CN114509938A - Single-effect lithium bromide unit load rapid tracking control method - Google Patents

Single-effect lithium bromide unit load rapid tracking control method Download PDF

Info

Publication number
CN114509938A
CN114509938A CN202210018964.3A CN202210018964A CN114509938A CN 114509938 A CN114509938 A CN 114509938A CN 202210018964 A CN202210018964 A CN 202210018964A CN 114509938 A CN114509938 A CN 114509938A
Authority
CN
China
Prior art keywords
control
output
time
increment
lithium bromide
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210018964.3A
Other languages
Chinese (zh)
Inventor
李益国
吴婧谌
张俊礼
沈炯
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southeast University
Original Assignee
Southeast University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southeast University filed Critical Southeast University
Priority to CN202210018964.3A priority Critical patent/CN114509938A/en
Publication of CN114509938A publication Critical patent/CN114509938A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a single-effect lithium bromide unit load rapid tracking control method, which comprises the following steps: obtaining an amplification state space model of the single-effect lithium bromide unit; setting controller parameters including a prediction time domain and a control time domain, initializing the controller, and estimating the current state of the system according to the output quantity of the current time; predicting the output of the system at the future prediction time domain limited moment by using a prediction model; constructing a performance index and correcting a deviation term weight in the comprehensive time and absolute error performance index; converting the nonlinear programming into the solving performance index of the linear programming to obtain the optimal control quantity increment; and calculating and updating the system output at the next moment according to the optimal control quantity increment. The invention improves the rapidity of the tracking process, is suitable for a multivariable system, reduces the online calculated amount, shortens the adjusting time and provides a feasible method for realizing the rapid load tracking control of large-delay energy supply equipment in the comprehensive energy system.

Description

Single-effect lithium bromide unit load rapid tracking control method
Technical Field
The invention relates to the field of automatic control of thermal engineering, in particular to a quick load tracking control method for a single-effect lithium bromide unit.
Background
The lithium bromide absorption refrigerating unit is a commonly used waste heat utilization device in a distributed comprehensive energy system. The lithium bromide absorption chiller contains multiple components, involving multiple heat exchange processes, and is typically a large delay target. The conventional PID control strategy belongs to post regulation, cannot give consideration to rapidity and stability of tracking, and is difficult to obtain satisfactory control performance when used for a large-delay object.
In the prior art, the existing control method for a delay object includes active disturbance rejection control, optimal control, and model-free adaptive prediction control. However, the load quick tracking capability of the above method is poor, and still needs to be further improved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a single-effect lithium bromide unit load rapid tracking control method, aiming at realizing rapid tracking of the set value, overcoming various disturbance influences and meeting the cold load requirements of users.
The technical scheme adopted by the invention is as follows:
a single-effect lithium bromide unit load rapid tracking control method comprises the following steps:
s1, obtaining an amplification state space model of the single-effect lithium bromide unit:
Figure BDA0003461077780000011
in the formula, xk、xk+1Respectively representing the amplified state quantities at the k moment and the k +1 moment, and respectively representing corresponding coefficient matrixes A, B and C;
Δxd，k、Δxd，k+1increment of state quantity at time k and k +1, yk、yk+1Output quantities at times k and k +1, DeltaukFor increments of control quantity at time k, OdIs ny x l dimensional zero matrix, ny and l are dimensions of output quantity and state quantity increment respectively, Iny×nyIs a ny dimension unit matrix;
s2, setting controller parameters including prediction time domain NpAnd control time domain Nc(ii) a Initializing a controller;
s3, estimating the current time state of the system according to the output quantity of the current time;
s4, predicting the future N of the system by using the following prediction modelpThe output of each time instant is predicted,
Yk＝Fxk+ΦΔUk
in the formula, YkVectors formed for output quantity predictors, xkΔ U is the amount of state after amplificationkFor future control of quantity UkA vector of increments of (a);
Figure BDA0003461077780000021
s5, constructing a performance index minJ:
minJ＝||Tq(Yk-Wk)||1+||λΔUk||1
Figure BDA0003461077780000022
wherein T is diag (T)s1p，2T s1p，…，NpTs1p) For temporal weighting coefficients of future errors, TsIn order to be the sampling period of time,
Figure BDA0003461077780000023
to the deviation Y of the outputk-WkThe weighting coefficient of (a) is determined,
Figure BDA0003461077780000024
Figure BDA0003461077780000025
for the weighting factor for the control quantity increment,
Figure BDA0003461077780000026
nu is the number of the control quantity;
Figure BDA0003461077780000027
Figure BDA0003461077780000028
for the future target value sequence, | | | | purple1Represents the 1-norm of the vector;Umin、Umax，ΔUmin、ΔUmax，Ymin、Ymaxrespectively corresponding upper and lower limits;
s6, calculating the optimal control quantity increment by solving the performance index;
and S7, calculating and updating the system output at the next moment according to the optimal control quantity increment, and repeating the steps S3 to S7 in each sampling period.
The further technical scheme is as follows:
in step S6, when the optimal control increment is solved, the performance index is converted from a nonlinear programming problem to a linear programming problem:
Figure BDA0003461077780000029
Figure BDA00034610777800000210
in the formula (I), the compound is shown in the specification,
Figure BDA00034610777800000211
Figure BDA00034610777800000212
I1is nu-order unit array; γ is the upper bound of the performance indicator;
Figure BDA0003461077780000031
all are non-negative vectors, which respectively represent the upper bound of the deviation of the output quantity and the upper bound of the increment of the control quantity, namely the following inequalities are provided:
Figure BDA0003461077780000032
in step S2, the control time domain N is setcNot greater than the prediction time domain Np。
The invention has the following beneficial effects:
compared with a PID control method, the method uses a model predictive control method, adopts an expanded state space model, and can be suitable for a multivariable object with constraint. The method can shorten the adjusting time under the condition of reducing the overshoot, and provides an effective method for realizing the rapid load tracking control of the large-delay energy supply equipment in the comprehensive energy system.
Compared with the traditional quadratic performance index, the invention corrects the deviation term weight in the performance index of Integrated Time and Absolute Error (ITAE), provides a solving method for converting the nonlinear programming into the linear programming, and reduces the on-line calculated amount.
Drawings
FIG. 1 is a schematic diagram of a control method according to an embodiment of the present invention.
FIG. 2 is a graph comparing the output of the control method of the present invention and the conventional quadratic form prediction control under the same conditions.
Fig. 3 is a control quantity comparison graph of the control method according to the embodiment of the present invention and the conventional quadratic form prediction control under the same conditions.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
The application provides a single-effect lithium bromide unit load rapid tracking control method, which comprises the following steps:
s1, (1) obtaining a transfer function model of the single-effect lithium bromide unit, selecting input variables and output variables to perform an open-loop step response experiment under a steady-state working condition, and setting sampling time TsAnd preprocessing the experimental data, identifying to obtain a transfer function model, and converting the transfer function model into a discrete state space model shown in a formula (1):
Figure BDA0003461077780000033
in the formula, xd，k、xd，k+1When represents k and k +1 respectivelyState quantities, y, of discrete state space models transformed from transfer function modelskChilled water outlet temperature (output) at time k, ukThe flow rate (control amount) of the heat source working medium at the time k, Ad，Bd，CdRespectively corresponding coefficient matrices. The subscript d represents the discretization.
In particular, the sampling time TsThe method can be selected according to Shannon sampling theorem, and ensures that the sampling frequency is not less than 2 times of the highest frequency in the frequency spectrum of the analog signal.
(2) In order to realize the non-static tracking performance, an amplification state space model of the single-effect lithium bromide unit is obtained according to the formula (1):
Figure BDA0003461077780000034
in the formula (2), xk、xk+1Respectively representing the amplified state quantities at the k moment and the k +1 moment, and respectively representing corresponding coefficient matrixes A, B and C;
Δxd，k、Δxd，k+1increment of state quantity at time k and k +1, yk、yk+1Output quantities at times k and k +1, DeltaukFor increments of control quantity at time k, OdIs ny x l dimensional zero matrix, ny and l are dimensions of output quantity and state quantity increment respectively, Iny×nyIs a ny dimension unit matrix;
s2, setting controller parameters including but not limited to a prediction time domain NpAnd control time domain NcInitializing the controller;
in particular, the time domain N is predictedpSelects the main dynamic characteristic of the coverage system and predicts the time domain NpNot less than the control time domain, i.e. Nc≤Np。
S3, estimating the current time state of the system according to the output quantity of the current time;
specifically, a kalman filter algorithm may be used to estimate the state.
S4, predicting the future output of the system by using the prediction model;
the prediction model is as follows:
Yk＝Fxk+ΦΔUk (3)
in the formula (3), xkFor the amplified state quantity, YkIs a vector composed of a predicted value of output (a predicted value of outlet temperature of chilled water), Δ UkFor future control quantity (heat source working medium flow) UkA vector of increments of (a);
Figure BDA0003461077780000041
wherein ny and nu are dimensions of the output quantity increment and the control quantity increment respectively.
In the formula (3), the reaction mixture is,
Figure BDA0003461077780000042
wherein N ispTo predict time domain, NcIs a control time domain;
s5, constructing a performance index minJ, and ensuring that (1) the controlled quantity can track a set value; (2) the fluctuation of the control amount is not too severe; (3) the adjusting time is shortened as much as possible, the three items are included in the design of the performance index, and the performance index min is designed as follows:
minJ＝||Tq(Yk-Wk)||1+||λΔUk||1 (4)
Figure BDA0003461077780000043
in the formula (4), T ═ diag (T)s1p，2T s1p，…，NpTs1p) For temporal weighting coefficients of future errors, TsIn order to be the sampling period of time,
Figure BDA0003461077780000044
to the deviation Y of the outputk-WkThe weighting coefficients (error weight matrix) of (a),
Figure BDA0003461077780000045
for the weighting coefficients for the control quantity increments (control weight matrix),
Figure BDA0003461077780000046
Figure BDA0003461077780000047
nu is the number of the control quantity;
Figure BDA0003461077780000048
for the future target value sequence, | | | | purple1Represents the 1-norm of the vector; u shapemin、Umax，ΔUmin、ΔUmax，Ymin、YmaxRespectively corresponding upper and lower limit values;
s6, solving the optimal control quantity increment, taking the first element of the optimal control quantity increment to act on the next moment, and calculating and updating the system output of the next moment; within each sampling period, steps S3 to S6 are repeated.
Specifically, solving the optimal control increment is a nonlinear programming problem, and in order to reduce the online calculation amount, the application provides a solving method for converting the nonlinear programming into the linear programming. The description is as follows:
setting up
Figure BDA0003461077780000051
The output quantity deviation and the control quantity increment in the formula (4) are both non-negative vectors and represent an upper bound of the output quantity deviation and an upper bound of the control quantity increment respectively, namely the following inequalities are provided:
Figure BDA0003461077780000052
wherein the content of the first and second substances,
Figure BDA0003461077780000053
γ is the upper bound of the performance index;
solving a linear programming problem that converts equation (4) to equation (6) based on equation (5):
Figure BDA0003461077780000054
S.T.
Figure BDA0003461077780000055
in the formula (6), the reaction mixture is,
Figure BDA0003461077780000056
I1is nu-order unit array;
equation (6) is converted to the standard linear programming problem:
Figure BDA0003461077780000057
Figure BDA0003461077780000058
in the formula (I), the compound is shown in the specification,
Figure BDA0003461077780000061
Figure BDA0003461077780000062
wherein, I represents an identity matrix,
Figure BDA0003461077780000063
the actual representation is nu × NcLine, nu × NcA matrix of columns;
the technical solution of the present application is further described below with specific examples.
The tracking prediction control method of the embodiment is applied to a single-effect lithium bromide system, and a basic architecture for realizing the method can refer to fig. 1. In the figure, Yr is the chilled water outlet temperature setpoint, U0 is the predictive controller output, d2 is the input disturbance, U is the actual heat source working fluid flow, d3 is the output disturbance, and Y is the actual chilled water outlet temperature.
The method comprises the following concrete implementation processes:
1) obtaining a transfer function model of a single-effect lithium bromide system:
the transfer function model of the lithium bromide unit from hot water flow (kg/s) to chilled water outlet temperature (DEG C) obtained by the identification method is as follows:
Figure BDA0003461077780000064
selecting a sampling period TsDiscretizing 10 a system matrix of a state space model
And (3) obtaining a system matrix of the state space model by scattering:
Figure BDA0003461077780000065
2) establishing an amplification state space model:
Figure BDA0003461077780000066
3) setting controller parameters:
Np＝20，Nc＝8，ΔUmin＝-2kg/s2、ΔUmax＝2kg/s2error weight matrix element
Figure BDA0003461077780000067
Control weight matrix element
Figure BDA0003461077780000068
WkThe softening coefficient α of (a) is 0.1.
4) Controller state initialization:
control quantity u0Control quantity increment Δ u of 000, expanded state space of initial stateThe model is x ═ 000]T；
5) Estimating the current time state by using a Kalman filtering method;
6) predicting future N according to the current state estimation value according to the established prediction modelpOutputting at each moment;
7) solving the linear programming problem of equation (7) to calculate future NcOptimum control increment DeltaU of each momentk；
8) Taking Delta UkAnd calculating the hot water flow rate at the time k by using u (k) ═ u (k-1) + Δ u (k), and outputting the hot water flow rate, wherein u (k) and u (k-1) are respectively control amounts at the time k and the time k-1. And then repeating the 5 th step to the 8 th step in each sampling period.
The effect of the optimized control scheme (improved ITAE predictive control) of the present embodiment was compared with the control effect of the conventional quadratic MPC control scheme by simulation.
Firstly, respectively changing the fixed value of the outlet temperature of the chilled water by 4 ℃ and-2 ℃ in steps at 10s and 400s, and inspecting the load tracking capacity of the system; then, 5kg/s and 2 ℃ input and output disturbances were applied to the system at 800s and 1250s, respectively, and the ability of the system to suppress various internal and external disturbances such as hot water flow, hot water temperature, and cooling water temperature was examined. The simulation results are shown in fig. 2 and 3.
Compared with simulation results of two prediction control methods, the method has the advantages that the regulation time of prediction control is shorter, overshoot hardly occurs, and the scheduling instruction given by the scheduling layer can be tracked more quickly and smoothly. Meanwhile, from the perspective of disturbance rejection, the predictive control of the embodiment can greatly reduce the dynamic deviation of the system under the condition of input disturbance, and for the condition of output disturbance, the adjustment time can be obviously shortened. In general, compared with the conventional quadratic predictive control algorithm, the predictive control method of the embodiment further improves the control performance. The fundamental reason for the improvement of the control performance is that the time-related weighting coefficient is added to the performance index of the predictive control, and the requirement for the adjustment time is strengthened while a relatively small dynamic deviation is pursued.

Claims (3)

1. A single-effect lithium bromide unit load rapid tracking control method is characterized by comprising the following steps:
s1, obtaining an amplification state space model of the single-effect lithium bromide unit:
Figure FDA0003461077770000011
in the formula, xk、xk+1Respectively representing the amplified state quantities at the k moment and the k +1 moment, and respectively representing corresponding coefficient matrixes A, B and C;
Δxd，k、Δxd，k+1increment of state quantity at time k and k +1, yk、yk+1The output quantities at the time points k and k +1, respectively, are Δ ukFor increments of control quantity at time k, OdIs ny x l dimensional zero matrix, ny and l are dimensions of output quantity and state quantity increment respectively, Iny×nyIs a ny dimension unit matrix;
s2, setting controller parameters including prediction time domain NpAnd control time domain Nc(ii) a Initializing a controller;
s3, estimating the current time state of the system according to the output quantity of the current time;
s4, predicting the future N of the system by using the following prediction modelpThe output of each time instant is predicted,
Yk＝Fxk+ΦΔUk
in the formula, YkVectors formed for output quantity predictors, xkDelta U as the amplified state quantitykFor future control of quantity UkA vector of increments of (a);
Figure FDA0003461077770000012
s5, constructing a performance index minJ:
minJ＝||Tq(Yk-Wk)||1+||λΔUk||1
Figure FDA0003461077770000013
wherein T is diag (T)s1p，2Ts1p，…，NpTs1p) For temporal weighting coefficients of future errors, TsIs a time period of the sampling, and,
Figure FDA0003461077770000014
to the deviation Y of the outputk-WkThe weighting coefficient of (a) is determined,
Figure FDA0003461077770000019
Figure FDA0003461077770000015
for the weighting factor for the control quantity increment,
Figure FDA0003461077770000016
nu is the number of the control quantity;
Figure FDA0003461077770000017
Figure FDA0003461077770000018
for the future target value sequence, | | | | purple1Represents the 1-norm of the vector; u shapemin、Umax，ΔUmin、ΔUmax，Ymin、YmaxRespectively corresponding upper and lower limits;
s6, calculating the optimal control quantity increment by solving the performance index;
and S7, calculating and updating the system output at the next moment according to the optimal control quantity increment, and repeating the steps S3 to S7 in each sampling period.
2. The single-effect lithium bromide unit load fast tracking control method according to claim 1, characterized in that in step S6, when solving the optimal control increment, the performance index is converted from a nonlinear programming problem to a linear programming problem:
Figure FDA0003461077770000021
Figure FDA0003461077770000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003461077770000023
Figure FDA0003461077770000024
I1is nu-order unit array; γ is the upper bound of the performance index;
Figure FDA0003461077770000025
the uniform vectors are non-negative vectors and respectively represent the upper bound of the output quantity deviation and the upper bound of the control quantity increment, namely the following inequalities are provided:
Figure FDA0003461077770000026
3. the method as claimed in claim 2, wherein in step S2, the control time domain N is setcNot greater than the prediction time domain Np。
CN202210018964.3A 2022-01-07 2022-01-07 Single-effect lithium bromide unit load rapid tracking control method Pending CN114509938A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210018964.3A CN114509938A (en) 2022-01-07 2022-01-07 Single-effect lithium bromide unit load rapid tracking control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210018964.3A CN114509938A (en) 2022-01-07 2022-01-07 Single-effect lithium bromide unit load rapid tracking control method

Publications (1)

Publication Number Publication Date
CN114509938A true CN114509938A (en) 2022-05-17

Family

ID=81549792

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210018964.3A Pending CN114509938A (en) 2022-01-07 2022-01-07 Single-effect lithium bromide unit load rapid tracking control method

Country Status (1)

Country Link
CN (1) CN114509938A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117747116A (en) * 2024-02-19 2024-03-22 天津市第五中心医院 Intelligent early warning method for physiological index of obstetrical department midwifery

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117747116A (en) * 2024-02-19 2024-03-22 天津市第五中心医院 Intelligent early warning method for physiological index of obstetrical department midwifery
CN117747116B (en) * 2024-02-19 2024-05-17 天津市第五中心医院 Intelligent early warning method for physiological index of obstetrical department midwifery

Similar Documents

Publication Publication Date Title
CN104375475B (en) The optimal control method of Batch reaction processes in batch reactor
Hazyuk et al. Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part II–Control algorithm
CN109212974A (en) The robust fuzzy of Interval time-varying delay system predicts fault tolerant control method
Lee et al. Generic model control—a case study
CN111336683A (en) MPC-PID cascade control method for air source heat pump temperature control system
CN110501909B (en) Fuzzy prediction control method based on enhanced robust characteristics of disturbance observer
Pipino et al. Nonlinear temperature regulation of solar collectors with a fast adaptive polytopic LPV MPC formulation
CN111123871B (en) Prediction function control method for genetic algorithm optimization of chemical process
Ferhatbegović et al. Model based predictive control for a solar-thermal system
CN114509938A (en) Single-effect lithium bromide unit load rapid tracking control method
Gouadria et al. Comparison between self-tuning fuzzy PID and classic PID controllers for greenhouse system
Mallaiah et al. A simulated annealing optimization algorithm based nonlinear model predictive control strategy with application
Jinyang et al. Temperature decoupling control of double-level air flow field dynamic vacuum system based on neural network and prediction principle
Lara et al. Offset-free model predictive control for an energy efficient tropical island hotel
CN109765950B (en) Control method for first-order pure time delay furnace temperature system
JP4177171B2 (en) Process control apparatus and process control method
Pataro et al. Hierarchical control based on a hybrid nonlinear predictive strategy for a solar-powered absorption machine facility
Vajpayee et al. Gain scheduled subspace predictive control of a pressurized water-type nuclear reactor
CN111221252B (en) Predictive controller parameter analysis setting method for industrial system with fractional hysteresis
Sheikhi et al. Design of nonlinear predictive generalized minimum variance control for performance monitoring of nonlinear control systems
Abdelbaky et al. Stable economic model-predictive control for TS fuzzy systems with persistent disturbances
Pataro et al. Optimal model-free adaptive control based on reinforcement Q-Learning for solar thermal collector fields
Kumavat et al. Analysis of CSTR Temperature Control with PID, MPC & Hybrid MPC-PID Controller
Siddiqui et al. A Direct Synthesis based Sliding Mode Control of a Nonlinear Continuous Stirred Tank Reactor
Kia et al. Implemention of LQR controller for HVAC systems and investigating effect of gains on improving performance

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination