CN109999270B

CN109999270B - Artificial pancreas self-adaptation auto-disturbance rejection controller based on blood sugar variation trend

Info

Publication number: CN109999270B
Application number: CN201910222692.7A
Authority: CN
Inventors: 史大威; 纪立农; 蔡德恒; 王军政; 蔡晓凌; 刘蔚
Original assignee: Peking University Peoples Hospital; Beijing Institute of Technology BIT
Current assignee: Peking University Peoples Hospital; Beijing Institute of Technology BIT
Priority date: 2019-03-22
Filing date: 2019-03-22
Publication date: 2020-09-04
Anticipated expiration: 2039-03-22
Also published as: CN109999270A

Abstract

The invention provides an artificial pancreas self-adaptive active disturbance rejection controller based on blood sugar variation trend, which comprises a tracking differentiator module, a dimension expansion observer module, a nonlinear feedback module and a constraint module, wherein the nonlinear feedback module comprises a nonlinear feedback model: u (-fhan (k))₁e₁,k₂e₂,r₂,a)‑z₃)/b₀Wherein k is₁,k₂A is a parameter adaptive according to the blood sugar variation trend, r₂Referred to as the control quantity gain; e.g. of the type₁And e₂Is an error signal between the blood glucose concentration and its rate of change set point and estimate, z₃Is an estimate of the total interference; b₀The gain factor is known. The invention attributes all uncertain factor action acting on the controlled object as unknown disturbance and uses input and output data of the object to estimate and compensate the unknown disturbance. Therefore, the controller algorithm has certain robustness on disturbance such as inaccurate personal parameters, uncertain models, eating interference, inaccurate pre-prandial dosage and the like.

Description

Artificial pancreas self-adaptation auto-disturbance rejection controller based on blood sugar variation trend

Technical Field

The invention relates to an artificial pancreas self-adaptive self-disturbance rejection controller based on a blood sugar change trend, and belongs to the technical field of artificial pancreas systems.

Background

The blood glucose concentration of a normal healthy person is synergistically regulated by insulin and glucagon. Glucagon is secreted by alpha cells in the pancreas, which can raise blood glucose concentrations, while insulin is secreted by beta cells in the pancreas, which can lower blood glucose concentrations. Type i diabetes is the condition when insulin is not secreted at all due to autoimmune destruction resulting in loss of function or death of beta cells, and type ii diabetes is the condition when beta cells are unable to produce sufficient amounts of insulin. Both type i and type ii diabetes are metabolic diseases characterized by hyperglycemia, and can cause serious long-term complications such as cardiovascular diseases, chronic kidney diseases, diabetic foot, retinopathy and the like, and are collectively called four major chronic diseases with cardiovascular diseases, respiratory diseases and tumors.

Thanks to the technical development of blood glucose sensors and insulin pumps, the artificial pancreas is implemented, more effective diabetes treatment is realized, and the blood glucose concentration is ensured to be within a normal range as much as possible: 70-180 mg/dl. The artificial pancreas system is a closed loop control system, as shown in fig. 1, and is mainly composed of three parts: dynamic blood glucose monitoring (blood glucose sensor), insulin pump capable of insulin infusion, and controller capable of adjusting the amount of insulin infusion in real time based on continuously measured blood glucose values. However, the control algorithm in the controller is a key core part of the artificial pancreas, and the design of the control algorithm faces many challenges:

1) controlled processes are difficult to model accurately. Due to the complexity of human body structure and dynamics, the blood sugar metabolic process of the human body is a complex, unsteady, multivariable, strong coupling and high-order nonlinear system, and the insulin sensitivity of individuals is different even in different time periods of the same individual, so that the system is also a time-varying and parameter-varying system.

2) Various types of interference. The activities of ingestion, exercise, drinking, and the like, as well as stress and emotional changes, which are involved in the normal life of the human body, cause disturbances in the blood glucose metabolic system, which are difficult to measure.

3) Asymmetric kinetics. The rise in blood glucose brought about by digestive absorption after ingestion is a fast-responding kinetic process, the decrease in blood glucose by absorption and action of subcutaneously injected insulin is a slow kinetic process, and there is also a time lag and inaccuracy in the measurement of blood glucose concentration by the blood glucose sensor through the difference in concentration of subcutaneous intercellular fluid and blood glucose in blood vessels.

4) Risk of asymmetry of hyperglycemia and hypoglycemia. Hyperglycemia is a major cause of long-term complications in diabetics, whereas the "insulin-blood sugar" system is a positive system, and insulin infusion values and system status values are only positive, when it is intended to eliminate hyperglycemia as soon as possible, there is a possibility that excessive insulin injection may cause subsequent hypoglycemia.

The existing closed-loop control algorithms entering clinical experiments mainly comprise PID control and Model Predictive Control (MPC). The PID is also used in the artificial pancreas system as an industrially practical control algorithm, and forms a feedback control quantity by using a weighted sum form of proportion, integral and differential of an error between a target value and an actual value of blood glucose concentration, and has the characteristics of simple structure and easy realization, but is also limited by the simple structure, the problems of the characteristics of the blood glucose metabolic system including the above consideration cannot be reflected in the design of a controller, and the integral saturation phenomenon easily causes the insulin injection overdose when the blood glucose continuously rises. MPC can directly process the control problem under various constraint conditions, has certain robustness to the system model, through predicting the future output, searches the optimal or suboptimal control quantity, can very conveniently process ingestion, insulin absorption delay and the like, has the characteristic of superior performance, but the algorithm complexity is higher, the controller occupies more computing resources during operation, and is not beneficial to the reliable realization in an embedded system. Therefore, how to design the controller which can be effectively compatible with the characteristics of simple structure of the PID controller and excellent performance of the MPC controller and ensure the safety has important significance for the artificial pancreas system.

Disclosure of Invention

The invention aims to overcome the defects and defects of the prior art, provides an artificial pancreas self-adaptive active disturbance rejection controller based on the blood sugar change trend by utilizing an active disturbance rejection control technology and combining a self-adaptive thought, and achieves the purposes of having the characteristics of simple structure, small calculated amount and excellent performance of a compatible MPC controller and ensuring the safety of an algorithm.

The invention is realized by the following technical scheme:

an artificial pancreas self-adaptive auto-disturbance rejection controller based on blood sugar variation trend comprises a tracking differentiator module, a dimension expansion observer module, a nonlinear feedback module and a constraint module, wherein,

the nonlinear feedback model of the nonlinear feedback module is as follows:

u＝(-fhan(k₁e₁,k₂e₂,r₂,a)-z₃)/b₀

wherein k is₁,k₂A is a parameter adaptive according to the blood sugar variation trend, r₂Referred to as the control quantity gain; e.g. of the type₁And e₂Is an error signal between the blood glucose concentration and its rate of change set point and estimate, z₃Is an estimate of the total interference; b₀The gain factor is known.

Furthermore, the tracking differentiator module receives a blood glucose concentration measuring signal acquired by a blood glucose sensor on a human body every other sampling period, outputs a blood glucose concentration prediction signal when the blood glucose concentration meets a design condition, and otherwise outputs a blood glucose concentration filtering signal; the design conditions are as follows: blood glucose concentration was maintained at the set value [ G ] during the ascending phase_h,G_H]Within the range, the blood glucose concentration is maintained at the set value [ G ] in the descending stage_LG_l]

In the range, G_hThe value range is 110mg/dl-150mg/dl, G_HThe value range is 200mg/dl-300mg/dl, G_LThe value range is 90mg/dl-120m/dl, G_lThe value range is 170mg/dl-200 mg/dl.

The dimension expansion observer module is used for processing the filtering signal or the prediction signal output by the tracking differentiator module to obtain a total interference estimation value, a blood glucose concentration deviation value and a change rate estimation value thereof, and then comparing the blood glucose concentration deviation value and the change rate estimation value thereof with a preset reference signal to obtain an error signal;

and the constraint module is used for controlling the insulin pump after constraining the output signal u according to the constraint condition, and injecting the insulin infusion amount corresponding to the control signal into the human body to form closed-loop control.

Further, if the change of the blood glucose concentration meets the design condition, the constraint module calculates the IOB constraint value by using the blood glucose concentration prediction signal, otherwise, the constraint module calculates the IOB constraint value by using the blood glucose concentration filtering signal.

Further, k according to the present invention₁,k₂And a, parameters self-adaptive according to the blood sugar change trend are as follows:

the idea of setting parameters: the total realization is that a proper amount of insulin is injected in advance in the blood sugar concentration rising stage, and the excessive injection of the insulin is prevented, and a proper amount of insulin is injected in the blood sugar concentration falling stage, so that the safety of the algorithm is ensured by the injection amount of the basic insulin and even stopping the injection;

blood glucose concentration rise Process

The first stage is as follows: when the blood glucose concentration is less than the threshold G_hWhen, will k₁,k₂Designing a function of the blood glucose concentration change rate, increasing along with the increase of the blood glucose concentration change rate, and keeping the function unchanged, designing a as the function of the blood glucose concentration, decreasing along with the increase of the blood glucose concentration, and keeping the function unchanged; (realize that when the blood sugar concentration is lower and rises slowly, the control response is relatively conservative, reach the effect of basically injecting with basic insulin quantity, weaken the influence of sensor noise, and when the blood sugar concentration rises gradually and fast, the control response is sensitive gradually, reach the effect that insulin injection quantity increases gradually from basic insulin injection quantity.)

And a second stage: when the blood glucose concentration is greater than the threshold G_hAnd is less than a threshold value G_HWhen k is₁,k₂Each maintaining a first phase constant value, and a is designed as a function of blood glucose concentration as blood glucose concentration increasesAnd is increased; (achieve the purpose of improving the response sensitivity of the controller in the initial stage of the rise of the blood sugar concentration, fully injecting a proper amount of insulin, and gradually reducing the injection amount of the insulin to prevent over-injection when the rise of the blood sugar approaches an upper threshold value.)

And a third stage: when the blood glucose concentration is greater than the threshold G_HWhen, let k₁,k₂A respectively keeping the end value of the second stage; (sufficient insulin has been injected in the first, second phase, thus achieving injection of the appropriate amount of insulin in this phase.)

Process of decreasing blood glucose concentration

The first stage is as follows: when the blood glucose concentration is greater than the threshold G_lThen, k will be designed₂As a function of the absolute value of the rate of change of blood glucose concentration, the greater the absolute value k₂The larger, and design k₁And a is kept constant; (to achieve the injection of a proper amount of insulin in a decreasing phase with a high blood glucose concentration, and to reduce the amount of insulin injected as the rate of decrease in blood glucose concentration increases.)

And a second stage: when the blood glucose concentration is less than the threshold G_lAnd is greater than a threshold value G_LAnd design k₁Is a constant value, a is the same as the first phase value, k₂Is the function used for the first segment; (achieving injection of a proper amount of insulin in a decreasing stage at a lower blood glucose concentration, and the amount of insulin injected is more decreased as the rate of decrease in blood glucose concentration increases.)

And a third stage: when the blood glucose concentration is less than the threshold G_LDesign k₁And a is the same as the value of the second stage, k₂Is a fixed value. (achieving injection of basal insulin alone, even stopping injection, and preventing hypoglycemia at lower blood glucose concentration.)

Advantageous effects

The invention provides an artificial pancreas self-adaptive active disturbance rejection controller based on a blood sugar change trend by utilizing an active disturbance rejection control technology and combining a self-adaptive thought.

(1) The most prominent feature of the active disturbance rejection control technology is that all uncertain factors acting on a controlled object are classified as unknown disturbance, and the unknown disturbance is estimated and compensated by input and output data of the object. Therefore, the controller algorithm has certain robustness on disturbance such as inaccurate personal parameters, uncertain models, eating interference, inaccurate pre-prandial dosage and the like.

(2) According to the controller algorithm, when the blood sugar rising and falling stages respectively meet the designed conditions, the tracking differentiator is utilized to start the prediction function, and the IOB constraint is self-adaptive, so that aiming at the asymmetric dynamics problem, the algorithm is fierce at the initial stage of the blood sugar concentration rising after eating, insulin is injected more in advance, the prediction function is started at the blood sugar concentration falling stage, the algorithm is conservative, insulin is injected less in advance, and even the injection is stopped. The design is simultaneously beneficial to solving the asymmetrical risk of high and low blood sugar, effectively leads the blood sugar concentration to return to the normal range as soon as possible, avoids the occurrence of hypoglycemia symptoms and ensures the safety of the algorithm.

(3) The controller algorithm introduces a self-adaptive thought, and parameters of a nonlinear feedback control law are designed based on the blood sugar variation trend, so that the controller algorithm has certain robustness on the measured noise, different processing modes in the blood sugar concentration rising and falling stages are realized, high sensitivity on high and low blood sugar is realized, and the safety, reasonability and effectiveness of the algorithm are ensured.

Drawings

FIG. 1 is a block diagram of an artificial pancreas system according to the present invention;

FIG. 2 is a schematic diagram of the architecture of the adaptive auto-disturbance-rejection controller of the present invention;

FIG. 3 is a graph of a function utilized for design parameter adaptation in an embodiment of the present invention;

FIG. 4 is a graph of a quartile curve and mean value of blood glucose concentration for simulation results with a bolus of insulin supplemented prior to a meal in an embodiment of the present invention;

FIG. 5 is a graph comparing simulation results of the present controller with two other MPC controllers for pre-meal bolus insulin supplementation in accordance with an embodiment of the present invention;

FIG. 6 is a graph of a quartile curve and mean value of blood glucose concentration for simulation results without bolus insulin supplementation prior to a meal in an embodiment of the present invention;

FIG. 7 is a graph comparing simulation results of the present controller and two other MPC controllers without bolus insulin supplementation before meal in accordance with an embodiment of the present invention.

Detailed Description

The invention is described in further detail below with reference to the following detailed description and accompanying drawings: the present example is carried out on the premise of the technical solution of the present invention, but the scope of the present invention is not limited to the following embodiments.

The design idea of the invention is as follows: according to the actual condition of the patient, determining the total insulin amount u required by the endocrinology specialist to maintain the blood sugar concentration approximately stable every day_TDIEstablished around this equilibrium steady state to achieve a blood glucose concentration output of G_bThe control model is 110mg/dl and is suitable for the implementation of the active disturbance rejection control technology, and the control model designed by the invention is as follows:

wherein t is time in minutes, and G is blood glucose concentration G_BGDeviation G_bA value of (i.e. G ═ G)_BG-G_bTo do so

Is the change rate of the deviation value, namely the change rate of the blood sugar concentration,

is composed of

D (t) is interference, e.g. feeding, model uncertainty, etc.

Is a function of blood glucose concentration and its rate of change, disturbance and time, the control quantity u being a deviation from the basal insulin injection rate u_bI.e. u-u_I-u_b，u_IFor the actual insulin injection rate, it should be guaranteed that the value is not negative. b is a gain factor, which can be written as u_TDIRelated known partB is divided into₀And perturbation portion Δ b.

Based on the above thought, the present embodiment is an artificial pancreas adaptive auto-disturbance rejection controller based on blood sugar variation trend, comprising a tracking differentiator module, a dimension expansion observer module, a nonlinear feedback module and a constraint module, wherein,

the tracking differentiator module receives blood glucose concentration measuring signals collected by a blood glucose sensor on a human body every other sampling period, outputs a blood glucose concentration prediction signal when the blood glucose concentration meets a design condition, and otherwise outputs a blood glucose concentration filtering signal; the design conditions are as follows: blood glucose concentration was maintained at the set value [ G ] during the ascending phase_h,G_H]Within the range, the blood glucose concentration is maintained at the set value [ G ] in the descending stage_LG_l]Within the range;

the nonlinear feedback model of the nonlinear feedback module is as follows:

u＝(-fhan(k₁e₁,k₂e₂,r₂,a)-z₃)/b₀

The specific process of each module is as follows:

(1) every other sampling period, the controller receives a blood sugar sensor measurement value CGM (k), a corresponding filtering signal and an approximate differential signal thereof are obtained through processing of the tracking differentiator, meanwhile, a self-adaptive thought is introduced, and according to different measurement values, when one of design conditions is met, a prediction function is started, and a blood sugar concentration prediction signal is obtained in a self-adaptive mode. There are various types of tracking differentiators, and the tracking differentiator described in document [1] (hangjieming. active disturbance rejection control technology, beijing, national defense industry press, 2008) includes a linear tracking differentiator and a nonlinear tracking differentiator (a fast tracking differentiator and a fastest tracking differentiator).

(2) Adaptively sending a filtering signal or a prediction signal of the blood glucose concentration into an extended dimension state observer, discretizing a control model, and carrying out adaptive control on the control model

Viewed as total interference d_tTo estimate, wherein the extended dimension state observer can adopt a linear state observer or a non-linear state observer, and the specific form and corresponding parameter determination can be found in the literature [1]]The extended state observer section can obtain the total interference d by using the extended dimension state observer_tAn estimate of blood glucose concentration deviation and an estimate of the rate of change thereof.

(3) Respectively comparing the blood glucose concentration and the change rate set value thereof with the blood glucose concentration deviation value and the change rate estimated value z estimated by the dimension extending observer₁And z₂Comparing to obtain an error signal e₁And e₂And total interference d_tIs estimated value z₃The data are provided to a nonlinear feedback module together, meanwhile, an adaptive thought is introduced, and an output signal u is generated in an adaptive mode based on parameters in a blood glucose change trend changing module, wherein the equation is as follows:

u＝(-fhan(k₁e₁,k₂e₂,r₂,a)-z₃)/b₀

wherein k is₁,k₂A is a parameter adaptive according to the blood sugar variation trend, r₂Called the control gain, is a fixed parameter, where fhan (-) is described in detail in document [1]]. From (1), the actual insulin quantity injected into the human body in one sampling period is u_IN＝(u+u_b) h. According to the document [1]]To simplify the design of the parameters, the parameter r is designed₂Always make the following expression hold

And

the approximate expression of the non-linear function fhan (-) is

Blood glucose level rise phase

When the blood glucose concentration is less than the threshold G_hWhen, will k₁,k₂Designing a function of the blood glucose concentration change rate, increasing along with the increase of the blood glucose concentration change rate, and keeping the function unchanged, designing a as the function of the blood glucose concentration, decreasing along with the increase of the blood glucose concentration, and keeping the function unchanged; when the blood sugar concentration is low and rises slowly, the algorithm is conservative, the influence of noise of the sensor is weakened, and when the blood sugar concentration rises gradually and quickly, the algorithm is gradually fierce.

When the blood glucose concentration is greater than the threshold G_hAnd is less than a threshold value G_HWhen k is₁,k₂Each maintaining a first phase constant value, and designing a as a function of blood glucose concentration, wherein the blood glucose concentration increases with the increase of the blood glucose concentration; and a prediction function is started by utilizing a tracking differentiator to obtain a prediction value, the prediction value is transmitted to the IOB module, the constraint is relaxed, the algorithm is enabled to be fierce at the initial stage of the rise of the blood sugar concentration, and insulin is fully injected.

When the blood glucose concentration is greater than the threshold G_HWhen, let k₁,k₂And a respectively keeps the end value of the second stage, so that the algorithm is gradually conserved, the insulin to be injected is gradually reduced, and the safety of the algorithm is ensured.

Blood glucose concentration lowering stage

When the blood glucose concentration is greater than the threshold G_lThen, k will be designed₂As a function of the absolute value of the rate of change of blood glucose concentration, the greater the absolute value k₂The larger, and design k₁And a is kept constant;

when the blood glucose concentration is less than the threshold G_lAnd is greater than a threshold value G_LAnd design k₁Is a constant value, a is the same as the first phase value, k₂Starting a prediction function for the function used in the first section, and tightening the constraint to realize more conservative insulin injection;

when the blood glucose concentration is less than the threshold G_LDesign k₁And a is the same as the value of the second stage, k₂Is a fixed value k₁,k₂And a is designed to be more sensitive to change rate and hypoglycemia, and when the blood sugar concentration is low and the blood sugar concentration still has a descending trend, the insulin infusion is stopped earlier in time, so that the safety of the algorithm is ensured.

(5) Certain constraint is applied to the output of the nonlinear feedback module, so that the reasonability and the safety of the algorithm are ensured. The restriction module includes non-negative and maximum limits, and an in vivo active insulin limit (IOB). The nonnegative and maximum limits are expressed by the formula: u is not less than 0_IN≤u_max. IOB estimation using literature [2](Gondhalekar R,Dassau E,Doyle IIIF.J.Velocity-weighting&velocity-penalty MPC of an artificial pancreas:Improved safety&performance[J]The method in Automatica,2018,91: 105-:

wherein a: -0.995, b: -0.04, c: -0.84 and

tau represents the time elapsed after insulin injection, T is the length of the curve, and is a function of the blood glucose concentration y, written as

T(y):＝max{min{-y/30+12,8},2}

Then T (y) ∈ [2,8 ]]In units of hours. Remember y_iThe blood glucose concentration value provided to the IOB module for the latest moment is the output of the tracking differentiatorThe obtained filtering or prediction value is divided into T (y) length according to the sampling period_i) Discretizing the attenuation curve values to corresponding vectors

The attenuation curve with the length of 4 hours is taken as the attenuation curve of the large dose of insulin additionally beaten after meals, and the vector obtained by discretization is recorded as

Note the book

The 8-hour historical data vector of the injection amount u h of the basal insulin injection amount subtracted from the injection amount of the pump into the human body in one sampling period is also understood as the output of the nonlinear feedback module subjected to nonnegative, maximum and last-time IOB limit constraints and the discretized value of the pump.

Vector of 8 hour historical data for boluses of insulin administered after meals. The estimate of IOB is calculated as follows:

u_IOB,i:＝max{_i-φ_i,0}

_i:＝(y_i-G_b)/C_F,i

in which the index i represents the most recent moment, C_F,i[mg/dl/U]If the blood glucose concentration is a correction factor for insulin, u.h.ltoreq.u should be satisfied for the time i_IOB,iWhen u is_IOB,i0 means the total amount of insulin u delivered in one sampling period after time i_INShould not exceed the amount that would be achieved at the basal insulin injection rate.

(6) Pump discretization

Determining the amount of insulin u to be finally infused in a sampling period after the sampling instant i_INThis value is then rounded to the nearest integer multiple of the minimum pump increase and decrease, and the process can be expressed as

Wherein u is_carry,iThe amount of the beat in the previous sampling period that is down by rounding, the minimum amount of increase and decrease,

to ultimately indicate the amount of insulin the insulin pump delivers subcutaneously to the body.

As shown in fig. 2, the following also presents various controller parameter variation curves designed according to the adaptive concept, but the scope of the present invention is not limited to these designed curves and implementation functions. The specific parameter values in this embodiment are determined based on the simulation of the FDA-certified UVA/Padova T1DM metabolic simulator.

Firstly, a control model which is individualized and suitable for the implementation of the active disturbance rejection control technology is designed for an individual, and a nominal gain parameter b is designed₀As follows

The control model established is

Wherein

For unknown and difficult modeling functions, d (t) and delta b are unknown bounded interference and parameter perturbation, and all uncertain factors are acted according to the active disturbance rejection control technology

Viewed as total disturbance d_tAnd evaluated and compensated as an expanded state variable.

In the present embodiment, the fastest tracking differentiator proposed in the document [1] is used, and the specific form thereof is:

fh＝fhan(x₁(k)-CGM(k),x₂(k),r₁,h₀)

x₁(k+1)＝x₁(k)+hx₂(k)

x₂(k+1)＝x₂(k)+hfh

y_i(k)＝x₁(k+1)+K_ix₂(k+1)

wherein h is a sampling period determined to be 5 minutes, and r is₁Determining the tracking speed, wherein the larger the tracking speed is, the faster the tracking speed is, the determined value is 2, x₁Tracking input signal CGM, then x₂Is an approximately differential signal of CGM, h₀The filter factor is properly larger than h, and the filter effect is enhanced and determined as h₀20, but will cause a certain phase lag and amplitude attenuation, and needs to be properly compensated, so when K is equal to_iTaking different values, the corresponding filtered or predicted signal value y is obtained_i(k) In that respect This example takes K₁Obtaining a filtered signal value y corresponding to the k time instant as 1₁(k) When the blood sugar level is in the rising stage and is greater than the threshold value G_hWhen the value is in the optional interval, K is taken₂Get the predicted signal value y for the rising phase at 3₂(k) When the blood sugar level is in the descending stage and is less than the threshold value G_lWhen the value is in the optional interval, K is taken₂Get the descent stage prediction signal value y as 2₂(k)。

In this embodiment, the dimension-extending state observer is a non-linear discrete observer, and the specific form of the non-linear discrete observer is as follows:

e＝z₁(k)-(y_i(k)-G_b)

z₁(k+1)＝z₁(k)+h(z₂(k)-β₁e)

z₂(k+1)＝z₂(k)+h(z₃(k)-β₂fe+b₀u)

z₃(k+1)＝z₃(k)+h(-β₃fe₁)

wherein z is₁And z₂Respectively, the deviation value of blood sugar concentration and the estimated value of the change rate thereof, z₃As a total interference d_tEstimated value of y_iThat is, the blood sugar concentration filtering or predicting signal obtained in the second step, when the blood sugar rises and the concentration is greater than G_hAnd a decrease in blood glucose and a concentration less than G_lThe extended dimension state observer receives the prediction signal y₂Otherwise receiving the filtered signal y₁，G_bThe reference blood sugar value in the designed model is 110mg/dl β₁,β₂,β₃For discrete observer parameters, according to document [1]]The extended state observer section is determined as β₁＝1/h，β₂＝1/(3*h²)，β₃＝2/(64*h³) And fe, fe₁The function fal (e, α,) utilized is

Taking fe as fal (e,2, h), fe₁Fal (e,1, h), where h is the sampling period.

In this embodiment, the parameters in the nonlinear feedback module adapt to the variation process according to the variation trend of blood glucose. Error signal is e₁＝G_r-(z₁+G_b) And

in the formula G_rFor the blood glucose concentration reference signal, this example takes 110mg/dl,

as a reference signal for the rate of change of blood glucose concentration, 0mg/dl/min was taken in this example. The nonlinear feedback control law is

u＝(-fhan(k₁e₁,k₂e₂,r₂,a)-z₃)/b₀

The control gain r in fhan (-) is designed in this embodiment₂Is always r₂The function used for designing other parameters is denoted as f, 10 being constant_a(x,), the function curve is shown in fig. 3, and the specific expression is as follows:

f_a(x,)＝min{a₁,exp{αx^β}+a₂-1}，x≥0

wherein ═ a₁,α,β,a₂Is the coefficient to be determined, where a₁,a₂The maximum (saturation) and minimum values of the function are determined separately, α together determining the steepness of the curve of the function.

a) And (3) a blood sugar rising stage: determining a threshold value G_hmg/dl, when the blood glucose concentration value is less than G_hWill k is₁,k₂The function designed to be the rate of change of blood glucose concentration is as follows:

k₁＝min{4,exp{2x₂ ²j +2-1, and k₂＝min{5,exp{2x₂ ³}+3-1}

In the formula, x₂I.e. the approximate differential signal of the blood sugar concentration provided by the tracking differentiator, and the function realizes k₁,k₂Increasing with increasing rate of change of blood glucose concentration. Design a as a function of blood glucose concentration as follows:

a＝min{30,exp{2×(150-y₁)²}+20-1}

in the formula, y₁For tracking the filtered signal provided by the differentiator, the function realization a decreases with increasing blood glucose concentration.

When the blood glucose concentration value is larger than G_hIs smaller than G_HWhen k is₁,k₂Each of which holds the value, k in this embodiment₁＝4,k₂A is designed as a function of blood glucose concentration, with 5 being constantThe following were used:

a＝70-min{50,exp{2×(200-y₁)³}+20-1}

the function is implemented near a larger value G of the blood glucose concentration_HWhen a is increased from 20 to 50, a is unchanged;

and a prediction function is started by utilizing a tracking differentiator to obtain a prediction value, and the prediction value is transmitted to the IOB module to relax the constraint. This overall design process allows the algorithm to be conservative, attenuating the effects of sensor noise, when the blood glucose concentration is low and changing slowly, and to be aggressive, injecting sufficient insulin at the initial stage of the blood glucose concentration increase as the blood glucose concentration increases.

When the blood sugar concentration rises to be greater than a certain larger value G_HRedesigning k₁,k₂A makes the algorithm gradually conservative, keeping k in this example₁＝3，k ₂3 and 50 are unchanged,

make the algorithm at blood glucose concentration greater than G_HIn time, the insulin to be delivered is reduced along with the reduction of the blood sugar concentration change rate, and the safety of the algorithm is ensured.

b) When the blood sugar is in the descending stage, namely the change rate of the blood sugar concentration is negative, the k is designed in three sections according to the blood sugar concentration₁,k₂,a；

When the blood glucose concentration is greater than the threshold G_lDesign k₂As a function of the rate of change of blood glucose concentration, i.e. k₂＝min{3,exp{0.5x₂ ²+1-1} and k is designed₁The constant keeping of 1 and 20 realizes that the proper amount of insulin is injected when the blood sugar concentration is still higher and the blood sugar concentration changes gently, and the insulin injection is stopped in time when the blood sugar concentration drops rapidly.

When the blood glucose concentration is lower than G_lAnd is higher than G_LStarting the prediction function of the tracking differentiator, tightening the IOB constraint and designing k₁K is held constant for 2 and a 40₂A more conservative insulin injection was achieved as a function of the used in the first paragraph.

When the blood glucose concentration decreases to a lower value G_LDesign k₁＝2,k ₂5 and 40 are kept unchanged, and control is realizedThe system is more sensitive to the change rate of the blood sugar concentration and hypoglycemia, and when the blood sugar concentration is low and still has a downward trend, the insulin infusion can be stopped earlier in time, and the safety of the algorithm is ensured.

In the embodiment, the constraint module imposes certain constraint on the output of the nonlinear feedback module to ensure the reasonability and safety of the algorithm, and comprises a nonnegative and maximum limiting module and an IOB module. In this example u_max0.5U, the non-negative and maximum limits are expressed by the equation: u is not less than 0_INLess than or equal to 0.5U. The sampling period in the IOB module is 5 minutes, and the blood glucose concentration is greater than G_hAnd when the blood glucose concentration change rate is positive, the IOB module receives the predicted value y of the blood glucose concentration₂At blood glucose concentrations less than G_lAnd when the change rate of the blood glucose concentration is negative, the IOB module also receives a predicted value y of the blood glucose concentration₂Otherwise receiving the filtered value y of blood glucose concentration₁Calculating the IOB limit u corresponding to each sampling time_IOB,iThen u.h is less than or equal to u in a sampling period after the time i_IOB,iWhere u is the output of the nonlinear feedback module.

Discretizing the control signal output by the constraint module, wherein the minimum increment and decrement of the pump is 0.05U in the embodiment, and finally calculating the insulin volume which finally indicates the pump to infuse the human body through the subcutaneous tissue

This example was simulated and verified in an FDA certified UVA/Padova T1DM metabolic simulator, and compared with a velocity-weighted model predictive Control algorithm in document [2] (Gondhalekar R, Dassau E, Doyle III F.J.velocity-weighting & velocity-weighting MPC of an innovative security & performance [ J ] Automatica,2018,91:105 ] 117.) and a velocity-weighted model predictive Control algorithm in document [3] (Shi DW, Dassau E, Doyle III F.J.zone model predictive Control with a glucose-dependent performance-weighted predictive Control algorithm, JJJ 29,2018). These two MPC algorithms are abbreviated as "Automatica 2018" and "ACC 2018" in fig. 5 and 7, respectively. The simulation started in the morning at 7:00 for two days for a total of 48 hours with three meals each day for a time period of 8: 00, 12: 00, 19: 00, the diet used contained 50g, 75g, 75g of carbohydrates. All three controllers utilize the adult patient group (containing 10 simulated adults) in the simulator based on the scene, change random seed in the simulator from 1 to 10 sequentially, realize 10 times of repeated simulation verification based on different additive CGM measurement noises, and respectively based on pre-meal large-dose insulin supplementation and non-pre-meal large-dose insulin supplementation. Each controller had a total of 200 simulations.

The simulation results of the bolus insulin supplementation before meal are shown in fig. 4 and 5, and the simulation results of the bolus insulin non-supplementation before meal are shown in fig. 6 and 7. From the results in the figures, it can be seen that the artificial pancreas adaptive disturbance rejection controller of the invention is close to or even superior to the modified MPC algorithm in the document [3] in the time ratio of 70-180mg/dl and the average blood glucose concentration, no matter based on the supplementation of large dose of insulin before meal or no insulin before meal, without significantly increasing the hypoglycemia risk, and achieves the purpose of having the characteristics of simple structure, small calculation amount and excellent performance of compatible MPC controller and ensuring the safety of the algorithm.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An artificial pancreas self-adaptive active disturbance rejection controller based on blood sugar variation trend is characterized by comprising a tracking differentiator module, a dimension expansion observer module, a nonlinear feedback module and a constraint module, wherein,

the tracking differentiator module receives blood sugar concentration measuring signals collected by a blood sugar sensor on a human body every other sampling period, outputs a blood sugar concentration prediction signal when the blood sugar concentration meets the design condition, and otherwise outputs a blood sugar concentration filtering signalNumber; the design conditions are as follows: blood glucose concentration was maintained at the set value [ G ] during the ascending phase_h,G_H]Within the range, the blood glucose concentration is maintained at the set value [ G ] in the descending stage_L，G_l]In the range, G_hThe value range is 110mg/dl-150mg/dl, G_HThe value range is 200mg/dl-300mg/dl, G_LThe value range is 90mg/dl-120m/dl, G_lThe value range is 170mg/dl-200 mg/dl;

the dimension expansion observer module processes the filtering signal or the prediction signal output by the tracking differentiator module to obtain a total interference estimation value, a blood glucose concentration deviation value and a change rate estimation value thereof, and then compares the blood glucose concentration deviation value and the change rate estimation value thereof with a preset reference signal to obtain an error signal;

the nonlinear feedback model of the nonlinear feedback module is as follows:

u＝(-fhan(k₁e₁,k₂e₂,r₂,a)-z₃)/b₀

where u is the output signal, k₁,k₂A is a parameter adaptive according to the blood sugar variation trend, r₂Referred to as the control quantity gain; e.g. of the type₁And e₂Is an error signal between the blood glucose concentration and its rate of change set point and estimate, z₃Is an estimate of the total interference; b₀Is a known gain factor;

the constraint module is used for controlling the insulin pump after constraining the output signal u according to the constraint condition, and injecting the insulin infusion amount corresponding to the control signal into the human body to form closed-loop control; if the change of the blood sugar concentration meets the design condition, the constraint module calculates the IOB constraint value of the in-vivo active insulin limit by using the blood sugar concentration prediction signal, otherwise, the constraint module calculates the IOB constraint value by using the blood sugar concentration filtering signal.

2. The adaptive disturbance-rejection controller for artificial pancreas based on blood glucose tendency of claim 1, wherein k is a function of the signal level₁,k₂And a, parameters self-adaptive according to the blood sugar change trend are as follows:

blood glucose concentration rise Process

The first stage is as follows: when the blood glucose concentration is less than the threshold G_hWhen, will k₁,k₂Designing a function of the blood glucose concentration change rate, increasing along with the increase of the blood glucose concentration change rate, and keeping the function unchanged, designing a as the function of the blood glucose concentration, decreasing along with the increase of the blood glucose concentration, and keeping the function unchanged;

and a second stage: when the blood glucose concentration is greater than the threshold G_hAnd is less than a threshold value G_HWhen k is₁,k₂Each maintaining a first phase constant value, and designing a as a function of blood glucose concentration, wherein the blood glucose concentration increases with the increase of the blood glucose concentration;

and a third stage: when the blood glucose concentration is greater than the threshold G_HWhen, let k₁,k₂A respectively keeping the end value of the second stage;

process of decreasing blood glucose concentration

The first stage is as follows: when the blood glucose concentration is greater than the threshold G_lThen, k will be designed₂As a function of the absolute value of the rate of change of blood glucose concentration, the greater the absolute value k₂The larger, and design k₁And a is kept constant;

and a second stage: when the blood glucose concentration is less than the threshold G_lAnd is greater than a threshold value G_LAnd design k₁Is a constant value, a is the same as the first phase value, k₂Is the function used for the first segment;

and a third stage: when the blood glucose concentration is less than the threshold G_LDesign k₁And a is the same as the value of the second stage, k₂Is a fixed value.