Single-effect lithium bromide unit load rapid tracking control method

Abstract

The invention discloses a method for rapid load tracking control of a single-effect lithium bromide unit, which includes: obtaining an augmented state space model of the single-effect lithium bromide unit; setting controller parameters, including a prediction time domain and a control time domain, and initializing the controller; estimating the state of the system at the current moment according to the output quantity at the current moment; predicting the output of the system at the moment limited by the future prediction time domain by using a prediction model; constructing a performance index and modifying the weight value of the deviation term in the comprehensive time and absolute error performance index; converting a nonlinear programming into a linear programming to solve the performance index to obtain an optimal control quantity increment; 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 and is applicable to a multivariable system, reduces the online calculation amount, shortens the adjustment time, and provides a feasible method for realizing rapid load tracking control of large-delay energy supply equipment in a comprehensive energy system.

Description

Technical Field

[0001] The present invention relates to the field of thermal automatic control, and in particular to a method for quickly tracking the load of a single-effect lithium bromide unit. Background Art

[0002] Lithium bromide absorption refrigeration units are commonly used waste heat utilization equipment in distributed integrated energy systems. Lithium bromide absorption refrigerators contain multiple components and involve multiple heat exchange processes, belonging to typical large-delay objects. Conventional PID control strategies belong to post-regulation and cannot balance the rapidity and stability of tracking. It is difficult to obtain satisfactory control performance when used for large-delay objects.

[0003] In the prior art, existing control methods for delay objects include active disturbance rejection control, optimal control, and model-free adaptive predictive control. However, the above methods have poor load rapid tracking ability and still need to be further improved. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a method for quickly tracking the load of a single-effect lithium bromide unit, aiming to achieve rapid tracking of the set value, while overcoming various disturbance effects to meet the user's cooling load demand in a timely manner.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for quickly tracking the load of a single-effect lithium bromide unit, comprising the following steps:

[0007] S1. Obtain the augmented state space model of the single-effect lithium bromide unit:

[0008]

[0009] In the formula, x k , x k+1 respectively represent the augmented state quantities at times k and k + 1, and A, B, and C respectively represent the corresponding coefficient matrices;

[0010] Δx d，k , Δx d，k+1 are respectively the state quantity increments at times k and k + 1, y k , y k+1 are respectively the output quantities at times k and k + 1, Δu k is the increment of the control quantity at time k, O d is an ny×l-dimensional zero matrix, where ny and l are the dimensions of the output quantity and the state quantity increment respectively, and I ny×ny is an ny-dimensional identity matrix;

[0011] S2. Set the controller parameters, including the prediction horizon N p and the control horizon Nc ; Initialize the controller;

[0012] S3. Estimate the current state of the system based on the output at the current moment;

[0013] S4. Use the following prediction model to predict the outputs of the system at the next N p moments,

[0014] Y k = Fx k + ΦΔU k

[0015] where Y k is the vector composed of predicted output values, x k is the augmented state quantity, and ΔU k is the vector composed of increments of the future control quantity U k ;

[0016]

[0017] S5. Construct the performance index minJ:

[0018] minJ = ||Tq(Y k - W k )||1 + ||λΔU k ||1

[0019]

[0020] where T = diag(T s 1 p , 2T s 1 p , …, N p T s 1 p ) is the time weighting coefficient for the future error, T s is the sampling period, is the weighting coefficient for the output deviation Y k - W k , is the weighting coefficient for the control quantity increment, nu is the number of control quantities; is the sequence of future target values, ||||1 represents the 1-norm of the vector; U min 、U max , ΔU min 、ΔU max , Y min 、Y max are the corresponding upper and lower limits respectively;

[0021] S6. Calculate the optimal control increment by solving the performance index;

[0022] S7. Calculate and update the system output at the next moment according to the optimal control increment, and repeat steps S3 to S7 within each sampling period.

[0023] A further technical solution is as follows:

[0024] In step S6, when solving the optimal control increment, transform the performance index from a non-linear programming problem into a linear programming problem:

[0025]

[0026]

[0027] In the formula,

[0028] I1 is a nu-order identity matrix; γ is the upper bound of the performance index;

[0029] are all non-negative vectors, respectively representing the upper bounds of the output deviation and the control increment, that is, there are the following inequalities:

[0030]

[0031] In step S2, set the control time domain N c not greater than the prediction time domain N p .

[0032] The beneficial effects of the present invention are as follows:

[0033] Compared with the PID control method, the present invention uses the model predictive control method and adopts an augmented form of the state space model, which can be applied to multi-variable objects with constraints. It can shorten the adjustment time while reducing overshoot, providing an effective method for realizing the fast load tracking control of large-delay energy supply equipment in the integrated energy system.

[0034] Compared with the traditional quadratic performance index, the present invention modifies the weight value of the deviation term in the Integrated Time and Absolute Error (ITAE) performance index, gives a solution method for transforming non-linear programming into linear programming, and reduces the online calculation amount. Description of the Drawings

[0035] Figure 1 It is a schematic diagram of the principle of the control method of a specific embodiment of the present invention.

[0036] Figure 2 Comparison diagram of the output of the control method of the specific embodiment of the present invention and the traditional quadratic prediction control under the same conditions.

[0037] Figure 3 Comparison diagram of the control quantity of the control method of the specific embodiment of the present invention and the traditional quadratic prediction control under the same conditions. Specific embodiments

[0038] The following describes the specific embodiments of the present invention with reference to the accompanying drawings.

[0039] A rapid load tracking control method for a single-effect lithium bromide unit of the present application includes the following steps:

[0040] S1. (1) Obtain the transfer function model of the single-effect lithium bromide unit. Under steady-state conditions, select the input variable and the output variable to conduct an open-loop step response experiment, and set the sampling time T s , preprocess the experimental data, identify the transfer function model, and convert it into the discrete state space model shown in formula (1):

[0041]

[0042] In the formula, x d，k , x d，k+1 respectively represent the state quantities of the discrete state space model converted from the transfer function model at time k and k + 1, y k is the chilled water outlet temperature (output quantity) at time k, u k is the heat source working medium flow rate (control quantity) at time k, A d , B d , C d are the corresponding coefficient matrices respectively. The subscript d represents discretization.

[0043] Specifically, the sampling time T s can be selected according to the Shannon sampling theorem to ensure that the sampling frequency is not less than 2 times the highest frequency in the analog signal spectrum.

[0044] (2) To achieve a zero-static error tracking performance, obtain the augmented state space model of the single-effect lithium bromide unit according to formula (1):

[0045]

[0046] In formula (2), x k , x k+1 respectively represent the augmented state quantities at time k and k + 1, and A, B, and C represent the corresponding coefficient matrices respectively;

[0047] Δx d，k , Δx d，k+1are the state quantity increments at times k and k + 1, respectively, and y k , y k+1 are the output quantities at times k and k + 1, respectively, and Δu k is the increment of the control quantity at time k, and O d is an ny×l dimensional zero matrix, where ny and l are the dimensions of the output quantity and the state quantity increment, respectively, and I ny×ny is the ny dimensional identity matrix;

[0048] S2. Set the controller parameters, including but not limited to the prediction horizon N p and the control horizon N c , and initialize the controller;

[0049] Specifically, the selection of the prediction horizon N p should cover the main dynamic characteristics of the system, and the prediction horizon N p should not be less than the control horizon, that is, N c ≤ N p .

[0050] S3. Estimate the current state of the system based on the output quantity at the current moment;

[0051] Specifically, the Kalman filter algorithm can be used to estimate the state.

[0052] S4. Use the prediction model to predict the future output of the system;

[0053] The prediction model is as follows:

[0054] Y k = Fx k + ΦΔU k (3)

[0055] In equation (3), x k is the augmented state quantity, Y k is the vector composed of the predicted output quantity (predicted chilled water outlet temperature), and ΔU k is the vector composed of the increments of the future control quantity (heat source working medium flow rate) U k ;

[0056]

[0057] Among them, ny and nu are the dimensions of the output quantity and the control quantity increment, respectively.

[0058] In equation (3),

[0059] Among them, N p is the prediction horizon, and N c is the control horizon;

[0060] S5. Construct performance index minJ to ensure that (1) the controlled quantity can track the set value; (2) the fluctuation of the controlled quantity will not be too drastic; (3) the adjustment time is shortened as much as possible. Incorporate these three items into the design of performance index. The performance index min is designed as:

[0061] minJ=||Tq(Y k -W k )||1+||λΔU k ||1 (4)

[0062]

[0063] In formula (4), T = diag (T s 1 p , 2T s 1 p ,…,N p T s 1 p ) is the time weighting coefficient for future errors, T s is the sampling period, The output deviation Y k -W k The weighting coefficients of (error weight matrix), is the weighting coefficient of the control quantity increment (control weight matrix), nu is the number of controlled quantities; is the future target value sequence, ||||1 represents the 1-norm of the vector; U min , U max , ΔU min , ΔU max , Y min , Y max are the corresponding upper and lower limits respectively;

[0064] S6. Solve the optimal control quantity increment, take the first element of the optimal control quantity increment and apply it to the next moment, calculate and update the system output at the next moment; repeat steps S3 to S6 in each sampling period.

[0065] Specifically, solving the optimal control increment is a nonlinear programming problem. In order to reduce the amount of online calculation, this application proposes a solution method that converts nonlinear programming into linear programming. The description is as follows:

[0066] set up are all non-negative vectors, representing the upper bound of the output deviation and the upper bound of the control increment in equation (4), that is, the following inequality exists:

[0067]

[0068] in, γ is the upper bound of the performance index;

[0069] Based on Equation (5), Equation (4) is transformed into a linear programming problem in Equation (6) for solution:

[0070]

[0071] S.T.

[0072]

[0073] In Equation (6), I1 is the nu - order identity matrix;

[0074] Equation (6) is transformed into a standard linear programming problem:

[0075]

[0076]

[0077] In the formula,

[0078]

[0079] Among them, I represents the identity matrix, actually represents a matrix of nu×N c rows and nu×N c columns;

[0080] The technical solution of the present application is further described below with specific embodiments.

[0081] The tracking and prediction control method of this embodiment is applied to a single - effect lithium bromide system. The basic architecture of the method implementation can refer to Figure 1 . In the figure, Yr is the set value of the chilled water outlet temperature, U0 is the output of the predictive controller, d2 is the input disturbance, U is the actual heat source working medium flow rate, d3 is the output disturbance, and Y is the actual chilled water outlet temperature.

[0082] The specific implementation process of the method is as follows:

[0083] 1) Obtain the transfer function model of the single - effect lithium bromide system:

[0084] The transfer function model of the lithium bromide unit from the hot water flow rate (kg / s) to the chilled water outlet temperature (°C) obtained by the identification method is:

[0085]

[0086] Select the sampling period T s = 10, and discretize to obtain the system matrix of the state - space model

[0087] Diverge to obtain the system matrix of the state-space model:

[0088]

[0089] 2) Establish an augmented state-space model:

[0090]

[0091] 3) Set the controller parameters:

[0092] N p = 20, N c = 8, ΔU min = -2 kg / s 2 、ΔU max = 2 kg / s 2 The error weight matrix element The control weight matrix element W k The softening coefficient α = 0.1.

[0093] 4) Initialize the controller state:

[0094] The control variable u0 = 0, the control variable increment Δu0 = 0, and the augmented state-space model of the initial state is x = [0 0 0] T ;

[0095] 5) Use the Kalman filtering method to estimate the state at the current moment;

[0096] 6) According to the established prediction model, predict the outputs at the next N p moments based on the state estimate at the current moment;

[0097] 7) Solve the linear programming problem in Equation (7) to calculate the optimal control increment ΔU c at the next N k moments;

[0098] 8) Take the first element Δu(k) of ΔU k and calculate and output the hot water flow rate at time k through u(k) = u(k - 1)+Δu(k), where u(k) and u(k - 1) are the control variables at times k and k - 1 respectively. Then, in each sampling period, repeat steps 5 to 8.

[0099] Compare the control effect of the optimized control scheme (improved ITAE predictive control) in this embodiment with that of the conventional quadratic MPC control scheme through simulation.

[0100] First, at 10 s and 400 s respectively, the set values of the chilled water outlet temperature are stepped by 4°C and -2°C respectively to investigate the load tracking ability of the system; then, at 800 s and 1250 s respectively, an input and output disturbance of 5 kg / s and 2°C is applied to the system to investigate the ability of the system to suppress various internal and external disturbances such as hot water flow rate, hot water temperature and cooling water temperature. The simulation results are as Figure 2 and Figure 3 shown.

[0101] Comparing the simulation results of the two predictive control methods, it can be seen that the adjustment time of the predictive control in this embodiment is shorter, with almost no overshoot, and it can track the scheduling instructions given by the scheduling layer more quickly and smoothly. At the same time, from the perspective of disturbance rejection, the predictive control in this embodiment can greatly reduce the dynamic deviation of the system under the condition of input disturbance, while for the case of output disturbance, the adjustment time can be significantly shortened. Generally speaking, compared with the conventional quadratic predictive control algorithm, the control performance of the predictive control method in this embodiment has been further improved. The fundamental reason for the improvement of the control performance is that a weighting coefficient related to time is added to the performance index of the predictive control, strengthening the requirement for the adjustment time while pursuing a relatively small dynamic deviation.

Claims

1. A rapid load tracking control method for a single-effect lithium bromide unit, characterized in that, It includes the following steps: S1. Obtain the augmented state space model of the single-effect lithium bromide unit: where x k , x k+1 represent the amplified state variables at times k and k + 1 respectively, and A, B, and C represent the corresponding coefficient matrices; Δx d，k and Δx d，k+1 are the state quantity increments at times k and k + 1 respectively, y k and y k+1 are the output quantities at times k and k + 1 respectively, Δu k is the increment of the control quantity at time k, O d is an ny×l zero matrix, where ny and l are the dimensions of the output quantity and the state quantity increment respectively, and I ny×ny is the ny-dimensional identity matrix; S2. Set the controller parameters, including the prediction horizon N p and the control horizon N c ; Initialize the controller; S3. Estimate the system state at the current moment according to the output quantity at the current moment; S4. Use the following prediction model to predict the outputs of the system at the next N p moments. Y k = Fx k + ΦΔU k where Y k is a vector composed of predicted output values, x k is the augmented state quantity, and ΔU k is a vector composed of increments of the future control quantity U k ; S5. Construct the performance index minJ: minJ = ||Tq(Y k -W k )||1 + ||λΔU k ||1 where \(T = \text{diag}(T s 1 p , 2T s 1 p , \cdots, NT p 1 s 1 p )\) is the time - weighting coefficient for future errors, \(T s \) is the sampling period, \) is the weighting coefficient for the output deviation \(Y k - W k \), \) is the weighting coefficient for the increment of the control variable, \(n_u\) is the number of control variables; \) is the sequence of future target values, \(\|\cdot\|_1\) represents the 1 - norm of a vector; \(U min \), \(U max , \Delta U min , \Delta U max , \(Y min , \(Y max \) are the corresponding upper and lower limits respectively; S6. Calculate the optimal control quantity increment by solving the performance index; S7. Calculate and update the system output at the next moment according to the optimal control quantity increment, and repeat steps S3 to S7 in each sampling period.

2. The rapid load tracking control method for a single-effect lithium bromide unit according to claim 1, wherein In step S6, when solving the optimal control increment, transform the performance index from a non-linear programming problem into a linear programming problem: In the formula, $I_1$ is an $n_u$-order identity matrix; γ is the upper bound of the performance index; They are all non - negative vectors, respectively representing the upper bounds of the output quantity deviation and the upper bound of the control quantity increment. That is, the following inequalities hold: 。 3. The single-effect lithium bromide unit load rapid tracking control method according to claim 2, characterized in that, In step S2, set the control time domain N c not greater than the prediction time domain N p .

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