CN103760931A - Oil-gas-water horizontal type three-phase separator pressure control method optimized through dynamic matrix control - Google Patents

Abstract

The invention discloses an oil-gas-water horizontal type three-phase separator pressure control method optimized through dynamic matrix control. The method comprises the steps that firstly, the model of a pressure object in an oil-gas-water horizontal type three-phase separator is built based on the step response data of the pressure object in the oil-gas-water horizontal type three-phase separator, and basic object characters are excavated out; then, the parameters of a corresponding PI-PD controller are set according to the character of the dynamic matrix control; finally, PI-PD control is carried out on the pressure object in the oil-gas-water horizontal type three-phase separator. The good control performance of the PI-PD control and the good control performance of the dynamic matrix control are combined, and the defects of a traditional control method are effectively overcome.

Description

Pressure control method of oil-gas-water horizontal three-phase separator optimized through dynamic matrix control

Technical Field

The invention belongs to the technical field of automation, and relates to a Dynamic Matrix Control (DMC) -optimization-based pressure proportional integral-proportional derivative (PI-PD) control method in an oil-gas-water horizontal three-phase separator.

Background

The PID controller has simple structure and convenient control, and is widely applied to various industrial control systems. However, for an integral, oscillatory or unstable control target, the PID sometimes has difficulty in satisfying higher control requirements. For example, large overshoot and oscillation often occur at step input, which may present a safety hazard to production. At present, PID control is mostly adopted for pressure control of the oil-gas-water horizontal three-phase separator, if PD control can be added to an inner ring, overshoot of the separator is inhibited firstly, and PI control is adopted for an outer ring, so that better production performance can be obtained. The dynamic matrix control algorithm is one of advanced control algorithms, has low requirement on a model and good control performance, and can further improve the efficiency of oil refining and natural gas collection if the dynamic matrix control and the PI-PD technology can be combined.

Disclosure of Invention

The invention aims to provide a PI-PD control method for pressure in an oil-gas-water horizontal three-phase separator based on dynamic matrix control optimization aiming at the defects of the existing PID controller, which is used for inhibiting overshoot so as to obtain better actual control performance. The PI-PD control method with the dynamic matrix control performance is obtained by combining the dynamic matrix control and the PI-PD control. The method not only inherits the excellent performance of dynamic matrix control, but also has simple form and can meet the requirement of actual industrial process.

Firstly, establishing a model of a pressure object in the oil-gas-water horizontal three-phase separator based on step response data of the pressure object in the oil-gas-water horizontal three-phase separator, and excavating basic object characteristics; then, setting parameters of a corresponding PI-PD controller according to the characteristics of dynamic matrix control; and finally, performing PI-PD control on a pressure object in the oil-gas-water horizontal three-phase separator.

According to the technical scheme, the PI-PD control method based on dynamic matrix control optimization is established by means of data acquisition, dynamic matrix establishment, prediction model establishment, prediction mechanism, optimization and the like, and can effectively inhibit overshoot and improve the stability of the system.

The method comprises the following steps:

step (1), establishing a model of a controlled object through real-time step response data of a process object, wherein the specific method comprises the following steps:

a. and (4) giving a step input signal to the controlled object, and recording a step response curve of the controlled object.

b. C, filtering the step response curve obtained in the step a, fitting the step response curve into a smooth curve, and recording step response data corresponding to each sampling moment on the smooth curve, wherein the first sampling moment is T_sThe time interval between two adjacent sampling time is T_sThe sampling time sequence is T_s、2T_s、3T_s… …, respectively; the step response of the controlled object will be at a certain time t_NAfter NT, it tends to be stable when a_i(i > N) and a_NWhen the error of (a) and the measurement error are of the same order of magnitude, a can be regarded as_NApproximately equal to the steady state value of the step response. Establishing a model vector a of an object:

a＝[a₁,a₂,…a_N]^Τ

where < T > is the transposed symbol of the matrix, a_iIs the data of the step response of the process object, and N is the modeling time domain.

Step (2), designing a PIPD controller of a controlled object, wherein the specific method comprises the following steps:

a. building a dynamic matrix of controlled objects

And (3) establishing a dynamic control matrix of the controlled object by using the model vector a obtained in the step (1) b, wherein the form of the dynamic control matrix is as follows:

$A=\left(\begin{array}{cccc}{a}_1& 0& ...& 0\\ a_2& a_1& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_P& a_{P-1}& ...& a_{P-M+1}\end{array}\right)$

wherein, A is a P multiplied by M order dynamic matrix of the controlled object, P is an optimized time domain of a dynamic matrix control algorithm, M is a control time domain of the dynamic matrix control algorithm, and M is more than P and less than N.

b. Calculating model prediction initial response value y of controlled object at current k moment_M(k)

Calculating a model predicted value y after adding a control increment delta u (k-1) at the time of k-1_p(k-1):

y_P(k-1)＝y_M(k-1)+A₀Δu(k-1)

Wherein,

$y_P(k-1)=\left[\begin{array}{c}{y}_1\left(k\right|k-1)\\ y_1(k+1|k-1)\\ .\\ .\\ .\\ y_1(k+N-1|k-1)\end{array}\right],y_M\left(k\right)=\left[\begin{array}{c}{y}_0\left(k\right|k-1)\\ y_0(k+1|k-1)\\ .\\ .\\ .\\ y_0(k+N-1|k-1)\end{array}\right],A_0=\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_N\end{array}\right]$

y₁(k|k-1),y₁(k+1|k-1),…,y₁(k + N-1| k-1) respectively represents the model predicted value of the controlled object after adding the control increment delta u (k-1) to k, k +1, …, k + N-1 at the time k-1, y₀(k|k-1),y₀(k|k-1),…y₀(k+N-1|k-1)Denotes the initial prediction value, A, at time k-1 versus time k, k +1, …, k + N-1₀For the matrix established for the step response data, Δ u (k-1) is the input control increment at time k-1.

Calculating a model prediction error value e (k) of the controlled object at the moment k:

ess(k)＝y(k)-y₁(k|k-1)

wherein y (k) represents the actual output value of the controlled object measured at the time k, y₁And (k | k-1) represents the model predicted value of the controlled object at the time k-1 to the time k after the control increment delta u (k-1) is added.

Calculating the correction value y of the model output at the moment k_cor(k):

y_cor(k)＝y_M(k-1)+h*ess(k)

Wherein,

<math> <mrow> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>h</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>&alpha;</mi> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mi>&alpha;</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

y_cor(k|k),y_cor(k+1|k),…y_corand (k + N-1| k) respectively represents the corrected value of the prediction model of the controlled object at the moment k, h is a weight matrix for error compensation, and alpha is an error correction coefficient.

Calculating initial response value y of model prediction at k moment_M(k)：

y_M(k)＝Sy_cor(k)

Wherein S is a state transition matrix of NxN order,

c. calculating the predicted output value y of the controlled object under M continuous control increments delta u (k), … and delta u (k + M-1)_PMThe specific method comprises the following steps:

y_PM(k)＝y_p0(k)+AΔu_M(k)

wherein,

<math> <mrow> <msub> <mi>y</mi> <mi>PM</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>P</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>&Delta;u</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>M</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

y_M(k+1|k),y_M(k+2|k),…,y_M(k + P | k) is the model predicted output value at time k versus time k +1, k +2, …, k + P, y₀(k+1|k),y₀(k+2|k-1),…y₀(k + N | k) represents the initial predicted value at time k versus time k +1, k +2, … k + P.

d. Let the control time domain M =1 of the controlled object, select the objective function j (k) of the controlled object, where j (k) is in the form:

<math> <mrow> <mi>min</mi> <mi>J</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mrow> <mo>(</mo> <mi>ref</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mi>PM</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>Q</mi> </msub> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>r</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mi>Q</mi> <msup> <mrow> <mo>(</mo> <mi>ref</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>P</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>A&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>r&Delta;u</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

ref(k)＝[ref₁(k),ref₂(k),…,ref_P(k)]^Τ

Q＝diag(q₁,q₂,…q_P)

r＝diag(r₁,r₂,…r_M)

ref_i(k)＝βⁱy(k)+(1-βⁱ)c(k)

wherein Q is an error weighting matrix, Q₁,q₂,…,q_PIs the addition of a weighting matrixA weight coefficient; beta is softening coefficient, c (k) is set value of process object; r is a control weight matrix, r₁,r₂,…r_MTo control the weighting coefficients of the weighting matrix, ref (k) is the reference trajectory of the system, ref_i(k) Is the value of the ith reference point in the reference track.

e. Converting the control quantity u (k):

e(k)＝c(k)-y(k)

u(k)＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-Kd(y(k)-2y(k-1)+y(k-2))＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-Kd(y(k)-y(k-1))+Kd(y(k-1)-y(k-2))

further processing u (k) to obtain

u(k)＝u(k-1)+w(k)^ΤE(k)

Wherein,

w(:,k)＝[K_p(k)+K_i(k),-K_p(k),-K_f(k)-K_d(k),K_d(k)]^Τ

E(k)＝(e(k),e(k-1),y(k)-y(k-1),y(k-1)-y(k-2))^Τ

Kp(k)、K_i(k)、K_f(k)、K_d(k) the proportional value of the outer ring, the integral of the outer ring, the proportional value of the inner ring and the differential parameter of the inner ring of the PI-PD controller at the moment k are respectively, e (k) is the error between a reference track value at the moment k and an actual output value, T is a transposed symbol of the matrix, and w (: k) is a matrix with four rows and k columns.

f. Substituting u (k) into the objective function in step d to solve the parameters in the PI-PD controller, we can obtain:

$w(:,k)=\frac{(\mathrm{ref}\left(k\right)-y_{p0}\left(k\right))\mathrm{QAE}}{(A^T\mathrm{QA}+r)E^{T}E}$

further, it is possible to obtain:

K_p(k)＝w(1,k)+w(2,k)

K_i(k)＝-w(2,k)

K_f(k)＝-w(3,k)-w(4,k)

K_d(k)＝w(4,k)

g. obtaining a parameter K of the PI-PD controller_p(k)、K_i(k)、K_f(k)、K_d(k) The subsequent constituent control quantity u (k) acts on the controlled object

u(k)＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-K_d(y(k)-2y(k-1)+y(k-2))。

h. At the next moment, the new parameter k of the PI-PD controller is continuously solved according to the steps from b to g_P(k+1)、k_i(k+1)、k_f(k+1)、k_dThe values of (k +1) are cycled through in sequence.

The invention provides a dynamic matrix control optimization-based PI-PD control method for pressure in an oil-gas-water horizontal three-phase separator, which combines good control performance of PI-PD control and dynamic matrix control, effectively improves the defects of the traditional control method, and promotes the development and application of an advanced control algorithm.

Detailed Description

Taking the process control of the pressure in the oil-gas-water horizontal three-phase separator as an example:

the control of the pressure in the oil-gas-water horizontal three-phase separator is a lag process, and the adjusting means adopts the control of the opening degree of an exhaust valve in a settling chamber.

Step (1), establishing a model of a controlled object through real-time step response data of a pressure object in an oil-gas-water horizontal three-phase separator, wherein the method comprises the following specific steps:

a. and (3) a step input signal is input to the oil-feeding gas-water horizontal three-phase separator, and a step response curve of the step input signal is recorded.

b. Filtering the corresponding step response curve, fitting the corresponding step response curve into a smooth curve, and recording the step response data corresponding to each sampling time on the smooth curve, wherein the first sampling time is T_sThe time interval between two adjacent sampling time is T_sThe sampling time sequence is T_s、2T_s、3T_s… …, respectively; the response will be at a certain time t_NAfter NT, it tends to be stable when a_i(i > N) and a_NWhen the error of (a) and the measurement error are of the same order of magnitude, a can be regarded as_NApproximately equal to the steady state value of the step response. Establishing a model vector a of a pressure object in the oil-gas-water horizontal three-phase separator:

a＝[a₁,a₂,…a_N]^Τ

where < T > is the transposed symbol of the matrix, a_iIs a step response of the pressure in the settling chamber of the oil-gas-water horizontal three-phase separatorData, N is the modeled time domain.

Step (2), designing a PI-PD controller of pressure in the oil-gas-water horizontal three-phase separator, wherein the specific method comprises the following steps:

a. and (2) establishing a dynamic matrix of the pressure in the oil-gas-water horizontal three-phase separator by using the model vector a obtained in the step (1) b, wherein the form of the dynamic matrix is as follows:

$A=\left(\begin{array}{cccc}{a}_1& 0& ...& 0\\ a_2& a_1& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_P& a_{P-1}& ...& a_{P-M+1}\end{array}\right)$

wherein A is a P multiplied by M order dynamic matrix of pressure in the oil-gas-water horizontal three-phase separator, P is an optimized time domain of a dynamic matrix control algorithm, M is a control time domain of the dynamic matrix control algorithm, and M is more than P and less than N.

b. Establishing an initial model prediction value y of the pressure in the oil-gas-water horizontal three-phase separator at the current k moment_M(k)

Calculating a model predicted value y of pressure in the oil-gas-water horizontal three-phase separator after adding a control increment delta u (k-1) at the time of k-1_p(k-1):

y_P(k-1)＝y_M(k-1)+A₀Δu(k-1)

Wherein,

$y_P(k-1)=\left[\begin{array}{c}{y}_1\left(k\right|k-1)\\ y_1(k+1|k-1)\\ .\\ .\\ .\\ y_1(k+N-1|k-1)\end{array}\right],A_0=\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_N\end{array}\right],y_M\left(k\right)=\left[\begin{array}{c}{y}_0\left(k\right|k-1)\\ y_0\left(k\right|k-1)\\ .\\ .\\ .\\ y_0(k+N-1|k-1)\end{array}\right]$

y₁(k|k-1),y₁(k+1|k-1),…,y₁(k + N-1| k-1) respectively represents a model predicted value y after delta u (k-1) is added to k, k +1, …, k + N-1 at the moment k-1 in the pressure in the oil-gas-water horizontal three-phase separator, and₀(k|k-1),y₀(k|k-1),…y₀(k + N-1| k-1) represents an initial predicted value of the pressure in the oil-gas-water horizontal three-phase separator at the moment k-1 to the moment k, k +1, …, k + N-1, A₀The delta u (k-1) is a matrix established by pressure step response data in a settling chamber of the oil-gas-water horizontal three-phase separator, and is the control increment of the opening degree of an exhaust valve in the oil-gas-water horizontal three-phase separator at the moment of k-1.

Calculating a model prediction error value ess (k) of the pressure in the oil-gas-water horizontal three-phase separator at the moment k:

ess(k)＝y(k)-y₁(k|k-1)

wherein y (k) represents the actual output value of the pressure in the oil-gas-water horizontal three-phase separator measured at the moment k, y₁And (k | k-1) represents the model predicted value of the pressure in the oil-gas-water horizontal three-phase separator at the moment k-1 to the moment k after the control increment delta u (k-1) is added.

Calculating the output correction value y of the pressure model in the oil-gas-water horizontal three-phase separator at the moment k_cor(k):

y_cor(k)＝y_M(k-1)+h*ess(k)

Wherein,

<math> <mrow> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>h</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>&alpha;</mi> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mi>&alpha;</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

y_cor(k|k),y_cor(k+1|k),…y_cor(k + N-1| k) respectively represents the pressure in the oil-gas-water horizontal three-phase separatorAnd the correction value of the model at the moment k, h is a weight matrix of error compensation, and alpha is an error correction coefficient.

Calculating the model prediction initial response value y of the pressure in the oil-gas-water horizontal three-phase separator at the moment k_M(k)：

y_M(k)＝Sy_cor(k)

Wherein S is a state transition matrix of NxN order,

c. calculating the predicted output value y of the pressure in the oil-gas-water horizontal three-phase separator under M continuous control increments delta u (k), … and delta u (k + M-1)_PMThe specific method comprises the following steps:

y_PM(k)＝y_P0(k)+AΔu_M(k)

wherein,

<math> <mrow> <msub> <mi>y</mi> <mi>PM</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>P</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>&Delta;u</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>M</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

y_P0(k) is y_M(k) The first P term, y_M(k+1|k),y_M(k+2|k),…,y_MAnd (k + P | k) is a model predicted output value of the pressure in the oil-gas-water horizontal three-phase separator at the k moment to the k +1, k +2, … and k + P moment.

d. And (3) setting the control time domain M as 1, and selecting an objective function J (k) of the pressure in the oil-gas-water horizontal three-phase separator, wherein the form of J (k) is as follows:

<math> <mrow> <mi>min</mi> <mi>J</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mrow> <mo>(</mo> <mi>ref</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mi>PM</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>Q</mi> </msub> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>r</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mi>Q</mi> <msup> <mrow> <mo>(</mo> <mi>ref</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>P</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>A&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>r&Delta;u</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

ref(k)＝[ref₁(k),ref₂(k),…,ref_P(k)]^Τ

Q＝diag(q₁,q₂,…q_P)

r＝diag(r₁,r₂,…r_M)

ref_i(k)＝βⁱy(k)+(1-βⁱ)c(k)

wherein Q is an error weighting matrix, Q₁,q₂,…,q_PWeighting coefficients for the error weighting matrix; beta is softening coefficient, c (k) is set value of pressure in oil-gas-water horizontal three-phase separator; r ═ diag (r)₁,r₂,…r_M) To control the weighting matrix, r₁,r₂,…r_MIn order to control the weighting coefficient of the weighting matrix, ref (k) is a reference track of the pressure in the oil-gas-water horizontal three-phase separator at the moment k, ref_i(k) Is the value of the ith reference point in the reference track.

e. Converting the control quantity u (k) of the opening degree of an exhaust valve in the oil-gas-water horizontal three-phase separator:

e(k)＝c(k)-y(k)

u(k)＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-Kd(y(k)-2y(k-1)+y(k-2))＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-Kd(y(k)-y(k-1))+Kd(y(k-1)-y(k-2))

further processing u (k) to obtain

u(k)＝u(k-1)+w(k)^ΤE(k)

Wherein,

w(:,k)＝[K_p(k)+K_i(k),-K_p(k),-K_f(k)-K_d(k),K_d(k)]

E(k)＝(e(k),e(k-1),y(k)-y(k-1),y(k-1)-y(k-2))^Τ

Kp(k)、K_i(k)、K_f(k)、K_d(k) the ratio of an outer ring, the integral of the outer ring, the ratio of an inner ring and differential parameters of the inner ring of the PI-PD controller are respectively, e (k) is an error between a reference track value at a moment k and an actual output value, T is a transposed symbol of the matrix, and w (: k) is a matrix with four rows and k columns.

f. Substituting u (k) into the objective function in the step d, and solving the parameters in the PI-PD controller to obtain:

$w(:,k)=\frac{(\mathrm{ref}\left(k\right)-y_{p0}\left(k\right))\mathrm{QAE}}{(A^T\mathrm{QA}+r)E^{T}E}$

further, it is possible to obtain:

K_p(k)＝w(1,k)+w(2,k)

K_i(k)＝-w(2,k)

K_f(k)＝-w(3,k)-w(4,k)

K_d(k)＝w(4,k)

g. obtaining a parameter K of the PI-PD controller_p(k)、K_i(k)、K_f(k)、K_d(k) The subsequent formation of control quantity u (k) acting on oil-gas-water horizontal three-phase separator

u(k)＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-Kd(y(k)-2y(k-1)+y(k-2))

h. At the next moment, the new parameter k of the PI-PD controller is continuously solved according to the steps from b to g_P(k+1)、k_i(k+1)、k_f(k+1)、k_dThe value of (k +1), which acts on the controlled object, cycles through.

Claims (1)

1. The pressure control method of the oil-gas-water horizontal three-phase separator optimized by dynamic matrix control is characterized by comprising the following specific steps:

step (1), establishing a model of a controlled object through real-time step response data of a process object, wherein the specific method comprises the following steps:

1-a, giving a step input signal to a controlled object, and recording a step response curve of the controlled object;

1-b, filtering the step response curve obtained in the step 1-a, fitting the step response curve into a smooth curve, and recording each step response curve on the smooth curveStep response data corresponding to sampling time, wherein the first sampling time is T_sThe time interval between two adjacent sampling time is T_sThe sampling time sequence is T_s、2T_s、3T_s… …, respectively; the step response of the controlled object will be at a certain time t_NAfter NT, it tends to be stable when a_iAnd a_NWhen the error of (a) and the measurement error are of the same order of magnitude, a can be regarded as_NApproximately equal to the steady state value of the step response, i > N; establishing a model vector a of an object:

a＝[a₁,a₂,…a_N]^Τ

where < T > is the transposed symbol of the matrix, a_iIs the data of the step response of the process object, and N is the modeling time domain;

step (2), designing a PIPD controller of a controlled object, wherein the specific method comprises the following steps:

2-a establishing dynamic matrix of controlled object

And (3) establishing a dynamic control matrix of the controlled object by using the model vector a obtained in the step (1-b), wherein the form of the dynamic control matrix is as follows:

$A=\left(\begin{array}{cccc}{a}_1& 0& ...& 0\\ a_2& a_1& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_P& a_{P-1}& ...& a_{P-M+1}\end{array}\right)$

a is a P multiplied by M order dynamic matrix of a controlled object, P is an optimized time domain of a dynamic matrix control algorithm, M is a control time domain of the dynamic matrix control algorithm, and M is more than P and less than N;

2-b, calculating the model prediction initial response value y of the controlled object at the current k moment_M(k)

Calculating a model predicted value y after adding a control increment delta u (k-1) at the time of k-1_p(k-1):

y_P(k-1)＝y_M(k-1)+A₀Δu(k-1)

Wherein,

$y_P(k-1)=\left[\begin{array}{c}{y}_1\left(k\right|k-1)\\ y_1(k+1|k-1)\\ .\\ .\\ .\\ y_1(k+N-1|k-1)\end{array}\right],y_M\left(k\right)=\left[\begin{array}{c}{y}_0\left(k\right|k-1)\\ y_0(k+1|k-1)\\ .\\ .\\ .\\ y_0(k+N-1|k-1)\end{array}\right],A_0=\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ .\\ a_N\end{array}\right]$

y₁(k|k-1),y₁(k+1|k-1),…,y₁(k + N-1| k-1) respectively represents the model predicted value of the controlled object after adding the control increment delta u (k-1) to k, k +1, …, k + N-1 at the time k-1, y₀(k|k-1),y₀(k|k-1),…y₀(k + N-1| k-1) represents the initial predicted value at time k-1 versus time k, k +1, …, k + N-1, A₀A matrix is established for the step response data, and delta u (k-1) is an input control increment at the moment of k-1;

calculating a model prediction error value e (k) of the controlled object at the moment k:

ess(k)＝y(k)-y₁(k|k-1)

wherein y (k) represents the actual output value of the controlled object measured at the time k, y₁(k | k-1) represents the model predicted value of the controlled object at the k-1 moment to the k moment after the control increment delta u (k-1) is added;

calculating the correction value y of the model output at the moment k_cor(k):

y_cor(k)＝y_M(k-1)+h*ess(k)

Wherein,

<math> <mrow> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>cor</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>h</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>&alpha;</mi> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mi>&alpha;</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

y_cor(k|k),y_cor(k+1|k),…y_cor(k + N-1| k) respectively represents the corrected value of the controlled object at the k moment prediction model, h is the weight matrix of error compensation, and alpha is the error correction systemCounting;

calculating initial response value y of model prediction at k moment_M(k)：

y_M(k)＝Sy_cor(k)

Wherein S is a state transition matrix of NxN order,

2-c, calculating the predicted output value y of the controlled object under M continuous control increments delta u (k), … and delta u (k + M-1)_PMThe specific method comprises the following steps:

y_PM(k)＝y_p0(k)+AΔu_M(k)

wherein,

<math> <mrow> <msub> <mi>y</mi> <mi>PM</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>P</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>&Delta;u</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>M</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

y_M(k+1|k),y_M(k+2|k),…,y_M(k + P | k) is the model predicted output value at time k versus time k +1, k +2, …, k + P, y₀(k+1|k),y₀(k+2|k-1),…y₀(k + N | k) represents the initial predicted value at time k versus time k +1, k +2, … k + P;

and 2-d, enabling the control time domain M =1 of the controlled object, and selecting a target function J (k) of the controlled object, wherein the form is as follows:

<math> <mrow> <mi>min</mi> <mi>J</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mrow> <mo>(</mo> <mi>ref</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mi>PM</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>Q</mi> </msub> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>r</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mi>Q</mi> <msup> <mrow> <mo>(</mo> <mi>ref</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>P</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>A&Delta;u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>r&Delta;u</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

ref(k)＝[ref₁(k),ref₂(k),…,ref_P(k)]^Τ

Q＝diag(q₁,q₂,…q_P)

r＝diag(r₁,r₂,…r_M)

ref_i(k)＝βⁱy(k)+(1-βⁱ)c(k)

wherein Q is an error weighting matrix, Q₁,q₂,…,q_PA weighting coefficient being a weighting matrix; beta is softening coefficient, c (k) is set value of process object; r is a control weight matrix, r₁,r₂,…r_MTo control the weighting coefficients of the weighting matrix, ref (k) is the reference trajectory of the system, ref_i(k) Is the value of the ith reference point in the reference track;

transforming the control quantity u (k):

e(k)＝c(k)-y(k)

u(k)＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-Kd(y(k)-2y(k-1)+y(k-2))＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-Kd(y(k)-y(k-1))+Kd(y(k-1)-y(k-2))

further processing u (k) to obtain

u(k)＝u(k-1)+w(k)^ΤE(k)

Wherein,

w(:,k)＝[K_p(k)+K_i(k),-K_p(k),-K_f(k)-K_d(k),K_d(k)]^Τ

E(k)＝(e(k),e(k-1),y(k)-y(k-1),y(k-1)-y(k-2))^Τ

Kp(k)、K_i(k)、K_f(k)、K_d(k) respectively is the proportion of an outer ring, the integral of the outer ring, the proportion of an inner ring and differential parameters of the inner ring of the PI-PD controller at the moment k, e (k) is the error between a reference track value at the moment k and an actual output value, T is a transposed symbol of the matrix, and w (: k) is a matrix with four rows and k columns;

substituting u (k) into the objective function in step 2-d to solve the parameters in the PI-PD controller, we can obtain:

$w(:,k)=\frac{(\mathrm{ref}\left(k\right)-y_{p0}\left(k\right))\mathrm{QAE}}{(A^T\mathrm{QA}+r)E^{T}E}$

further obtaining:

K_p(k)＝w(1,k)+w(2,k)

K_i(k)＝-w(2,k)

K_f(k)＝-w(3,k)-w(4,k)

K_d(k)＝w(4,k)

obtaining parameter K of PI-PD controller_p(k)、K_i(k)、K_f(k)、K_d(k) The subsequent constituent control quantity u (k) acts on the controlled object

u(k)＝u(k-1)+K_p(k)(e(k)-e(k-1))+K_i(k)e(k)-K_f(k)(y(k)-y(k-1)-K_d(y(k)-2y(k-1)+y(k-2))；

At the next moment, continuously solving a new parameter k of the PI-PD controller according to the steps 2-b to 2-g_P(k+1)、k_i(k+1)、k_f(k+1)、k_dThe values of (k +1) are cycled through in sequence.