Ultra-high-precision aerodynamic force servo system and intelligent control parameter optimization method therefor

Abstract

An ultra-high-precision aerodynamic force servo system and an intelligent control parameter optimization method therefor. The aerodynamic servo system is mainly composed of a double-acting air-floating friction-free cylinder (10) and a pressure control system. The effect of friction on the output force control precision can be removed by using the air-floating friction-free cylinder (10); in the pressure control system, ultra-high-precision control over the pressure is realized by means of a fuzzy PI controller optimized on the basis of a new improved particle swarm algorithm; a Gaussian mutation policy and a fuzzy control theory are fused in the new improved particle swarm algorithm; and optimized fuzzy PI control parameters are obtained by using the new improved particle swarm algorithm, ultra-high-precision pressure control over a cavity of the air-floating friction-free cylinder (10) is executed on the basis of the parameters, and an ultra-high-precision force output of the system can be realized. The aerodynamic force servo system can be applied to occasions with very high requirements for force control precision, and expands the application range of the aerodynamic force servo system.

Description

An ultra-high-precision pneumatic servo system and intelligent optimization method for its control parameters Technical Field

[0001] The present invention belongs to the field of pneumatic technology, and in particular relates to an ultra-high precision pneumatic servo system and an intelligent optimization method for control parameters thereof. Background Art

[0002] With the advancement of technology, force servo systems have found widespread application in the industrial field. Currently, high-precision force servo systems typically use electric cylinders as actuators. In pneumatic servo systems, the complex friction generated by conventional cylinders during movement results in low precision control of pneumatic output force. To address this issue, existing technologies, such as those in the literature "Research on Frictionless Cylinders and High-Precision Pneumatic Load Systems," "Research on Key Technologies for Zero-Gravity Environment Simulation Pneumatic Suspension Systems," and patent CN113700696B, have proposed novel air-floating frictionless cylinders with various structures. These cylinders exhibit extremely low friction and, in theory, are capable of high-precision pneumatic output force control. However, these cylinders are single-acting and can only achieve a single force output. The present invention proposes to employ the double-acting air-floating frictionless cylinder disclosed in Chinese patent application number 201711223571.1 as the actuator for a pneumatic servo system. Due to its independent air supply, the cylinder maintains a frictionless state during switching, enabling high-precision alternating thrust and pull output. In view of the use of air-floating frictionless cylinder, the output force of the cylinder can be equivalent to the pressure control in the cylinder cavity.

[0003] Fuzzy PI control offers advantages such as simple algorithms, efficient control, and robustness. Therefore, the present invention proposes to employ a fuzzy PI control algorithm to achieve high-precision pressure control. However, in practical applications, the selection of fuzzy PI controller parameters often relies on a trial-and-error approach. This results in a significant degree of randomness in the selection, making it difficult to select more precise parameters and resulting in low control accuracy. Currently, simple manual random parameter adjustment is no longer sufficient to meet the demands of high-precision or even ultra-high-precision control. The rapid development of swarm intelligence algorithms has provided an intelligent approach to complex parameter adjustment, namely, finding an optimal set of parameters through multiple iterations to achieve the most satisfactory control results. Ant colony algorithms, genetic algorithms, and particle swarm algorithms are relatively common swarm intelligence algorithms. Among them, the particle swarm algorithm, with its advantages of simplicity and ease of implementation and a small number of adjustment parameters, has been widely used in the optimization field and can address the parameter selection problem of fuzzy PI controllers. However, traditional particle swarm algorithms cannot effectively balance global and local search, and particles may become trapped in local optima and be unable to effectively escape, which seriously affects optimization efficiency and accuracy.

[0004] Therefore, how to provide an ultra-high precision pneumatic servo system and an intelligent optimization method for its control parameters is an urgent problem that needs to be solved by those skilled in the art.

[0005] Summary of the Invention

[0006] The purpose of the present invention is to break the conventional concept that pneumatic actuator systems cannot achieve ultra-high precision pneumatic output force control. To this end, an ultra-high precision pneumatic servo system and an intelligent optimization method for its control parameters are provided.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] An ultra-high-precision pneumatic servo system, characterized in that it includes an actuator module, a pressure control module, an air source module and an air supply module; the actuator module is a double-acting air-floating frictionless cylinder; the pressure control module includes an industrial computer, a data acquisition card, a three-position five-way solenoid valve, a two-position three-way solenoid valve 1, a two-position three-way solenoid valve 2, a high-precision pressure sensor 1, a high-precision pressure sensor 2, a small gas tank 1 and a small gas tank 2; the air supply module includes a pressure reducing valve 1, a pressure reducing valve 2, a small gas tank 3, a small gas tank 4, an air dryer and a precision filter; the air source module includes an air source, a pressure reducing valve 3 and a large air tank;

[0009] The compressed air generated by the air source is transported to the large air tank through the third action of the pressure reducing valve to provide compressed air for each pneumatic branch; the pressure reducing valve 1, the small air tank 3, the air dryer and the precision filter form the branch 1 to supply air to the air bearing of the air-floating frictionless cylinder, and the pressure reducing valve 2 and the small air tank 4 form the branch 2 to supply air to the air-floating piston of the air-floating frictionless cylinder, so that the air-floating frictionless cylinder can work normally;

[0010] The upstream of the three-position five-way solenoid valve is connected to the large gas tank as branch three; the two interfaces of the three-position five-way solenoid valve are connected to the small gas tank one and the small gas tank two respectively through the two-position three-way solenoid valve one and the two-position three-way solenoid valve two; the small gas tank one and the rodless cavity of the air-floating frictionless cylinder constitute the controlled cavity one, and the small gas tank two and the rod cavity of the air-floating frictionless cylinder constitute the controlled cavity two; the high-precision pressure sensor one and the high-precision pressure sensor two respectively feed back the pressure information in the cavity one and the cavity two to the industrial control computer through the data acquisition card, and the industrial control computer executes its own fuzzy PI control algorithm and outputs the voltage signal to the three-position five-way solenoid valve through the data acquisition card.

[0011] Furthermore, the maximum valve port opening of the two-position three-way solenoid valve 1 and the two-position three-way solenoid valve 2 is greater than or equal to the maximum valve port opening of the three-position five-way solenoid valve.

[0012] Furthermore, the inner diameters of all air pipes between the three-position five-way solenoid valve and the air-floating frictionless cylinder cavity are larger than the diameters of the two-position three-way solenoid valve one, the two-position three-way solenoid valve two and the three-position five-way solenoid valve.

[0013] The method for intelligently optimizing control parameters of an ultra-high-precision pneumatic servo system is characterized in that small gas tank 1 and the rodless cavity of the air-floating frictionless cylinder constitute controlled cavity 1, small gas tank 2 and the rod cavity of the air-floating frictionless cylinder constitute controlled cavity 2, high-precision pressure sensor 1 and high-precision pressure sensor 2 respectively feed back pressure information in cavity 1 and cavity 2 to an industrial computer via a data acquisition card, and the industrial computer executes its respective fuzzy PI control algorithms and outputs a voltage signal to a three-position five-way solenoid valve via the data acquisition card; the method is characterized in that the control parameters of the fuzzy PI control algorithm are optimized by a new improved particle swarm algorithm in the following steps:

[0014] S1: Construct a fuzzy PI pressure controller and determine the variables to be optimized;

[0015] S2: Determine the search space of the variables to be optimized by trial and error;

[0016] S3: Determine the objective function in the optimization process;

[0017] S4: Iterative optimization using a new improved particle swarm algorithm;

[0018] S5: Cavity 1 and cavity 2 are respectively taken as controlled objects, and their respective optimized fuzzy PI control parameters are optimized.

[0019] Furthermore, the objective function in step S3 is selected as follows: in the rising stage of the system step response, it is set to the first T1 second, and the ITAE evaluation index function is used; when the system enters the steady-state stage, it is set to T1 to T2 seconds, and the ITSE evaluation index function is used. The specific expression is:

[0020] Where: f is the objective function; t is time; e is the pressure control error.

[0021] Furthermore, it also includes incorporating a penalty function into the objective function, as follows: if a particle has not completed the rising stage of the system step response after T1 seconds, the current control is stopped and the particle is sentenced to "death", that is, the particle is given an extremely poor fitness value; when the input voltage of the three-position five-way solenoid valve reaches 0V or 10V three times, it is determined that the system is oscillating at this time, and the current control is stopped and the particle is sentenced to "death".

[0022] Furthermore, the iterative optimization process in step S4 is as follows:

[0023] S41: Set the basic parameters of the new improved particle swarm optimization algorithm and initialize it;

[0024] S42: Randomly initialize particle position and velocity vectors in the search space;

[0025] S43: Calculate the fitness value of each particle;

[0026] S44: Compare the fitness values ​​to obtain the individual historical optimal particle position and the global optimal particle position;

[0027] S45: Update particles using the velocity update formula and the new position update formula;

[0028] S46: Check whether each particle has crossed the boundary. If so, retain the state of the particle before the update.

[0029] S47: If the number of iterations reaches the maximum number of iterations, proceed to the next step, otherwise proceed to step S43;

[0030] S48: The operation ends and the optimized fuzzy PI control parameters are output.

[0031] The speed update formula and the new position update formula in step S45 are as follows:

[0032] Where: is the position of the i-th particle after t iterations; is the individual historical optimal position of the i-th particle after t iterations; is the global optimal position of the entire group after t iterations; is the velocity of the i-th particle after t iterations; is the velocity of the i-th particle after (t+1) iterations; w is the inertia weight; c1 and c2 are the individual learning factor and the social learning factor respectively; r1, r2, r3 and r α are random numbers in the range of [0,1]; β is the determination coefficient, which is determined by the standard deviation of the individual's historical optimal fitness. When the standard deviation is greater than 1, it is 0.1, otherwise it is 0.5; v and u are random numbers that obey Gaussian distribution; λ imax (t) is and The weight of the maximum difference in all dimensions is expressed as follows:

[0033] Where: x ik (t) is the k-th dimension position value of the i-th particle at the t-th iteration; x gbk (t) is the k-th dimension value of the global optimal position at the t-th iteration; λ ik (t) is the k-th dimension difference weight of the i-th particle at the t-th iteration;

[0034] The formulas of random numbers u and v that obey Gaussian distribution introduced in the improved particle swarm update formula are as follows:

[0035] Where: r4 is a random number in the range of [-1.5, 1.5]; r5 is a random number in the range of [0, 1]; σ u and σ v are the variances of Gaussian distributions u and v respectively.

[0036] Furthermore, the parameters w, c1, c2 and σ in the new position update formula u The adaptive control system is realized by fuzzy control system, which is as follows: the number of iterations t and the maximum difference weight λ imax (t) as the input variable and the corresponding quantization factor Q t and Q λ After multiplication, it is input into the fuzzy system and then processed by fuzzy and proportional factor P w 、P c1 、P c2 and P σu After multiplication, the output increments Δw, Δc1, Δc2 and Δσ u , parameters w, c1, c2 and σ u It can be obtained by the following formula

[0037] Where: w0, c 10 、c 20 and σ u0 are the initial values ​​of each parameter.

[0038] Variables t, λ imax (t), Δw, Δc1, Δc2 and Δσ u The domain of discourse is set to [0,6], and the quantization factor Q t and Q λ and the scaling factor P w 、P c1 、P c2 and P σu Set to 6 / t respectively max , 6*rand, where rand is a random number in the range [0,1], (1 / 6)*rand, 1 / 3, 1 / 3 and 1 / (6*rand), and the initial values ​​w0, c 10 and c 20 are set to 0.3, 0.5 and 0.5 respectively; and for σ u0 , if t / t max <rand, take cos(πt / t max ), where t max is the maximum number of iterations, if t / t max ≥rand, its value is 1E-15.

[0039] Furthermore, by using the fuzzy PI control parameters of the cavity one system obtained by optimizing the new improved particle swarm algorithm to perform ultra-high precision pressure control of cavity one, ultra-high precision thrust output of the air-floating frictionless cylinder can be achieved; by using the fuzzy PI control parameters of the cavity two system obtained by optimizing the new improved particle swarm algorithm to perform ultra-high precision pressure control of cavity two, ultra-high precision tension output of the air-floating frictionless cylinder can be achieved.

[0040] Furthermore, by using the fuzzy PI control parameters of the cavity one system and the fuzzy PI control parameters of the cavity two system obtained by optimization based on the new improved particle swarm algorithm, ultra-high precision pressure control of cavity one and cavity two is alternately performed, which can achieve ultra-high precision alternating output of thrust and pull of the air-floating frictionless cylinder.

[0041] The ultra-high-precision pneumatic servo system and the intelligent optimization method for its control parameters proposed in this invention have the following beneficial effects compared with the prior art:

[0042] 1. The pneumatic actuator used in the present invention is a new type of air-floating frictionless cylinder with independent air supply. Compared with ordinary cylinders, this cylinder avoids the influence of friction on the force servo control accuracy. In addition, due to the working mode of the cylinder's independent air supply, the frictionless state of the cylinder is not affected during the reversing process. Compared with the existing single-acting air-floating frictionless cylinder, this cylinder can achieve alternating output of thrust and pull.

[0043] 2. The present invention proposes a new and improved particle swarm algorithm, which makes up for the shortcomings of traditional particle swarm algorithms, such as their inability to effectively balance exploration and development capabilities and their inability to effectively escape local optimality. In addition, the present invention uses this algorithm to optimize the parameters of the fuzzy PI pressure controller of the pneumatic servo system, which can avoid the problem of low control accuracy caused by the randomness and subjectivity of parameter adjustment through trial and error, thereby ultimately achieving ultra-high-precision force control of the air-floating frictionless cylinder.

[0044] 3. In the optimization of fuzzy PI pressure control parameters based on the new improved particle swarm algorithm, the present invention establishes corresponding penalty mechanisms for particles with poor control accuracy and oscillation. This can effectively reduce the experimental optimization time on the one hand, and on the other hand, it can stop the system in time when oscillation occurs, thereby improving the life of the experimental device. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] FIG1 is a schematic diagram of the pneumatic servo system of the present invention;

[0046] FIG2 is a schematic diagram of the fuzzy PI pressure controller of the present invention;

[0047] FIG3 is an optimization flow chart of the novel improved particle swarm algorithm of the present invention;

[0048] FIG4 is a convergence curve diagram of the multi-dimensional unimodal function optimization in Example 1 of the present invention;

[0049] FIG5 is a convergence curve diagram of the multi-dimensional multi-modal function optimization in Example 1 of the present invention;

[0050] FIG6 is a convergence curve diagram of fuzzy PI pressure control optimization in Example 1 of the present invention;

[0051] FIG7 is a graph showing a continuous step thrust response in the first embodiment of the present invention;

[0052] FIG8 is a graph showing a continuous step thrust error in the first embodiment of the present invention. DETAILED DESCRIPTION

[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0054] Example 1:

[0055] 1 , the ultra-high precision pneumatic servo system of the present invention includes an actuator module, a pressure control module, an air source module and an air supply module; the actuator module is a universal double-acting air-floating frictionless cylinder 10 disclosed in patent application number 201711223571.1; the pressure control module includes an industrial computer 1, a data acquisition card 2, a three-position five-way solenoid valve 3, a two-position three-way solenoid valve 1 4, a two-position three-way solenoid valve 2 7, a high-precision pressure sensor 1 6, a high-precision pressure sensor 2 9, a small gas tank 1 5 and a small gas tank 2 8; the air supply module includes a pressure reducing valve 1 11, a pressure reducing valve 2 15, a small gas tank 3 12, a small gas tank 4 16, an air dryer 13 and a precision filter 14; the air source module includes an air source 17, a pressure reducing valve 3 18 and an atmospheric tank 19.

[0056] The compressed air generated by the air source 17 is transported to the large air tank 19 through the action of the pressure reducing valve 3 18, providing compressed air for each pneumatic branch; the pressure reducing valve 11, the small air tank 3 12, the air dryer 13 and the precision filter 14 form the branch 1 to supply air to the air bearing of the air-floating frictionless cylinder 10, and the pressure reducing valve 2 15 and the small air tank 4 16 form the branch 2 to supply air to the air-floating piston of the air-floating frictionless cylinder 10, thereby enabling the air-floating frictionless cylinder 10 to work normally.

[0057] The upstream end of the 5 / 3-way solenoid valve 3 is connected to the large air tank 19 as branch line 3. The two ports of the 5 / 3-way solenoid valve 3 are connected to the small air tank 1 5 and small air tank 2 8, respectively, via the 3 / 2-way solenoid valve 1 4 and the 3 / 2-way solenoid valve 2 7. The maximum valve openings of the 3 / 3-way solenoid valve 1 4 and the 3 / 2-way solenoid valve 2 7 should be greater than or equal to the maximum valve openings of the 5 / 3-way solenoid valve 3 to avoid affecting the intake air flow. The small air tank 1 5 and the rodless chamber of the air-floating frictionless cylinder 10 form the controlled chamber 1, while the small air tank 2 8 and the rod chamber of the air-floating frictionless cylinder 5 form the controlled chamber 2. The inner diameter of all air pipes between the 5 / 3-way solenoid valve 3 and the air-floating frictionless cylinder 5 cavity should be larger than the diameters of the 3 / 2-way solenoid valve 1 4, the 3 / 2-way solenoid valve 2 7, and the 5 / 3-way solenoid valve 3, and the aspect ratio of all air pipes should be as small as possible to reduce pressure loss along the way. High-precision pressure sensor 1 6 and high-precision pressure sensor 2 9 respectively feed back the pressure information in cavity 1 and cavity 2 to the industrial computer 1 through the data acquisition card 2. After the industrial computer 1 executes its own fuzzy PI control algorithm, it outputs the voltage signal to the three-position five-way solenoid valve 3 through the data acquisition card 2.

[0058] The fuzzy PI pressure control parameters are optimized by a novel improved particle swarm algorithm, and the steps are as follows:

[0059] S1: Referring to Figure 2, a fuzzy PI pressure controller is constructed and the variables to be optimized are determined, including:

[0060] S11: Pressure error e and pressure error change rate e c is the input variable, and the increment of PI controller parameter ΔK p and ΔK i is the output variable, and the domain of the variable is set to [-3,3], and the fuzzy set is set to {NB, NM, NS, ZE, PS, PM, PB};

[0061] S12: Set variables e and e c Respectively with the quantization factor Q e and Q ec After multiplication, the data are input into the fuzzy system and fuzzified using the triangular membership function;

[0062] S13: referring to Table 1 and Table 2, a fuzzy reasoning rule base is established, and fuzzy reasoning is performed using the Mamdani method;

[0063] Table 1 Output variable ΔK p Fuzzy rules

[0064] Table 2 Output variable ΔK i Fuzzy rules

[0065] S14: Use the area center method to defuzzify, and then add the proportional factor P Kp and P Ki After multiplication, the output is ΔK p and ΔK i ;

[0066] S15: Update parameter K according to formula (1) p and K i , in order to adjust the parameters of the PI controller;

[0067] Where: K p0 and K i0 K p and K i The initial value of

[0068] S16: Determine the K in the fuzzy PI controller p0 , K i0 , Q ec 、P Kp and P Ki is the optimization variable.

[0069] S2: Determine the search space of the variables to be optimized by trial and error;

[0070] S3: Determine the objective function in the optimization process. In the rising stage of the system step response (set to the first T1 seconds), the ITAE evaluation index function is used; when the system enters the steady-state stage (set to T1 to T2 seconds), the ITSE evaluation index function is used. The specific expression is:

[0071] In addition, a penalty function is integrated into the objective function. If a particle has not completed the rising phase of the system step response after T1 seconds, the control is stopped and the particle is sentenced to death, that is, the particle is given an extremely poor fitness value. When the input voltage of the three-position five-way solenoid valve reaches 0V or 10V three times, it is determined that the system is oscillating, and the control is stopped and the particle is sentenced to death.

[0072] S4: Referring to Figure 3, the novel improved particle swarm algorithm is used for iterative optimization, specifically including:

[0073] S41: Set the basic parameters of the new improved particle swarm optimization algorithm and initialize it;

[0074] S42: Randomly initialize particle position and velocity vectors in the search space;

[0075] S43: Calculate the fitness value of each particle;

[0076] S44: Compare the fitness values ​​to obtain the individual historical optimal particle position and the global optimal particle position;

[0077] S45: Update particles using the velocity update formula (3) and the new position update formula (4);

[0078] Where: is the position of the i-th particle after t iterations; is the individual historical optimal position of the i-th particle after t iterations; is the global optimal position of the entire group after t iterations; is the velocity of the i-th particle after t iterations; is the velocity of the i-th particle after (t+1) iterations; w is the inertia weight; c1 and c2 are the individual learning factor and the social learning factor respectively; r1, r2, r3 and r α are random numbers in the range of [0,1]; β is the determination coefficient, which is determined by the standard deviation of the individual's historical optimal fitness. When the standard deviation is greater than 1, it is 0.1, otherwise it is 0.5; v and u are random numbers that obey Gaussian distribution; λ imax (t) is and The weight of the maximum difference in all dimensions. In formula (4), the coefficient β set according to the individual optimal position is to increase the probability of using the proposed new position update formula in the later iteration. Furthermore, when the maximum difference weight of the particle is less than r α When λ is used, it is considered that these particles are very close to the global optimal position. Introducing a random number v that follows a Gaussian distribution can effectively prevent particles from falling into the local optimum. In addition, even if the new position update formula is used in the early iterations, the design of u can also ensure that the algorithm has a stronger exploration ability. imax The specific expression of (t) is as follows:

[0079] Where: x ik (t) is the k-th dimension position value of the i-th particle at the t-th iteration; x gbk (t) is the k-th dimension value of the global optimal position at the t-th iteration; λ ik (t) is the k-th dimension difference weight of the i-th particle at the t-th iteration.

[0080] The formulas of random numbers u and v that obey Gaussian distribution introduced in the improved particle swarm update formula are as follows:

[0081] Where: r4 is a random number in the range of [-1.5, 1.5]; r5 is a random number in the range of [0, 1].

[0082] In order to realize w, c1, c2 and σ u Adaptive adjustment of parameters, integrating fuzzy theory into the new improved particle swarm optimization algorithm, specifically including:

[0083] S451: The number of iterations t and the maximum difference weight λ imax (t) is the input variable, with parameter increments Δw, Δc1, Δc2 and Δσ u is the output variable, and the variable domain is set to [0,6], and the fuzzy sets are set to {NB, NM, NS, ZE, PS, PM, PB};

[0084] S452: Variables t and λ imax (t) and the quantization factor Q t and Q λ After multiplication, the data are input into the fuzzy system and fuzzified using the triangular membership function;

[0085] S453: referring to Tables 3 to 6, establishing a fuzzy reasoning rule base and performing fuzzy reasoning;

[0086] Table 3 Fuzzy rules for output variable Δw

[0087] Table 4 Fuzzy rules for output variable Δc1

[0088] Table 5 Fuzzy rules for output variable Δc2

[0089] Table 6 Output variables Δσ u Fuzzy rules

[0090] S454: Use the centroid method to defuzzify, and then use the proportional factor P w 、P c1 、P c2 and P σu After multiplication, the output is Δw, Δc1, Δc2 and Δσ u ;

[0091] S455: Update parameters w, c1, c2 and σ according to formula (7) u , in order to realize the adjustment of the parameters of the new improved particle swarm algorithm;

[0092] Where: w0, c 10 、c 20 and σ u0 are the initial values ​​of each parameter.

[0093] Specifically, the quantization factor Q t and Qλ and a scale factor P w , P c1 , P c2 and P σu are respectively set to 6 / t max , 6*rand (where rand is a random number within the range of [0, 1]), (1 / 6)*rand, 1 / 3, 1 / 3, and 1 / (6*rand), and the initial values w0, c 10 and c 20 are respectively set to 0.3, 0.5, and 0.5; for σ u0 , if t / t max <rand, take cos(πt / t max )(where t max is the maximum number of iterations), if t / t max ≥rand, its value is taken as 1E-15; where introducing random numbers into the control parameters of the fuzzy controller is to improve the diversity of particle movement during the optimization process. For the initial value of σ u0 , in the first half of the optimization, it is set as a function that decreases with the number of iterations, in order to make the algorithm have stronger exploration ability and have a higher tolerance for particles far from the global optimum; while in the second half of the optimization, the initial value is set to a very small value, hoping that the algorithm has stronger exploitation ability.

[0094] For the proposed new improved particle swarm algorithm, the algorithms in the papers "Comparing inertia weights and constriction factors in particle swarm optimization" (PSO-LDIW), "Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients" (HPSO-TVAC), "Tracking and optimizing dynamic systems with particle swarms" (PSO-RIW), "A particle swarm optimization algorithm with random learning mechanism and Levy flight for optimization of atomic clusters" (RPSOLF) and "HEPSO: high exploration particle swarm optimization" (HEPSO) were selected to compare and verify the following two functions.

[0095] Multidimensional unimodal function: The variable range is [-100, 100], the maximum number of iterations of each algorithm is set to 2500, the population size is set to 50, and the population dimension is set to 30. Each optimization algorithm is run independently 30 times, and the average, standard deviation, optimal solution and worst solution of the 30 optimization results are recorded.

[0096] Referring to Table 7 and Figure 4 for the algorithm optimization results, it can be found that the proposed new improved particle swarm algorithm found the optimal solution 0 of the function, while the other algorithms were unable to find 0, and the new improved particle swarm algorithm has a very fast convergence speed.

[0097] Table 7 Optimization results for multidimensional unimodal functions

[0098] Multidimensional multimodal function: The variable range is [-500, 500], the maximum number of iterations of each algorithm is set to 2500, the population size is set to 50, and the population dimension is set to 30. Each optimization algorithm is run independently 30 times, and the average, standard deviation, optimal solution and worst solution of the 30 optimization results are recorded.

[0099] The algorithm optimization results refer to Table 8 and Figure 5. It can be found that the proposed new improved particle swarm optimization algorithm still has the highest optimization accuracy and the fastest convergence speed compared with several other optimization algorithms.

[0100] Table 8 Optimization results for multidimensional and multimodal functions

[0101] S46: Check whether each particle has crossed the boundary. If so, retain the state of the particle before the update.

[0102] S47: If the number of iterations reaches the maximum number of iterations, proceed to the next step, otherwise proceed to step S43;

[0103] S48: The operation ends and the optimized fuzzy PI control parameters are output.

[0104] S5: Cavity 1 and cavity 2 are respectively taken as controlled objects, and their respective optimized fuzzy PI control parameters are optimized.

[0105] When the pneumatic servo system is required to output ultra-high-precision thrust, the industrial computer 1 controls the two-position three-way solenoid valve 1 4 to switch to the open state through the data acquisition card 2, so that the three-position five-way solenoid valve 3 forms a passage with the cavity 1, and at the same time keeps the two-position three-way solenoid valve 2 7 in the closed state, so that the cavity 2 is connected to the atmosphere; then, the voltage control quantity is obtained by calculating the cavity 1 control parameters obtained by the constructed cavity 1 system fuzzy PI controller and the cavity 1 control parameters obtained by optimization based on the new improved particle swarm algorithm, and is output to the three-position five-way solenoid valve 3 through the data acquisition card 2 to execute ultra-high-precision pressure control of the cavity 1, thereby realizing ultra-high-precision pneumatic thrust output.

[0106] When the pneumatic servo system is required to output ultra-high-precision pulling force, the industrial computer 1 controls the two-position three-way solenoid valve 2 7 to switch to the open state through the data acquisition card 2, so that the three-position five-way solenoid valve 3 forms a passage with the cavity 2, and at the same time keeps the two-position three-way solenoid valve 1 4 in the closed state, so that the cavity 1 is connected to the atmosphere; then, the voltage control quantity is obtained by calculating the cavity 2 system fuzzy PI controller constructed and the cavity 2 control parameters obtained by optimization based on the new improved particle swarm algorithm, and is output to the three-position five-way solenoid valve 3 through the data acquisition card 2 to execute ultra-high-precision pressure control of the cavity 2, thereby realizing ultra-high-precision pneumatic pulling force output.

[0107] For this embodiment, an experimental method will be used to perform parameter optimization verification.

[0108] In the experiment of this embodiment, the step response rising stage is 10 seconds, that is, T1 is 10 seconds; the step response stabilization stage is 20 seconds, that is, T2 is 30 seconds; the pressure sensor adopts the pressure sensor of Keller model PAA-33X, and the three-position five-way solenoid valve adopts the proportional directional valve of Festo model MPYE-5-1 / 8LF-010.

[0109] Set the number of particles and the number of iterations of the new improved particle swarm optimization algorithm to 20, and the quantization factor Q e The value of depends primarily on the control system and is set to 80,000. The optimization results are shown in Table 9 and Figure 6. As shown in the figure, the proposed improved particle swarm optimization algorithm found the theoretically optimal control parameters for the fuzzy PI pressure controller in the ninth iteration. The optimized parameters were rounded (or trimmed) and used in aerodynamic servo experiments.

[0110] Table 9 Parameters obtained by optimizing the fuzzy PI controller using the new improved particle swarm optimization algorithm and the rounded (or trimmed) parameters

[0111] In the experiment, the air bearing and piston of the air-floating frictionless cylinder were supplied with gas at pressures of 0.4 MPa and 0.2 MPa respectively by air supply branch 1 and air supply branch 2. In addition, the thrust output of the air-floating frictionless cylinder is obtained by multiplying the pressure in the rodless cavity of the air-floating frictionless cylinder by the effective area of ​​the rodless cavity (the effective area is 807.2665 mm without considering the machining error). 2 Continuous step thrust control is performed on the pneumatic servo system, and the controller parameters are the optimized and rounded parameters, as shown in Table 3.

[0112] 7 and 8 , it can be seen that the actual continuous step output force response curve of the output force servo system fits the target curve. Within the output force variation range of 80 N to 240 N, the steady-state error of the system when it reaches stability is less than 0.023 N (equivalent to a system accuracy of 0.01% FS. Therefore, the proposed pneumatic servo system achieves the goal of ultra-high precision). Therefore, the method proposed in the present invention achieves the control goal of ultra-high precision thrust of the air-floating frictionless cylinder.

[0113] Example 2:

[0114] This embodiment differs from the first embodiment in that the fuzzy PI control parameters of the cavity one system and the fuzzy PI control parameters of the cavity two system obtained by optimization based on the new improved particle swarm algorithm are used to alternately perform ultra-high-precision pressure control of cavity one and cavity two, thereby achieving ultra-high-precision alternating output of thrust and pull of the air-floating frictionless cylinder. The details are as follows: the industrial computer 1 first controls the two-position three-way solenoid valve 1 4 to switch to the open state through the data acquisition card 2, so that the three-position five-way solenoid valve 3 forms a passage with the cavity 1, and at the same time controls the two-position three-way solenoid valve 2 7 to switch to the closed state to quickly empty the gas in the cavity 2, and uses the cavity 1 system fuzzy PI controller optimized based on the new improved particle swarm algorithm to control the three-position five-way solenoid valve 3 to inflate the cavity 1 for a period of time; then, the industrial computer 1 controls the two-position three-way solenoid valve 2 7 to switch to the open state through the data acquisition card 2, so that the three-position five-way solenoid valve 3 forms a passage with the cavity 2, and controls the two-position three-way solenoid valve 1 4 to switch to the closed state to quickly empty the gas in the cavity 1, and uses the cavity 2 system fuzzy PI controller optimized based on the new improved particle swarm algorithm to control the three-position five-way solenoid valve 3 to inflate the cavity 2 for the same period of time; in this way, a cycle of alternating thrust and pull output is executed, and the cycle action can be repeated to output continuous alternating force.

Claims

1. An ultra-high precision pneumatic servo system, characterized in that: It includes an actuator module, a pressure control module, an air source module and an air supply module; the actuator module is a double-acting air-floating frictionless cylinder 10; the pressure control module includes an industrial computer 1, a data acquisition card 2, a three-position five-way solenoid valve 3, a two-position three-way solenoid valve 1 4, a two-position three-way solenoid valve 2 7, a high-precision pressure sensor 1 6, a high-precision pressure sensor 2 9, a small gas tank 1 5 and a small gas tank 2 8; the air supply module includes a pressure reducing valve 1 11, a pressure reducing valve 2 15, a small gas tank 3 12, a small gas tank 4 16, an air dryer 13 and a precision filter 14; the air source module includes an air source 17, a pressure reducing valve 3 18 and an air tank 19; Compressed air generated by air source 17 is transported to large air tank 19 through pressure reducing valve 3 18 to provide compressed air for each pneumatic branch. Pressure reducing valve 1 1 1 , small air tank 3 12 , air dryer 13 and precision filter 14 form branch 1 to supply air to the air bearing of air-floating frictionless cylinder 10 . Pressure reducing valve 2 15 and small air tank 4 16 form branch 2 to supply air to the air-floating piston of air-floating frictionless cylinder 10 , thereby ensuring the normal operation of air-floating frictionless cylinder 10 . The upstream of the three-position five-way solenoid valve 3 is connected to the large air tank 19 as branch three; the two interfaces of the three-position five-way solenoid valve 3 are connected to the small air tank 1 5 and the small air tank 2 8 respectively through the two-position three-way solenoid valve 1 4 and the two-position three-way solenoid valve 2 7; the small air tank 1 5 and the rodless cavity of the air-floating frictionless cylinder 10 constitute the controlled cavity 1, and the small air tank 2 8 and the rod cavity of the air-floating frictionless cylinder 5 constitute the controlled cavity 2; the high-precision pressure sensor 1 6 and the high-precision pressure sensor 2 9 respectively feed back the pressure information in the cavity 1 and the cavity 2 to the industrial control computer 1 through the data acquisition card 2, and the industrial control computer 1 executes its respective fuzzy PI control algorithms and outputs the voltage signal to the three-position five-way solenoid valve 3 through the data acquisition card 2.

2. The servo system according to claim 1, characterized in that The maximum valve opening of the two-position three-way solenoid valve 1 4 and the two-position three-way solenoid valve 2 7 is greater than or equal to the maximum valve opening of the three-position five-way solenoid valve 3 .

3. The servo system according to claim 1, wherein: The inner diameters of all air pipes between the three-position five-way solenoid valve 3 and the cavity of the air-floating frictionless cylinder 5 are larger than the diameters of the two-position three-way solenoid valve 1 4 , the two-position three-way solenoid valve 2 7 and the three-position five-way solenoid valve 3 .

4. The intelligent optimization method for control parameters of an ultra-high precision pneumatic servo system according to claim 1 is characterized in that: The small gas tank 1 5 and the rodless cavity of the air-floating frictionless cylinder 10 constitute the controlled cavity 1, and the small gas tank 2 8 and the rod cavity of the air-floating frictionless cylinder 5 constitute the controlled cavity 2. The high-precision pressure sensor 1 6 and the high-precision pressure sensor 2 9 respectively feed back the pressure information in the cavity 1 and cavity 2 to the industrial computer 1 through the data acquisition card 2. After the industrial computer 1 executes its own fuzzy PI control algorithm, it outputs the voltage signal to the three-position five-way solenoid valve 3 through the data acquisition card 2. The characteristic is that the control parameters of the fuzzy PI control algorithm are optimized by the new improved particle swarm algorithm, and the steps are as follows: S1: Construct a fuzzy PI pressure controller and determine the variables to be optimized; S2: Determine the search space of the variables to be optimized by trial and error; S3: Determine the objective function in the optimization process; S4: Iterative optimization using a new improved particle swarm algorithm; S5: Cavity 1 and cavity 2 are respectively taken as controlled objects, and their respective optimized fuzzy PI control parameters are optimized.

5. The method according to claim 4, characterized in that The objective function in step S3 is selected as follows: in the rising stage of the system step response, it is set to the first T1 seconds, and the ITAE evaluation index function is used; when the system enters the steady-state stage, it is set to T1 to T2 seconds, and the ITSE evaluation index function is used. The specific expression is: Where: f is the objective function; t is time; e is the pressure control error.

6. The method according to claim 5, characterized in that It also includes incorporating a penalty function into the objective function, as follows: if a particle has not completed the rising phase of the system's step response after T1 seconds, the control is stopped and the particle is sentenced to death, that is, the particle is given an extremely poor fitness value; if the input voltage of the three-position five-way solenoid valve reaches 0V or 10V three times, it is determined that the system is oscillating, and the control is stopped and the particle is sentenced to death.

7. The method according to claim 4, characterized in that The iterative optimization process in step S4 is as follows: S41: Set the basic parameters of the new improved particle swarm optimization algorithm and initialize it; S42: Randomly initialize particle position and velocity vectors in the search space; S43: Calculate the fitness value of each particle; S44: Compare the fitness values ​​to obtain the individual historical optimal particle position and the global optimal particle position; S45: Update particles using the velocity update formula and the new position update formula; S46: Check whether each particle has crossed the boundary. If so, retain the state of the particle before the update. S47: If the number of iterations reaches the maximum number of iterations, proceed to the next step, otherwise proceed to step S43; S48: The operation ends and the optimized fuzzy PI control parameters are output; The speed update formula and the new position update formula in step S45 are as follows: Where: is the position of the i-th particle after t iterations; is the individual historical optimal position of the i-th particle after t iterations; is the global optimal position of the entire group after t iterations; is the velocity of the i-th particle after t iterations; is the velocity of the i-th particle after (t+1) iterations; w is the inertia weight; c1 and c2 are the individual learning factor and the social learning factor respectively; r1, r2, r3 and r α are random numbers in the range of [0,1]; β is the determination coefficient, which is determined by the standard deviation of the individual's historical optimal fitness. When the standard deviation is greater than 1, it is 0.1, otherwise it is 0.5; v and u are random numbers that obey Gaussian distribution; λ imax (t) is and The weight of the maximum difference in all dimensions is expressed as follows: Where: x ik (t) is the k-th dimension position value of the i-th particle at the t-th iteration; x gbk (t) is the k-th dimension value of the global optimal position at the t-th iteration; λ ik (t) is the k-th dimension difference weight of the i-th particle at the t-th iteration; The formulas of random numbers u and v that obey Gaussian distribution introduced in the improved particle swarm update formula are: Where: r4 is a random number in the range of [-1.5, 1.5]; r5 is a random number in the range of [0, 1]; σ u and σ v are the variances of Gaussian distributions u and v respectively.

8. The method according to claim 7, characterized in that The parameters w, c1, c2 and σ in the new position update formula u The adaptive control system is realized by fuzzy control system, which is as follows: the number of iterations t and the maximum difference weight λ imax (t) as the input variable and the corresponding quantization factor Q t and Q λ After multiplication, it is input into the fuzzy system and then processed by fuzzy and proportional factor P w 、P c1 、P c2 and P σu After multiplication, the output increments Δw, Δc1, Δc2 and Δσ u , parameters w, c1, c2 and σ u It can be obtained by the following formula Where: w0, c 10 、c 20 and σ u0 are the initial values ​​of each parameter; Variables t, λ imax (t), Δw, Δc1, Δc2 and Δσ u The domain of discourse is set to [0,6], and the quantization factor Q t and Q λ and the scaling factor P w 、P c1 、P c2 and P σu Set to 6 / t respectively max , 6*rand, where rand is a random number in the range [0,1], (1 / 6)*rand, 1 / 3, 1 / 3 and 1 / (6*rand), and the initial values ​​w0, c 10 and c 20 are set to 0.3, 0.5 and 0.5 respectively; and for σ u0 , if t / t max <rand, take cos(πt / t max ), where t max is the maximum number of iterations, if t / t max ≥rand, its value is 1E-15.

9. The method according to claim 1, characterized in that By using the fuzzy PI control parameters of cavity one system obtained by optimizing the new improved particle swarm algorithm to perform ultra-high precision pressure control of cavity one, ultra-high precision thrust output of the air-floating frictionless cylinder can be achieved; by using the fuzzy PI control parameters of cavity two system obtained by optimizing the new improved particle swarm algorithm to perform ultra-high precision pressure control of cavity two, ultra-high precision tension output of the air-floating frictionless cylinder can be achieved.

10. The method according to claim 1, characterized in that By using the fuzzy PI control parameters of cavity one and cavity two obtained by optimizing the new improved particle swarm algorithm, ultra-high-precision pressure control of cavity one and cavity two is performed alternately, which can achieve ultra-high-precision alternating output of thrust and pull of the air-floating frictionless cylinder.

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