Multi-objective optimization control method for variable frequency centrifugal units

Abstract

The invention discloses a multi-objective optimization control method for a variable frequency centrifugal unit, and relates to the technical field of automatic control or optimization control. The method comprises: step 1: defining a multi-dimensional state space of the variable frequency centrifugal unit, and taking each operation data and control input as an element in the multi-dimensional state space; step 2: defining an energy consumption dynamic model, a vibration dynamics equation and a temperature distribution model of the variable frequency centrifugal unit; defining a total objective function of a multi-objective optimization model of the variable frequency centrifugal unit; step 3: based on the total objective function, estimating the state of the variable frequency centrifugal unit in real time; step 4: iteratively solving the optimization problem through a non-dominated sorting genetic algorithm II, realizing real-time control, and making real-time adjustments according to feedback. The invention realizes efficient and stable operation of the variable frequency centrifugal unit under complex working conditions.

Description

Technical Field

[0001] The invention relates to the technical field of automatic control or optimization control, and in particular to a multi-objective optimization control method for a variable frequency centrifugal unit. Background Art

[0002] As an important equipment widely used in industrial production, variable frequency centrifugal units are usually used for large-scale separation, concentration and filtration of liquids, gases or other media. With the continuous development of industrial technology, the application scenarios of variable frequency centrifugal units are becoming more and more extensive, and their performance has a vital impact on production efficiency, energy consumption level and equipment stability. The operation of traditional centrifugal units relies on fixed control parameters and preset operating conditions. As production needs change, factors such as equipment load, operating conditions, and operating time are also changing dynamically, making it difficult for traditional centrifugal units to achieve efficient and stable operation under complex conditions.

[0003] In the existing variable frequency centrifugal unit control technology, many devices use simple PID control to adjust the speed and frequency, thereby controlling energy consumption and equipment vibration. This method can achieve certain results under certain specific working conditions, but its limitations are also obvious. First of all, traditional PID control relies on precise mathematical models. When the nonlinear factors in the system increase, the effect of PID control will decrease significantly, and it is difficult to effectively cope with the nonlinear dynamic changes of complex systems. For centrifugal units, there are complex physical processes involved, including fluid mechanics, temperature conduction, pressure changes, mechanical vibrations and other mutually coupled factors. The nonlinear characteristics of these factors are difficult to effectively adjust through traditional PID control.

[0004] Secondly, there is less attention paid to multi-objective optimization in the prior art. In the industrial production process, the operation of the variable frequency centrifugal unit often involves multiple conflicting objectives, such as the need to control temperature rise and mechanical vibration while optimizing energy consumption. However, traditional control methods usually focus only on a single goal, such as minimizing energy consumption, while ignoring the optimization needs of other goals. This single-objective optimization control method is prone to cause imbalance in the system during operation. For example, in the process of reducing energy consumption, if the effects of temperature and vibration are not considered, the equipment may operate at high temperature or strong vibration, thereby affecting the stability and service life of the equipment. Furthermore, the monitoring and estimation capabilities of the real-time status of the equipment in the prior art are also relatively limited. When the variable frequency centrifugal unit is operating under complex working conditions, its internal state is often difficult to obtain through direct measurement, and traditional control systems often rely on data obtained by external sensors for control. These data are affected by noise, sensor accuracy and external interference, resulting in deviations between the actual state and the measured state of the system, which in turn affects the control effect. At the same time, the existing state observation technology can usually only estimate part of the state of the system, and the estimation accuracy is low, making it difficult to timely and accurately reflect the global state of the system in a dynamic environment. Summary of the invention

[0005] The purpose of the present invention is to provide a multi-objective optimization control method for a variable frequency centrifugal unit, thereby achieving efficient and stable operation of the variable frequency centrifugal unit under complex working conditions.

[0006] In order to solve the above technical problems, the present invention provides a multi-objective optimization control method for a variable frequency centrifugal unit, the method comprising:

[0007] Step 1: define the multidimensional state space of the variable frequency centrifugal unit, collect the operating data of the variable frequency centrifugal unit at each time, and take each operating data and control input as an element in the multidimensional state space;

[0008] Step 2: Define the energy consumption dynamic model, vibration dynamics equation and temperature distribution model of the variable frequency centrifugal unit; combine the energy consumption dynamic model, vibration dynamics equation and temperature distribution model to define the total objective function of the multi-objective optimization model of the variable frequency centrifugal unit;

[0009] Step 3: Based on the total objective function, the collaborative optimization control law of the variable frequency centrifugal unit is obtained through variational method and iterative optimization; a state observer is constructed to estimate the state of the variable frequency centrifugal unit in real time;

[0010] Step 4: Iteratively solve the optimization problem through non-dominated sorting genetic algorithm II to obtain the optimal control strategy; according to the optimal control strategy, design the actual controller of the variable frequency centrifugal unit to achieve real-time control and make real-time adjustments based on feedback.

[0011] Furthermore, it is characterized in that the operating data includes: inverter frequency , variable frequency centrifugal unit pressure , Unit speed ,vibration and temperature ; For time; The control input of time is , and obtain a multidimensional state space for:

[0012] ;

[0013] in, is the preset state transfer matrix; Input matrix for preset control; is the time step.

[0014] Furthermore, the energy consumption dynamic model of the variable frequency centrifugal unit defined in step 2 is Use the following formula to express it:

[0015] ;

[0016] in, is the preset friction loss coefficient; is the preset modulation index; is the nonlinear coupling term of speed and vibration is a preset positive number to avoid the singularity of the logarithmic function; A coefficient that represents the vibration energy loss; It is the preset temperature suppression index, which represents the negative feedback effect of temperature on friction loss.

[0017] Furthermore, the vibration dynamics equation of the variable frequency centrifugal unit defined in step 2 is expressed using the following formula:

[0018] ;

[0019] in, It is vibration The fractional derivative of represents the memory effect of the variable frequency centrifugal unit; is the fractional order, ; represents the nonlinear damping effect of vibration, is the damping coefficient, which is used to quantify the effect of damping on vibration; is a positive integer index, indicating the nonlinear degree of speed and pressure coupling. This reflects that when the pressure increases, the effect of the rotation speed on the vibration gradually weakens; is the initial temperature; Indicates from the initial time to the time The time between the frequency conversion centrifugal unit and the vibration It is expressed by the vibration dynamics equation.

[0020] Furthermore, the temperature distribution model defined in step 2 Use the following formula to express it:

[0021] ;

[0022] The temperature distribution model Indicates at location Place, time Temperature at is the Fourier heat conduction term; is the thermal diffusivity, which describes the thermal conductivity of a material. The larger the thermal diffusivity, the faster the heat spreads; The temperature distribution model The Laplace operator represents the second-order derivative of temperature with space, quantifying the variation of temperature at different spatial locations; It indicates the inhibitory effect of rotation speed on temperature distribution. When it is higher, the convection effect in the variable frequency centrifugal unit is enhanced, resulting in a decrease in the temperature gradient; is the effective length of the variable frequency centrifugal unit; It is the coupling coefficient of frequency, pressure and vibration. It is a dimensionless constant that represents the strength of the nonlinear coupling between these variables. When the frequency and pressure increase, the increase in vibration will lead to a significant increase in temperature.

[0023] Furthermore, the total objective function of the multi-objective optimization model of the variable frequency centrifugal unit defined in step 2 is Use the following formula to express it:

[0024] ;

[0025] in, is the square term of the rate of change of the temperature distribution model, indicating that the energy dissipation of the variable frequency centrifugal unit increases when the temperature is rapidly increased or decreased, and the more drastic the temperature change, the greater the value of the objective function, thus promoting the maintenance of temperature stability during the optimization process; It represents the feedback effect of temperature on frequency, pressure and vibration coupling. When it increases, this item decreases, indicating that under high temperature conditions, the influence of the vibration of the variable frequency centrifugal unit on the objective function will be amplified, thereby reducing the vibration during the optimization process and maintaining the temperature stability; Describes the effects of frequency, speed and pressure on vibration. , speed or pressure When increasing, vibration The nonlinear growth of will be limited by the logarithmic function, reducing its growth rate.

[0026] Furthermore, the collaborative control optimization rule in step 3 is expressed using the following formula:

[0027] ;

[0028] in, is the preset feedback gain matrix; is the initial control input.

[0029] Furthermore, the state observer constructed in step 3 Calculated by the following formula:

[0030] ;

[0031] in, is the observer gain matrix; is the observation matrix; is the output of the variable frequency centrifugal unit; the state observer The status of the variable frequency centrifuge unit as a real-time estimate.

[0032] Furthermore, in step 4, the optimization problem is iteratively solved by non-dominated sorting genetic algorithm II to find the Pareto optimal solution among multiple performance objectives and obtain the optimal control strategy; the formula for iterative solution is:

[0033] ;

[0034] in, For the generation of control inputs, through the previous generation And the overall objective function of the previous generation Gradient Make updates; is the learning rate or step size coefficient, which controls the adjustment amplitude of the control input in each iterative solution; For the The optimal control input is determined by judging the convergence of the control input. If the change in the control input If it is less than the preset threshold, it is considered to have converged and the optimal control input is output ; The implementation formula of the controller is:

[0035] ;

[0036] in, is the control input for the next moment, and the optimal control input after optimization is Update with feedback adjustments; is the optimal control input obtained by iterative solution; To provide feedback adjustment, use the current multidimensional state space and estimated status of variable frequency centrifugal unit Adjust the difference between is the feedback adjustment coefficient, which controls the impact of the feedback term.

[0037] The multi-objective optimization control method of the variable frequency centrifugal unit of the present invention has the following beneficial effects: most of the traditional centrifugal unit control methods focus on the optimization of a single objective, such as minimizing energy consumption or speed stability, while ignoring the control of other key indicators such as temperature and vibration. In industrial applications, the operation of the variable frequency centrifugal unit involves multiple competing objectives, such as reducing energy consumption may lead to temperature increase or vibration intensification. The present invention adopts the NSGA-II algorithm, and through the multi-objective optimization model, finds the best balance point between multiple objectives to ensure that the system can maintain temperature stability and effectively suppress vibration while operating efficiently. By balancing energy consumption, temperature and vibration, the present invention can reduce the mechanical loss and heat loss of the system, extend the service life of the equipment, and ensure that the equipment can avoid failures or damage caused by excessive vibration or excessive temperature while operating efficiently. The present invention improves the control accuracy and response speed of the system through a state observer. The state (such as speed, pressure, temperature, vibration, etc.) of the centrifugal unit during operation is complex and difficult to measure directly, especially in an environment with large external interference and noise, the measurement error of the sensor may cause the control system to feedback inaccurately on the state. In order to solve this problem, the present invention introduces a state observer, which corrects the state estimation of the system in real time through a feedback mechanism. The state observer uses the output information of the current measurement combined with the dynamic model of the system to estimate the internal state that cannot be directly measured, thereby providing more accurate state information for the control system. Through this method, the present invention not only improves the accuracy of state estimation, but also enhances the real-time response capability of the system, allowing the control system to quickly make adjustments based on accurate state information, ensuring the stable operation of the system under different working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0039] Figure 1 A method flow chart of a multi-objective optimization control method for a variable frequency centrifugal unit provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] Example 1: Reference Figure 1 , a multi-objective optimization control method for a variable frequency centrifugal unit, the method comprising:

[0042] Step 1: define the multidimensional state space of the variable frequency centrifugal unit, collect the operating data of the variable frequency centrifugal unit at each time, and take each operating data and control input as an element in the multidimensional state space;

[0043] The operation process of the variable frequency centrifugal unit involves multiple key parameters, which not only reflect the current state of the unit, but also have an important impact on energy consumption, efficiency, stability and other aspects. In order to effectively optimize the control, it is first necessary to abstract these complex physical processes and parameters into a multidimensional state space. In this state space, each dimension represents a key operating data of the variable frequency centrifugal unit, such as speed, vibration amplitude, temperature, energy consumption, load, etc., and the control input signals, such as frequency and voltage changes, must also be considered. By integrating these operating data and control inputs into the multidimensional state space, the operating state of the unit under different times and conditions can be fully reflected. The construction of this state space helps to capture the dynamic characteristics of the system, especially in complex physical equipment such as variable frequency centrifugal units, where there are often complex coupling relationships between multiple variables. For example, the frequency change of the unit not only affects energy consumption, but also has a chain effect on vibration and temperature. Therefore, integrating the operating data at each time point into an element in the multidimensional state space can systematically describe the interaction between these variables. By continuously collecting these operating data, the system can track the state changes of the centrifugal unit in real time and provide basic data support for subsequent multi-objective optimization. The definition of multidimensional state space is not only the collection of data, but more importantly, it provides a mathematical framework so that the state of the centrifugal unit can be modeled and analyzed. Under this framework, the operating state of the variable frequency centrifugal unit is no longer isolated, but embedded in a higher dimensional space, where all variables interact and jointly affect the overall performance of the unit. Compared with traditional single variable or few variable control methods, the advantage of multidimensional state space lies in its adaptability and flexibility to complex systems. Previous control methods usually rely on the optimization of a single state, such as only focusing on the reduction of energy consumption or temperature, ignoring the changes of other important factors. In the present invention, by taking into account the multidimensional state of each time step, the system can comprehensively optimize multiple goals during operation. In addition, the inclusion of the control input signal enables the system to not only monitor the operating state of the centrifugal unit, but also predict the state changes under different input conditions, so as to better make control decisions. Such a multidimensional description method lays the foundation for subsequent optimization, so that the control strategy can be dynamically adjusted according to the actual operating conditions to ensure that the system always operates in the optimal state.

[0044] Step 2: Define the energy consumption dynamic model, vibration dynamics equation and temperature distribution model of the variable frequency centrifugal unit; combine the energy consumption dynamic model, vibration dynamics equation and temperature distribution model to define the total objective function of the multi-objective optimization model of the variable frequency centrifugal unit;

[0045] The energy consumption dynamic model is one of the foundations of the entire system. The operating energy consumption of the variable frequency centrifugal unit is directly related to its frequency, load, temperature and other variables. By constructing an energy consumption dynamic model, the energy consumption changes of the centrifugal unit under different operating conditions can be accurately quantified and predicted. Generally speaking, the energy consumption of the centrifugal unit increases under high load and high frequency, and changes in temperature and vibration may also affect the energy consumption level. Therefore, the energy consumption dynamic model not only needs to reflect the basic operating laws of the unit, but also needs to be coupled with other physical variables to ensure that the dynamic changes of energy consumption can be correctly described under different working conditions. This provides a basis for subsequent optimization control, that is, to reduce energy consumption as much as possible while meeting other conditions, thereby improving the operating efficiency of the equipment. Secondly, the construction of the vibration dynamics equation is an important link to ensure the stability of the system. During the operation of the centrifugal unit, vibration is inevitable due to the high-speed rotation of its internal rotating parts. The magnitude of the vibration directly affects the stability and life of the equipment. If the vibration is too large, it may cause damage to the equipment or abnormal operation. Therefore, the establishment of the vibration dynamics equation aims to optimize the control strategy by describing the vibration behavior of the equipment under different working conditions, so that the vibration is maintained within a safe range. This equation is usually based on the physical properties of the centrifuge, such as its mass, stiffness, damping, etc. Through the effect of these parameters, the vibration dynamics equation can accurately predict the vibration amplitude and frequency of the equipment under different loads and frequencies. By coupling with the energy consumption dynamic model, the vibration can be reduced while minimizing the impact on energy consumption to achieve the purpose of optimization control. The temperature distribution model is another optimization target that cannot be ignored. During the operation of the variable frequency centrifugal unit, due to energy conversion and friction, various parts of the equipment will accumulate heat to varying degrees. If the temperature is too high, it may cause the equipment to overheat, thereby affecting its performance or even damaging the equipment. The temperature distribution model can accurately describe the temperature changes of the centrifuge during operation by modeling the heat conduction and heat radiation processes of different parts of the equipment. Through this model, the temperature of the equipment can be monitored and predicted in real time during operation to prevent the temperature from being too high or too low. At the same time, the temperature distribution model also needs to be combined with the energy consumption model and the vibration model, because temperature changes may affect vibration and energy consumption, and the coupling relationship between the three is complex. Therefore, these factors need to be considered simultaneously during the optimization process to ensure a balance between different goals. Based on the above three models, the present invention proposes a multi-objective optimization model, which aims to comprehensively optimize energy consumption, vibration and temperature at the same time. Traditional single-objective optimization methods often cannot meet the multi-dimensional requirements of complex equipment, while the multi-objective optimization model introduces multiple objective functions to weigh and coordinate between various objectives. The overall objective function unifies the optimization objectives of energy consumption, vibration and temperature in a weighted manner. The setting of the weight coefficient is very important, which determines the priority of each objective in the optimization process.For example, in some operating conditions, energy saving may be the primary goal, while in other operating conditions, temperature control or vibration reduction may need to be prioritized. Therefore, the weight design of the overall objective function needs to be flexibly adjusted according to the actual application scenario to ensure the optimal operating state under different operating conditions.

[0046] Step 3: Based on the total objective function, the collaborative optimization control law of the variable frequency centrifugal unit is obtained through variational method and iterative optimization; a state observer is constructed to estimate the state of the variable frequency centrifugal unit in real time;

[0047] The core of the collaborative optimization control law is to consider multiple optimization objectives such as energy consumption, vibration and temperature at the same time, and adjust the optimization requirements under different working conditions in real time. For example, when the system is in a high-load state, it may be necessary to pay more attention to vibration control to avoid mechanical failure of the equipment due to excessive vibration; while under low-load conditions, the system may be more inclined to optimize energy consumption to ensure that energy consumption is reduced as much as possible under the premise of meeting basic operating conditions. The design of the collaborative optimization control law aims to balance the weights of different objectives and dynamically adjust the control strategy so that the system always remains in the optimal operating state. In order to achieve this goal, the calculus of variations is introduced as an important tool for optimization control. The calculus of variations analyzes the influence of different variables on the optimization objectives by deriving the objective function, and then derives the optimal control strategy. In the present invention, the multi-objective optimization model of the variable frequency centrifugal unit has complex nonlinear characteristics, involving multiple state variables and dynamic changes of control inputs. Therefore, the application of the calculus of variations can help find the optimal relationship between these variables and ensure the effectiveness of the control strategy. Through the iterative optimization method, the collaborative optimization control law can continuously correct the control input so that it is in the optimal state at every time point and adapts to the dynamic changes of the system. This dynamic adjustment capability enables the system to respond quickly to changes in external working conditions and improve control accuracy through real-time optimization. In addition to the collaborative optimization control law, the state observer also plays a vital role in this step. The role of the state observer is to monitor the operating state of the variable frequency centrifugal unit in real time and provide the current state estimate of the system. Since the data collected by the sensor may be interfered by noise, delay, etc. in actual operation, relying solely on the data of the sensor for control may lead to error accumulation and control inaccuracy. The state observer can estimate the current system state more accurately and compensate for the errors in the sensor data by filtering and correcting the collected data, combined with the state space model of the system. Common state observers include Kalman filters and extended Kalman filters, which gradually improve the accuracy of state estimation by continuously iterating and correcting the estimated value. The combination of the state observer and the collaborative optimization control law enables the present invention to not only accurately control the current state of the centrifugal unit, but also optimize and adjust in advance by predicting the future state. For example, when the state observer finds that the current state is about to exceed the set safety range, the system can adjust the control input in advance to prevent the state from continuing to deteriorate. This forward-looking control method improves the real-time response capability of the control strategy while improving the stability and safety of the system. Compared with the prior art, traditional control systems usually rely on fixed control laws and cannot be adjusted dynamically in real time. The present invention solves this problem by introducing a state observer and a collaborative optimization control law, thus enabling the system to have adaptive capabilities.

[0048] Step 4: Iteratively solve the optimization problem through non-dominated sorting genetic algorithm II to obtain the optimal control strategy; according to the optimal control strategy, design the actual controller of the variable frequency centrifugal unit to achieve real-time control and make real-time adjustments based on feedback.

[0049] The NSGA-II algorithm is a very effective evolutionary algorithm in the field of multi-objective optimization. It can optimize multiple conflicting objectives at the same time and find a set of solutions that take into account each objective, namely, the Pareto optimal solution set. In the present invention, the control problem of the variable frequency centrifugal unit involves three interrelated and even conflicting objectives: energy consumption, vibration and temperature. The traditional single-objective optimization method is difficult to balance these objectives, while the advantage of the NSGA-II algorithm is that it can gradually approach the optimal trade-off point between multiple objectives through the evolutionary process of the genetic algorithm. In the context of the present invention, the application of the NSGA-II algorithm first initializes a population containing multiple candidate control strategies, which represent different variable frequency centrifugal unit control inputs. In each iteration, the algorithm generates new candidate strategies through genetic operations such as selection, crossover and mutation. These strategies are evaluated based on the energy consumption, vibration and temperature objective functions in the multi-objective optimization model. NSGA-II adopts the concept of non-dominated sorting, and sorts the candidate solutions according to the Pareto optimal criterion, that is, if a solution is not inferior to another solution in all objectives, it is considered to be non-dominated. Through this sorting mechanism, the algorithm can find a balance point between multiple objectives, namely the Pareto frontier, where the solution on this frontier is the optimal compromise between multiple objectives. During the optimization process, NSGA-II also avoids the algorithm from falling into the local optimal solution by retaining the diversity of the population. This is achieved through the crowding distance sorting mechanism, which calculates the distribution of solutions to ensure that the solution set is evenly distributed in the multi-objective space, thereby improving the algorithm's ability to find the global optimal solution. For variable frequency centrifugal units, this diversity is very important because the operating state of the system may change at any time, and the optimization strategy must be flexible and adaptable to cope with different operating conditions. In practical applications, the multiple Pareto optimal solution sets generated by the NSGA-II algorithm represent different control strategies, and the differences between these strategies reflect different trade-offs between energy consumption, vibration and temperature objectives. The Pareto frontier solution set obtained by the NSGA-II algorithm not only provides an optimal solution, but also provides a rich selection space for designing actual controllers. According to the current operating conditions of the system, a control strategy suitable for the current optimization needs can be selected from the Pareto frontier solution set. For example, when the system is under high load, a solution that performs better on the vibration target can be selected to ensure the stability of the equipment, while when the load is light, a control strategy with better energy consumption optimization can be prioritized. This multi-strategy selection mechanism based on the Pareto frontier makes the control system of the variable frequency centrifugal unit extremely flexible and adaptable, and can achieve the best operating state under different working conditions. Once the optimal control strategy is determined, the system designs the actual controller through the strategy to achieve real-time control of the unit.The controller generates control signals based on the optimization strategy and adjusts the operating status of the unit, such as adjusting the frequency, load or temperature management parameters to ensure that the unit is always in the optimal operating state. At the same time, the system also has a real-time feedback function, which can dynamically adjust the control strategy according to the actual operating data of the unit. When the state observer feedback system state deviation or change, the controller can quickly adjust the control input to ensure the stable operation of the system under uncertain conditions.

[0050] Embodiment 2: It is characterized in that the operating data includes: frequency converter frequency , variable frequency centrifugal unit pressure , Unit speed ,vibration and temperature ; For time; The control input of time is , and obtain a multidimensional state space for:

[0051] ;

[0052] in, is the preset state transfer matrix; Input matrix for preset control; is the time step.

[0053] Specifically, in this state space model, the system is currently Status From the previous moment Status and the current control input This means that the state of the system is not only affected by the past state, but also depends on the current control strategy. An important feature of this description is its time-varying nature, that is, the state of the system at each moment may be different and may change at different time steps. Through this formula, the present invention can accurately capture the dynamic behavior of the variable frequency centrifugal unit at different time points and respond to different control inputs in a timely manner, thereby achieving multi-objective optimization control. State transfer equation Through the matrix and Describes the relationship between states and the impact of control input on the system. Here, the matrix represents the internal dynamic evolution of the system without external control input. It captures the natural state changes of the centrifuge unit, such as speed changes due to inertia effects or temperature changes due to energy transfer. Therefore, the matrix It is a simplified expression of the inherent dynamic characteristics of the system. It can be pre-set based on the physical characteristics of the equipment and prior knowledge, or obtained by fitting historical operating data, reflecting the evolution law of the system under different states. Control input matrix It is a linear mapping of the system response control input, describing the current control input How to affect the state of the system. In the variable frequency centrifugal unit, the control input It may be the adjustment of the frequency of the inverter, or the optimization of the energy consumption and stability of the system by adjusting the speed of the unit. It plays a bridging role here, mapping the externally applied control quantity to the various state variables of the system, directly reflecting the impact of the control strategy on the operation of the unit. , the system can quickly adjust parameters such as frequency, speed, temperature, etc. according to the real-time optimization control strategy to ensure the stable and efficient operation of the unit. This model of the present invention plays a vital role in multi-objective optimization control, because it can dynamically adjust the system state in real time to ensure that the system achieves the optimal operating state under different working conditions. For example, when the unit is operating under high load, the system may face problems of vibration and temperature rise. At this time, the control input can reduce the vibration amplitude and control the temperature increase by adjusting the frequency or speed. Under low load conditions, the control input can prioritize energy consumption to ensure that the system maintains normal operation with the lowest energy consumption. Through the state transfer matrix in the formula and the control input matrix The system can flexibly respond to different working conditions and achieve multi-objective optimization control. It also plays an important role. It defines the frequency of system status updates, which usually needs to be small enough to ensure that the system can respond to state changes in a timely manner. The choice of depends on the operating characteristics and control requirements of the system. A smaller time step can improve the control accuracy of the system, reduce response delays, and ensure that the system can still maintain stable operation under sudden or rapidly changing conditions.

[0054] Example 3: Dynamic energy consumption model of the variable frequency centrifugal unit defined in step 2 Use the following formula to express it:

[0055] ;

[0056] in, is the preset friction loss coefficient; is the preset modulation index; is the nonlinear coupling term of speed and vibration, is a preset positive number to avoid the singularity of the logarithmic function; A coefficient that represents the vibration energy loss; It is the preset temperature suppression index, which represents the negative feedback effect of temperature on friction loss.

[0057] Specifically, the first term in the formula Emphasized the pressure and speed During the operation of the variable frequency centrifugal unit, the change in pressure is often directly related to the speed, and the impact of these two on energy consumption is significant. By introducing the time derivative of pressure , which not only takes into account the absolute value of pressure, but also describes the contribution of the pressure change rate to energy consumption. The addition further enhances the physical interpretation of the model, since the rotational speed directly affects the power demand of the device. , then the frequency is introduced The nonlinear relationship between pressure and speed captures the fluctuating effect of frequency regulation on energy consumption. Mathematically, the sine function can well describe periodic changes, and physically, it reflects the periodic effect of frequency regulation on the internal operating state of the centrifuge. In general, this term expresses how the changes in pressure and speed over time jointly affect the energy consumption of the system through frequency regulation. Next, the second term in the formula The frequency is introduced With vibration Here, the parameter is the friction loss coefficient, which represents the energy loss caused by mechanical friction in the system. Due to the coupling effect of vibration and speed, mechanical friction will dynamically adjust with the changes in frequency and vibration, resulting in fluctuations in energy consumption. The modulation index Operate with power, the formula describes the nonlinear effect of frequency on friction loss. As the frequency increases, the energy consumption increases nonlinearly, which is consistent with the actual situation, because higher operating frequencies are usually accompanied by more friction and heat accumulation. It is particularly noteworthy that this term also includes This nonlinear term, is a constant used to avoid singularities in the logarithmic function. This term captures the nonlinear coupling effect between speed and vibration, indicating that when the speed and vibration When the speed or vibration changes, the system energy consumption will change in a logarithmic form. The introduction of the logarithmic function enables the model to more effectively describe the impact of smaller vibrations or speed differences on energy consumption. In the case of low frequency or low vibration, this term has little impact on energy consumption, but as the speed or vibration increases, the growth rate of the logarithmic function accelerates, causing the energy consumption to rise rapidly. Therefore, this coupling term adds more complexity and accuracy to the energy consumption model. The third term Pay attention to the rate of change of vibration Impact on energy consumption. Vibration is one of the key factors in the operation of variable frequency centrifugal units. Changes in vibration amplitude and frequency will significantly affect the stability and energy consumption of the equipment. By introducing the square term of the vibration change rate, the model expands the impact of dynamic changes in vibration to reflect the sharp increase in energy consumption when the vibration changes more violently. The coefficient in this term represents the intensity of vibration energy loss, and its magnitude depends on the structural design of the system and the operating environment. The introduction of the square term not only amplifies the impact of vibration changes, but also ensures that the value of this term is always positive, indicating that an increase in vibration will definitely increase energy consumption. The last term Represents the inhibitory effect of temperature on friction loss. It is one of the important variables that affect the operation of the equipment. The increase in temperature usually leads to a change in the friction coefficient of the material, thus affecting the energy consumption performance of the system. The model introduces the negative power term of temperature , describes the negative feedback effect of temperature on friction loss, which means that at high temperatures, friction loss will be relatively reduced. This negative feedback mechanism is consistent with physical reality, because high temperatures will cause thermal expansion of materials and reduce friction. Parameters It represents the sensitivity of temperature to friction loss, and its size can be adjusted according to experimental data.

[0058] Embodiment 4: The vibration dynamics equation of the variable frequency centrifugal unit defined in step 2 is expressed using the following formula:

[0059] ;

[0060] in, It is vibration The fractional derivative of represents the memory effect of the variable frequency centrifugal unit; is the fractional order, ; represents the nonlinear damping effect of vibration, is the damping coefficient, which is used to quantify the effect of damping on vibration; is a positive integer index, indicating the nonlinear degree of speed and pressure coupling. This reflects that when the pressure increases, the effect of the rotation speed on the vibration gradually weakens; is the initial temperature; Indicates from the initial time to the time The time between the frequency conversion centrifugal unit and the vibration It is expressed by the vibration dynamics equation.

[0061] Specifically, the fractional derivative of the vibration is one of the core parts of this formula, which describes the "memory effect" of vibration in the form of fractional calculus. In traditional vibration models, integer-order derivatives are usually used to represent the change of vibration over time, which means that the system only considers the state and its rate of change at the current moment, without involving the state in the past. However, for complex equipment such as variable frequency centrifugal units, vibration is not only affected by the current operating conditions, but also closely related to the historical state. The introduction of fractional-order derivatives can describe this memory effect, indicating that vibration is the result of a cumulative effect, and the past state will have an impact on the current vibration. Parameters Determines the strength of this memory effect. The smaller the value, the greater the impact of the historical state on the current vibration. The closer it is to 1, the weaker the memory effect of the system is, and it mainly depends on the current state. This memory effect is particularly important in centrifugal units that run for a long time, because vibrations are often cumulative, and the operating conditions of the equipment in the early stages may have a significant impact on the stability in the later stages.

[0062] Secondly, the nonlinear damping effect in the vibration dynamics formula is given by Expression. Damping is responsible for dissipating vibration energy in a mechanical system, thereby ensuring the stability of the system. Linear damping terms are often used in traditional models, that is, the damping force is proportional to the vibration velocity. However, this linear assumption often cannot fully capture the nonlinear characteristics of high-frequency vibrations in practical applications. By adopting the square root form of the vibration velocity, the formula of the present invention can better describe the nonlinear damping behavior under high-frequency vibrations. Especially when the variable frequency centrifugal unit is running at high speed, the damping does not increase linearly, but presents more complex nonlinear characteristics as the vibration velocity changes. Parameters is used to quantify the strength of this damping effect. The larger the damping coefficient, the stronger the system's ability to suppress vibration. Through this term, the formula can more accurately predict the dissipation rate of vibration, thus providing a more reliable basis for vibration control. Next, the coupling term in the formula The coupling effect of speed and pressure on vibration is described. is one of the key factors affecting vibration. Generally, as the speed increases, the vibration will also increase. However, this coupling term introduces pressure As the pressure increases, the influence of speed on vibration gradually weakens. This reflects the strength of this nonlinear coupling. When running at high load, the pressure inside the centrifugal unit rises, which has a certain inhibitory effect on vibration, which is manifested in the pressure At higher speeds, The influence on vibration is weakened. Through this coupling term, the present invention can more flexibly adjust the vibration control strategy under different operating conditions to ensure that the equipment can still maintain a stable vibration level under high load and high pressure conditions. The last part of the formula is an integral term, which is used to describe the temperature change. Long-term effects on vibration. This term reflects the temperature by accumulating changes in temperature and pressure. With initial temperature How the difference between affects the dynamic behavior of vibration. Temperature often affects the physical properties of materials (such as elastic modulus and friction coefficient) during equipment operation, which in turn affects the performance of vibration. As the temperature rises, the physical properties of the material may change, causing vibration suppression or enhancement effects. Through the integral term, the formula can capture the long-term effect of temperature on vibration, allowing the control system to predict and adjust vibration based on real-time temperature changes. Indicates the speed of pressure change, which together with temperature change has a complex effect on vibration. For example, when the system temperature is significantly higher than the initial temperature When the temperature is too low, the vibration may be attenuated by the feedback effect of temperature.

[0063] Example 5: Temperature distribution model defined in step 2 Use the following formula to express it:

[0064] ;

[0065] The temperature distribution model Indicates at location Place, time Temperature at is the Fourier heat conduction term; is the thermal diffusivity, which describes the thermal conductivity of a material. The larger the thermal diffusivity, the faster the heat spreads; The temperature distribution model The Laplace operator represents the second-order derivative of temperature with space, quantifying the variation of temperature at different spatial locations; It indicates the inhibitory effect of rotation speed on temperature distribution. When it is higher, the convection effect in the variable frequency centrifugal unit is enhanced, resulting in a decrease in the temperature gradient; is the effective length of the variable frequency centrifugal unit; It is the coupling coefficient of frequency, pressure and vibration. It is a dimensionless constant that represents the strength of the nonlinear coupling between these variables. When the frequency and pressure increase, the increase in vibration will lead to a significant increase in temperature.

[0066] Specifically, the core part of the formula is the Fourier heat conduction term . In this item It is the thermal diffusion coefficient, which determines the speed at which heat propagates in the material. The larger the thermal diffusion coefficient, the better the thermal conductivity of the material, and the faster the heat can diffuse from the high temperature area to the low temperature area. For the variable frequency centrifugal unit, this means that if the thermal conductivity of the material is strong, the temperature distribution inside the equipment will be more uniform, reducing the possibility of local overheating. On the other hand, is the second derivative of temperature with respect to space, indicating how the temperature varies at different spatial locations. This term quantifies the presence of temperature gradients—that is, the temperature in some areas changes faster or slower than in other areas. The Fourier heat conduction term provides a basic framework for temperature distribution models, through which we can understand how heat is transmitted at different locations within the system. Next, the formula in Item indicates speed The inhibitory effect on temperature distribution. When the speed is high, the air or liquid inside the variable frequency centrifugal unit will form stronger convection, and the strengthening of convection helps to quickly dissipate heat. This means that when the speed is high, the air or liquid inside the variable frequency centrifugal unit will form stronger convection, and the strengthening of convection helps to quickly dissipate heat. When the speed increases, the temperature gradient of the system will be flattened, the temperature distribution tends to be uniform, and the possibility of local overheating is reduced. Through this item, the present invention can describe the impact of speed changes on temperature, which is very important for optimizing temperature management during control. Especially when running at high load, the increase in speed can significantly reduce the risk of temperature accumulation.

[0067] also, The item reveals the pressure The coupling effect of speed and pressure on temperature distribution. The greater the pressure, the more significant the friction and compression heat, which leads to higher temperature. , which also takes into account the temperature over the length of the unit The sine function is a common tool for describing periodic spatial distributions. Here, it represents the fluctuation of temperature at different locations in the unit. For example, the temperature at both ends of the unit may be different. This term reflects the nonlinear effect of the local pressure change in the system coupled with the speed on the temperature. Another important component in the formula is , which captures the effect of vibration on temperature. Here, is the rate of change of vibration over time, indicating that changes in the intensity of vibration will have a direct impact on temperature. The more intense the vibration, the greater the loss of mechanical energy, which is often released in the form of heat, causing the temperature to rise. By introducing the logarithmic function The model also reflects the coupling relationship between temperature and vibration. The logarithmic function helps to describe the gradual amplification effect of vibration on temperature change, especially when the temperature is close to the initial temperature. When the temperature is significantly higher than The effect of vibration is significantly amplified when the temperature is too high. This nonlinear relationship is very practical because at higher temperatures, the physical properties of the material change and vibration may further increase the heat generation. Finally, the formula describes the complex coupling between frequency, pressure, and vibration. Here, frequency Change and pressure and vibration The interaction of and determines the temperature increase. The square form of this term shows that the influence of these variables is nonlinear, and the increase in frequency and pressure will lead to an increase in vibration, which will significantly increase the temperature. This reflects the actual situation: when the operating frequency and pressure of the equipment increase, the friction and collision inside the mechanical system will become more intense, generating more heat. Parameters As a dimensionless constant, it is used to quantify the strength of this nonlinear coupling effect, and its magnitude depends on the specific design and material properties of the system.

[0068] Example 6: The overall objective function of the multi-objective optimization model of the variable frequency centrifuge unit defined in step 2 Use the following formula to express it:

[0069] ;

[0070] in, is the square term of the rate of change of the temperature distribution model, indicating that the energy dissipation of the variable frequency centrifugal unit increases when the temperature is rapidly increased or decreased, and the more drastic the temperature change, the greater the value of the objective function, thus promoting the maintenance of temperature stability during the optimization process; It represents the feedback effect of temperature on frequency, pressure and vibration coupling. When it increases, this item decreases, indicating that under high temperature conditions, the influence of the vibration of the variable frequency centrifugal unit on the objective function will be amplified, thereby reducing the vibration during the optimization process and maintaining the temperature stability; Describes the effects of frequency, speed and pressure on vibration. , speed or pressure When increasing, vibration The nonlinear growth of will be limited by the logarithmic function, reducing its growth rate.

[0071] Specifically, the objective function The term describes the energy consumption With vibration The energy consumption of variable frequency centrifugal units is often closely related to vibration. The greater the vibration, the greater the energy consumption of the system. The effect of vibration is introduced so that when vibration increases, the contribution of energy consumption to the objective function is amplified. This design is intended to force the optimization process to minimize vibration, thereby reducing energy consumption while reducing the destructive impact of vibration on the system. Since vibration not only affects the energy consumption of the system, but may also cause mechanical wear, fatigue or other long-term operating problems, this item acts as a constraint in the optimization process to ensure that the system finds a balance between high energy efficiency and low vibration. Secondly, the objective function includes The term is the square of the rate of change of the temperature distribution model, which represents the magnitude of the temperature change over time. The more drastic the temperature change, the greater the energy dissipation, which is not conducive to the stability of the system. Therefore, through this term, the objective function imposes constraints on the system that heats up or cools down quickly, prompting the optimization algorithm to maintain a stable temperature change. When the temperature fluctuates too much, the value of the objective function will rise rapidly, forcing the optimization process to adjust the control input This design is very important in practical applications, because drastic temperature fluctuations may cause the equipment to overheat or overcool, thus affecting the operating efficiency and safety of the centrifuge unit. The term captures the feedback effect of temperature on frequency, pressure, and vibration. When increases, the value of this item decreases, indicating that under high temperature conditions, the impact of vibration on the objective function will be amplified. Such a design reflects the fragility of the system under high temperature. Temperature increases are often accompanied by increased vibration, and the impact of vibration on the system is more significant under high temperature conditions. Therefore, this item amplifies the impact of vibration under high temperature, prompting the optimization algorithm to reduce vibration, thereby maintaining the stability and safety of the system under high temperature conditions. This mechanism is of great significance in avoiding equipment failure or damage due to excessive temperature. The term describes the frequency , speed and pressure Vibration The nonlinear influence of. With the increase of frequency, speed or pressure, the vibration usually grows nonlinearly, which poses a threat to the stability of the system. However, by introducing the logarithmic function, the growth rate of the vibration is effectively controlled. The characteristic of the logarithmic function is that it can limit the rapid growth of the input value, thereby suppressing the sharp increase of vibration during the optimization process and ensuring that the system remains stable at high frequency, high speed or high pressure. Especially in actual industrial applications, centrifugal units usually need to work under high load and high speed, so effectively suppressing the nonlinear growth of vibration is crucial to the long-term operation of the equipment. In addition, The term is an important supplement in the optimization model. It further strengthens the constraint of the objective function on vibration control through the coupling effect of frequency, pressure and vibration. and pressure When increasing, vibration The influence of becomes more significant, and the square form of this term amplifies this effect, prompting the system to pay more attention to vibration control during the optimization process. is a dimensionless constant used to quantify the strength of this coupling effect. By introducing this term, the system can effectively suppress vibration under the combined effect of multiple coupling factors, thereby improving the overall stability of the system.

[0072] Example 7: The collaborative control optimization rule in step 3 is expressed using the following formula:

[0073] ;

[0074] in, is the preset feedback gain matrix; is the initial control input.

[0075] Specifically, the formula Indicates that based on the current state Here, is the preset feedback gain matrix, which determines how the system adjusts the control input in different states Feedback control is a common strategy in industrial control systems. Feedback to the controller can dynamically adjust the system input to ensure that the system's operating state always remains within the expected range. The function of negative feedback is to amplify or reduce the state error of the system, thereby generating corresponding control actions. The form of indicates that when the system state deviates from the target, the controller will make timely adjustments through the feedback mechanism to suppress the system deviation and pull it back to the desired state. This feedback mechanism is the core of the entire control system, ensuring that the system can still maintain stable operation under various disturbance conditions. Secondly, the formula is the initial control input, which indicates the system at time The initial control input is usually set based on the initial estimation of the system, which provides an initial state for the system to start. As the system runs for a certain period of time, the feedback mechanism and subsequent optimization parts will gradually take over the control tasks and adjust the control input To adapt to the actual operating conditions. Initial control input The selection of is very important for the system startup and initial stability. A reasonable initial value can reduce the fluctuation and oscillation in the startup phase. Next, the integral term in the formula is the key part of the collaborative control optimization law, which captures the objective function Status The partial derivative of the objective function is the gradient of the objective function with the state change. This gradient indicates how the system's control strategy affects the results of multi-objective optimization, thus providing a basis for the dynamic adjustment of the control input. By calculating the rate of change of the objective function with respect to the state, the controller can optimize the control input in real time according to the current state change of the system. This integral term reflects the system's The control strategy for the current moment , it combines the historical control effect with the current state feedback to achieve global collaborative optimization. The physical meaning of this item is that during the continuous operation of the system, its control strategy should be adjusted as the state changes, and this adjustment does not depend solely on the state information at the current moment, but is based on the global optimization result of the objective function. In this way, the system can balance the conflicts between different objectives, such as energy consumption, vibration, and temperature control, within the framework of multi-objective optimization. Therefore, the introduction of the integral term provides the system with a temporal collaborative control mechanism, enabling the system to gradually optimize its own control strategy and adapt to changes in different working conditions. The main goal of collaborative control optimization is to ensure that the control input of the system can not only stabilize the operation of the system, but also optimize multiple performance indicators. In variable frequency centrifugal units, these performance indicators usually include energy consumption, temperature, and vibration. By optimizing the objective function , the system can meet these performance goals at the same time. The design of the integral term ensures that the system can gradually correct the control strategy according to the state information of the previous time in each time step, so as to achieve the global optimum. This optimization strategy can effectively prevent the system from falling into the local optimum and ensure that the global optimal control strategy can still be found under complex working conditions. Compared with traditional control methods, the collaborative control optimization law of the present invention achieves a more efficient control effect by combining feedback control with objective function optimization. Traditional methods usually rely on pre-set control laws and are difficult to adapt to complex, multi-objective optimization requirements. The present invention uses the feedback matrix Combined with the objective function gradient, the control system can make adaptive adjustments in a dynamic environment to ensure the system's operating efficiency and stability. At the same time, the introduction of the integral term also enhances the controller's memory of historical states, allowing the system to make more precise adjustments based on past operating results. will be generated dynamically through real-time calculation, and the feedback gain matrix The setting can be adjusted according to the physical characteristics and design requirements of the system. The calculation of the objective function gradient ensures that the system can gradually approach the optimal control strategy. Through this collaborative control mechanism, the variable frequency centrifugal unit can maintain the optimal operating state under different working conditions, achieving the goals of minimum energy consumption, minimum vibration and stable temperature.

[0076] Example 8: The state observer constructed in step 3 Calculated by the following formula:

[0077] ;

[0078] in, is the observer gain matrix; is the observation matrix; is the output of the variable frequency centrifugal unit; the state observer The status of the variable frequency centrifuge unit as a real-time estimate.

[0079] Specifically, this formula constructs a feedback mechanism through the state estimation method, which enables the system to The state observer is introduced to make real-time and accurate estimates, thereby enhancing the performance of the control system. The global state of the system is estimated by using the dynamic model of the control system. This estimation is particularly critical in complex systems such as variable frequency centrifugal units, because some states may not be obtained through direct measurement, or the measurement may be noisy and delayed. First, the observation matrix in the formula Used to convert the actual status With output Usually, the output of the system is measured by sensors, and the state It contains all the internal variables of the system, including speed, pressure, vibration, etc. Some variables in these states may not be directly measured, so the matrix Relate these unmeasurable states to measurable outputs. Represents the observation matrix From the status Projected onto the output model, this term describes how the state affects the output of the system. Next, the observer gain matrix It is the key to the entire observer design. The gain matrix The error correction speed used to adjust the state estimate determines the observer's sensitivity to state errors. The state observer continuously adjusts its estimate through a feedback mechanism to get as close to the actual system state as possible. The error term in the formula Indicates the measurement output The output of the observer estimate The difference between the two, this error reflects the deviation between the observer and the real system. The observer's state estimate is corrected based on this error. When the error is large, This error will be amplified, causing the observer's estimate to adjust quickly; when the error is small, the adjustment is relatively gentle. This feedback mechanism ensures that the observer can dynamically adapt to changes in the system and achieve real-time and accurate estimation of the state. is the observer's estimate of the system output. The state observer uses the estimated state at the current moment and the observation matrix , and estimate the output of the system and compare it with the actual output for comparison. This error feedback mechanism can not only dynamically correct the state estimate, but also filter out the influence of sensor noise and external interference on the system output, thereby improving the estimation accuracy. The design of the observer combines the system output with the internal state model, so that when some states of the system cannot be measured or measured inaccurately, it can still achieve accurate estimation of the global state of the system. Especially in complex industrial systems such as variable frequency centrifugal units, the actual measuring equipment may be affected by noise, delay or error, and it is often unrealistic to directly obtain all state information. Therefore, the introduction of the state observer greatly improves the controllability and reliability of the system. By correcting the state estimate in real time, the observer ensures that the system can respond quickly to external changes under different operating conditions and enhances the robustness of the entire system. At the same time, the construction of the state observer also provides data support for multi-objective optimization control. In multi-objective optimization control, the actual state of the system is an important basis for the optimization algorithm decision-making. Through the state observer , the control system can obtain accurate state estimates even when it cannot directly measure all states, and then use these estimates to adjust the control inputs during the optimization process. , ensuring that the system runs in the optimal state. The design of the observer also provides an important guarantee for the real-time control of the system. Whether in high-frequency vibration control, temperature management or energy consumption optimization, the state observer can output the real-time Providing accurate state estimation enables the controller to make adjustments based on accurate state information. This not only reduces the reliance on sensor accuracy, but also enhances the system's operational stability in uncertain environments. Compared with traditional control methods, the state observer of the present invention introduces the observation matrix and the gain matrix Dynamic feedback control is realized, which significantly improves the adaptability and response speed of the system. Traditional control methods often rely on accurate state measurement, but in actual industrial environments, direct measurement is often subject to various physical limitations and interferences. Through the design of the state observer, the present invention can still accurately estimate the system state in the absence of direct measurement, providing a more flexible and reliable solution for the optimization of the control system.

[0080] Embodiment 9: In step 4, the optimization problem is iteratively solved by non-dominated sorting genetic algorithm II to find the Pareto optimal solution between multiple performance objectives and obtain the optimal control strategy; the formula for iterative solution is:

[0081] ;

[0082] in, For the The control input of the previous generation And the overall objective function of the previous generation Gradient Make updates; is the learning rate or step size coefficient, which controls the adjustment amplitude of the control input in each iterative solution; For the The optimal control input is determined by judging the convergence of the control input. If the change in the control input If it is less than the preset threshold, it is considered to have converged and the optimal control input is output ; The implementation formula of the controller is:

[0083] ;

[0084] in, is the control input for the next moment, and the optimal control input after optimization is Update with feedback adjustments; is the optimal control input obtained by iterative solution; To provide feedback adjustment, use the current multidimensional state space and estimated status of variable frequency centrifugal unit Adjust the difference between is the feedback adjustment coefficient, which controls the impact of the feedback term.

[0085] Specifically, the principle of Example 9 is to iteratively solve the multi-objective optimization problem of the variable frequency centrifugal unit through the non-dominated sorting genetic algorithm II (NSGA-II), aiming to balance the conflicts between multiple performance objectives, and finally find the Pareto optimal solution of the system and output the optimal control strategy. This process not only relies on the evolutionary optimization mechanism of the genetic algorithm, but also realizes the dynamic optimization control of the complex system through iterative adjustment of the control input, state estimation feedback, gradient descent and learning rate regulation. The multi-objective optimization control method in the present invention combines the multi-dimensional state space and multi-performance indicators of the centrifugal unit to ensure that the system can simultaneously achieve the best energy consumption, temperature stability and vibration suppression effect under various operating conditions. The introduction of NSGA-II is to provide an effective solution when facing multiple conflicting objectives. For variable frequency centrifugal units, the optimization control problem usually involves multiple competing objectives, such as minimizing energy consumption, temperature control and reducing vibration. Traditional single-objective optimization methods can often only focus on optimizing a specific performance, while ignoring the optimization requirements of other performances, which easily leads to a decline in the overall performance of the system. As a multi-objective optimization algorithm, NSGA-II can find a balance point between multiple performance objectives through an evolutionary mechanism to form a Pareto optimal solution set. A Pareto optimal solution means that there is no other solution that can be better than the current solution in all objectives at the same time, thus ensuring that no objective is excessively sacrificed during the multi-objective optimization process. In order to achieve this optimization process, the iterative update formula of the control input is the core of the optimization system. Through the control input in the formula , the system can gradually adjust the control input of each generation to move towards a better objective function Direction of development. Gradient It describes the direction of the impact of the current control input on the objective function, that is, how an increase or decrease in the control input will affect the multi-objective performance of the system in the current state. By calculating this gradient, the system can identify the optimal adjustment direction and adjust the control input in each generation of iteration. This adjustment strategy ensures the directionality of the optimization and enables the system to quickly converge to the Pareto frontier solution, that is, a set of optimal solutions that achieve balance in multi-objective optimization. Learning rate It plays an important regulatory role in this optimization process. The learning rate controls the adjustment range of each generation of control input, and its setting directly affects the speed and convergence of optimization. Too large a learning rate may cause the system to overshoot or oscillate during the optimization process, that is, the change in the control input is too large and it cannot stably converge to the optimal solution; while too small a learning rate will make the optimization process too slow and increase the computational cost. Therefore, choosing a suitable learning rate is crucial to the efficiency and effect of the optimization control process. In the variable frequency centrifugal unit control of the present invention, the setting of the learning rate is usually adjusted according to the dynamic characteristics of the system and the actual operating requirements to ensure that the system can find the global optimal solution within a reasonable time range. The convergence of the control input is a key judgment criterion in the iterative optimization process. In each generation of iteration, the change in the control input is calculated. , it can be determined whether the system has converged to the optimal solution. If the change in the control input is less than a preset threshold, it means that the control input of the current iteration is close enough to the optimal solution, and the system optimization process can be stopped. At this point, the system believes that the optimal control input has been found. This judgment mechanism can effectively avoid lengthy iterative calculation processes and ensure that the control input of the system achieves the optimal balance in the multi-objective optimization process. Find the optimal control input After that, the next step of the system is to adjust the control input through feedback to make it more suitable for the actual operating state of the system. The implementation formula of the controller is , where the feedback adjustment term is introduced , used to correct the actual state of the system and estimated state The feedback adjustment mechanism ensures that the system can adjust the control strategy in real time in a complex dynamic environment, thereby improving the robustness and stability of the control system. Multidimensional state space Represents the actual operating status of the variable frequency centrifugal unit, including key physical quantities such as system speed, pressure, temperature, vibration, etc. is the estimated value of the system state through the state observer. Since the actual measured state may be disturbed by noise, sensor error, etc., the estimated value of the observer Possible and actual status By introducing feedback adjustment items, the system can adjust the optimal control input according to these deviations. Make real-time corrections so that the control input at the next moment More accurate and reliable. The introduction of this feedback mechanism enhances the system's ability to adapt to external disturbances, ensuring that the system can maintain the optimal operating state even under complex and dynamic conditions. Feedback adjustment coefficient Controls the strength of the feedback term, which directly affects the magnitude of the feedback adjustment. Will make the feedback adjustment faster, and the system can correct the state error faster; while the smaller This means that the feedback adjustment is gentler and the system correction process will be smoother. It can be adjusted dynamically to adapt to different operating conditions. In the actual operation of the variable frequency centrifugal unit, the system usually operates under different loads, frequencies and environmental conditions, so a flexible feedback adjustment mechanism is required to ensure the stability and optimization effect of the system. In general, the principle of Example 9 realizes the multi-objective optimization control of the variable frequency centrifugal unit through the combination of the NSGA-II optimization algorithm and the control input feedback adjustment. This process not only depends on the iterative update of the control input, but also continuously adjusts the optimal solution through the feedback mechanism, so that the system can simultaneously achieve multiple goals such as minimization of energy consumption, temperature stability and vibration suppression under the multi-objective optimization framework. The introduction of the NSGA-II algorithm enables the system to find the best balance between multiple conflicting goals, and the feedback adjustment mechanism ensures the accuracy and reliability of the system in actual operation. Compared with traditional control methods, the optimization control method of the present invention has higher flexibility and adaptability. Traditional methods can usually only optimize for a single target, while ignoring the optimization requirements of other performance indicators. The present invention can optimize multiple targets at the same time through the NSGA-II algorithm, and realizes real-time control of complex dynamic systems through gradient descent and feedback adjustment. In addition, the flexible adjustment of the learning rate and feedback adjustment coefficient enables the system to adapt to different operating conditions, further improving the robustness of the control strategy.

[0086] The present invention is described in detail above. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A multi-objective optimization control method for a variable frequency centrifugal unit, characterized in that: The method comprises: Step 1: define the multidimensional state space of the variable frequency centrifugal unit, collect the operating data of the variable frequency centrifugal unit at each time, and take each operating data and control input as an element in the multidimensional state space; Step 2: Define the energy consumption dynamic model, vibration dynamics equation and temperature distribution model of the variable frequency centrifugal unit; combine the energy consumption dynamic model, vibration dynamics equation and temperature distribution model to define the total objective function of the multi-objective optimization model of the variable frequency centrifugal unit; Step 3: Based on the total objective function, the collaborative optimization control law of the variable frequency centrifugal unit is obtained through variational method and iterative optimization; a state observer is constructed to estimate the state of the variable frequency centrifugal unit in real time; Step 4: Iteratively solve the optimization problem through non-dominated sorting genetic algorithm II to obtain the optimal control strategy; according to the optimal control strategy, design the actual controller of the variable frequency centrifugal unit to achieve real-time control and make real-time adjustments according to feedback; the operating data includes: frequency converter frequency , variable frequency centrifugal unit pressure , Unit speed ,vibration and temperature ; For time; The control input of time is , and obtain a multidimensional state space for: ； in, is the preset state transfer matrix; Input matrix for preset control; is the time step; the energy consumption dynamic model of the variable frequency centrifugal unit defined in step 2 Use the following formula to express it: ； in, is the preset friction loss coefficient; is the preset modulation index; is the nonlinear coupling term of speed and vibration, is a preset positive number to avoid the singularity of the logarithmic function; A coefficient that represents the vibration energy loss; is the preset temperature suppression index, which indicates the negative feedback effect of temperature on friction loss; the vibration dynamics equation of the variable frequency centrifugal unit defined in step 2 is expressed using the following formula: ； in, It is vibration The fractional derivative of represents the memory effect of the variable frequency centrifugal unit; is the fractional order, ; represents the nonlinear damping effect of vibration, is the damping coefficient, which is used to quantify the effect of damping on vibration; is a positive integer index, indicating the nonlinear degree of speed and pressure coupling. This reflects that when the pressure increases, the effect of the rotation speed on the vibration gradually weakens; is the initial temperature; Indicates from the initial time to the time The time between the frequency conversion centrifugal unit and the vibration Represented by vibration dynamics equations; temperature distribution model defined in step 2 Use the following formula to express it: ； The temperature distribution model Indicates at location Place, time Temperature at is the Fourier heat conduction term; is the thermal diffusivity, which describes the thermal conductivity of the material; the larger the thermal diffusivity, the faster the heat spreads; The temperature distribution model The Laplace operator represents the second-order derivative of temperature with space, quantifying the variation of temperature at different spatial locations; It indicates the inhibitory effect of rotation speed on temperature distribution. When it is higher, the convection effect in the variable frequency centrifugal unit is enhanced, resulting in a decrease in the temperature gradient; is the effective length of the variable frequency centrifugal unit; is the coupling coefficient of frequency, pressure and vibration, which is a dimensionless constant and represents the nonlinear coupling strength between these variables. When the frequency and pressure increase, the increase of vibration will lead to a significant increase in temperature. The total objective function of the multi-objective optimization model of the variable frequency centrifugal unit defined in step 2 is Use the following formula to express it: ； in, is the square term of the rate of change of the temperature distribution model, indicating that the energy dissipation of the variable frequency centrifugal unit increases when the temperature is rapidly increased or decreased, and the more drastic the temperature change, the greater the value of the objective function, thus promoting the maintenance of temperature stability during the optimization process; It represents the feedback effect of temperature on frequency, pressure and vibration coupling. When it increases, this item decreases, indicating that under high temperature conditions, the influence of the vibration of the variable frequency centrifugal unit on the objective function will be amplified, thereby reducing the vibration during the optimization process and maintaining the temperature stability; Describes the effects of frequency, speed and pressure on vibration. , speed or pressure When increasing, vibration The nonlinear growth of will be limited by the logarithmic function, reducing its growth rate; the collaborative control optimization law in step 3 is expressed by the following formula: ； in, is the preset feedback gain matrix; is the initial control input.

2. The multi-objective optimization control method of the variable frequency centrifugal unit according to claim 1, characterized in that: The state observer constructed in step 3 Calculated by the following formula: ； in, is the observer gain matrix; is the observation matrix; is the output of the variable frequency centrifugal unit; the state observer The status of the variable frequency centrifuge unit as a real-time estimate.

3. The multi-objective optimization control method of the variable frequency centrifugal unit according to claim 2, characterized in that: In step 4, the optimization problem is iteratively solved by non-dominated sorting genetic algorithm II to find the Pareto optimal solution among multiple performance objectives and obtain the optimal control strategy; the formula for iterative solution is: ； in, For the The control input of the previous generation And the overall objective function of the previous generation Gradient Make updates; is the learning rate or step size coefficient, which controls the adjustment amplitude of the control input in each iterative solution; For the The optimal control input is determined by judging the convergence of the control input. If the change in the control input If it is less than the preset threshold, it is considered to have converged and the optimal control input is output ; The implementation formula of the controller is: ； in, is the control input for the next moment, and the optimal control input after optimization is Update with feedback adjustments; is the optimal control input obtained by iterative solution; To provide feedback adjustment, use the current multidimensional state space and estimated status of variable frequency centrifugal unit Adjust the difference between is the feedback adjustment coefficient, which controls the impact of the feedback term.

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