A chemical four-tank system output compensation control method based on perturbation decomposition technology

Abstract

The application discloses a chemical four-tank system output compensation control method based on a disturbance decomposition technique. The method firstly establishes a mathematical model of the chemical four-tank system based on a Laplace inverse transform method, classifies matched disturbances and unmatched disturbances possibly existing in the chemical four-tank system affected by multiple disturbances, and performs disturbance decomposition on the matched disturbances. In the condition that the state of the chemical four-tank system is unknown, the method then considers observing and compensating each feature of the disturbances based on an output value observer. The method can be applied to a non-ideal system affected by uncertainty, nonlinearity and multiple disturbances, and can be improved by considering cost on the basis of observation and compensation control.

Description

Technical Field

[0001] This invention relates to a control method for a four-tank chemical system, specifically to an output compensation control method for a four-tank chemical system based on disturbance decomposition technology. Background Technology

[0002] Due to the complexity of the scenario, chemical four-tank systems are difficult to handle, as the inability to collect the internal state of the tanks leads to a decrease in system performance, and strong disturbances and strong coupling affect the output measurement error. In order to stabilize the safety of chemical four-tank equipment and ensure the stability of the control system, it is necessary to establish multiple appropriate disturbance observers for control compensation, which can effectively address the robustness and safety issues of chemical four-tank systems.

[0003] The use of disturbance decomposition technology is a bold attempt at overall disturbance observation and control, which greatly improves the observation effect of disturbance and state. However, the excessive number of observer devices makes it impossible to guarantee cost control, which is the focus of future research. Therefore, it is necessary to use relevant experience and theoretical knowledge to study new observation and control algorithms. Summary of the Invention

[0004] The purpose of this invention is to propose an output compensation control method for a four-tank chemical system based on perturbation decomposition technology. This method can effectively utilize relevant experience and theoretical knowledge to observe unknown perturbations and states as much as possible, even when the system has multiple perturbation nonlinear terms.

[0005] The specific technical solution of the present invention is as follows: A method for output compensation control of a four-tank chemical system based on perturbation decomposition technology, comprising the following steps:

[0006] The output compensation control method for a four-tank chemical system based on perturbation decomposition technology is characterized by establishing a control system model using the inverse Laplace transform:

[0007]

[0008] In the formula, x(t) is the relevant state vector of the four-tank chemical system, and u(t) is the control input of the four-tank chemical system. r(t) represents the matched interference from an external excitation source with unknown information or nonlinear band influence at the controller end; w(t) represents the unmatched interference due to external bounded interference; y(t) represents the actual output value received by the sensor; ΔA(t) = UJ(t)G represents the uncertainty measure caused by parameter uncertainty during the modeling process; and A, B, C, and E are the system matrices obtained by establishing a mathematical model for the four-tank chemical system.

[0009]

[0010]

[0011] Among them, the time constant T of tank 1 s1 Tank 2 time constant T s2 Tank 3 time constant T s3 Tank 4 time constant T s4 Cross-sectional area of ​​tank 1 Cross-sectional area of ​​tank 2 Cross-sectional area of ​​tank 3 Cross-sectional area of ​​tank 4 Valve 1 is set with parameter l1, valve 2 is set with parameter l2, valve 1 has a unit flow velocity φ1, valve 2 has a unit flow velocity φ2, and the flow rate per unit length is k. c ;

[0012] Decomposing the matching perturbation yields the perturbation features:

[0013] For model perturbations, state-space equations are used to model them, which are then transformed into Jordan canonical form and diagonally decomposed to generate the following perturbation excitation sub-models for matching perturbations:

[0014]

[0015] in, M i F i S i T i It is the system matrix that decomposes the perturbation excitation model into N perturbation excitation sub-models with respect to perturbation characteristics, satisfying the following conditions:

[0016] (1) And p(t) represents any unknown external signal disturbance that may exist;

[0017] (2) All the established perturbation excitation sub-model systems are observable;

[0018] N disturbance observers are established for the decomposed disturbance excitation sub-model as follows:

[0019]

[0020] Among them, L 1i ε is the observation gain of N perturbation observers. i (t) represents N intermediate observer variables generated by N differences. In a given perturbation observer, interconnection terms with other N-1 perturbation observers are considered. Since N perturbation observers are designed to observe N perturbation features, consistent solutions are not possible. To reduce the computational workload of LMI and decrease the conservatism of the solution, augmentation and dimension expansion are performed, which leads to the following conditions:

[0021] (1) M = diag{M1, M2, ..., M} N}

[0022] (2) F = diag{F1, F2, ..., F} N}

[0023] (3) S = diag{S1, S2, ..., S} N}

[0024] (4)T = (T1, T2, ..., T) N )

[0025] (5)

[0026] (6)

[0027] For mismatched interference caused by external environmental influences or frequency disturbances, H∞ control is used to suppress the mismatched disturbance.

[0028] Design a Luenberger observer to observe the unknown state of a four-tank chemical system; the model of the state observer is as follows:

[0029]

[0030] Where: L2 is the controller gain of the state observer.

[0031] The control rate of the design compensation control value and feedback control is...

[0032] Analyze the effectiveness of the design methodology:

[0033] C001: Establish an error system for the designed observer and controller:

[0034] C002: To establish an error system, the internal state of the control system must first be able to converge.

[0035] C003:

[0036] C004: Establish an error system and then ensure that the observation errors of numerous disturbance observers converge;

[0037] C005:

[0038] C006: Standardize the error system;

[0039] C007:

[0040] C008: The observation error of the final state observer of the established error system can converge;

[0041] C009:

[0042] C010: Establish an error system for the designed observer and controller:

[0043] C011: in

[0044] C012:

[0045] C013: and

[0046] C014: Select a suitable Lyapunov functional as follows:

[0047] C015: ν(t)=μ T (t)Pμ(t);

[0048] C016: Where P = diag{P1, P2, P3};

[0049] C017: The following inequality holds true through stability analysis:

[0050] C018:

[0051] C019: Among them, For measurement output;

[0052] C020: Decoupling is achieved using techniques such as Schul complement, Young's inequality, and structural separation. A feasible solution for the following LMI is obtained through the LMI toolbox:

[0053] C021:

[0054] C022: Among them,

[0055] C023:

[0056] C024: Among them, and The controller gain and observer gain that satisfy all effects are obtained by solving the LMI in B004.

[0057] C025: Therefore, based on C003, C004, and C005, the stability of the error system under this model can be proven:

[0058] C026: According to C006, the convergence of the state of the four-tank chemical system and the convergence of observation errors can be guaranteed.

[0059] C027: According to C009, it can be proven that the perturbation decomposition technique can capture the characteristics of the perturbation and reduce the observation error of the perturbation, that is, reduce the impact of the perturbation observation error on the state observation error system. Attached Figure Description

[0060] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0061] Figure 2 This is a simplified diagram of the experimental equipment according to an embodiment of the present invention;

[0062] Figure 3 The example uses the method proposed in this invention to process the state response diagrams of states 1-4.

[0063] Figure 4 This is a comparison chart of the interference observation errors of the method proposed in this invention and the global observation method in the example embodiment;

[0064] Figure 5 The example image shows the interference observation of the first local interference source feature using the method proposed in this invention.

[0065] Figure 6 The example image shows the interference observation of the second local interference source characteristics using the method proposed in this invention.

[0066] Figure 7 The example image shows the interference observation of the third local interference source characteristics using the method proposed in this invention.

[0067] Figure 8 The following is an example of an interference observation diagram of the overall disturbance using the method proposed in this invention; Detailed Implementation

[0068] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0069] like Figure 1 As shown, a method for output compensation control of a four-tank chemical system based on perturbation decomposition technology includes the following steps:

[0070] Step 1: Set the parameters: Among them, the time constant T of the four-tank chemical system s1 =0.5, T s2 =1,Ts3 =2,T s4 =1; Cross-section of the four-tank tank The dual valve settings are: l1 = 0.7, l2 = 0.6; unit flow velocity at the valve φ1 = 3 cm. 3 / V·s, φ2=3.5cm 3 / V·s; flow rate per unit length k c =1V / cm,

[0071] Step 2: Import the status observation values ​​of the four chemical tank systems into the controller and update them;

[0072] Step 3: Repeat Step 2. Continue operation after the four-tank chemical system has stabilized.

[0073] The following is a real-world example:

[0074] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a simplified diagram of the experimental equipment according to an embodiment of the present invention; Figure 3 The example uses the method proposed in this invention to process the state response diagrams of states 1-4. Figure 4 This is a comparison chart of the interference observation errors of the method proposed in this invention and the global observation method in the example embodiment; Figure 5-7 The example image shows the interference observation of the characteristics of the first to third local interference sources using the method proposed in this invention. Figure 8 The following is an example of an interference observation diagram of the overall disturbance using the method proposed in this invention;

[0075] As can be seen from the figure, the designed method can achieve satisfactory control and observation performance.

[0076] References

[0077] [1]Shen M, Zhang H, Nguang SK, et al.H∞output anti-disturbance control of stochastic Markov jump systems with multiple disturbances[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2020, 51(12): 7633-7643.

[0078] [2]Liu L,Chen M,Li T,et al.Composite Anti-Disturbance Reference ModelL 2-L∞L_∞Control for Helicopter Slung Load System[J].Journal ofIntelligent&Robotic Systems,2021,102:1-21.

Claims

1. A method for output compensation control of a four-tank chemical system based on perturbation decomposition technology, characterized in that, Includes the following steps: A mathematical model of the four-tank chemical system is established using the inverse Laplace transform method, and a control system model is also established using the inverse Laplace transform method. ， In the formula, This represents the relevant state vector of a four-tank chemical system. For the control input of the four-tank chemical system, This is to address the matched interference from external excitation sources that are affected by unknown information or nonlinear bands at the controller end. This is due to externally bounded unmatched interference. The actual output value received by the sensor. This refers to the measurement of uncertainty caused by parameter uncertainty during the modeling process. The system matrix obtained by establishing a mathematical model for a four-tank chemical system. in: ， ， ， ， Among them, the time constant of tank 1 Tank 2 time constant Tank 3 time constant Tank 4 time constant Cross-sectional area of ​​tank 1 The cross-sectional area of ​​tank 2 The cross-sectional area of ​​tank 3 Cross-sectional area of ​​tank 4 Valve 1 setting parameters Valve 2 setting parameters Valve 1 unit flow rate Valve 2 unit flow rate Flow rate per unit length ; Decomposing matched perturbations yields perturbation features, while unmatched perturbations are handled using... Control and suppression, specifically: separating matchable perturbations and defining perturbation characteristics: For model perturbations, state-space equations are used to model them, which are then transformed into Jordan canonical form and diagonally decomposed to generate the following perturbation excitation sub-models for matching perturbations: in, , It separates the perturbation excitation model into The system matrix of the perturbation excitation sub-model with respect to perturbation characteristics satisfies the following conditions: (1) ,and This is to account for potential unknown external signal disturbances; (2) All the established perturbation excitation sub-model systems are observable; Establish the perturbation excitation sub-model after decomposition The disturbance observers are as follows: ， in, yes The observation gain of each perturbation observer yes The difference generates An intermediate observer variable, considered in a certain disturbance observer, is compared with other variables. The interconnection terms of the disturbance observers, due to the design A disturbance observer pair Since the perturbation characteristics of each sub-model are observed, a consistent solution cannot be achieved. To reduce the computational workload of LMI and the conservatism of the solution, augmentation and dimension expansion are performed, which will lead to the following conditions: ⑴ ； ⑵ ； ⑶ ； ⑷ ； ⑸ ； ⑹ ； For mismatched interference caused by external environmental influences or frequency disturbances, the mismatched disturbance is addressed by employing... Control and inhibition; The disturbance is compensated for by observing various features based on the output value, and the state observations obtained by the Luenberger observer are used for feedback control.

2. According to claim 1, a method for output compensation control of a four-tank chemical system based on perturbation decomposition technology is used to design a Luenberger observer to observe the unknown state of the four-tank chemical system; the model of the state observer is as follows: in: It is the state observer gain; The control rate for designing compensation control and feedback control is based on the state observation values ​​and disturbance observation values ​​obtained from the state observer. ; Analyze the effectiveness of the design methodology: B001: Establish an error system for the designed observer and controller: ， in, , , and ; B002: Select a suitable Lyapunov functional as follows: ,in ; B003: The following inequality holds true through stability analysis: in, For measurement output; B004: Decoupling is achieved using Schul complement, Young's inequality, and structural separation techniques. A feasible solution for the following LMI is obtained through the LMI toolbox: ;in, and, B005: Among them, , and To obtain the controller gain and observer gain that satisfy various effects by solving the LMI in B004; B006: Therefore, based on B003, B004, and B005, the stability of the error system under this model can be proven: B007: According to B006, the convergence of the state of the four-tank chemical system and the convergence of observation errors can be guaranteed; B008: According to B001, it can be proven that the perturbation decomposition technique can capture the characteristics of the perturbation and reduce the observation error of the perturbation, that is, reduce the impact of the perturbation observation error on the state observation error system.

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