CN116974206B - Mill control method based on predictive fuzzy control algorithm - Google Patents
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Abstract
The invention provides a mill control method based on a predictive fuzzy control algorithm, which comprises the following steps: s1: establishing a mathematical model of a mill control system and a predicted performance reference curve; judging whether the model of the mill control system is mismatched or not through a predicted performance reference curve, and judging the tracking performance and robustness condition of the mill control system; s2: designing a predictive controller based on a mathematical model of a mill control system; s3: setting filter parameters of the prediction controller by adopting a fuzzy control algorithm; s4: substituting the optimal value of the filter parameter after setting into a prediction controller to obtain the optimal output value of the mill control system. The prediction-fuzzy control algorithm is used for setting and optimizing parameters of the prediction controller through the establishment of the prediction controller and the fuzzy control algorithm, so that the problem that tracking performance and robustness of a mill control system cannot be well balanced is solved.
Description
Technical Field
The invention relates to the technical field of mine final equipment control systems, in particular to a mill control method based on a predictive fuzzy control algorithm.
Background
Mill control systems are an important control system in mine engineering. However, the conventional mill control system is low in working efficiency, consumes a large amount of manpower and material resources, and is difficult to establish an accurate mathematical model due to complexity of a mill grinding process, time variability of parameters and large hysteresis characteristics, and cannot quantitatively judge the working state and ore properties of the mill, and only can qualitatively or tendently judge, so that accurate control of the mill cannot be realized.
Although the fuzzy control is successfully applied to the automatic control of the mill at present, certain defects exist in the practical application process, and the problems of fuzzy control parameter setting, algorithm optimization and the like are mainly reflected, meanwhile, the optimal working condition area of the mill control system is narrow, the tracking performance and the robustness of the mill control system cannot be well balanced, the processing capacity of the mill is reduced, and the process indexes such as the fineness, the concentration and the like of the mill are influenced.
In summary, it is necessary to provide a mill control method based on a predictive fuzzy control algorithm, to improve the balance problem of tracking performance and robustness of a mill control system, and to improve the processing capacity and process index of the mill.
Disclosure of Invention
In view of this, the present invention proposes a mill control method with better feedback tracking capability that incorporates a fuzzy controller and predictive model.
The technical scheme of the invention is realized as follows: the invention provides a mill control method based on a predictive fuzzy control algorithm, which comprises the following steps:
s1: establishing a mathematical model of a mill control system and a predicted performance reference curve; judging whether the model of the mill control system is mismatched or not through a predicted performance reference curve, and judging the tracking performance and robustness condition of the mill control system;
s2: designing a predictive controller based on a mathematical model of a mill control system;
s3: setting filter parameters of the prediction controller by adopting a fuzzy control algorithm;
s4: substituting the optimal value of the filter parameter after setting into a prediction controller to obtain the optimal output value of the mill control system.
On the basis of the above technical solution, preferably, in the step S1, the mathematical model of the mill control system is established, where the output of the mill is y (S), the set value of the mill control system is r (S), the external disturbance of the mill is d (S), the transfer function of the mathematical model of the mill is G (S), and the predictive controller is G m (s) the predicted model transfer function of the mill is G' p (s), s is Laplacian, and the input-output relation expression of the mill control system is:the input-output relation expression of the disturbance of the mill control system is as follows: />Wherein the open loop transfer function->The transfer function G(s) of the mathematical model of the mill is developed with: />Wherein K is p To be proportional to the amplification factor, T 1 And T 2 Is a time constant, τ is a time lag, e -τs For time-lag term, ->
Preferably, the step S1 of establishing the predicted performance reference curve is performed by the predictive controller G m The filter f(s) is introduced into(s),T f k is an adjusting parameter introduced into the filter, and n is an order; then predict controller G m (s) rewriting as: />Wherein [ G ]' p- (s)] -1 Is the transfer function G 'with minimum phase characteristics' p- Reciprocal of(s), G' p+ (s) is the transfer function of an all-pass filter and satisfies G' p (s)＝G′ p+ (s)·G′ p- (s); then G c (s) rewriting as: />
Let the transfer function G(s) of the mathematical model of the mill and the predicted model transfer function G 'of the mill' p (S) equality, i.e. the model of the mill control system is not mismatched, let the sensitivity function of the mill control system be S (S), expressed as:respectively selecting absolute value error integral IAE and sensitivityDegree M s As an index for measuring the tracking performance and the robust performance of the mill control system, the smaller the value of the absolute value error integral IAE is, the better the tracking performance of the mill control system tracking performance is; sensitivity M s The smaller the more robust the mill control system is; respectively calculating absolute value error integral IAE and sensitivity M s And at IAE-M s And establishing a predicted performance reference curve on the plane, judging whether the model of the mill control system is mismatched according to the predicted performance reference curve, and judging the tracking performance and the robustness of the mill control system.
Further preferably, the determining whether the model of the mill control system is mismatched according to the predicted performance reference curve, and determining the tracking performance and robustness of the mill control system is defined by integrating the absolute value error IAE as follows:wherein e (t) represents a deviation of the actual output from the desired output, t being time; sensitivity M s Is defined as:wherein S (j omega) is obtained by replacing S in the sensitivity function S (S) with j omega, the former term of j omega is an imaginary unit, and the latter term is an angular frequency;
if the model of the mill control system has no mismatch, G(s) =G 'is satisfied' p (s) when the mill control system makes steps with the amplitude r and sinusoidal tracking under the zero initial condition, the absolute value error integral IAE is as follows:sensitivity M s Is thatFor a given time lag τ and amplitude r, let the tuning parameter T introduced into the filter f In the case of the (0-s), ++ infinity) in in a variation of the method, the device, taking absolute value error integral IAE as a horizontal axis and sensitivity M s Is taken as a vertical axis to construct ME-M s Plane, and at ME-M s Establishing a predicted performance reference curve in a plane;
when G(s) =g' p (s) when there is no mismatch in the model of the mill control system, the mill output y(s) is: y(s) =g(s) G m (s)[r(s)-d(s)]+d(s); if the mill control system is stable and G(s) noteqG' p (s), predictive controller G m (s) only the static gain G needs to be satisfied m (0) Static gain G 'for a predictive model transfer function of a mill' p (0) Inverse of (G) m (0)＝G′ p (0) -1 The mill control system has no steady-state deviation for constant value interference and step input, and the equation for obtaining the closed-loop deviation e(s) of the predictive control system is as follows: e(s) =r(s) -y(s), the steady state deviation e (≡) is:
still further preferably, the sensitivity M s The value range of (2) is [1,2 ]]。
Still more preferably, the step S2 of designing the predictive controller based on the mathematical model of the mill control system is based on a transfer function G 'of the predictive model of the mill' p (s)＝G′ p+ (s)·G′ p- (s) and introducing a filter f(s), for the predictive controller G m (s) rewriting the filter f(s) to 2 order, there isSubstituting the input-output relation expression of the mill control system and the input-output relation expression of the disturbance of the mill control system into the input-output relation expression of the mill control system:when the model of the mill control system is not mismatched, G(s) =G 'is satisfied' p (s), and G' p (s)＝G′ p- (s), the mill control system input-output relation expression and the mill control system disturbance input-output relation expression can be simplified into: />
Further preferably, step S3 uses a fuzzy control algorithm to adjust the filter parameters of the prediction controller according to the output y (S) of the mill and the output y of the transfer function link of the prediction model of the mill p The error E and the error change rate EC between the two are used as the input of a fuzzy control algorithm and are based on a predictive controller G m (s) introduction of a FilterPresence of T f ＝T f0 +T f1 ，K＝K 0 +K 1 ，T f And K is the adjustment parameter introduced into the filter f(s), T f0 And K 0 Is a preset initial value; t (T) f1 And K 1 Is the output of the fuzzy control algorithm, and the T is obtained by a defuzzification method f1 And K 1 Is set to the optimum value of (2).
Still more preferably, T is obtained by a defuzzification method f1 And K 1 The optimal value of (2) is that the membership function of the fuzzy set C of the fuzzy output Z obtained by the fuzzy control algorithm according to the fuzzy rule table is mu C (Z) let membership function μ C The weighted average value of (Z) is dF (Z), and the weighted average value dF (Z) is taken as the clear value of the fuzzy output Z,a and b are constants, T is taken as f1 And K 1 Substituting the fuzzy output Z to obtain T f1 And K 1 The optimal value is sent to the predictive controller G m (s)。
Compared with the prior art, the mill control method based on the predictive fuzzy control algorithm has the following beneficial effects:
the predictive fuzzy control algorithm provided by the application judges whether the model of the mill control system is mismatched or not by establishing a predictive controller and adopting absolute value error integration IAE and sensitivity MS as indexes for measuring the tracking performance and the robust performance of the mill control system, and adjusts and optimizes parameters of the predictive controller through the fuzzy control algorithm, so that the problem that the tracking performance and the robust performance of the mill control system cannot be balanced well is solved; can simultaneously improve the processing capacity of the mill and meet the requirements of process indexes such as grinding fineness, concentration and the like.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a control flow chart of a mill control method based on a predictive fuzzy control algorithm of the present invention.
Detailed Description
The following description of the embodiments of the present invention will clearly and fully describe the technical aspects of the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, are intended to fall within the scope of the present invention.
As shown in fig. 1, the invention provides a mill control method based on a predictive fuzzy control algorithm, which comprises the following steps:
s1: establishing a mathematical model of a mill control system and a predicted performance reference curve; judging whether the model of the mill control system is mismatched or not through the predicted performance reference curve, and judging the tracking performance and the robustness condition of the mill control system.
S11: first, a mathematical model of a mill control system needs to be built, and referring to fig. 1, fig. 1 is a negative feedback closed loop system. Let the output of the mill be y(s), the set value of the mill control system be r(s), the external disturbance of the mill be d(s), the transfer function of the mathematical model of the mill be G(s), the predictive controller be G m (s) predictive model transfer function for millThe number is G' p (s), s is the Laplacian, then there are:
the input-output relation expression of the mill control system is as follows:equation 1;
the input-output relation expression of the disturbance of the mill control system is as follows:equation 2; wherein the open loop transfer function->Equation 3; developing the transfer function G(s) of the mathematical model of the mill to obtain:wherein K is p To be proportional to the amplification factor, T 1 And T 2 Is a time constant, τ is a time lag, e -τs In order to make the time-lag term,equation 4. It follows that the denominator of the transfer function G(s) of the mathematical model of the mill of the present solution is a quadratic term.
S12: establishing a predictive performance benchmark curve at the predictive controller G m The filter f(s) is introduced into(s),T f k is an adjusting parameter introduced into the filter, and n is an order; then predict controller G m (s) rewriting as:equation 5; wherein [ G ]' p- (s)] -1 Is the transfer function G 'with minimum phase characteristics' p- Reciprocal of(s), G' p- (s) stably excluding predicted items; g'. p+ (s) is the transfer function of an all-pass filter and satisfies G' p (s)＝G′ p+ (s)·G′ p- (s); then G c (s) rewriting as: />Equation 6.
The process of establishing the predicted performance reference curve is as follows: let the transfer function G(s) of the mathematical model of the mill and the predicted model transfer function G 'of the mill' p (S) equality, i.e. the model of the mill control system is not mismatched, let the sensitivity function of the mill control system be S (S), expressed as:equation 7; respectively selecting absolute value error integral ME and sensitivity M s As an index for measuring the tracking performance and the robust performance of the mill control system, the smaller the value of the absolute value error integral ME is, the better the tracking performance of the mill control system tracking performance is; sensitivity M s The smaller the more robust the mill control system is; respectively calculating absolute value error integral ME and sensitivity M s And at ME-M s And establishing a predicted performance reference curve on the plane, judging whether the model of the mill control system is mismatched according to the predicted performance reference curve, and judging the tracking performance and the robustness of the mill control system.
S13: judging whether the model of the mill control system is mismatched according to the predicted performance reference curve, and judging the tracking performance and robustness of the mill control system, wherein the absolute value error integral IAE is defined as:equation 8; wherein e (t) represents a deviation of the actual output from the desired output, t being time; sensitivity M s Is defined as: />Equation 9; where S (jω) is obtained by substituting S in the sensitivity function S (S) for ω, the former term of jω being the imaginary unit j and the latter term being the angular frequency, in this application the sensitivity M s The value range of (2) is [1,2 ]]。
Assuming that the model of the mill control system is not mismatched, then G(s) =g 'is satisfied' p (s) when the mill control system makes steps with the amplitude r and sinusoidal tracking under the zero initial condition, the absolute value error integral IAE is as follows:equation 10; sensitivity M s Is thatEquation 11; for a given time lag τ and amplitude r, let the tuning parameter T introduced into the filter f In the case of the (0-s), ++ infinity) in in a variation of the method, the device, calculating IAE value and M using equation 10 and equation 11 s Takes the absolute value error integral IAE as the horizontal axis and takes the sensitivity M as the value of s Is taken as a vertical axis to construct IAE-M s Plane, and in IAE-M s Establishing a predicted performance reference curve in a plane;
when the model of the mill control system is not mismatched, i.e. G(s) =g' p At(s), the mill output y(s) at this time is: y(s) =g(s) G m (s)[r(s)-d(s)]+d(s), equation 12; if the mill control system is stable and G(s) noteqG' p (s), predictive controller G m (s) only the static gain G needs to be satisfied m (0) Static gain G 'for a predictive model transfer function of a mill' p (0) Inverse of (G) m (0)＝G′ p (0) -1 The mill control system has no steady-state deviation for constant value interference and step input, and the equation for obtaining the closed-loop deviation e(s) of the predictive control system is as follows: e(s) =r(s) -y(s), equation 13; the steady state deviation e (≡) is:equation 14. The closed loop deviation and steady state deviation of the predictive control system can be calculated according to formulas 13 and 14, if the formulas are satisfied, the model of the mill control system is not mismatched; if not, a model mismatch of the mill control system is indicated. Based on the value sum M of IAE calculated in practice s The extent to which the value of (a) deviates from the predicted performance reference curve, e.g. inAnd if the vertical axis direction deviates from the predicted performance reference curve by more than a set distance threshold, judging that the tracking performance and the robustness of the mill control system are poor if the vertical axis direction deviates from the predicted performance reference curve by more than 0.2-0.5. The set distance threshold may be set as desired.
S2: the predictive controller is designed based on a mathematical model of the mill control system.
Rewriting formula 3 to obtainEquation 15. Transfer function G 'according to a predictive model of the mill' p (s)＝G′ p+ (s)·G′ p- (s), decomposition is performed in equation 16, G' p- (s) is a transfer function with minimum phase characteristics, G' p- (s) stably excluding predicted items; g'. p+ (s) is a transfer function of an all-pass filter including all time lags and right half-plane zero points, satisfying |G 'for all frequencies' p+ (jω)|＝0。
Introducing a filter f(s) into the predictive controller G m (s) overwriting, the order of introduction of the filter f(s) was discussed above as 2, then there isEquation 17; substituting into equations 1 and 2 is:
equation 18;
equation 19.
When the model of the mill control system is not mismatched, G(s) =G 'is satisfied' p (s), and G' p (s)＝G′ p- (s), then equation 18 and equation 19 can be reduced to:
equation 20; />Equation 21.
It follows that the performance of the closed loop control system of the mill is dependent on the introduction of the filter f(s).
S3: and setting the filter parameters of the prediction controller by adopting a fuzzy control algorithm.
Specifically, as shown in FIG. 1, the output y of the transfer function link is based on the output y(s) of the mill and the predictive model of the mill p The error E and the error change rate EC between the two are used as the input of a fuzzy control algorithm and are based on a predictive controller G m (s) introduction of a FilterPresence of T f ＝T f0 +T f1 ，K＝K 0 +K 1 ，T f And K is the adjustment parameter introduced into the filter f(s), T f0 And K 0 Is a preset initial value; to ensure the stability of the mill control system, T f0 The upper limit is determined by the robust performance of the mill system and the lower limit is determined by the closed loop performance of the mill system. K (K) 0 The value of (2) is determined by the steady state error of the mill system.
T f1 And K 1 Is the output of the fuzzy control algorithm, and the T is obtained by a defuzzification method f1 And K 1 Is set to the optimum value of (2).
The T is obtained by a defuzzification method f1 And K 1 Firstly, establishing a fuzzy control algorithm and a fuzzy rule table. The error E and the error change rate EC are respectively quantized in seven levels according to fuzzy set theory, and the language variables are [ NB, NM, NS, Z, PS, PM, PB ]]Respectively represent [ negative big, negative middle, negative small, zero, positive small, median, positive big ]]The method comprises the steps of carrying out a first treatment on the surface of the The membership functions of the error E and the error change rate EC are all in the form of combining triangle, S-type and Z-type membership functions, the membership of the E and the EC is calculated, and the domains of input and output of a fuzzy control algorithm are selected and adjusted according to the actual condition of the mill.
T f1 And K 1 Seven-level language quantization is also performed, and the language variables are [ VB, B, BM, M, MS, Z ]]Respectively represent [ maximum, large, medium, middle, small, medium and small, zero ]]。
T is calculated using the following table f1 And K 1 And further performing a defuzzification operation according to the fuzzy output quantity to obtain a clear value of the fuzzy output quantity.
Table 1T f1 Fuzzy rule table
Table 2K 1 Is a fuzzy rule table of (a)
The membership function of the fuzzy set C of the fuzzy output Z obtained by the fuzzy control algorithm according to the fuzzy rule table is mu C (Z) let membership function μ C The weighted average value of (Z) is dF (Z), and the weighted average value dF (Z) is taken as the clear value of the fuzzy output Z,equation 22; wherein a and b are constants, T is taken as f1 And K 1 Substituting the fuzzy output according to the fuzzy rule table into the fuzzy output Z to obtain T f1 And K 1 The optimal value is sent to the predictive controller G m (s)。
S4: substituting the optimal value of the filter parameter after setting into a prediction controller to obtain the optimal output value of the mill control system.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (5)
1. A mill control method based on a predictive fuzzy control algorithm is characterized by comprising the following steps:
s1: establishing a mathematical model of a mill control system and a predicted performance reference curve; judging whether the model of the mill control system is mismatched or not through a predicted performance reference curve, and judging the tracking performance and robustness condition of the mill control system;
s2: designing a predictive controller based on a mathematical model of a mill control system;
s3: setting filter parameters of the prediction controller by adopting a fuzzy control algorithm;
s4: substituting the optimal value of the set filter parameter into a prediction controller to obtain an optimal output value of a mill control system;
in the step S1, a mathematical model of a mill control system is established, wherein the output of the mill is y (S), the set value of the mill control system is r (S), the external disturbance of the mill is d (S), the transfer function of the mathematical model of the mill is G (S), and the predictive controller is G m (s) the predicted model transfer function of the mill is [ G ]' p (s)]S is Laplacian, the input-output relation expression of the mill control system is:the input-output relation expression of the disturbance of the mill control system is as follows:wherein the open loop transfer function->The transfer function G(s) of the mathematical model of the mill is developed with: />Wherein K is p To be proportional to the amplification factor, T 1 And T 2 Is a time constant, τ is a time lag, e -τs For time-lag term, ->
In step S1, a predictive performance reference curve is established in the predictive controller G m The filter f(s) is introduced into(s),T f k is an adjusting parameter introduced into the filter, and n is an order; then predict controller G m (s) rewriting as:wherein [ G ]' p- (s)] -1 Is a transfer function [ G 'with minimum phase characteristics' p- (s)]Inverse of [ G ]' p+ (s)]Is a transfer function of an all-pass filter and satisfies [ G ]' p (s)]＝[G′ p+ (s)]·[G′ p- (s)]The method comprises the steps of carrying out a first treatment on the surface of the Then G c (s) rewriting as: />
Let the transfer function G(s) of the mathematical model of the mill and the predictive model transfer function of the mill [ G ]' p (s)]Equality, i.e. the model of the mill control system has no mismatch, let the sensitivity function of the mill control system be S (S), its expression is:respectively selecting absolute value error integral IAE and sensitivity M s As an index for measuring the tracking performance and the robust performance of the mill control system, the smaller the value of the absolute value error integral IAE is, the better the tracking performance of the mill control system tracking performance is; sensitivity M s The smaller the more robust the mill control system is; respectively calculating absolute value error integral IAE and sensitivity M s And at IAE-M s Establishing a predicted performance reference curve on a plane, and judging whether the model of the mill control system is mismatched according to the predicted performance reference curveJudging the tracking performance and robustness of the mill control system;
step S2, designing a predictive controller based on a mathematical model of the mill control system according to a transfer function [ G 'of the predictive model of the mill' p (s)]＝[G′ p+ (s)]·[G′ p- (s)]And introducing a filter f(s) to the predictive controller G m (s) rewriting the filter f(s) to 2 order, there isSubstituting the input-output relation expression of the mill control system and the input-output relation expression of the disturbance of the mill control system into the input-output relation expression of the mill control system:
when the model of the mill control system is not mismatched, G(s) = [ G ]' p (s)]And [ G ]' p (s)]＝[G′ p- (s)]The mill control system input-output relationship expression and the mill control system disturbance input-output relationship expression can be simplified into:
2. the method for controlling a mill based on a predictive fuzzy control algorithm according to claim 1, wherein the determining whether the model of the mill control system is mismatched according to the predictive performance reference curve, and determining the tracking performance and the robustness of the mill control system is defined by integrating the absolute value error IAE as:wherein e (t) represents a deviation of the actual output from the desired output, t being time; sensitivity M s Is defined as: />Wherein S (jω) isSubstituting S in the sensitivity function S (S) with jω, wherein the former term of jω is an imaginary unit, and the latter term is an angular frequency;
if the model of the mill control system has no mismatch, G(s) = [ G ]' p (s)]When the mill control system is in zero initial condition to make step and sine tracking with amplitude r, its absolute value error integral IAE is:sensitivity M s Is thatFor a given time lag τ and amplitude r, let the tuning parameter T introduced into the filter f Is changed within (0, ++ -infinity), taking absolute value error integral IAE as a horizontal axis and sensitivity M s Is taken as a vertical axis to construct IAE-M s Plane, and in IAE-M s Establishing a predicted performance reference curve in a plane;
when G(s) = [ G ]' p (s)]When there is no mismatch in the model of the mill control system, the output y(s) of the mill is: y(s) =g(s) G m (s)[r(s)-d(s)]+d(s); if the mill control system is stable and G(s) +. p (s)]Predictive controller G m (s) only the static gain G needs to be satisfied m (0) Static gain [ G 'for a predictive model transfer function of a mill' p (0)]Inverse of (G) m (0)＝[G′ p (0)] -1 The mill control system has no steady-state deviation for constant value interference and step input, and the equation for obtaining the closed-loop deviation e(s) of the predictive control system is as follows: e(s) =r(s) -y(s), the steady state deviation e (≡) is:
3. the mill control method based on the predictive fuzzy control algorithm of claim 2, wherein the sensitivity M s The value range of (2) is [1,2 ]]。
4. The method for controlling a mill based on a predictive fuzzy control algorithm according to claim 1, wherein the step S3 of adjusting the filter parameters of the predictive controller by using the fuzzy control algorithm is based on the output y (S) of the mill and the output y of the transfer function link of the predictive model of the mill p The error E and the error change rate EC between the two are used as the input of a fuzzy control algorithm and are based on a predictive controller G m (s) introduction of a FilterPresence of T f ＝T f0 +T f1 ，K＝K 0 +K 1 ，T f And K is the adjustment parameter introduced into the filter f(s), T f0 And K 0 Is a preset initial value; t (T) f1 And K 1 Is the output of the fuzzy control algorithm, and the T is obtained by a defuzzification method f1 And K 1 Is set to the optimum value of (2).
5. The method of claim 4, wherein T is obtained by a fuzzy decomposition method f1 And K 1 The optimal value of (2) is that the membership function of the fuzzy set C of the fuzzy output Z obtained by the fuzzy control algorithm according to the fuzzy rule table is mu C (Z) let membership function μ C The weighted average value of (Z) is dF (Z), and the weighted average value dF (Z) is taken as the clear value of the fuzzy output Z,a and b are constants, T is taken as f1 And K 1 Substituting the fuzzy output Z to obtain T f1 And K 1 The optimal value is sent to the predictive controller G m (s)。
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