An ultra-high precision pneumatic servo system and intelligent optimization method of its control parameters

Abstract

The present invention provides an ultra-high precision pneumatic servo system and an intelligent optimization method for its control parameters. The pneumatic servo system is mainly composed of a double-acting air-floating frictionless cylinder and a pressure control system. The air-floating frictionless cylinder can be used to eliminate the influence of friction on the output force control accuracy. The pressure control system uses a fuzzy PI controller optimized based on a new improved particle swarm algorithm to achieve ultra-high precision control of pressure. The new improved particle swarm algorithm integrates Gaussian variation strategy and fuzzy control theory. The optimized fuzzy PI control parameters are obtained using the new improved particle swarm algorithm and ultra-high precision pressure control of the air-floating frictionless cylinder cavity is performed based on the parameters, so as to achieve ultra-high precision force output of the system. The pneumatic servo system proposed by the present invention can be used in occasions with high requirements for force control accuracy, thereby expanding the application range of the pneumatic servo system.

Description

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 development of science and technology, force servo systems have been widely used in the industrial field. At present, high-precision force servo systems usually use electric cylinders as actuators. In pneumatic servo systems, the complex friction generated by ordinary cylinders during movement makes the pneumatic output force control accuracy low. In order to solve this problem, existing technologies such as the literature "Research on Frictionless Cylinders and High-Precision Pneumatic Load Systems", "Research on Key Technologies for Simulating Pneumatic Suspension Systems in Zero Gravity Environments", and patent CN113700696B have proposed new air-floating frictionless cylinders with different structures. Such cylinders have the characteristics of extremely low friction and can theoretically achieve high-precision pneumatic output force control. However, these cylinders are single-acting cylinders and can only achieve a single force output. The present invention intends to use the double-acting air-floating frictionless cylinder disclosed in the Chinese patent with patent application number 201711223571.1 as the actuator of the pneumatic servo system. 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, thereby making it possible to output high-precision thrust and pull alternatingly. In view of the use of air-floating frictionless cylinders, the output force of the cylinder can be equivalent to the pressure control in the cylinder cavity.

[0003] Fuzzy PI control has the advantages of simple algorithm, efficient control and good robustness, so the present invention intends to use fuzzy PI control algorithm to achieve high-precision control of pressure. However, in practical applications, the selection of fuzzy PI controller parameters often adopts trial and error, which leads to greater randomness in the selection, making it difficult to select more accurate parameters, resulting in low control accuracy. At present, simple manual random parameter adjustment can no longer meet the needs of high-precision control or even ultra-high-precision control, and the rapid development of swarm intelligence algorithms provides an intelligent method for complex parameter adjustment, that is, to find a set of optimal parameters through multiple iterations, so as to obtain satisfactory control effects as much as possible. Ant colony algorithm, genetic algorithm and particle swarm algorithm are more common swarm intelligence algorithms. Among them, particle swarm algorithm has the advantages of simple implementation and few adjustment parameters, and has been widely used in the field of optimization, which can solve the problem of fuzzy PI controller parameter selection. However, the traditional particle swarm algorithm cannot effectively balance the global search and local search, and the particles fall into the local optimum and cannot effectively jump out, which seriously affects the 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 to be solved by those skilled in the art. Summary of the invention

[0005] 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.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] An ultra-high precision pneumatic servo system, characterized in that it comprises 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 comprises 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 comprises 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 comprises an air source, a pressure reducing valve 3 and a large gas tank;

[0008] 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;

[0009] 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 respectively connected to the small gas tank one and the small gas tank two 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.

[0010] Furthermore, the maximum valve opening of the two-position three-way solenoid valve one and the two-position three-way solenoid valve two is greater than or equal to the maximum valve opening of the three-position five-way solenoid valve.

[0011] 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.

[0012] The method for intelligent optimization of control parameters of an ultra-high precision pneumatic servo system is characterized in that the small gas tank 1 and the rodless cavity of the air-floating frictionless cylinder constitute the controlled cavity 1, the small gas tank 2 and the rod cavity of the air-floating frictionless cylinder constitute the controlled cavity 2, the high-precision pressure sensor 1 and the high-precision pressure sensor 2 respectively feed back the pressure information in the cavity 1 and the cavity 2 to the industrial computer through the data acquisition card, and the industrial 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; the control parameters of the fuzzy PI control algorithm are optimized by the new improved particle swarm algorithm, and the steps are as follows:

[0013] S1: Construct a fuzzy PI pressure controller and determine the variables to be optimized;

[0014] S2: Determine the search space of the variables to be optimized by trial and error;

[0015] S3: Determine the objective function in the optimization process;

[0016] S4: Iterative optimization using a new improved particle swarm algorithm;

[0017] S5: respectively taking cavity one and cavity two as controlled objects, and optimizing their respective optimized fuzzy PI control parameters.

[0018] 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 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:

[0019]

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

[0021] Furthermore, it also includes incorporating the penalty function into the objective function, as follows: when 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 oscillates at this time, then 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, keep the state of the particle before the update.

[0029] S47: If the number of iterations reaches the maximum number of iterations, execute the next step, otherwise execute 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]

[0033]

[0034] Where: is the position of the ith particle after t iterations; is the individual historical optimal position of the ith particle after t iterations; is the global optimal position of the entire group after t iterations; is the velocity of the ith particle after y iterations; is the velocity of the ith 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 takes 0.1, otherwise it takes 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:

[0035]

[0036] 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 best position at the t-th iteration; λ ik(t) is the k-th dimension difference weight of the ith particle at the y-th iteration;

[0037] The formulas of random numbers u and v that obey Gaussian distribution introduced in the improved particle swarm update formula are:

[0038]

[0039] 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.

[0040] 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, 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 then combined with the 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

[0041]

[0042] Where: w0, c 10 、c 20 and σ u0 are the initial values ​​of each parameter.

[0043] Variables t, λ imax (t), Δw, Δc1, Δc2 and Δσ u The domain of 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 ou 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), 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 / tmax <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.

[0044] Furthermore, 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.

[0045] Furthermore, by utilizing the fuzzy PI control parameters of cavity one system and the fuzzy PI control parameters of cavity two system obtained by optimizing the novel improved particle swarm algorithm, ultra-high precision pressure control of cavity one and cavity two is performed alternately, thereby realizing the alternating output of ultra-high precision thrust and pull of the air-floating frictionless cylinder.

[0046] Compared with the prior art, the ultra-high precision pneumatic servo system and the intelligent optimization method of control parameters thereof proposed in the present invention have the following beneficial effects:

[0047] 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 independent air supply of the cylinder, the frictionless state during the cylinder switching process is not affected. Compared with the existing single-acting air-floating frictionless cylinder, this cylinder can achieve alternating output of thrust and pull.

[0048] 2. The present invention proposes a new improved particle swarm algorithm, which makes up for the shortcomings of the traditional particle swarm algorithm, such as the inability to effectively balance the exploration and development capabilities and the inability to effectively jump out of the local optimum; in addition, the present invention uses the algorithm to realize the parameter optimization 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 realizing ultra-high precision force control of the air-floating frictionless cylinder.

[0049] 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 it oscillates, thereby increasing the life of the experimental device. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a schematic diagram of the pneumatic servo system of the present invention;

[0051] Figure 2 It is the principle diagram of the fuzzy PI pressure controller of the present invention;

[0052] Figure 3 It is an optimization flow chart of the novel improved particle swarm algorithm of the present invention;

[0053] Figure 4 is a convergence curve diagram of multi-dimensional unimodal function optimization in the first embodiment of the present invention;

[0054] Figure 5 is a convergence curve diagram of multi-dimensional multi-peak function optimization in the first embodiment of the present invention;

[0055] Figure 6 is a convergence curve diagram of fuzzy PI pressure control optimization in the first embodiment of the present invention;

[0056] Figure 7 is a continuous step thrust response curve diagram in the first embodiment of the present invention;

[0057] Figure 8 4 is a continuous step thrust error curve diagram in the first embodiment of the present invention. DETAILED DESCRIPTION

[0058] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0059] Embodiment 1:

[0060] Reference Figure 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.

[0061] 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 three 18, providing compressed air for each pneumatic branch; the pressure reducing valve one 11, the small air tank three 12, the air dryer 13 and the precision filter 14 form the branch one to supply air to the air bearing of the air-floating frictionless cylinder 10, and the pressure reducing valve two 15 and the small air tank four 16 form the branch two to supply air to the air-floating piston of the air-floating frictionless cylinder 10, so that the air-floating frictionless cylinder 10 can work normally.

[0062] The upstream of the three-position five-way solenoid valve 3 is connected to the large gas tank 19 as branch three; the two interfaces of the three-position five-way solenoid valve 3 are connected to the small gas tank 15 and the small gas tank 28 respectively through the two-position three-way solenoid valve 14 and the two-position three-way solenoid valve 27; the maximum valve opening of the two-position three-way solenoid valve 14 and the two-position three-way solenoid valve 27 should be greater than or equal to the maximum valve opening of the three-position five-way solenoid valve 3, so as not to affect the intake flow. The small gas tank 15 and the rodless cavity of the air-floating frictionless cylinder 10 constitute the controlled volume chamber 1, and the small gas tank 28 and the rod cavity of the air-floating frictionless cylinder 5 constitute the controlled volume chamber 2; the inner diameter of all air pipes between the three-position five-way solenoid valve 3 and the cavity of the air-floating frictionless cylinder 5 should be greater than the diameter of the two-position three-way solenoid valve 14, the two-position three-way solenoid valve 27 and the three-position five-way solenoid valve 3, and the length-to-diameter ratio of all air pipes should be as small as possible, so as to reduce the 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 industrial computer 1 through 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 data acquisition card 2.

[0063] The fuzzy PI pressure control parameters are optimized by a novel improved particle swarm algorithm, the steps are as follows:

[0064] S1: Reference Figure 2 , construct a fuzzy PI pressure controller and determine the variables to be optimized, including:

[0065] S11: Pressure error e and pressure error change rate e c is the input variable, with the increment ΔK of the PI controller parameter p and ΔK i is the output variable, and the domain of the variable is set to [-3, 3], and the fuzzy sets are set to {NB, NM, NS, ZE, PS, PM, PB};

[0066] 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;

[0067] S13: referring to Table 1 and Table 2, a fuzzy reasoning rule base is established, and the Mamdani method is used for fuzzy reasoning;

[0068] Table 1 Output variable ΔK p Fuzzy rules

[0069]

[0070] Table 2 Output variable ΔK i Fuzzy rules

[0071]

[0072] 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 ;

[0073] S15: Update parameter K according to formula (1) p and K i , in order to adjust the parameters of the PI controller;

[0074]

[0075] Where: K p0 and K i0 K p and K i The initial value of

[0076] S16: Determine the K in the fuzzy PI controller p0 , K i0 , Q ec , P Kp and P Ki is the optimization variable.

[0077] S2: Determine the search space of the variables to be optimized by trial and error;

[0078] 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:

[0079]

[0080] In addition, the penalty function is integrated into the objective function. When a particle has not completed the rising stage 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 oscillates at this time, then the control is stopped and the particle is sentenced to "death".

[0081] S4: Reference Figure 3 , using the new improved particle swarm algorithm for iterative optimization, including:

[0082] S41: Set the basic parameters of the new improved particle swarm optimization algorithm and initialize it;

[0083] S42: Randomly initialize particle position and velocity vectors in the search space;

[0084] S43: Calculate the fitness value of each particle;

[0085] S44: Compare the fitness values ​​to obtain the individual historical optimal particle position and the global optimal particle position;

[0086] S45: Update particles using the velocity update formula (3) and the new position update formula (4);

[0087]

[0088]

[0089] Where: is the position of the ith particle after t iterations; is the individual historical optimal position of the ith particle after t iterations; is the global optimal position of the entire group after t iterations; is the velocity of the ith particle after t iterations; is the velocity of the ith 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 takes 0.1, otherwise it takes 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 is set according to the individual optimal position 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 αWhen λ is used, it is considered that these particles are very close to the global optimal position. Then, the introduction of random numbers v that obey the 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:

[0090]

[0091] 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 best position at the t-th iteration; λ ik (t) is the k-th dimension difference weight of the ith particle at the t-th iteration.

[0092] The formulas of random numbers u and v that obey Gaussian distribution introduced in the improved particle swarm update formula are:

[0093]

[0094] 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].

[0095] In order to achieve w, c1, c2 and σ u Adaptive adjustment of parameters, integrating fuzzy theory into the new improved particle swarm optimization algorithm, including:

[0096] S451: with 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};

[0097] S452: Set 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;

[0098] S453: referring to Tables 3 to 6, establishing a fuzzy reasoning rule base and performing fuzzy reasoning;

[0099] Table 3 Fuzzy rules for output variable Δw

[0100]

[0101] Table 4 Fuzzy rules for output variable Δc1

[0102]

[0103] Table 5 Fuzzy rules for output variable Δc2

[0104]

[0105]

[0106] Table 6 Output variables Δσ u Fuzzy rules

[0107]

[0108] S454: Use the centroid method to defuzzify and then add the proportional factor P w , P c1 , P c2 and P σu After multiplication, the outputs are Δw, Δc1, Δc2 and Δσ u ;

[0109] S455: Update parameters w, c1, c2 and σ according to equation (7) u , in order to achieve the adjustment of the parameters of the new improved particle swarm algorithm;

[0110]

[0111] Where: w0, c 10 、c 20 and σ u0 are the initial values ​​of each parameter.

[0112] Specifically, 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), 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; the random number is introduced into the control parameters of the fuzzy controller to improve the diversity of particle motion during the optimization process. u0 In the first half of the optimization search, it is set to a function that decreases with the number of iterations in order to make the algorithm have stronger exploration capabilities and a higher tolerance for particles far away from the global optimum; in the second half of the optimization search, the initial value is set to a very small value in the hope that the algorithm has stronger development capabilities.

[0113] For the proposed new improved particle swarm algorithm, the algorithms in the literature "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.

[0114] 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.

[0115] The algorithm optimization results refer to Table 7 and Figure 4 , it can be found that the proposed new improved particle swarm algorithm finds the optimal solution 0 of the function, while the other algorithms cannot find 0, and the new improved particle swarm algorithm has a very fast convergence speed.

[0116] Table 7 Optimization results for multidimensional unimodal functions

[0117]

[0118] 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.

[0119] The algorithm optimization results refer to Table 8 and Figure 5 , it can be found that the proposed new improved particle swarm algorithm still has the highest optimization accuracy and the fastest convergence speed compared with several other optimization algorithms.

[0120] Table 8 Optimization results for multidimensional multimodal functions

[0121]

[0122] S46: Check whether each particle has crossed the boundary. If so, keep the state of the particle before the update.

[0123] S47: If the number of iterations reaches the maximum number of iterations, execute the next step, otherwise execute step S43;

[0124] S48: The operation ends and the optimized fuzzy PI control parameters are output.

[0125] S5: respectively taking cavity one and cavity two as controlled objects, and optimizing their respective optimized fuzzy PI control parameters.

[0126] 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 amount is obtained by using the constructed cavity 1 system fuzzy PI controller and the cavity 1 control parameters obtained by the optimization based on the new improved particle swarm algorithm, and outputted 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.

[0127] 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 amount is obtained by using the constructed cavity 2 system fuzzy PI controller and the cavity 2 control parameters obtained by the optimization based on the new improved particle swarm algorithm, and outputted 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, so as to achieve ultra-high precision pneumatic pulling force output.

[0128] For this embodiment, an experimental method will be used to perform parameter optimization verification.

[0129] 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 model PAA-33X of Keller Company, and the three-position five-way solenoid valve adopts the proportional directional valve model MPYE-5-1 / 8LF-010 of Festo Company.

[0130] 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 mainly on the control system and is set to 80000. The optimization results are shown in Table 9 and Figure 6 As can be seen from the figure, the proposed new improved particle swarm optimization algorithm found the theoretical optimal control parameters of the fuzzy PI pressure controller in the ninth iteration. After the optimized parameters were rounded (or trimmed), the pneumatic servo experiment was carried out based on this set of parameters.

[0131] Table 9 Parameters obtained by optimizing the fuzzy PI controller using the new improved particle swarm optimization algorithm and the rounded (or trimmed) parameters

[0132]

[0133] In the experiment, the air bearing and air piston of the air-floating frictionless cylinder are supplied with gas at pressures of 0.4MPa and 0.2MPa respectively by air supply branch 1 and air supply branch 2. In addition, the thrust output 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 807.2665mm without considering the processing error). 2 ). The pneumatic servo system is subjected to continuous step thrust control, and the controller parameters are the optimized and rounded parameters, as shown in Table 3.

[0134] Reference Figure 7 and Figure 8It can be seen that at this time, the actual continuous step output force response curve of the output force servo system fits the target curve. In the output force variation range of 80N to 240N, the steady-state error of the system when it reaches stability is less than 0.023N (equivalent to the system accuracy reaching 0.01% FS, so 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.

[0135] Embodiment 2:

[0136] This embodiment is different from the first embodiment in that the ultra-high precision pressure control of cavity one and cavity two is alternately performed by utilizing the fuzzy PI control parameters of the cavity one system and the fuzzy PI control parameters of the cavity two system obtained by optimizing the novel improved particle swarm algorithm, thereby realizing the alternating output of ultra-high precision 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 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 output of thrust and pull is executed, and continuous alternating force can be output by repeating this cycle.

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 a large gas tank 19; 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, so as to provide compressed air for each pneumatic branch; the pressure reducing valve 1 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, so that the air-floating frictionless cylinder 10 can work normally; The upstream of the three-position five-way solenoid valve 3 is connected to the large gas tank 19 as branch three; the two interfaces of the three-position five-way solenoid valve 3 are respectively connected to the small gas tank 1 5 and the small gas tank 2 8 through the two-position three-way solenoid valve 1 4 and the two-position three-way solenoid valve 2 7; 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 10 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 computer 1 through the data acquisition card 2, and the industrial computer 1 executes its own fuzzy PI control algorithm 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, characterized in that: 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 control parameter intelligent optimization method of an ultra-high precision pneumatic servo system according to claim 1 is characterized in that: The rodless cavity of the small gas tank 15 and the air-floating frictionless cylinder 10 constitutes the controlled cavity 1, and the rod cavity of the small gas tank 28 and the air-floating frictionless cylinder 10 constitutes the controlled cavity 2. The high-precision pressure sensor 16 and the high-precision pressure sensor 29 respectively feed back the pressure information in the cavity 1 and the 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; it is characterized in 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: respectively taking cavity one and cavity two as controlled objects, and optimizing their respective optimized fuzzy PI control parameters.

5. The control parameter intelligent optimization 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 the time; e is the pressure control error.

6. The control parameter intelligent optimization method according to claim 5, characterized in that: It also includes incorporating the penalty function into the objective function, as follows: when 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 oscillates at this time, then the current control is stopped and the particle is sentenced to "death".

7. The control parameter intelligent optimization 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, keep the state of the particle before the update. S47: If the number of iterations reaches the maximum number of iterations, execute the next step, otherwise execute 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 ith particle after t iterations; is the individual historical optimal position of the ith particle after t iterations; is the global optimal position of the entire group after t iterations; is the velocity of the ith particle after t iterations; is the velocity of the ith 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 takes 0.1, otherwise it takes 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 best position at the t-th iteration; λ ik (t) is the k-th dimension difference weight of the ith 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 control parameter intelligent optimization method according to claim 7, characterized in that: The parameters w, c1, c2 and σ in the novel position update formula u The adaptive control system is realized by fuzzy control system, 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 then combined with the 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 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), 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 control parameter intelligent optimization method according to claim 4, 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 control parameter intelligent optimization method according to claim 4, characterized in that: By using the fuzzy PI control parameters of cavity one system and cavity two system optimized 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 the alternating output of ultra-high precision thrust and pull of the air-floating frictionless cylinder.

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