Research on multi-objective collaborative control of complex product development in equipment manufacturing industry

Equipment manufacturing involves the integration of multiple technologies and is a complex product system. In the independent innovation of complex product systems, product development is the most important way. Multi-objective cooperative control has been applied to various industries with remarkable results. In this paper, high quality research and development of complex products in equipment manufacturing industry is the main goal. Inspired by the dimensional parameters of the key structures of the product and the structure of the endocrine regulation network, a multi-objective collaborative controller consisting of a speed and position coordinator, a module consisting of a speed and position coordinator, a hormone discriminator, a hormone optimizer


Introduction
The equipment manufacturing industry is to provide technical equipment for the national economy and national defense construction the industry.This industry is the basis of national economic development, especially industrial development [1][2][3][4].China's equipment manufacturing industry has long been locked in the low end of the global value chain, leading to its low international competitiveness [5][6][7].The international competitiveness of China's productive service industry is also not high due to its small and fragmented size and the imperfect industrial system [8][9].Achieving the competitiveness of the equipment manufacturing industry and productive service industry, especially achieving the global value chain climbing of the former, has become an important issue in China's economic field [10].Seizing the favorable opportunities of increasing economic globalization and integration, continuous international industrial transfer and international redistribution of labor, enhancing the core competitiveness of the industry and achieving strategic upgrading of the industrial structure and its value chain has become an important development strategy for China at present [11][12][13][14][15].
Scholars from various countries around the world have studied the equipment manufacturing industry of global value chains, and the analysis of the research results obtained presents different situations.The literature [16] proposed that the development of AI technology provides new development opportunities for the transformation and upgrading of the industry.A panel data regression model constructed is used to measure the financing efficiency and influencing factors of the industry.It is proved by the data that the average financing efficiency of the industry is moderate, and external financing has positive and negative effects on the financing efficiency and labor input of enterprises, respectively.The literature [17] formulated the scheduling problem of a multi-energy consuming system in manufacturing as a MLRM and designed an energy management system with an economic and greenhouse gas emission focus.Then, the gray theory is combined with ordinary MLRM and load fluctuation, total cost and environmental pollution value are used as reference standards to measure the effectiveness of the gray optimization method.The MLRM is applied to the optimization of energy supply plans and its performance is verified by numerical examples.The validation results satisfy the conditions for the optimal operation of multi-energy microgrid systems.The literature [18] verified the importance of economic theory in constituting manufacturing outputs and inputs using a factorial model based on the proposed standard model.In addition, the functional structure was defined to adequately represent the manufacturing output of Chile.The literature [19] shows that the equipment manufacturing industry suffers from an irrational industrial structure and high pollution dilemma.Using data from 30 Chinese provinces, a composite pollution indicator was calculated in estimating the potential pollution reduction from industrial structure optimization, and the reasonable level of capital allocation for each province and industry was assessed using nonlinear programming and stochastic frontier methods.The results of the literature [20] show that with the gradual deepening of equipment manufacturing industry participation in the global value chain, the industry deepens its economic low-end lock.From a segmentation point of view, the degree of locking physical location is deepest at the lower end of manufacturing metal products and electrical equipment.The above literature examines issues such as the development of artificial intelligence technology, energy management consumption, industrial structure and high pollution from the perspective of the equipment manufacturing industry.However, none of them mentioned the use and results of multiobjective cooperative control in the development of complex products in the industry.
The process of complex products in the industry has special characteristics, and its R&D process is different from that of mass-produced products.After years of research and development of multiobjective cooperative control, various multi-objective cooperative control strategies have been combined with control algorithms and applied to various industries with great success.Therefore, this paper tries to incorporate multi-objective cooperative control technology in complex products of the equipment manufacturing industry.Correlation analysis of variance data, multi-level uniform description sampling method and Nawaf transformation method is used to extract the key dimensional parameters of complex products.According to the selected relative velocity, distance error between structures or components, acceleration control amount, acceleration change rate, and reference acceleration performance indexes, the multi-objective cooperative controller is designed from the mechanism of speed and position coordinator, hormone discriminator, hormone optimizer, controller and other modules.The research results aim to improve the development quality of complex products in the equipment manufacturing industry and drive the development of the whole industrial economy by enhancing the spillover effect and marginal output of factors in the equipment manufacturing industry.
2 Controller structure design under multi-objective cooperative control study

Dimensional parameter extraction
Correlation analysis of variance data was used to extract key structural dimensional parameters by distinguishing the differences between test results caused by changes in sample values of structural dimensional parameters of complex products from changes in test errors [21][22][23].The sample data of each structural dimensional parameter sampled by the multilevel uniform description sampling method were solved by calculating the statistical matrix of the multiparameter response function after the Nawaf transformation.The correlation coefficient between each initial structural dimension parameter and the response target can be calculated based on the standard deviation and variance values of the response target.Its correlation coefficient R is calculated as [24][25].
The sample standard deviation of The sample standard deviation of Y .
When the value is 0 to 1, the correlation R is positive.When the value is -1 to 0, the correlation R is negative.
According to the calculation of the correlation coefficient formula, the closer the absolute value of R is to 1, the stronger the association between the initial structural dimensional parameters and the response target, and the greater the degree of influence.The closer the absolute value of R is to 0, the weaker the association between the initial structural dimensional parameters and the response target, and the smaller the degree of influence [26].

The utility function and performance indicator function
The utility function, also known as the local cost function, is a very important indicator.It reflects the control effect of each step and must fully reflect the requirements of all aspects of the controlled system, and the utility function can be defined based on the control requirements [27].The performance indicator function is a function that maps one or more performance indicators to a real number that visually represents the "cost" associated with the performance indicator.Relative velocity, distance error between structures or components, acceleration control amount, acceleration rate of change, and reference acceleration are taken as performance metrics, respectively [28][29].Scalar-valued utility functions and multi-objective performance indicator functions ( 4) and ( 5) are defined according to Eqs. ( 2) and (3). Where  is the corresponding weight factor and   u k is the acceleration control quantity output by the controller.

Multi-objective cooperative control model
According to the endocrine system regulation structure inspired by the structure size parameters of complex products in the equipment manufacturing industry, a multi-objective collaborative controller is proposed.The multi-objective synergistic controller is mainly designed in terms of the mechanism of the modules such as speed and bit coordinator, hormone discriminator, hormone optimizer and controller.

Speed and bit coordinator
Set speed Set location Where r denotes the distance between the real position to the target position.
C r is a set distance constant to indicate the switch from the bit-velocity regulation mode to the bit-position regulation mode when the controlled object runs to a certain position.Thus the speed and bit cooperative algorithm of the cooperative unit can be designed as: Here, Where   1 U t is the output of the synergistic unit, and the position error signal        is a position switching factor.

C
K is a conversion factor to eliminate the instability of the control signal jump during the switching from bit-rate regulation mode to bit-position regulation mode.(2) Initial PID controller.The IOCU uses a PID controller as the main controller module, and its control parameters are optimized by a hormone discriminator and a hormone optimizer.The controller selects the traditional continuous control algorithm.
Where   2 U t is the output signal of the IOCU, i.e., the PID controller.0 j K , , , are the parameter of this controller in the default state.
(3) Hormone discriminator.In the endocrine system, the gland can enhance the recognition ability and control the accuracy of hormone secretion within the working range.When the stimulus signal exceeds its recognition limit, the hormone can only be secreted at a certain maximum value.Similarly, the hormone discriminator designed by this method is also in line with this rule.The process is as follows: firstly, solve for the absolute value of parameter   2 e t , and then the error is mapped to the corresponding control range, and when the error exceeds this control range, the maximum value is selected instead.The process of error mapping can be expressed as follows: Here  is the post-mapping error, and max e and min e are the upper and lower limits of the optimal control range of the error, respectively.Next, the hormone up and down-regulation factors are calculated based on the mapped errors.Hormone secretion is usually non-negative and monotonic.Monotonic upward secretion indicates positive control, while monotonic downward indicates reverse control.Therefore, it's rising and falling regulation process is consistent with the Hill function property.The ascending factor Here 1 n and 2 n denote Hill coefficients, respectively.
(4) Hormone improver.If the regulation of hormone A is under the control of hormone B, then the expression of the relationship between them is shown below: Where Applying this regulatory mechanism to the adaptive optimization of controller parameters, the following equation is obtained: Where   S t denotes the real-time optimized value, 0 S denotes the initial value, and H S and L S denote the most suitable upper and lower parameter values corresponding to the error at the upper and lower limit values, respectively.It is noteworthy that Eq. 9 can be expressed as follows when 1 2 n n  in Eq. 14: Ultimately, equation 16 is applied to the controller parameter optimization.For example, when the control   Where denotes the optimized parameter, and denote the upper and lower parameter limits for larger and smaller control errors, respectively.At this point, Eq. 12 is improved as: 3 Multi-objective collaborative control uses effect evaluation

Position/velocity cooperative control
Experimental study of multi-objective cooperative control of position/velocity for complex products.When no controller is added, Fig. 2(a) and Fig. 2(b) show the position and velocity response sinusoidal signal curve, respectively, in which the solid and dashed curves each refer to the input and output signals.The given amplitude of the position signal sinusoidal input is 9mm with a period of 2s, and the given amplitude of the velocity signal is 63.7mm/s with a period of 1s.As can be seen in Fig. 2(a), when no multi-objective cooperative control is implemented, the position output curve of the product vibrates more and has a significant overshoot compared to the given position signal.Moreover, there is a phase lag in the output signal, and even the steady-state deviation is relatively large.In terms of the velocity output curve of the complex product, compared to the given velocity, the vibration and shock are larger, and there are both significant oscillation phenomena, which will also have serious adverse effects on the stability of the overall operating state of the product.In Fig 2(b), the output of product speed deviates from the input curve significantly, because the control signals of both position and speed have a certain correlation, so that when the product position signal changes, the speed control signal will also change.To deeply examine the effect of product position/velocity cooperative control, the following is to add the designed controller to further study it.
Taking the PID parameters of the position control section as [3,1,2], the PID controller does not work at this time.After adding the multi-objective cooperative controller to the speed control section, the parameter of the proportional part (e-input part) is 0.7, the parameter of the differential part (etc.input part) is 0.04, and the parameter of the controller output part is 0.8.
The PID controller does not work when the PID controller is taken as [2,1,3].At this time, the multiobjective co-controller plays the main control role for the velocity control part and the overall cocontrol of position and velocity.When comparing Fig. 2(b) and Fig. 2(a), it is obvious that the velocity output curve of the complex product after adding the multi-objective cooperative controller has significantly improved compared with the velocity output curve of the complex product without adding the controller.The velocity output curve in Fig. 2(b) has been very effectively controlled in terms of the vibration of the velocity signal at all times.While the control effect of the speed control part is improved, the control effect of the position control part is also improved to some extent, but not too obviously, this can be seen by comparing the trend of the curves in the two subplots of Fig 2.
The optimized position control effect is achieved through the synergistic relationship between the velocity and position signals, and the optimization of the velocity signal will inevitably enhance the position signal control capability.

Force/position synergy control
Experimental study of force/position cooperative control of a complex product using a PID controller and a multi-objective cooperative controller.When the multi-objective cooperative controller is not added to the force/position cooperative control process, a given sinusoidal signal is used as input.The position input amplitude of the given sinusoidal signal is 9mm with a period of 2s, and the corresponding force input amplitude is 100N with a period of 2s.Fig 3(a) shows the position and the force response graph for the sinusoidal signal, where the solid line and the dashed line represent the input signal and the output signal.The following two graphs are taken from 4s to 6s, the same as in the position/velocity cooperative control experiments, and the complex product has reached a steady state during this time.At this time, the simulation graphs can better present the actual characteristics of the complex product.It avoids the impact of vibration and shock on the experimental results caused by the instability of the complex product at the beginning of the simulation and the spool not being in the neutral position and the nonlinearity of the complex product.
As can be seen from the fig below, when the controller is not added, the steady-state deviation of the position output curve and the force output curve of the experimental table is very large, and the operation state of the system is not very stable, which will seriously affect the control effect of the complex product in the working process.As can be seen from Fig. 3(b), in the sinusoidal response curve of the force, there is only the upper part and not the lower part.This is because the load part is in intermittent contact with the outside world during the experiment, and the complex product only has force when it is in contact with the outside world.The result is that the force output part of the product is zero when there is no contact between the complex product and the outside world.The multi-objective co-operative controller is used to control the force of the product, the parameters of the PID are taken as [3,1,2], and the PID controller does not work at this time.To make the designed multi-objective cooperative controller effectively control the force control part and reduce the vibration and shock generated by the complex product during the force control process, the parameters of the proportional part (e input part) of this controller are taken as 2, the parameters of the differential part (etc.input part) are taken as 0.05, and the parameters of the output part of the controller are taken as 0.7.The response curves of the position and force control parts of the complex product under sinusoidal signal excitation are shown in Fig. 3(b), where the solid and the dashed curve represent the input signal and the output signal.
Comparing Fig. 3(a) and Fig. 3(b), it is obvious that the force output curve of the complex product with the controller is significantly better than that without the controller, and the vibration and shock in the force output signal are significantly suppressed, and the steady-state deviation of the complex product is significantly reduced.It shows that the designed multi-objective cooperative control model has a good control ability on the vibration and shock phenomenon in the force control process.

Multi-objective distributed cooperative control experiment for complex products
In this section, platform experiments are conducted for implementing a multi-objective distributed cooperative control method.The radius of connectivity is chosen as , the radius of collision avoidance , the radius of untouchable area 0.07 , and the controller parameters as 0.03 . The black curve corresponds to the number one component of the complex product, specified as the navigator, and the number two and three components correspond to the blue and red curves, respectively.The part trajectory fitting curves are given, and it can be seen that both the red and blue curves of the follower appear jittered on the left side of the trajectory plot so that the follower trajectory is always constrained by connectivity with the navigator.The result can be seen that the distance between the No. 2 component and the navigator is always smaller than the connectivity radius 1.When the obstacle enters the collision avoidance range 2, the collision avoidance constraint is effective so that the distance between the part and the obstacle is always greater than z d .Therefore, it is concluded that this collaborative controller can achieve the optimization and improvement of the control index of complex products.

Conclusion
In this paper, the key structural dimensional parameters of complex products are extracted from multiobjective cooperative control research.A multi-objective collaborative controller is designed based on the utility function and performance index function, combined with the controller structure inspired by the endocrine regulatory network structure.Experimental research on position/velocity and force/position cooperative control for complex products, and multi-objective distributed cooperative control experiments for three components of a product.When the controller parameters [3, 1, 2], the speed control proportional parameter is 0.7, the differential parameter is 0.04, and the controller output parameter is 0.8.Force control proportional parameter 2, differential parameter 0.05, controller output parameter 0.7.The experimental curves of synergistic control of displacement/velocity and force/position illustrate that the controller has good control over the overall position and velocity of the product, as well as the vibration and shock phenomena that occur during force control.Of the three components, the navigator moves in a uniform circular motion or uniform linear motion at [ 1 ,  1 ]  = [0.06,0.09] .Vector form  2 = [0.4,0.4] ,  3 = [−0.1,0.2] .Both the red and blue curves of the follower show jitter so that the follower trajectory always maintains connectivity constraints with the navigator and the follower shows good tracking performance.The controller provides good distributed and cooperative control of multiple components of complex products.

Figure 1 .
Figure 1.Structure of multi-objective cooperative controller system.(1) Synergy unit.The synergy unit contains a speed/bit coordinator, capable of receiving the set velocity signal   in V t , the set position signal   in P t and the real-time position signal   P t , and switch t indicates the switching moment point of the control strategy.

C
denote the secretion rate and solubility of the two hormones, respectively.0 A S denotes the initial secretion rate of hormone A, and the  

2 e t error1 is large, the initial proportional gain factor 0 PKKK
should be decreased toward H P K to moderate the control drive to reduce overshoot.Conversely, when   quickly to eliminate the error and improve control accuracy.The initial integral 0 differential coefficients have a similar tuning pattern.The parameter optimization adjustment process can be expressed as follows:

( a )Figure 2 .
Figure 2. The experimental curve of displacement/velocity cooperative control.

( a )Figure 3 .
Figure 3.The experimental curve of force/position cooperative control.

Figure 4 .
Figure 4. Experimental data of circular trajectory tracking by parts.
fitting curves for the three components to achieve circular trajectory tracking experiments are given in Fig [ 1 ,  1 ]  = [0.06,0.09] .The navigator moves in a uniform circular motion with 1.The expected formation is in vector form  2 = [0.4,0.4] , and the expected value is represented by the pink line in Fig 4.

Figure 5 .Finally
Figure 5.The fitting curve of experimental data of linear trajectory tracking realized by parts