Self-adaptive backstepping control construction method for air handling unit

Abstract

The invention relates to the technical field of intelligent temperature control of air handling units, in particular to a self-adaptive backstepping control construction method for an air handling unit, which comprises the following steps of: constructing a dynamic system of the air handling unit, setting a tracking error, and defining a smooth strict incremental function to transform the tracking error so as to update the system. The method comprises the following steps: performing approximation processing on a bounded continuous nonlinear function, processing the bounded continuous nonlinear function, defining an error variable, defining a plurality of Lyapunov candidate functions, updating a derivative or a time derivative of each Lyapunov candidate function, and determining a control design strategy for the dynamic system of the air handling unit. And simulation verification is carried out to complete construction of a self-adaptive backstepping control strategy for the air handling unit. According to the invention, the controller based on the sampling data is designed through the adaptive fuzzy backstepping technology, so that the system can guarantee that the obtained closed-loop system is kept stable, and the energy management efficiency in building management is effectively improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent temperature control technology for air handling units, and in particular to a method for constructing an adaptive backstepping control for air handling units. Background Technology

[0002] Air handling units (AHUs) in heating, ventilation, and air conditioning (HVAC) systems are typically designed for advanced building infrastructure to maintain a consistent and comfortable ambient temperature. However, given the increasing emphasis on energy conservation, effective control strategies for AHUs in HVAC systems are crucial, as these devices account for approximately 50% of a building's electrical energy consumption during operation. Various AHU control strategies have been developed in recent decades, relying on integer-order mathematical models to improve building temperature regulation and energy efficiency. Among the various temperature control methods for AHUs, proportional-integral-derivative (PID) control is the most commonly used due to its simple algorithm and ease of implementation, simplifying its practical application.

[0003] However, the nonlinear and time-varying behavior observed in air conditioning temperature modes can affect PID control. Incorrect PID parameter configuration can lead to significant overshoot problems, errors in maintaining steady state, and longer settling times, which in turn result in reduced energy efficiency and increased operating costs.

[0004] Accurate mathematical models of AHU systems based on building thermodynamics are crucial for the development of efficient control systems. Existing technologies use integer-order representations to create dynamic models of AHUs in HVAC systems. However, when constructing AHU models using integer nonlinear methods, a trade-off must be struck between accurately representing system complexity and maintaining model simplicity. Otherwise, complex control designs based on real-world, complex integer-order AHU models may generate significant computational demands and energy consumption.

[0005] Fractional dynamics in existing technologies, due to their inherent memory effect, can more concisely represent complex real-world models, including those related to heat transfer. Furthermore, since nonlinear fractional models require fewer parameters than integer-order models, using nonlinear fractional models to effectively and accurately characterize the thermal dynamics of air handling units (AHUs) within buildings is a natural tendency. However, current research on fractional AHUs primarily focuses on modeling, with insufficient development of temperature control strategies utilizing accurate and concise fractional AHU models. Consequently, when unpredictable temperature gradients occur within the cooling components of the AHU system, existing solutions cannot respond quickly or adjust strategies accordingly, failing to meet design requirements in terms of both transient and steady-state performance, thus leading to reduced energy management efficiency in building management. Summary of the Invention

[0006] Therefore, the present invention provides an adaptive backstepping control construction method for air handling units to overcome the problems in the prior art.

[0007] To achieve the above objectives, the present invention provides a method for constructing an adaptive backstepping control for air handling units, comprising: Step S1: Construct the dynamic system of the air handling unit. The dynamic system of the air handling unit is a fractional-order non-homogeneous AHU system, as shown in equation (3): (3) in, For system output, set For supply air temperature, Given the system input, calculate the derivative order. =0.96, Given constants, Set unknown system parameters To account for the uncertainty of the temperature gradient in the cooling unit, It is a bounded, continuous, nonlinear function. For unknown time-varying bounded disturbances, Let be the uncertain constant used to represent the unknown airflow caused by sensor malfunction. For ambient temperature, For indoor space volume, For the volume of the heat exchanger, The specific heat capacity of air. It is the enthalpy of vaporization. For saturated water enthalpy, For sensible heat load, Humidity intensity, air mass density, The humidity ratio of the air supply space. The outdoor air humidity ratio, The indoor humidity ratio; Step S2, set the tracking error And it satisfies the condition shown in equation (4): (4) in, For specified parameters and For a smooth decreasing performance function, ,in, ; Step S3, define a smooth, strictly increasing function. ,in, The tracking error is transformed, and the transformed tracking error is shown in equation (5): , in, The transformed tracking error is then fed into the dynamic system of the air handling unit for updating. The updated dynamic system of the air handling unit is shown in equation (6). (6); Step S4, use a fuzzy logic system to update the dynamic system of the air handling unit. After approximation processing, the fuzzy logic system is shown in equation (7): (7) in, For membership functions, For fuzzy sets, For fuzzy basis functions, Center of mass, ; Step S5, update the dynamic system of the air handling unit according to the second lemma. Perform processing and set the processed value. ,in, Through unknown positive numbers Upper bound constraint; Step S6, Define the error variable : (8) (9) in, The virtual control signal to be designed; Step S7, define the first Lyapunov candidate function. And calculate its time derivative based on the error variable. ,for For the virtual control signal Perform the design and update the time derivative based on the virtual control signal of the design. ; Step S8, define the second Lyapunov candidate function. Calculate its derivative ,for Designed for The second adaptive law is used, and the derivative is updated according to the second adaptive law and Young's inequality. ; Step S9, define the third Lyapunov candidate function. Calculate its derivative Update the derivative according to the first lemma The derivative is updated twice based on the first and second lemmas. ; Step S10, define the fourth Lyapunov candidate function. Calculate its time derivative ,for Designed separately for The fourth adaptive law and virtual control signal The time derivative is updated using the fourth adaptive law and the virtual control signal. ; Step S11, define the fifth Lyapunov candidate function. ,for Designed for The fifth adaptive law, designed to control input based on sampled data. The fifth Lyapunov candidate function is calculated based on the fifth adaptive law and Young's inequality. derivative ; Step S12: Determine the control design strategy for the dynamic system of the air handling unit based on each of the adaptive laws, and verify it through simulation. When the verification is successful, complete the construction of the adaptive backstepping control strategy for the air handling unit.

[0008] Furthermore, the first lemma includes that for any ,satisfy ,in, The Euclidean norm.

[0009] Furthermore, the second lemma includes the following: for a definition in a compact set... Continuous functions on ,exist In the case that there exists a fuzzy logic system, such that .

[0010] Furthermore, the first definition includes: For any function Its Caputo fractional derivative The calculation is shown in equation (1): , in, .

[0011] Furthermore, in step S7, the time derivative is updated. The process includes: Step S71, set the first Lyapunov candidate function Its time derivative is calculated as shown in equation (10): (10) in, ; Step S72, for the The designed virtual control signal As shown in equation (11): (11) in, The estimated value, The estimated value, The estimated value; Step S73, using the designed virtual control signal Update the time derivative The updated time derivative is shown in equation (12): (12) in, .

[0012] Furthermore, in step S8, the derivative is updated. The process includes: Step S81, set the second Lyapunov candidate function, Its derivative is calculated as shown in equation (13): (13) Step S82, for The second adaptive law designed includes The adaptive laws are shown in equations (14)-(16): (14) (15) (16) in, express At any moment The sampled values; Step S83: Update the derivative according to the second adaptive law and Young's inequality. The updated derivative As shown in equation (17): (17) in .

[0013] Furthermore, in step S9, the derivative is updated. The process includes: Step S91: Set the third Lyapunov candidate function. Calculate its derivative ,in, The calculation is shown in equation (18): (18) The calculation is shown in equation (19): (19); Step S92, obtain the following conditions according to the first lemma, including The derivative is updated twice using the above conditions. The derivative after the second update As shown in equation (20): (20) in ; Step S93, obtain the following conditions according to the second lemma, including ,in, Unknown, and Through an unknown positive real number Upper bound constraint; Step S94: Calculate the term in equation (20) based on the acquired conditions. The calculation process is shown in equation (21): (twenty one) in, ; Step S95, the terms in the above formula (20) are... Represented as Calculate the virtual controller fractional derivative and design ,in, The estimated value, The virtual control signal to be designed.

[0014] Furthermore, in step S10, the time derivative is updated. The process includes: Step S101: Set the fourth Lyapunov candidate function. ,in, ,calculate The time derivative is calculated as shown in equation (22): (twenty two); Step S102, for The design is aimed at the aforementioned The fourth adaptive law signal As shown in equation (23): (twenty three) Design for virtual control signals As shown in equation (24): (twenty four) in, express symbols, The estimated value, The estimated value, The estimated value, The estimated value; Step S103, for ,definition Based on the above The above and Young's inequality updates the time derivative. Updated time derivative As shown in equation (27): (27) in, .

[0015] Furthermore, in step S11, the derivative is updated. The process includes: Step S111: Define the fifth Lyapunov candidate function, where Design the function The fifth adaptive law includes The adaptive laws are shown in equations (28)-(31): (28) (29) (30) (31); Step S112, according to the fifth adaptive law, with respect to the updated time derivative In The conditions for setting the item are as shown in equation (32): (32); Step S113, according to the first definition and the convolution operator Design actual sampling data control input The design is as shown in equation (33): (33) in, This is obtained by replacing the values ​​in equation (24) with their sampled data; Step S114, for ,when , and when hour, Bounded, the function is calculated according to the fifth adaptive law and the pattern inequality. derivative The calculation is shown in equation (34): (34) in, ; Step S115, for positive constants, Under the following circumstances, the following conditions must be met: (35) in, .

[0016] Furthermore, the Young's inequality includes: (25) (26).

[0017] Compared with existing technologies, the beneficial effects of this invention are that it designs a sampled data-based controller for fractional-order non-homogeneous AHUs systems using adaptive fuzzy back-calculation technology. This ensures that even with uncertainties and external disturbances, the resulting closed-loop system remains stable, and all signals are bounded. It can track the reference indoor temperature very well. To avoid violating The occurrence of the specified output performance effectively improves the transient and steady-state performance of the system constructed by the method described in this invention, while also effectively improving the energy management efficiency in building management.

[0018] Furthermore, by setting up a sampling data-based control method for non-homogeneous fractional-order uncertain AHU systems, this invention can ensure that, under predefined output performance and various system uncertainties and external unknown factors, rigorous theoretical analysis is performed based on actual fractional-order systems to improve indoor temperature management. This further enhances the transient and steady-state performance of the system constructed by the method described in this invention, while also improving the energy management efficiency in building management.

[0019] Furthermore, compared to existing technologies that adjust the temperature in an integer AHU system based solely on an unknown humidity level, the method of this invention considers multiple real-world variables, including time-varying unknown heat loads, fluctuating humidity parameters, outdoor temperature changes, and humidity changes in the external air environment. By combining fuzzy logic systems to approximate these parameters, the method further improves the transient and steady-state performance of the system constructed using the method of this invention, while also enhancing the efficiency of energy management in building management.

[0020] Meanwhile, the method described in this invention estimates system uncertainties and external factors by designing an adaptive law, which can effectively offset the influence of uncertain control coefficients in the model caused by unpredictable temperature gradients in the cooling components of the AHU system on the controller design process. This further improves the transient and steady-state performance of the system constructed by the method described in this invention, while also improving the energy management efficiency in building management.

[0021] Furthermore, compared to the existing backstepping-based sampling data control schemes that only apply to homogeneous nonlinear fractional systems, the scheme of this invention introduces an adaptive backstepping sampling data control method for nonlinear uncertain nonhomogeneous fractional AHU systems to provide accurate model descriptions. A detailed theoretical analysis is conducted, carefully considering the unique characteristics of fractional calculus. This further improves the transient and steady-state performance of the system constructed using the method of this invention, while also enhancing the energy management efficiency in building management.

[0022] Furthermore, the solution described in this invention, based on the combination of an adaptive fuzzy backstepping fractional-order control scheme based on sampled data and a specified performance limit technique, strictly limits the transient and steady-state performance of the tracking error of the non-homogeneous fractional-order system output to predefined limits. This further improves the transient and steady-state performance of the system constructed by the method described in this invention, while also further improving the energy management efficiency in building management.

[0023] Furthermore, compared to existing technologies that analyze based on the transformed integer-order system, the method of this invention performs rigorous theoretical analysis based on the original fractional-order system. This allows for further constraints on the transient and steady-state properties of the tracking error of the non-homogeneous fractional-order system output. Consequently, while further improving the transient and steady-state properties of the system constructed using the method of this invention, it also further enhances the energy management efficiency in building management. Attached Figure Description

[0024] Figure 1 This is a flowchart of an adaptive backstepping control construction method for air handling units according to an embodiment of the present invention; Figure 2 The temperature tracking error curves are those of the method described in the embodiments of the present invention and the PID control method. Figure 3 The integral curves of the squared temperature tracking error of the method described in the embodiments of the present invention and the PID control method are shown. Figure 4 The integral curves of the absolute values ​​of the control inputs of the method described in the embodiments of the present invention and the PID control method are shown. Figure 5 The curve represents the system uncertainty estimation curve under the method described in the embodiments of the present invention. Detailed Implementation

[0025] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0026] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0027] Please see Figure 1 The diagram shows a flowchart of an adaptive backstepping control construction method for air handling units according to an embodiment of the present invention. The process of the adaptive backstepping control construction method for air handling units according to the present invention includes: Step S1: Construct the dynamic system of the air handling unit. The dynamic system of the air handling unit is a fractional-order non-homogeneous AHU system, as shown in equation (3): (3) in, For system output, set For supply air temperature, Given the system input, calculate the derivative order. =0.96, Given constants, Set unknown system parameters To account for the uncertainty of the temperature gradient in the cooling unit, It is a bounded, continuous, nonlinear function. For unknown time-varying bounded disturbances, Let be the uncertain constant used to represent the unknown airflow caused by sensor malfunction. For ambient temperature, For indoor space volume, For the volume of the heat exchanger, The specific heat capacity of air. It is the enthalpy of vaporization. For saturated water enthalpy, For sensible heat load, Humidity intensity, air mass density, The humidity ratio of the air supply space. The outdoor air humidity ratio, The indoor humidity ratio; Step S2, set the tracking error And it satisfies the condition shown in equation (4): (4) in, For specified parameters and For a smooth decreasing performance function, ,in, ; Step S3, define a smooth, strictly increasing function. ,in, The tracking error is transformed, and the transformed tracking error is shown in equation (5): , in, The transformed tracking error is then fed into the dynamic system of the air handling unit for updating. The updated dynamic system of the air handling unit is shown in equation (6). (6); Step S4, use a fuzzy logic system to update the dynamic system of the air handling unit. After approximation processing, the fuzzy logic system is shown in equation (7): (7) in, For membership functions, For fuzzy sets, For fuzzy basis functions, Center of mass, ; Step S5, update the dynamic system of the air handling unit according to the second lemma. Perform processing and set the processed value. ,in, Through unknown positive numbers Upper bound constraint; Step S6, Define the error variable : (8) (9) in, The virtual control signal to be designed; Step S7, define the first Lyapunov candidate function. And calculate its time derivative based on the error variable. ,for For the virtual control signal Perform the design and update the time derivative based on the virtual control signal of the design. ; Step S8, define the second Lyapunov candidate function. Calculate its derivative ,for Designed for The second adaptive law is used, and the derivative is updated according to the second adaptive law and Young's inequality. ; Step S9, define the third Lyapunov candidate function. Calculate its derivative Update the derivative according to the first lemma The derivative is updated twice based on the first and second lemmas. ; Step S10, define the fourth Lyapunov candidate function. Calculate its time derivative ,for Designed separately for The fourth adaptive law and virtual control signal The time derivative is updated using the fourth adaptive law and the virtual control signal. ; Step S11, define the fifth Lyapunov candidate function. ,for Designed for The fifth adaptive law, designed to control input based on sampled data. The fifth Lyapunov candidate function is calculated based on the fifth adaptive law and Young's inequality. derivative ; Step S12: Determine the control design strategy for the dynamic system of the air handling unit based on each of the adaptive laws, and verify it through simulation. When the verification is successful, complete the construction of the adaptive backstepping control strategy for the air handling unit.

[0028] It is understood that the air handling unit categories applied in the embodiments of the present invention include heat exchangers, chilled water piping systems, filters, supply and return air fans, control valves, air mixing units, dehumidification units, and humidification units. The embodiments of the present invention are only applied to air handling unit systems operating in cooling mode, wherein ideal gases are fully mixed through the heat exchanger at a fresh air to return air ratio of 0.25, and in the absence of air leakage, the effect of wind speed changes on area pressure is negligible.

[0029] It is understood that the embodiments of the present invention also include two assumptions to enable the fractional-order non-homogeneous AHUs system to complete backstepping tracking control based on integer and fractional orders. The assumptions include a first assumption and a second assumption, wherein: The first assumption is that the interference... From an unknown nonnegative constant Upper bound constraints, and interference. of fractional derivatives As a boundary, ,in It is another unknown nonnegative constant; The second assumption is that, It is bounded, smooth, and known.

[0030] Specifically, the virtual control signal to be designed described in the embodiments of the present invention Control signals based on sampled data at sampling time Updated sequentially, among which .

[0031] Specifically, the Young's inequalities described in the embodiments of the present invention include: (25) (26).

[0032] Specifically, the first lemma includes that for any ,satisfy ,in, The Euclidean norm; The second lemma includes the following: for a defined on a compact set... Continuous functions on ,exist In the case that there exists a fuzzy logic system, such that .

[0033] Specifically, the first definition includes: For any function Its Caputo fractional derivative The calculation is shown in equation (1): , in, .

[0034] Specifically, in step S7, the time derivative is updated. The process includes: Step S71, set the first Lyapunov candidate function Its time derivative is calculated as shown in equation (10): (10) in, ; Step S72, for the The designed virtual control signal As shown in equation (11): (11) in, The estimated value, The estimated value, The estimated value; Step S73, using the designed virtual control signal Update the time derivative The updated time derivative is shown in equation (12): (12) in, .

[0035] Specifically, the last inequality in inequality (10) is derived through the first lemma.

[0036] Specifically, in step S8, the derivative is updated. The process includes: Step S81, set the second Lyapunov candidate function, Its derivative is calculated as shown in equation (13): (13) Step S82, for The second adaptive law designed includes The adaptive laws are shown in equations (14)-(16): (14) (15) (16) in, express At any moment The sampled values; Step S83: Update the derivative according to the second adaptive law and Young's inequality. The updated derivative As shown in equation (17): (17) in .

[0037] Specifically, in step S9, the derivative is updated. The process includes: Step S91: Set the third Lyapunov candidate function. Calculate its derivative ,in, The calculation is shown in equation (18): (18) The calculation is shown in equation (19): (19); Step S92, obtain the following conditions according to the first lemma, including The derivative is updated twice using the above conditions. The derivative after the second update As shown in equation (20): (20) in ; Step S93, obtain the following conditions according to the second lemma, including ,in, Unknown, and Through an unknown positive real number Upper bound constraint; Step S94: Calculate the term in equation (20) based on the acquired conditions. The calculation process is shown in equation (21): (twenty one) in, ; Step S95, the terms in the above formula (20) are... Represented as Calculate the virtual controller fractional derivative and design ,in, The estimated value, The virtual control signal to be designed.

[0038] Specifically, the derivative Items in This is derived from the semigroup property of Caputo fractional derivatives.

[0039] Specifically, in step S10, the time derivative is updated. The process includes: Step S101: Set the fourth Lyapunov candidate function. ,in, ,calculate The time derivative is calculated as shown in equation (22): (twenty two); Step S102, for The design is aimed at the aforementioned The fourth adaptive law signal As shown in equation (23): (twenty three) Design for virtual control signals As shown in equation (24): (twenty four) in, express symbols, The estimated value, The estimated value, The estimated value, The estimated value; Step S103, for ,definition Based on the above The above and Young's inequality updates the time derivative. Updated time derivative As shown in equation (27): (27) in, .

[0040] Specifically, in step S11, the derivative is updated. The process includes: Step S111: Define the fifth Lyapunov candidate function, where Design the function The fifth adaptive law includes The adaptive laws are shown in equations (28)-(31): (28) (29) (30) (31); Step S112, according to the fifth adaptive law, with respect to the updated time derivative In The conditions for setting the item are as shown in equation (32): (32); Step S113, according to the first definition and the convolution operator Design actual sampling data control input The design is as shown in equation (33): (33) in, This is obtained by replacing the values ​​in equation (24) with their sampled data; Step S114, for ,when , and when hour, Bounded, the function is calculated according to the fifth adaptive law and the pattern inequality. derivative The calculation is shown in equation (34): (34) in, ; Step S115, for positive constants, Under the following circumstances, the following conditions must be met: (35) in, .

[0041] It is understandable that, in reality, the rate of change of physical values ​​is limited, therefore and Bounded, the stated Bounded.

[0042] Specifically, before the control design strategy is simulated and verified in step S12, a stability analysis is performed on it based on the first theorem, wherein the first theorem is: Based on the fractional-order uncertain AHU in equation (3) and the sampled data driven by the adaptive laws in equations (14) to (16), (23), and (28) to (31), the fractional-order control scheme in equation (33) ensures the uniform boundedness of the closed-loop signal, and the indoor temperature can track the reference indoor temperature well. Furthermore, the tracking error e always remains within the given performance limits.

[0043] Proof: For ,remember Define a Lyapunov function. .because ,therefore , Calculate in this way derivative The calculation is shown in equation (36): (36)

[0044] Wherein, the sampling interval satisfies ,and .

[0045] Integrating both sides of equation (36) yields This indicates Uniformly bounded, Bounded, Bounded.

[0046] from The design and the definition of fractional integrals in the second definition are obtained. Because when hour, Monotonically decreasing to 0, and Bounded, therefore It is continuous and bounded. Bounded. Because Bounded, according to As can be seen from its characteristics, for any initial error Through appropriate selection The value and make sure Therefore, the condition shown in formula (4) is for Established.

[0047] Specifically, in step S12, the control design strategy is simulated and verified. In this embodiment of the invention, the simulation verification is limited to the operation of the AHU in cooling mode during summer to ensure the generality of the simulation verification. The specific construction steps of the control design strategy in this embodiment are as follows: The target reference temperature used for simulation verification is set to be time-varying: ; Assign values ​​to the various parameters in the system shown in formula (3) and set them. Dry air; based on the actual maximum flow rate of chilled water, the control input will be... The upper limit is set at 0.41. ; Assign values ​​to unknown parameters / time-varying variables in the controller, and set... ,in, A unit step function representing time in seconds; The tracking error The boundary is defined as ,in Assign values ​​to each design parameter and set them. ; The first fuzzy logic system by As input, and define six uniformly distributed... Gaussian membership function on; second fuzzy logic system use and As input, each input is defined with the above. Same membership function; Define the system variables and the initial conditions for estimation: .

[0048] To highlight the efficiency of the method described in the embodiments of the present invention, the pre-configured system described above is compared with a system having… Compared with traditional PID controllers.

[0049] Please see Figure 2 As shown, it is the tracking error curve of the method described in the embodiments of the present invention and the PID control method; from Figure 2 It can be seen that the proposed method can perfectly achieve the control objective, while the PID method fails due to exceeding the specified limits. However, it failed to meet the output performance requirements. Conversely, the tracking error limit for the PID control scheme is... In comparison, its steady-state limit is larger and its convergence speed is slower, which intuitively demonstrates the advantages of the developed method in achieving improved control performance, since the PID control scheme can only ensure that the tracking error is within a more relaxed limit.

[0050] Please see Figure 3As shown in Figure 3, it is the integral curve of the squared temperature tracking error of the method described in the embodiment of the present invention and the PID control method; the data shown in Figure 3 further demonstrates the advantages of the control strategy constructed by the method described in the embodiment of the present invention, which has a very small cumulative tracking error compared with the PID controller.

[0051] Please see Figure 4 As shown in Figure 4, the integral curves of the absolute values ​​of the control inputs of the method described in this embodiment and the PID control method are shown. From the data shown in Figure 4, it can be found that regardless of whether the system is under our developed controller or a traditional PID controller, the cumulative control quantity is similar to each other. Therefore, it is similar to... Figure 2 and Figure 3 Together, it is shown that, compared with the existing widely used PID control methods, the studied scheme can achieve enhanced control performance without introducing additional required control force.

[0052] Please see Figure 5 As shown in Figure 5, it represents the estimated value curve of the system's uncertain variables under the method described in the embodiments of the present invention. The data shown in Figure 5 can effectively verify the boundedness of the strategy constructed by the method described in the embodiments of the present invention under closed-loop signals.

[0053] By comparing and verifying with commonly used PID control schemes, it can be concluded that the strategy constructed by the method described in this embodiment of the invention is effective and efficient for nonlinear uncertain nonhomogeneous AHUs. The method described in this embodiment of the invention is for nonlinear uncertain fractional nonhomogeneous AHUs with various system uncertainties and unknown time-varying disturbances. Based on the adaptive fuzzy backstepping method, a novel sampled data temperature tracking control scheme with predefined performance is constructed, which ensures the stability of the obtained closed-loop system and the compliance of the tracking error with the specified performance. Through simulation comparison with traditional and widely used PID control methods, the effectiveness of the multiple research schemes is verified.

[0054] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0055] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing adaptive backstepping control for air handling units, characterized in that, include: Step S1: Construct the dynamic system of the air handling unit. The dynamic system of the air handling unit is a fractional-order non-homogeneous AHU system, as shown in equation (3): （3） in, For system output, set For supply air temperature, Given the system input, calculate the derivative order. =0.96, Given constants, Set unknown system parameters To account for the uncertainty of the temperature gradient in the cooling unit, It is a bounded, continuous, nonlinear function. For unknown time-varying bounded disturbances, Let be the uncertain constant used to represent the unknown airflow caused by sensor malfunction. For ambient temperature, For indoor space volume, For the volume of the heat exchanger, The specific heat capacity of air. It is the enthalpy of vaporization. For saturated water enthalpy, For sensible heat load, Humidity intensity, air mass density, The humidity ratio of the air supply space. The outdoor air humidity ratio, The indoor humidity ratio; Step S2, set the tracking error And it satisfies the condition shown in equation (4): （4） in, For specified parameters and For a smooth decreasing performance function, ,in, ; Step S3, define a smooth, strictly increasing function. ,in, The tracking error is transformed, and the transformed tracking error is shown in equation (5): ， in, The transformed tracking error is then fed into the dynamic system of the air handling unit for updating. The updated dynamic system of the air handling unit is shown in equation (6). （6）； Step S4, use a fuzzy logic system to update the dynamic system of the air handling unit. After approximation processing, the fuzzy logic system is shown in equation (7): （7） in, For membership functions, For fuzzy sets, For fuzzy basis functions, Center of mass, ; Step S5, update the dynamic system of the air handling unit according to the second lemma. Perform processing and set the processed value. ,in, Through unknown positive numbers Upper bound constraint; Step S6, Define the error variable : （8） （9） in, The virtual control signal to be designed; Step S7, define the first Lyapunov candidate function. And calculate its time derivative based on the error variable. ,for For the virtual control signal Perform the design and update the time derivative based on the virtual control signal of the design. ; Step S8, define the second Lyapunov candidate function. Calculate its derivative ,for Designed for The second adaptive law is used, and the derivative is updated according to the second adaptive law and Young's inequality. ; Step S9, define the third Lyapunov candidate function. Calculate its derivative Update the derivative according to the first lemma The derivative is updated twice based on the first and second lemmas. ; Step S10, define the fourth Lyapunov candidate function. Calculate its time derivative ,for Designed separately for The fourth adaptive law and virtual control signal The time derivative is updated using the fourth adaptive law and the virtual control signal. ; Step S11, define the fifth Lyapunov candidate function. ,for Designed for The fifth adaptive law, designed to control input based on sampled data. The fifth Lyapunov candidate function is calculated based on the fifth adaptive law and Young's inequality. derivative ; Step S12: Determine the control design strategy for the dynamic system of the air handling unit based on each of the adaptive laws, and verify it through simulation. When the verification is successful, complete the construction of the adaptive backstepping control strategy for the air handling unit.

2. The adaptive backstepping control construction method for air handling units according to claim 1, characterized in that, The first lemma includes that for any ,satisfy ,in, The Euclidean norm.

3. The adaptive backstepping control construction method for air handling units according to claim 2, characterized in that, The second lemma includes the following: for a defined on a compact set... Continuous functions on ,exist In the case that there exists a fuzzy logic system, such that .

4. The adaptive backstepping control construction method for air handling units according to claim 1, characterized in that, The first definition includes: For any function Its Caputo fractional derivative The calculation is shown in equation (1): ， in, .

5. The adaptive backstepping control construction method for air handling units according to claim 1, characterized in that, In step S7, the time derivative is updated. The process includes: Step S71, set the first Lyapunov candidate function Its time derivative is calculated as shown in equation (10): （10） in, ; Step S72, for the The designed virtual control signal As shown in equation (11): （11） in, The estimated value, The estimated value, The estimated value; Step S73, using the designed virtual control signal Update the time derivative The updated time derivative is shown in equation (12): （12） in, .

6. The adaptive backstepping control construction method for air handling units according to claim 1, characterized in that, In step S8, the derivative is updated. The process includes: Step S81, set the second Lyapunov candidate function, Its derivative is calculated as shown in equation (13): （13） Step S82, for The second adaptive law designed includes The adaptive laws are shown in equations (14)-(16): （14） （15） （16） in, express At any moment The sampled values; Step S83: Update the derivative according to the second adaptive law and Young's inequality. The updated derivative As shown in equation (17): （17） in .

7. The adaptive backstepping control construction method for air handling units according to claim 3, characterized in that, In step S9, the derivative is updated. The process includes: Step S91: Set the third Lyapunov candidate function. Calculate its derivative ,in, The calculation is shown in equation (18): （18） The calculation is shown in equation (19): （19）； Step S92, obtain the following conditions according to the first lemma, including The derivative is updated twice using the above conditions. The derivative after the second update As shown in equation (20): （20） in ; Step S93, obtain the following conditions according to the second lemma, including ,in, Unknown, and Through an unknown positive real number Upper bound constraint; Step S94: Calculate the term in equation (20) based on the acquired conditions. The calculation process is shown in equation (21): （21） in, ; Step S95, the terms in the above formula (20) are... Represented as Calculate the virtual controller fractional derivative and design ,in, The estimated value, The virtual control signal to be designed.

8. The adaptive backstepping control construction method for air handling units according to claim 4, characterized in that, In step S10, the time derivative is updated. The process includes: Step S101: Set the fourth Lyapunov candidate function. ,in, ,calculate The time derivative is calculated as shown in equation (22): （22）； Step S102, for The design is aimed at the aforementioned The fourth adaptive law signal As shown in equation (23): （23） Design for virtual control signals As shown in equation (24): （24） in, express symbols, The estimated value, The estimated value, The estimated value, The estimated value; Step S103, for ,definition Based on the above The above and Young's inequality updates the time derivative. Updated time derivative As shown in equation (27): （27） in, .

9. The adaptive backstepping control construction method for air handling units according to claim 8, characterized in that, In step S11, the derivative is updated. The process includes: Step S111: Define the fifth Lyapunov candidate function, where Design the function The fifth adaptive law includes The adaptive laws are shown in equations (28)-(31): （28） （29） （30） （31）； Step S112, according to the fifth adaptive law, with respect to the updated time derivative In The conditions for setting the item are as shown in equation (32): （32）； Step S113, according to the first definition and the convolution operator Design actual sampling data control input The design is as shown in equation (33): （33） in, This is obtained by replacing the values ​​in equation (24) with their sampled data; Step S114, for ,when , and when hour, Bounded, the function is calculated according to the fifth adaptive law and the pattern inequality. derivative The calculation is shown in equation (34): （34） in, ; Step S115, for positive constants, Under the following circumstances, the following conditions must be met: （35） in, .

10. The method for constructing adaptive backstepping control for air handling units according to any one of claims 1-9, characterized in that, Young's inequalities include: （25） （26）。

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