process_sWhen known, it can be calculated according to above formulaControl bandwidth ω_c.In view of system actually enter and expectation there are certain errors, therefore there are allowance in adjusting, enable: ω_c=8/t_sFormula (2.11)

K is thus calculated again_pAnd k_dValue.

Optionally, described that parameter tuning is carried out to controller gain parameter, control bandwidth and observation bandwidth respectively, it determines certainlyThe yield value of resistance controller and extended state observer, comprising:

As observer state z₃(s) in the case where perfect tracking f (s), it is special that automatic disturbance rejection controller can obtain expected dynamicProperty, simultaneous observer expression formula (1.1) and system always disturb expression formula (1.5) and can obtain:

The first row and formula (2.12) of formula (1.1) are carried out Laplace to convert:

sz₁(s)=z₂+β₁[y(s)-z₁(s)] formula (2.13)

F (s)=z₃(s)+β₂[y(s)-z₁(s)]+[s²y(s)-sz₂(s)] formula (2.14)

The merging of two formulas can obtain:

F (s)=z₃(s)+β₂[y(s)-z₁(s)]+β₁s[y(s)-z₁(s)]+s²[y(s)-z₁(s)] formula (2.15)

Carrying out Laplace transformation to formula (1.1) the third line can obtain

sz₃(s)=β₃[y(s)-z₁(s)] formula (2.16)

Simultaneous (4.35) and (4.36) can obtain:

F (s) s=(β₃+β₂s+β₁s²+s³)[y(s)-z₁(s)] formula (2.17)

Simultaneous (2.16) and (2.17), available z₃(s) transmission function between f (s):

For actual control scene, the often low frequency signal mainly influenced caused on system control effect, and in it is lowThe factor beta of frequency signal₂And β₃Often it is much larger than high-frequency signal factor beta₁With 1, therefore high-frequency signal item is given up, approximate description z₃(s) relationship between f (s) is as follows:

WhereinK value is bigger, and observation, that is, tracking velocity of extended mode observer is faster, accuracy of observationIt is also faster with the response speed of corresponding system；

Define observer state z₃(s) lag time for tracking f (s) is T_t, according to first-order system behavioral characteristics, from formula(2.19) it can be obtained in:

T_t≈ 4/k formula (2.20)

In the design of automatic disturbance rejection controller, in order to guarantee that the tracking of observer did not had large time delay, T is generally required_t<t_s,It is available by formula (2.13):

β₁=3 ω_o,β₂=3 ω_o²β₃=ω_o³Formula (2.21)

Substituting into formula (2.19) can obtain: k ≡ ω_o/3；

In actual controller design, ω_oValue it is generally not too big by system stability constraint requirements, to extensionThe parameter setting of state observer is as follows, need to only adjust ω_oThe adjusting to observer parameter, β can be realized with the value of k₁=3ω_o,β₂=3 ω_o²β₃=k β₂Formula (2.22).

Technical solution provided by the invention has the benefit that

1, the automatic disturbance rejection controller used has stronger robustness and anti-interference energy while guaranteeing system tracking performancePower；

2, compared to other automatic disturbance rejection controllers, parameter tuning method of the invention reduces to setting parameters, givesGo out adjusting step, optimizes adjusting efficiency.

Detailed description of the invention

It, below will be to attached drawing needed in embodiment description in order to illustrate more clearly of technical solution of the present inventionIt is briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, general for this fieldFor logical technical staff, without creative efforts, it is also possible to obtain other drawings based on these drawings.

Fig. 1 is the flow diagram provided by the present invention for the Active Disturbance Rejection Control parameter tuning method of pH N-process；

Fig. 2 is initial automatic disturbance rejection controller structure control block diagram provided by the invention；

Fig. 3 is the simple system structure chart of common pH N-process provided by the invention；

Fig. 4 is control result figure provided by the invention；

Fig. 5 is the control effect of automatic disturbance rejection controller provided by the invention and PID controller when process stream disturbs；

Fig. 6 is the control effect of automatic disturbance rejection controller provided by the invention and PID controller when buffer stream disturbs.

Specific embodiment

To keep structure and advantage of the invention clearer, structure of the invention is made further below in conjunction with attached drawingDescription.

Embodiment one

The present invention provides the Active Disturbance Rejection Control parameter tuning methods for pH N-process, as shown in Figure 1, the parameterSetting method, comprising:

11, initial automatic disturbance rejection controller structural model is established, is obtained corresponding with initial automatic disturbance rejection controller structural modelClosed loop transfer function, expression formula carries out formal argument to closed loop transfer function, expression formula based on closed-loop system fast convergence condition,It determines to setting parameter；

12, it on the basis of ensuring that automatic disturbance rejection controller corresponds to the response speed and stability of control system, treats one by oneSetting parameter carries out adjusting processing, determines in automatic disturbance rejection controller each to the calculation of setting parameter；

13, based on charge and carbide ionic equilibrium principle establish in pH and model, in conjunction with determining active disturbance rejection controlEach pH N-process parameter is adjusted to the calculation of setting parameter in device processed；

Wherein, described to setting parameter includes yield value, control bandwidth and observation bandwidth.

In an implementation, why Active Disturbance Rejection Control scheme is used in pH N-process, is because Active Disturbance Rejection Control hasVery strong robustness and anti-interference ability can be applied effectively in this nonlinear processes of pH N-process, and be suitable forSolve the factors such as the big interference being widely present in actual industrial process and uncertainty.In addition, specific pH N-process is faced,Mathematical models of the automatic disturbance rejection controller independent of controlled device, and controller architecture is simple, is suitable for most ofIndustrial processes device.Finally, heretofore described its corresponding parameter tuning side of pH N-process automatic disturbance rejection controllerThe parameter of method, required adjusting is less compared to common automatic disturbance rejection controller, and parameter tuning process is more simple and effective.

The initial automatic disturbance rejection controller structure control block diagram established in step 11 is as shown in Fig. 2, wherein G_pIndicate controlledObject, r indicate the setting value of controlled device, and d indicates external interference.TD (TrackingDifferentiator) is tracking differentialDevice, it can produce the differential signal of system transient process, tracks input to setting value by the characteristic of its low-pass filtering and carries outNoise suppressed, while transient process can be effectively improved, reduce the overshoot of transient process.ESO(Extended StateObserver) it is called extended state observer, is used to that estimating system itself is non-linear or uncertain and external noiseAnd disturbance, in (Active Disturbance Rejection Controller, ADRC) Active Disturbance Rejection Control, these are unitedReferred to as system always disturbs.The input of ESO is the output y of system control signal u and system, and exporting is the 3 of extended state observerA quantity of state z₁,z₂,z₃。K_p,K_d,b₀For the parameter of ADRC controller.

Based on establishing initial automatic disturbance rejection controller structural model, it is also necessary to obtain and initial automatic disturbance rejection controller structural modelCorresponding closed loop transfer function, expression formula carries out form to closed loop transfer function, expression formula based on closed-loop system fast convergence conditionTransformation, determination are specifically included to setting parameter, that is, step 11:

111, the automatic disturbance rejection controller structural model including Nonlinear Tracking Differentiator and extended state observer is established, based on certainly anti-Disturb the initial function expression that control amount and output quantity in controller architecture model determine extended mode observer；

112, it is pushed away based on initial function expression of the working principle of automatic disturbance rejection controller to extended state observerIt leads, obtains extended state observer more new-standard cement；

113, closed function expression formula is determined according to the hierarchical structure in automatic disturbance rejection controller structural model, in closed-loop systemAfter being rewritten under the conditions of fast convergence to closed function expression formula, obtain to setting parameter.

Here the operating process proposed in step 111 is based on derivation made by initial automatic disturbance rejection controller model, specificallyInclude:

Shown in the function expression of extended state observer such as formula (1.1)

In formula, β₁、β₂And β₃Indicate the observer parameter in extended state observer, z₁,z₂,z₃For extended state observerQuantity of state, u be system control signal and system output y, b₀For yield value.

Optionally, it is described based on the working principle of automatic disturbance rejection controller to the initial function expression of extended state observerIt is derived, obtains extended state observer more new-standard cement, comprising:

Based on the corresponding expansion state detector of formula (1.1), when the corresponding control system of automatic disturbance rejection controller structural modelWhen controlled device is single order purely retarded model in system, f, yield value b that the system of being defined as was subject to always disturb₀Expression formula differenceFor shown in formula (1.2), formula (1.3)

It is obtained according to formula (1.2) and (1.3)

Formula (1.4) is rewritten as state-space expression form shown in formula (1.5)

U is introduced on the basis of formula (1.5)₀=f+b₀U obtains the extended mode equation as shown in formula (1.6)

Determine the control rate expression formula of automatic disturbance rejection controller

u₀=k_p(r-z₁)-k_dz₂Formula (1.7)

U=(u₀-z₃)/b₀Formula (1.8)

When extended mode observer is correctly adjusted, formula (1.7) and (1.8) are substituted into formula (1.4), obtained

It can be in the hope of the expectation closed-loop dynamic characteristic equation of system, to closed-loop dynamic feature by formula (1.9) substitution (1.7)Equation carries out the transmission function expression formula that Laplace converts the expected equation of available system

Based on initial automatic disturbance rejection controller structure, be expanded state observer equation

It enables formula (1.6) and formula (1.11) to make poor, obtains error equation expression formula

Wherein, L is the gain vector of observer,

Obtain the characteristic equation of system:

Three parameters of observer are adjusted according to characteristic equation, so that it may design corresponding automatic disturbance rejection controller extensionState observer.

Based on above-mentioned derivation process, the main thought for the parameter tuning method that the present embodiment proposes is to existing active disturbance rejectionController architecture improves, and treats setting parameter and is simplified.The pH N-process automatic disturbance rejection controller of conventional structure needsThe observer and controller parameter of adjusting at least 6, present invention employs improved Active Disturbance Rejection Control structures, and to parameterTuning process is optimized, and reduces the number of parameters for needing to adjust, and the parameter adjusted can be closed directly according to desiredRing property provides, so that parameter tuning process is more intuitive, adjusting result is more accurate effective.

Here simplification process specifically:

The expression of the closed function as shown in formula (2.1) is determined based on the hierarchical structure in automatic disturbance rejection controller structural modelFormula

In formula, A₁(s)=s³+(β₁+k_d)s²+(β₁k_d+β₂) s,

A₂(s)=k_ps³+(β₃+β₂k_d+β₁k_p)s²+(β₃k_d+β₂k_p)s+β₃k_p；

It can analyze the stability of system, the necessary condition of closed-loop system fast convergence according to the closed loop transfer function, of systemBe this characteristic equation characteristic root all in negative half-plane, therefore formula (1.13) is rewritten are as follows:

s³+β₁s²+β₂s+β₃=(s+ ω_o)³Formula (2.3)

Equally, formula (1.10) is rewritten into following form:

Therefore there is s²+k_ds+k_p=(s+ ω_c)²Formula (2.5)

Formula (2.1) is only left 3 independent parameters, yield value b at this time₀, control bandwidth ω_cWith observation bandwidth ω_o。

Three are being determined after setting parameter, is next needing to solve to each to setting parameter:

1) to yield value b₀Solution

During parameter tuning, b₀It can be according to the K, T of the approximate first-order lag model parameter of controlled device_p, T_dComeAdjusting.Because automatic disturbance rejection controller is stronger to the tolerance of time lag, generally for the response speed for guaranteeing adjusting system, b₀Value can be taken as

b₀=K/ (T_p×T_d') formula (2.6)

T in formula_d'=0.1 × T_d；

By formula (2.4) it is found that k_pAnd k_dDetermine the expection dynamical equation of Active Disturbance Rejection Control system；

By that can be obtained with formula (2.5): k_p=ω_c², k_d=2 ω_c。

2) control bandwidth ω_cSolution

Under unit step input, it is contemplated that the pull-type transformation of dynamical equation output are as follows:

The unit-step response of system can be obtained are as follows:

It is defined according to regulating time:

|y(t_s)-y (∞) |=△ formula (2.9)

As y (∞)=1,When,It solves:

t_s=5.85/ ω_cFormula (2.10)

As the regulating time t of system requirements it can be seen from above-mentioned derivation process_sWhen known, it can be calculated according to above formulaControl bandwidth ω_c.In view of system actually enter and expectation there are certain errors, therefore there are allowance in adjusting, enable: ω_c=8/t_sFormula (2.11)

K is thus calculated again_pAnd k_dValue.

3) to observation bandwidth ω_oSolution

As observer state z₃(s) in the case where perfect tracking f (s), it is special that automatic disturbance rejection controller can obtain expected dynamicProperty, simultaneous observer expression formula (1.1) and system always disturb expression formula (1.5) and can obtain:

The first row and formula (2.12) of formula (1.1) are carried out Laplace to convert:

sz₁(s)=z₂+β₁[y(s)-z₁(s)] formula (2.13)

F (s)=z₃(s)+β₂[y(s)-z₁(s)]+[s²y(s)-sz₂(s)] formula (2.14)

The merging of two formulas can obtain:

F (s)=z₃(s)+β₂[y(s)-z₁(s)]+β₁s[y(s)-z₁(s)]+s²[y(s)-z₁(s)] formula (2.15)

Carrying out Laplace transformation to formula (1.1) the third line can obtain

sz₃(s)=β₃[y(s)-z₁(s)] formula (2.16)

Simultaneous (4.35) and (4.36) can obtain:

F (s) s=(β₃+β₂s+β₁s²+s³)[y(s)-z₁(s)] formula (2.17)

Simultaneous (2.16) and (2.17), available z₃(s) transmission function between f (s):

For actual control scene, the often low frequency signal mainly influenced caused on system control effect, and in it is lowThe factor beta of frequency signal₂And β₃Often it is much larger than high-frequency signal factor beta₁With 1, therefore high-frequency signal item is given up, approximate description z₃(s) relationship between f (s) is as follows:

WhereinK value is bigger, and observation, that is, tracking velocity of extended mode observer is faster, accuracy of observationIt is also faster with the response speed of corresponding system；

Define observer state z₃(s) lag time for tracking f (s) is T_t, according to first-order system behavioral characteristics, from formula(2.19) it can be obtained in:

T_t≈ 4/k formula (2.20)

In the design of automatic disturbance rejection controller, in order to guarantee that the tracking of observer did not had large time delay, T is generally required_t<t_s,It is available by formula (2.13):

β₁=3 ω_o,β₂=3 ω_o²β₃=ω_o³Formula (2.21)

Substituting into formula (2.19) can obtain: k ≡ ω_o/3；

In actual controller design, ω_oValue it is generally not too big by system stability constraint requirements, to extensionThe parameter setting of state observer is as follows, need to only adjust ω_oThe adjusting to observer parameter, β can be realized with the value of k₁=3ω_o,β₂=3 ω_o²β₃=k β₂Formula (2.22).

For general controlled device, T is chosen_t1 second or so, i.e. k=3.At this point, for most controlled devices,Work as ω_o=3 ω_cWhen, that is, can guarantee system has enough tracking velocities, meet the performance indicator of system dynamic response, thus intoOne step simplifies the parameter tuning of automatic disturbance rejection controller.

Finally steps are as follows for the automatic disturbance rejection controller parameter tuning in the summary present invention:

1. according to ω_c≈10/t_s^*With the desired regulating time t of system_s^*Calculate control bandwidth ω_c。

2. according to desired tracking lag time and T_t≈ 4/k, ω_o=3 ω_c(general controlled device value), calculates sightSurvey bandwidth omega_o。

3. according to ω_cAnd ω_oCalculate controller gain k_p,k_dWith observer gain β₁, β₂And β₃。

k_p=ω_c² k_d=2 ω_c β₁=3 ω_o β₂=3 ω_o² β₃=k β₂

4. according to b₀=K/ (T_p×T_d), by estimating that controlled device transfer function model finds out b₀.Work as plant modelWhen unknown, b can be incrementally increased₀Until system dynamic response performance index is met the requirements.

Three are being determined after the calculation of setting parameter, is being introduced first in pH to be treated with model.

It is the simple system structure chart of certain common pH N-process shown in Fig. 3.Wherein, q₁q₂q₃Respectively process stream(HNO3), buffer stream (NaHCO3) and neutralized stream (NaOH, NaHCO3 mixed solution) flow, q₄To flow out liquid inventory.W_ai、W_biIt respectively indicates charge balance and carbide ionic equilibrium assumes that solution quickly sufficiently reacts in reaction kettle, by adjusting neutralized stream streamIt measures and the pH value of outflow solution is controlled.

PH N-process nonlinear model is established according to charge and carbide ionic equilibrium principle.Define charge and carbideIonic equilibrium is respectively as follows:

The dynamic equilibrium expression formula of [Na+] and [NO3-] is as follows in efflux:

It can be released by formula (3.1) (2-37) to formula (2-41) (3.4):

In buffer, H₂The ionization process of CO3 is as follows:

It is as follows to define its Dissociation equilibrium constant:

It is defined according to formula (3.9) and formula (3.10):

pk₁=-lgK_a1Formula (3.11)

pk₂=-lgK_a2Formula (3.12)

It can be pushed away by the above process:

Formula (3.5) (3.6) and (3.13) are the mathematical model of pH N-process.Wherein, neutralized stream flow is control amount,Efflux pH is system output.Table 1 lists parameter and operating condition in model:

Parameter	Value	Parameter	Value
				pk1	6.35	pk2	10.25
Wa1	0.003mol·L~ 1	Wa2	-0.03mol·L~ 1
				Wa3	-0.00305mol·L~ 1	Wb1	0.0mol·L~ 1
Wb2	0.03mol·L~ 1	Wb3	0.00005mol·L~ 1
				q1	16.6ml·s~ 1	q2	0.55ml·s~ 1
q3	15.6ml·s~ 1	V	2900ml
				θ	30s	pHsp	7

The model parameter and operating condition of 1 system of table

It is whole using aforementioned automatic disturbance rejection controller and corresponding parameter according to hereinbefore established pH N-process mathematical modelMethod is determined, after being designed to pH N-process Active Disturbance Rejection Control scheme and going forward side by side line control unit parameter tuning, after obtaining adjustingParameter b₀=1, w_c=0.15, and widely used pH N-process PID controller in control effect and industry is compared.

The tracking performance of controller is verified first.PH setting value is within a certain period of time from acidic region (low setting value)Differential gap is slowly improved, then is increased to basic region (high setting value), readjustment arrives original state, control result such as Fig. 4 institute again laterShow.It can be seen from the figure that pH N-process active disturbance rejection control designed either in acidic region or basic region, the present inventionDevice processed can non-overshoot quick tracking fixed valure, tracking effect is substantially better than traditional PID controller.

The anti-interference ability of controller and robustness are verified later.For process flow disturbance, in t=4min,Change process stream q₁=16.6+2mls^-1, as t=10min, q₁=16.6-2mls^-1.Automatic disturbance rejection controller and PID controlControl effect of the device processed when process stream disturbs is as shown in Figure 5.As can be seen that in the case where disturbing, active disturbance rejectionThe oscillation that controller receives is significantly less than PID controller, and can converge to setting value faster, have better anti-interference ability andRobustness.

For buffering flow disturbance, equally in t=4min, change q₂=0.55-0.05mls^-1, as t=10min,q₂=0.55+0.05mls^-1.The control effect of automatic disturbance rejection controller and PID controller when buffer stream disturbs such as Fig. 6It is shown.As can be seen that in the case where buffer stream disturbs, automatic disturbance rejection controller equally have better anti-interference ability andStronger robustness, control effect are more preferable.

The present invention realizes the control of pH N-process using automatic disturbance rejection controller, real using relatively simple control structureThe requirement to controlled device tracking performance and robust performance is showed.The parameter tuning method of automatic disturbance rejection controller is changed simultaneouslyInto reducing the quantity to setting parameter, quantitative gives the setting algorithm of automatic disturbance rejection controller, improves adjusting efficiency.Its major advantage is:

The automatic disturbance rejection controller of use has stronger robustness and anti-interference ability while guaranteeing system tracking performance；

Controller architecture is simple, and parameter tuning is convenient, is easy to implement to come into operation in industry spot；

Compared to other automatic disturbance rejection controllers, parameter tuning method of the invention reduces to setting parameters, providesAdjusting step, optimizes adjusting efficiency；

Parameter tuning method in the present invention uses quantitative analysis, can be according to desired system closed loop characteristic response indexIt calculates and obtains with plant model, tuning process is easy, there is stronger theoretical basis.

Each serial number in above-described embodiment is for illustration only, the assembling for not representing each component or the elder generation in use processSequence afterwards.

The above description is only an embodiment of the present invention, is not intended to limit the invention, all in the spirit and principles in the present inventionWithin, any modification, equivalent replacement, improvement and so on should all be included in the protection scope of the present invention.

Claims (8)

1. being used for the Active Disturbance Rejection Control parameter tuning method of pH N-process, which is characterized in that the parameter tuning method, packetIt includes:

Initial automatic disturbance rejection controller structure is established, closed loop transfer function, expression corresponding with initial automatic disturbance rejection controller structure is obtainedFormula carries out formal argument to closed loop transfer function, expression formula based on closed-loop system fast convergence condition, determines to setting parameter；

On the basis of ensuring that automatic disturbance rejection controller corresponds to the response speed and stability of control system, setting parameter is treated one by oneAdjusting processing is carried out, is determined in automatic disturbance rejection controller each to the calculation of setting parameter；

Based on charge and carbide ionic equilibrium principle is established in pH and model, in conjunction with each in determining automatic disturbance rejection controllerCalculation to setting parameter is adjusted the parameter of pH N-process automatic disturbance rejection controller；

Wherein, described to setting parameter includes yield value, control bandwidth and observation bandwidth.

2. the Active Disturbance Rejection Control parameter tuning method according to claim 1 for pH N-process, which is characterized in that instituteIt states and establishes initial automatic disturbance rejection controller structure, obtain closed loop transfer function, expression corresponding with initial automatic disturbance rejection controller structureFormula carries out formal argument to closed loop transfer function, expression formula based on closed-loop system fast convergence condition, determines to setting parameter packetIt includes:

The automatic disturbance rejection controller structure including Nonlinear Tracking Differentiator and extended state observer is established, automatic disturbance rejection controller structure is based onIn control amount and output quantity determine the initial function expression of extended mode observer；

It is derived, is expanded based on initial function expression of the working principle of automatic disturbance rejection controller to extended state observerOpen state observer more new-standard cement；

According to automatic disturbance rejection controller structure determination closed function expression formula, to closed function under the conditions of closed-loop system fast convergenceAfter expression formula is rewritten, obtain to setting parameter.

3. the Active Disturbance Rejection Control parameter tuning method according to claim 2 for pH N-process, which is characterized in that instituteIt states and establishes the automatic disturbance rejection controller structural model including Nonlinear Tracking Differentiator and extended state observer, be based on automatic disturbance rejection controller knotControl amount and output quantity in structure determine the function expression of extended state observer, comprising:

Shown in the function expression of extended state observer such as formula (1.1)

In formula, β₁、β₂And β₃Indicate the observer parameter in extended state observer, z₁,z₂,z₃For the shape of extended state observerState amount, u are the output y, b of system control signal and system₀For yield value.

4. the Active Disturbance Rejection Control parameter tuning method according to claim 2 for pH N-process, which is characterized in that instituteIt states the working principle based on automatic disturbance rejection controller to derive the initial function expression of extended state observer, be expandedState observer more new-standard cement, comprising:

Based on the corresponding expansion state detector of formula (1.1), when in the corresponding control system of automatic disturbance rejection controller structural modelWhen controlled device is single order purely retarded model, f, yield value b that the system of being defined as was subject to always disturb₀Expression formula be respectively public affairsShown in formula (1.2), formula (1.3)

It is obtained according to formula (1.2) and (1.3)

Formula (1.4) is rewritten as state-space expression form shown in formula (1.5)

U is introduced on the basis of formula (1.5)₀=f+b₀U obtains the extended mode equation as shown in formula (1.6)

Determine the control rate expression formula of automatic disturbance rejection controller

u₀=k_p(r-z₁)-k_dz₂Formula (1.7)

U=(u₀-z₃)/b₀Formula (1.8)

When extended mode observer is correctly adjusted, formula (1.7) and (1.8) are substituted into formula (1.4), obtained

It can be in the hope of the expectation closed-loop dynamic characteristic equation of system, to closed-loop dynamic characteristic equation by formula (1.9) substitution (1.7)Carry out the transmission function expression formula that Laplace converts the expected equation of available system

Based on initial automatic disturbance rejection controller structural model, be expanded state observer equation

It enables formula (1.6) and formula (1.11) to make poor, obtains error equation expression formula

Wherein, L is the gain vector of observer,

Obtain the characteristic equation of system:

Three parameters of observer are adjusted according to characteristic equation, so that it may design corresponding automatic disturbance rejection controller extended modeObserver.

5. the Active Disturbance Rejection Control parameter tuning method according to claim 3 for pH N-process, which is characterized in that instituteIt states according to automatic disturbance rejection controller structure determination closed function expression formula, to closed function table under the conditions of closed-loop system fast convergenceAfter being rewritten up to formula, obtain to setting parameter, including

Based on automatic disturbance rejection controller structure determination closed function expression formula as shown in formula (2.1)

In formula, A₁(s)=s³+(β₁+k_d)s²+(β₁k_d+β₂) s,

A₂(s)=k_ps³+(β₃+β₂k_d+β₁k_p)s²+(β₃k_d+β₂k_p)s+β₃k_p；

It can analyze the stability of system according to the closed loop transfer function, of system, the necessary condition of closed-loop system fast convergence is thisThe characteristic root of system features equation is all in negative half-plane, therefore formula (1.13) is rewritten are as follows:

s³+β₁s²+β₂s+β₃=(s+ ω_o)³Formula (2.3)

Equally, formula (1.10) is rewritten into following form:

Therefore there is s²+k_ds+k_p=(s+ ω_c)²Formula (2.5)

Formula (2.1) is only left 3 independent parameters, yield value b at this time₀, control bandwidth ω_cWith observation bandwidth ω_o。

6. the Active Disturbance Rejection Control parameter tuning method according to claim 4 for pH N-process, which is characterized in that instituteIt states and parameter tuning is carried out to controller gain parameter, control bandwidth and observation bandwidth respectively, determine from resistance controller and expansionOpen the yield value of state observer, comprising:

During parameter tuning, b₀It can be according to the K, T of the approximate first-order lag model parameter of controlled device_p, T_dCome wholeIt is fixed, because automatic disturbance rejection controller is stronger to the tolerance of time lag, generally for the response speed for guaranteeing adjusting system, b₀'sValue can be taken as

b₀=K/ (T_p×T_d') formula (2.6)

T in formula_d'=0.1 × T_d；

By formula (2.4) it is found that k_pAnd k_dDetermine the expection dynamical equation of Active Disturbance Rejection Control system；

Substituting into formula (2.5) can obtain: k_p=ω_c², k_d=2 ω_c。

7. the Active Disturbance Rejection Control parameter tuning method according to claim 3 for pH N-process, which is characterized in that instituteIt states and parameter tuning is carried out to controller gain parameter, control bandwidth and observation bandwidth respectively, determine from resistance controller and expansionOpen the yield value of state observer, comprising:

Under unit step input, it is contemplated that the pull-type transformation of dynamical equation output are as follows:

The unit-step response of system can be obtained are as follows:

It is defined according to regulating time:

|y(t_s)-y (∞) |=△ formula (2.9)

As y (∞)=1,When,It solves:

t_s=5.85/ ω_cFormula (2.10)

As the regulating time t of system requirements it can be seen from above-mentioned derivation process_sWhen known, control can be calculated according to above formulaBandwidth omega processed_c, it is contemplated that system actually enter and expectation there are certain errors, therefore there are allowance in adjusting, enable: ω_c=8/t_sFormula (2.11)

K is thus calculated again_pAnd k_dValue.

8. the Active Disturbance Rejection Control parameter tuning method according to claim 4 for pH N-process, which is characterized in that instituteIt states and parameter tuning is carried out to controller gain parameter, control bandwidth and observation bandwidth respectively, determine from resistance controller and expansionOpen the yield value of state observer, comprising:

As observer state z₃(s) in the case where perfect tracking f (s), automatic disturbance rejection controller can obtain expected dynamic characteristic, connectionVertical observer expression formula (1.1) and system always disturb expression formula (1.5) and can obtain:

The first row and formula (2.12) of formula (1.1) are carried out Laplace to convert:

sz₁(s)=z₂+β₁[y(s)-z₁(s)] formula (2.13)

F (s)=z₃(s)+β₂[y(s)-z₁(s)]+[s²y(s)-sz₂(s)] formula (2.14)

The merging of two formulas can obtain:

F (s)=z₃(s)+β₂[y(s)-z₁(s)]+β₁s[y(s)-z₁(s)]+s²[y(s)-z₁(s)] formula (2.15)

Carrying out Laplace transformation to formula (1.1) the third line can obtain

sz₃(s)=β₃[y(s)-z₁(s)] formula (2.16)

Simultaneous (4.35) and (4.36) can obtain:

F (s) s=(β₃+β₂s+β₁s²+s³)[y(s)-z₁(s)] formula (2.17)

Simultaneous (2.16) and (2.17), available z₃(s) transmission function between f (s):

For actual control scene, the often low frequency signal mainly influenced is caused on system control effect, and middle low frequency is believedNumber factor beta₂And β₃Often it is much larger than high-frequency signal factor beta₁With 1, therefore high-frequency signal item is given up, approximate description z₃(s) andRelationship between f (s) is as follows:

WhereinK value is bigger, and observation, that is, tracking velocity of extended mode observer is faster, accuracy of observation and phaseThe response speed of corresponding system is also faster；

Define observer state z₃(s) lag time for tracking f (s) is T_t, according to first-order system behavioral characteristics, from formula(2.19) it can be obtained in:

T_t≈ 4/k formula (2.20)

In the design of automatic disturbance rejection controller, in order to guarantee that the tracking of observer did not had large time delay, T is generally required_t<t_s, by public affairsFormula (2.13) is available:

β₁=3 ω_o,β₂=3 ω_o²β₃=ω_o³Formula (2.21)

Substituting into formula (2.19) can obtain: k ≡ ω_o/3；

In actual controller design, ω_oValue it is generally not too big by system stability constraint requirements, to extended modeThe parameter setting of observer is as follows, need to only adjust ω_oThe adjusting to observer parameter, β can be realized with the value of k₁=3 ω_o,β₂=3 ω_o²β₃=k β₂Formula (2.22).