Fault Tolerant Control and Parameter Optimization Method for Pressure Sensing in Pneumatic Position Servo System

Abstract

The present invention proposes a pressure sensing fault tolerance control and parameter optimization method for a pneumatic position servo system, including the steps of: S1. Establish a mathematical model of the pneumatic position servo system by combining the cylinder kinematic model, the system thermodynamics model and the proportional direction valve model; S2. Design a fractional-order fast generalized super-twisting sliding mode controller based on the mathematical model of the pneumatic position servo system; S3. Design a pressure sensing fault tolerance control method for the pneumatic position servo system based on a pressure observer; S4. Design a fault tolerance control parameter optimization method based on a novel improved sparrow search algorithm; S5. Use the control parameters of the fractional-order fast generalized super-twisting sliding mode controller and the fault tolerance controller obtained by the novel improved sparrow search algorithm to perform fault tolerance control on the pneumatic position servo system, and realize position control under pressure sensing faults. The novel improved sparrow search algorithm of the present invention ensures an effective balance between the exploration and development capabilities of the algorithm and improves the optimization performance of the algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of pneumatic technology, and particularly relates to a pressure sensing fault tolerance control and parameter optimization method for a pneumatic position servo system. Background Technique

[0002] Pneumatic systems have been widely used in the modern industrial field due to many advantages such as simple structure, clean and environmentally friendly, low cost, high flexibility, wide application range, and large power-to-weight ratio. Taking the valve-controlled cylinder pneumatic system as an example, if high-precision motion control is to be achieved, generally, model-based nonlinear control algorithms are adopted, and such algorithms require obtaining the full state information of the system. However, in such systems, pressure sensor failures are quite common, seriously affecting the normal operation of the system. In the context of the increasingly complex and expanding scale of today's systems, once a failure occurs but is not detected and isolated in time, it may cause great economic losses. Therefore, it is particularly necessary to carry out real-time fault diagnosis and implement fault tolerance control for the system.

[0003] In addition, currently in nonlinear controllers and fault tolerance controllers, the tuning of control parameters generally relies on the empirical trial-and-error method. However, the control parameters determined by this method often have strong subjectivity, contingency, and randomness, and it is difficult to obtain control parameters that enable the system to achieve the best performance. In contrast, using meta-heuristic optimization algorithms to optimize the above parameters has significant advantages. The sparrow search algorithm is a popular optimization algorithm and has been applied in fields such as path planning, engineering design, image processing, and parameter optimization. In view of the deficiencies of the basic sparrow search algorithm, such as slow convergence speed, easy to fall into local optimal solutions, and origin approaching property, it is necessary to improve it. Summary of the Invention

[0004] In view of the above problems, the present invention provides a pressure sensing fault tolerance control and parameter optimization method for a pneumatic position servo system, aiming to enable the system to still achieve high position servo control accuracy in the case of a pressure sensor failure.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A pressure sensing fault tolerance control and parameter optimization method for a pneumatic position servo system, comprising the following steps:

[0007] S1: Combine the cylinder kinematic model, the system thermodynamics model, and the proportional direction valve model to establish a mathematical model of the pneumatic position servo system;

[0008] S2: Design a fractional-order fast generalized super-twisting sliding mode controller based on the mathematical model of the pneumatic position servo system;

[0009] S3: Design a pressure sensing fault-tolerant control method for the pneumatic position servo system based on a pressure observer;

[0010] S4: Design a fault-tolerant control parameter optimization method based on a novel improved sparrow search algorithm;

[0011] S5: Use the control parameters of the fractional-order fast generalized super-twisting sliding mode controller and the fault-tolerant controller obtained by the novel improved sparrow search algorithm to perform fault-tolerant control of the pneumatic position servo system, and achieve position control under pressure sensing faults.

[0012] Furthermore, the pneumatic position servo system includes an actuator module, a gas supply module, and a control system module; the actuator module uses a piston-type cylinder; the control system module includes a proportional direction valve with an air outlet connected to the rodless cavity and the rod cavity of the piston-type cylinder, a pressure sensor one, a pressure sensor two, and a displacement sensor for monitoring the pressure and piston displacement information in the rodless cavity and the rod cavity of the piston-type cylinder, a data acquisition card for transmitting information, and an industrial control computer for equipment control; the gas supply module includes a gas storage tank, a precision pressure reducing valve, and a gas source connected in sequence; the gas storage tank is connected to the air inlet of the proportional direction valve.

[0013] Furthermore, in the step S1, the mathematical model of the pneumatic position servo system is as follows:

[0014]

[0015] Where: x is the displacement of the piston; M is the effective mass of the moving part of the cylinder; p a and p b are the pressures in the rodless cavity and the rod cavity of the cylinder respectively; X is the state vector including the displacement, velocity, acceleration of the piston, and the pressures in the rodless cavity and the rod cavity of the cylinder; A a and A b are the force areas of the pistons in the rodless cavity and the rod cavity respectively; V a and V b are the volumes of the rodless cavity and the rod cavity respectively; F f is the friction force of the cylinder; F 1 is the external load force on the cylinder; c is the specific heat ratio of air; R is the ideal gas constant; T 0 is the atmospheric temperature; and are the mass flow rates flowing into the rodless chamber and the rod chamber respectively; and are the mass flow rates flowing out of the rodless chamber and the rod chamber respectively. The specific expressions of the compressed air mass flow rates flowing into and out of each chamber are as follows:

[0016]

[0017] In the formula: p d and p u are the pressures downstream and upstream of the proportional direction valve respectively; C 1 and C d are a constant and a gas flow correction coefficient respectively; T u is the temperature upstream of the valve port; b is the critical pressure ratio; δ is the pressure ratio when the gas exhibits laminar flow; u is the control voltage of the proportional direction valve; A ( u ) is the effective valve port area, which is determined by the relationship curve between the opening area of the proportional direction valve and the control voltage.

[0018] Furthermore, the specific content of step S2 is as follows:

[0019] Introduce an exponential term into the fractional-order sliding mode surface to design a new type of fractional-order fast sliding mode surface, and its specific expression is as follows:

[0020]

[0021] In the formula: c 1 and c 2 are positive real numbers; sgn is the sign function; α is the exponent, and α >1; β is the fractional order, and 1 < β <2; D β represents the calculus operator; e 1 is the tracking error of the piston displacement;

[0022] Introduce a proportional coefficient, a variable gain coefficient, and a saturation function into the super-twisting algorithm to design an improved generalized super-twisting algorithm, and its specific expression is as follows:

[0023]

[0024]

[0025]

[0026]

[0027] Wherein: k 1, k 2, a and b are positive real numbers; s is the sliding mode surface; and are the non - linear stability terms; q is the proportionality coefficient, and 0 < q < 1; sat is the saturation function; g is the variable gain coefficient.

[0028] Furthermore, the specific content of step S3 is as follows:

[0029] When the absolute value of the difference between the measured value of the pressure sensor and the predicted value of the pressure observer is greater than the set threshold, the pressure observer is used for pressure monitoring, otherwise, the pressure sensor continues to be used for monitoring. The specific expression is as follows:

[0030]

[0031] Wherein: p ac and p bc are the pressures of the rodless chamber and the rod chamber monitored by the pressure sensor respectively; g a and g b are the fault - tolerance control thresholds of the rodless chamber and the rod chamber respectively; and are the pressures of the rodless chamber and the rod chamber predicted by the pressure observer respectively. The specific expressions are as follows:

[0032]

[0033] Wherein: k a and k b are the control parameters of the pressure observers for the rodless chamber and the rod chamber respectively; and are the predicted mass flow rates flowing into the rodless chamber and the rod chamber respectively; and are the predicted mass flow rates flowing out of the rodless chamber and the rod chamber respectively; T a and T b are the temperatures in the rodless chamber and the rod chamber respectively; and They are the differentials of the volumes of the rodless chamber and the rod chamber respectively.

[0034] Furthermore, in step S4, the parameters of the fractional-order fast generalized super-twisting sliding mode controller and the fault-tolerant controller are optimized by the new improved sparrow search algorithm in sequence. The specific steps are as follows:

[0035] S41: Determine the variables to be optimized for the sliding mode controller and the fault-tolerant controller;

[0036] S42: Determine the search range of the variables to be optimized by the trial-and-error method;

[0037] S43: Establish the objective functions for each optimization stage;

[0038] S44: Use the new improved sparrow search algorithm to iteratively optimize the parameters of the sliding mode controller and the pressure observer in sequence;

[0039] S45: Optimize the control parameters of the sliding mode controller in the state where the pressure sensor works normally;

[0040] S46: Based on the control parameters of the optimized sliding mode controller, perform position control and further optimize the control parameters of the fault-tolerant controller.

[0041] Furthermore, in step S43, the maximum absolute error is used as the evaluation index in the parameter optimization stage of the sliding mode controller; the integral time absolute error is used as the evaluation index in the parameter optimization stage of the pressure observer. The specific expressions are as follows:

[0042]

[0043] In the formula: f 1 and f 2 are the objective functions for the parameter optimization of the sliding mode controller and the pressure observer respectively, e 1 is the displacement control error of the piston, T is the test duration.

[0044] Furthermore, step S44 is specifically:

[0045] S441: Set the basic parameters of the new improved sparrow search algorithm and initialize;

[0046] S442: Randomly initialize the positions of the sparrow population in the search space;

[0047] S443: Calculate the fitness value of each sparrow individual, and find the optimal position and the worst position;

[0048] S444: Divide the discoverers and joiners in the sparrow group;

[0049] S445: Update the position of the discoverer using the new discoverer position update formula;

[0050] S446: Update the position of the joiner using the new joiner position update formula;

[0051] S447: Identify the early warning sparrows in the sparrow group;

[0052] S448: Update the position of the early warning sparrows using the early warning sparrow position update formula;

[0053] S449: If the number of iterations reaches the maximum number of iterations, output the optimized control parameters; otherwise, execute step S443;

[0054] In the said step S445, the new discoverer position update formula is as follows:

[0055]

[0056] In the formula: r 1 and r 2 are random numbers within the range [0, 1]; I is a random number in the set {1, 2}; n is the current number of iterations; Q is a random number subject to the standard normal distribution, ST represents the safety threshold, which is a random number within the range [0.5, 1]; L is a 1× d matrix with all elements equal to 1, and d is the dimension of the search space; X n i,j is the value of the i th sparrow after n iterations in the j th dimension; SX is a solution randomly selected from the target set generated by the improved sparrow algorithm, and its specific expression is as follows:

[0057]

[0058] In the formula: FP i is the target set of the m th sparrow; F i is the i th sparrow's fitness value, X best is the position of the individual with the optimal fitness value;

[0059] In the step S446, the position update formula for the new joiner is as follows:

[0060]

[0061] Where: X worst is the worst position in the current sparrow group; X p is the best position of the discoverer; r 3 is a random number within the range [0, 1]; N is the maximum number of iterations; A is a 1× d matrix with each value randomly assigned 1 or -1, and A * = A T ( AA T ) -1 ; r 4 is a random number subject to a Gaussian distribution, and its specific expression is as follows:

[0062]

[0063] Where: r 5 is a random number within the range [-2, 2];

[0064] In the step S448, the position update formula for the early warning sparrow is as follows:

[0065]

[0066] Where: K is a random number within the range [-1, 1]; β represents the update step size and is a random number subject to a standard normal distribution; f i is the fitness value of the i th sparrow individual; f g and f w are the global best fitness value and the global worst fitness value respectively; ε is a value equal to 1E - 50.

[0067] Furthermore, in the step S447, the early warning sparrow selects a random selection strategy, and the number of early warning sparrows is determined by a non - linear adaptive factor, and its specific expression is as follows:

[0068]

[0069] Where: SDis the number of early warning personnel, SD max and SD min are the maximum and minimum values of the number of early warning personnel respectively, N is the maximum number of iterations, round is the rounding function.

[0070] The pneumatic position servo system pressure sensing fault tolerance control and parameter optimization method proposed by the present invention has the following beneficial effects compared with the prior art:

[0071] 1) The present invention proposes a new fractional-order fast generalized super-twisting sliding mode controller. On the one hand, a new fractional-order fast sliding mode surface is designed to accelerate the system convergence by introducing an exponential term; on the other hand, an improved generalized super-twisting reaching law is proposed to accelerate the convergence by varying the exponential coefficient, and the proportional coefficient and saturation function are used to ensure the convergence and weaken the chattering.

[0072] 2) The present invention proposes a new improved sparrow search algorithm, which integrates three improvement strategies of Gaussian mutation strategy, osprey optimization algorithm and adaptive factor on the basis of the basic sparrow search algorithm to enhance the diversity of the algorithm, ensure the effective balance between the exploration and development capabilities of the algorithm, and improve the optimization ability of the algorithm.

[0073] 3) The present invention provides a pneumatic position servo system pressure sensing fault tolerance control method. In the case of pressure sensing fault, the pressure observer is used to replace the sensor for pressure monitoring, so as to ensure the high-precision control of the pneumatic position servo system in case of fault. Description of the Drawings

[0074] Figure 1 is the pneumatic schematic diagram of the pneumatic position servo system proposed by the present invention.

[0075] Figure 2 is the step diagram of the pneumatic position servo system pressure sensing fault tolerance control and parameter optimization method of the present invention.

[0076] Figure 3 is the optimization flow chart of the new improved sparrow search algorithm proposed by the present invention.

[0077] Figure 4 is the fitness convergence curve of the optimized sliding mode controller in the embodiment of the present invention.

[0078] Figure 5 is the fitness convergence curve of the optimized fault tolerance controller in the embodiment of the present invention.

[0079] Figure 6 is the position control result using the optimized parameters in the case of pressure sensor fault in the embodiment of the present invention.

[0080] Attached drawing reference numerals:

[0081] 1 - Piston - type cylinder; 2 - Proportional direction valve; 3 - Pressure sensor 1; 4 - Pressure sensor 2; 5 - Displacement sensor; 6 - Data acquisition card; 7 - Industrial control computer; 8 - Air storage tank; 9 - Pressure reducing valve; 10 - Air source. Specific implementation manners

[0082] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the examples of the present application. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0083] Refer to Figure 1 , the pneumatic position servo system of the present invention includes an actuator module, a gas supply module, and a control system module; the actuator module uses a piston - type cylinder 1; the control system module includes a proportional direction valve 2, a pressure sensor 1 3, a pressure sensor 2 4, a displacement sensor 5, a data acquisition card 6, and an industrial control computer 7; the gas supply module includes an air storage tank 8, a pressure reducing valve 9, and an air source 10.

[0084] The compressed air generated by the air source 10 is transported to the air storage tank 8 through the action of the pressure reducing valve 9 to provide compressed air for the piston - type cylinder 1. The pressure sensors 1 3, pressure sensors 2 4, and displacement sensor 5 transmit the pressure information of the rod - end chamber and non - rod - end chamber of the piston - type cylinder 1 and the displacement information of the piston to the industrial control computer 7 through the data acquisition card 6. After the industrial control computer 7 executes the fractional - order fast generalized super - twisting sliding - mode control algorithm, it outputs a control signal to the proportional direction valve 2 through the data acquisition card 6. Then, the proportional direction valve 2 is used to control the intake and exhaust of the non - rod - end chamber and rod - end chamber of the piston - type cylinder 1 to achieve high - precision position servo control. When the pressure sensors 1 3 and pressure sensors 2 4 fail, the fault - tolerant controller replaces the sensors to monitor the pressure of the non - rod - end chamber and rod - end chamber of the piston - type cylinder 1.

[0085] Refer to Figure 2 , the fault - tolerant control and parameter optimization method for pressure sensing faults of a pneumatic position servo system includes the following steps:

[0086] S1: Combining the cylinder kinematic model, the system thermodynamics model, and the proportional direction valve model, the mathematical model of the pneumatic position servo system can be obtained as shown below:

[0087]

[0088] In the formula: x is the displacement of the piston; M is the effective mass of the moving part of the cylinder; pa and p b are the pressures in the rodless chamber and the rod chamber of the cylinder, respectively; X is the state vector including the displacement, velocity, acceleration of the piston and the pressures in the rodless chamber and the rod chamber of the cylinder; A a and A b are the force - bearing areas of the pistons in the rodless chamber and the rod chamber, respectively; V a and V b are the volumes of the rodless chamber and the rod chamber, respectively; F f is the frictional force of the cylinder; F 1 is the external load force on the cylinder; c is the specific heat ratio of air; R is the ideal gas constant; T 0 is the atmospheric temperature; and are the mass flow rates into the rodless chamber and the rod chamber, respectively; and are the mass flow rates out of the rodless chamber and the rod chamber, respectively. The specific expressions for the compressed air mass flow rates into and out of each chamber are as follows:

[0089]

[0090] In the formula: p d and p u are the pressures downstream and upstream of the proportional direction valve, respectively; C 1 and C d are a constant and a gas flow correction coefficient, respectively; T u is the temperature upstream of the valve port; b is the critical pressure ratio; δ is the pressure ratio when the gas shows laminar flow; u is the control voltage of the proportional direction valve; A ( u ) is the effective valve port area, which is determined by the relationship curve between the opening area of the proportional direction valve and the control voltage.

[0091] S2: Based on the mathematical model of the pneumatic position servo system, design a fractional - order fast generalized super - twisting sliding - mode controller; in order to improve the convergence speed of the system, an exponential term is introduced into the fractional - order sliding - mode surface, and a new type of fractional - order fast sliding - mode surface is designed. Its specific expression is as follows:

[0092]

[0093] In the formula: c 1 and c 2 are positive real numbers; sgn is the sign function; α is the exponent, and α > 1; β is the fractional order, and 1 < β < 2; D β represents the calculus operator; e 1 is the tracking error of the piston displacement;

[0094] In order to reduce the adjustment step of the controlled quantity when the system is close to the equilibrium point and weaken the system jitter, a proportional coefficient, a variable gain coefficient, and a saturation function are introduced into the super-twisting algorithm, and an improved generalized super-twisting algorithm is designed. Its specific expression is as follows:

[0095]

[0096] In the formula: k 1, k 2, a and b are positive real numbers; s is the sliding mode surface; and are the non-linear stability terms; q is the proportional coefficient, and 0 < q < 1; sat is the saturation function; g is the variable gain coefficient.

[0097] S3: Design a pressure sensing fault-tolerant control method for the pneumatic position servo system based on a pressure observer; when the absolute value of the difference between the measured value of the pressure sensor and the predicted value of the pressure observer is greater than the set threshold, the pressure observer is used for pressure monitoring, otherwise the pressure sensor is continued to be used for monitoring. Its specific expression is as follows:

[0098]

[0099] In the formula: p ac and p bc are the pressures of the rodless chamber and the rod chamber monitored by the pressure sensor, respectively; g a and g b are the fault-tolerant control thresholds of the rodless chamber and the rod chamber, respectively; and are the pressures of the rodless chamber and the rod chamber predicted by the pressure observer, respectively. Its specific expression is as follows:

[0100]

[0101] In the formula: k a and k b are the control parameters of the pressure observers for the rodless chamber and the rod chamber, respectively; and are the estimated mass flow rates flowing into the rodless chamber and the rod chamber, respectively; and are the estimated mass flow rates flowing out of the rodless chamber and the rod chamber, respectively; T a and T b are the temperatures in the rodless chamber and the rod chamber, respectively; and are the differentials of the volumes of the rodless chamber and the rod chamber, respectively.

[0102] S4: Design a fault-tolerant control parameter optimization method based on a novel improved sparrow search algorithm; the parameters of the fractional-order fast generalized super-twisting sliding mode controller and the fault-tolerant controller are optimized by the novel improved sparrow search algorithm in sequence, and the specific steps are as follows:

[0103] S41: Determine the variables to be optimized for the sliding mode controller and the fault-tolerant controller.

[0104] S42: Determine the search range of the variables to be optimized by the trial-and-error method.

[0105] S43: Establish the objective function for each optimization stage. The maximum absolute error is used as the evaluation index in the parameter optimization stage of the sliding mode controller; the integral time absolute error is used as the evaluation index in the parameter optimization stage of the pressure observer, and its specific expression is as follows:

[0106]

[0107] In the formula: f 1 and f 2 are the objective functions for the parameter optimization of the sliding mode controller and the pressure observer, respectively, e 1 is the displacement control error of the piston, T is the test duration.

[0108] S44: Use the novel improved sparrow search algorithm to iteratively optimize the parameters of the sliding mode controller and the pressure observer in sequence. Referring to Figure 3 , the specific iterative optimization process is as follows:

[0109] S441: Set the basic parameters of the novel improved sparrow search algorithm and initialize it.

[0110] S442: Randomly initialize the positions of the sparrow population in the search space.

[0111] S443: Calculate the fitness value of each sparrow individual, and find the optimal position and the worst position.

[0112] S444: Divide the discoverers and joiners in the sparrow group.

[0113] S445: Update the positions of the discoverers using the new discoverer position update formula. The new discoverer position update formula is as follows:

[0114]

[0115] Where: r 1 and r 2 are random numbers within the range [0, 1]; I is a random number in the set {1, 2}; n is the current iteration number; Q is a random number obeying the standard normal distribution, ST represents the safety threshold, which is a random number within the range [0.5, 1]; L is a 1× d matrix with all elements equal to 1, and d is the dimension of the search space; X n i,j is the i th sparrow's value at the n th iteration in the j th dimension; SX is a solution randomly selected from the target set generated by the improved sparrow algorithm, and its specific expression is as follows:

[0116]

[0117] Where: FP i is the target set of the m th sparrow; F i is the i th sparrow's fitness value, X best is the position of the individual with the optimal fitness value.

[0118] S446: Update the positions of the joiners using the new joiner position update formula. The new joiner position update formula is as follows:

[0119]

[0120] Where:X worst is the worst position in the current sparrow group; X p is the best position of the discoverer; r 3 is a random number within the range [0, 1]; N is the maximum number of iterations; A is a 1× matrix with each value randomly assigned 1 or -1, and d ; A * = A T ( AA T ) -1 ; r 4 is a random number following a Gaussian distribution, and its specific expression is as follows:

[0121]

[0122] In the formula: r 5 is a random number within the range [-2, 2].

[0123] S447: Divide the warning sparrows in the sparrow group. The warning sparrows choose to adopt a random selection strategy, and the number of warning sparrows is determined by a non-linear adaptive factor, and its specific expression is as follows:

[0124]

[0125] In the formula: SD is the number of warning sparrows, SD max and SD min are the maximum and minimum values of the number of warning sparrows respectively, N is the maximum number of iterations, round is the rounding function;

[0126] S448: Update the positions of the warning sparrows using the warning sparrow position update formula. The warning sparrow position update formula is as follows:

[0127]

[0128] In the formula: K is a random number within the range [-1, 1]; β represents the update step size and is a random number following a standard normal distribution; f i is the i th fitness value of the sparrow individual; f g and f wThey are the global best fitness value and the global worst fitness value respectively; ε is a value equal to 1E-50.

[0129] S449: If the number of iterations reaches the maximum number of iterations, output the optimized control parameters, otherwise execute step S443.

[0130] S45: Optimize the control parameters of the sliding mode controller under the condition that the pressure sensor is working normally.

[0131] S46: Based on the control parameters of the optimized sliding mode controller, perform motion control and further optimize the control parameters of the fault-tolerant controller.

[0132] S5: Use the control parameters of the fractional-order fast generalized super-twisting sliding mode controller and the fault-tolerant controller obtained by the novel improved sparrow search algorithm to perform fault-tolerant control of the pneumatic position servo system, and high-precision position control under pressure sensor failure can be achieved.

[0133] In this implementation case, the pressure sensor selected is a high-precision pressure sensor of model 511.930002741 from HUBA Company, the proportional direction valve is a three-position five-way solenoid valve of model MPYE-5-1 / 8-HF-010-B from FESTO Company, the displacement sensor is a displacement sensor of model HG-C1200 from Panasonic Company, the cylinder uses a standard profile cylinder of model DSBC-32-PPVA-N3 from FESTO Company, and the data acquisition card is a data acquisition card of model PCI-1716 from Advantech Company.

[0134] In the optimized fractional-order fast generalized super-twisting sliding mode controller, a multi-frequency sine function is selected x ( t ) = 40[sin(π t ) + sin(0.5π t ) + sin(2π t / 7) + sin(π t / 6) + sin(2π t / 17)] mm is used as the reference trajectory. The parameter settings of the novel improved sparrow search algorithm are as follows: the sparrow population size is 20, the maximum number of iterations is 30, the number of discoverers is 4, the number of joiners is 16, SD max and SD min are 4 and 2 respectively. Select c 1, c 2, β 、 k 1, k 2 andq The control parameters are optimization variables, where c 1, c 2, k the search spaces of 1 and k 2 are [0, 50], β the search space of is [1, 2], q the search space of is [0, 1]. The other control parameters are set as follows, α = 2, a = 1.5, b = 0.5. Figure 4 is the convergence curve of the optimized fractional-order fast generalized super-twisting sliding mode controller in the implementation case. It can be seen that the novel improved sparrow search algorithm found the optimal parameters of the sliding mode controller at the 13th iteration.

[0135] In the optimized fault-tolerant controller, the sine function x ( t ) = 30sin(π t ) mm is selected as the reference trajectory. The parameter settings of the novel improved sparrow search algorithm are the same as above. Select k a and k b in the fault-tolerant controller, and the control parameters are optimization variables, and their search spaces are both [1, 1.4]. Figure 5 are the convergence curves of the optimized rodless cavity and rod cavity fault-tolerant controllers in the implementation case. It can be seen that the novel improved sparrow search algorithm found the optimal parameters of the fault-tolerant controller at the 18th iteration and the 12th iteration respectively.

[0136] Using the control parameters of the optimized fractional-order fast generalized super-twisting sliding mode controller and the fault-tolerant controller, a position servo control experiment is carried out under the condition of rodless cavity and rod cavity pressure sensor faults. Figure 6 are the experimental results of tracking the reference trajectory under the condition of rodless cavity and rod cavity pressure sensor faults. The results show that the optimized fault-tolerant controller can continue to monitor the pressure when a fault occurs, so as to ensure that the system control accuracy does not decrease significantly. Therefore, the method proposed by the present invention can continue to achieve high-precision position servo control of the cylinder under the condition of pressure sensor faults.

Claims

1. A pneumatic position servo system pressure sensing fault tolerance control and parameter optimization method, characterized in that, Including the following steps: S1: Combine the cylinder kinematic model, system thermodynamic model and proportional direction valve model to establish the mathematical model of the pneumatic position servo system; S2: Based on the mathematical model of the pneumatic position servo system, design a fractional-order fast generalized super-twisting sliding mode controller; S3: Design a pressure sensing fault-tolerant control method for the pneumatic position servo system based on a pressure observer; S4: Design a fault-tolerant control parameter optimization method based on a novel improved sparrow search algorithm; S5: Use the control parameters of the fractional-order fast generalized super-twisting sliding mode controller and the fault-tolerant controller obtained by the novel improved sparrow search algorithm to perform fault-tolerant control on the pneumatic position servo system, and achieve position control under pressure sensing faults; The specific content of step S2 is as follows: Introduce an exponential term into the fractional-order sliding mode surface to design a novel fractional-order fast sliding mode surface, and its specific expression is as follows: ， where: c 1 and c 2 are positive real numbers; sgn is the sign function; α is the exponent and α > 1; β is the fractional order and 1 < β < 2; D β represents the calculus operator; e 1 is the tracking error of the piston displacement; Introduce a proportional coefficient, a variable gain coefficient and a saturation function into the super-twisting algorithm to design an improved generalized super-twisting algorithm, and its specific expression is as follows: ， ， ， ， where: k 1, k 2, a and b are positive real numbers; s is the sliding mode surface; and are the nonlinear stabilizing terms; q is the proportionality coefficient, and 0 < q < 1; sat is the saturation function; g is the variable gain coefficient; The specific content of step S3 is as follows: When the absolute value of the difference between the measured value of the pressure sensor and the predicted value of the pressure observer is greater than the set threshold, use the pressure observer for pressure monitoring, otherwise continue to use the pressure sensor for monitoring, and its specific expression is as follows: ， In the formula: p ac and p bc are the pressures of the rodless cavity and the rod cavity monitored by the pressure sensor respectively; g a and g b are the fault tolerance control thresholds of the rodless cavity and the rod cavity respectively; and are the pressures of the rodless cavity and the rod cavity estimated by the pressure observer respectively, and their specific expressions are as follows: ， Wherein: k a and k b are the control parameters of the pressure observers for the rodless chamber and the rod chamber, respectively; and are the estimated mass flow rates flowing into the rodless chamber and the rod chamber, respectively; and are the estimated mass flow rates flowing out of the rodless chamber and the rod chamber, respectively; T a and T b are the temperatures in the rodless chamber and the rod chamber, respectively; and are the differentials of the volumes of the rodless chamber and the rod chamber, respectively; In step S4, the parameters of the fractional-order fast generalized super-twisting sliding mode controller and the fault-tolerant controller are optimized by the novel improved sparrow search algorithm in turn, and its specific steps are as follows: S41: Determine the variables to be optimized for the sliding mode controller and the fault-tolerant controller; S42: Determine the search range of the variables to be optimized by the trial and error method; S43: Establish the objective function for each optimization stage; S44: Use the novel improved sparrow search algorithm to iteratively optimize the parameters of the sliding mode controller and the pressure observer in turn; S45: Optimize the control parameters of the sliding mode controller in the state where the pressure sensor is working normally; S46: Based on the control parameters of the optimized sliding mode controller, perform position control, and further optimize the control parameters of the fault-tolerant controller.

2. The pressure sensing fault-tolerant control and parameter optimization method for the pneumatic position servo system according to claim 1, characterized in that, The pneumatic position servo system includes an actuator module, a gas supply module and a control system module; the actuator module uses a piston cylinder (1); the control system module includes a proportional direction valve (2) with an air outlet connected to the rodless cavity and the rod cavity of the piston cylinder (1), a pressure sensor one (3), a pressure sensor two (4) and a displacement sensor (5) for monitoring the pressures and piston displacements of the rodless cavity and the rod cavity of the piston cylinder (1), a data acquisition card (6) for transmitting information, and an industrial control computer (7) for device control; the gas supply module includes a gas storage tank (8), a precision pressure reducing valve (9) and a gas source (10) connected in sequence; the gas storage tank (8) is connected to the air inlet of the proportional direction valve (2).

3. The pressure sensing fault-tolerant control and parameter optimization method for the pneumatic position servo system according to claim 1, wherein In step S1, the mathematical model of the pneumatic position servo system is as follows: ， Wherein: x is the displacement of the piston; M is the effective mass of the moving part of the cylinder; p a and p b are the pressures in the rodless chamber and the rod chamber of the cylinder respectively; X is the state vector including the displacement, velocity, acceleration of the piston and the pressures in the rodless chamber and the rod chamber of the cylinder; A a and A b are the force areas of the pistons in the rodless chamber and the rod chamber respectively; V a and V b are the volumes of the rodless chamber and the rod chamber respectively; F f is the frictional force of the cylinder; F 1 is the external load force on the cylinder; c is the specific heat ratio of air; R is the ideal gas constant; T 0 is the atmospheric temperature; and are the mass flow rates into the rodless chamber and the rod chamber respectively; and are the mass flow rates out of the rodless chamber and the rod chamber respectively. The specific expressions for the compressed air mass flow rates into and out of each chamber are as follows: ， In the formula: p d and p u are the pressures downstream and upstream of the proportional directional valve respectively; C 1 and C d are a constant and a gas flow correction coefficient respectively; T u is the temperature upstream of the valve port; b is the critical pressure ratio; δ is the pressure ratio when the gas exhibits laminar flow; u is the control voltage of the proportional directional valve; A ( u ) is the effective valve port area, which is determined by the relationship curve between the opening area of the proportional directional valve and the control voltage.

4. The pressure sensing fault-tolerant control and parameter optimization method for the pneumatic position servo system according to claim 1, characterized in that, In the step S43, the maximum absolute error is used as the evaluation index in the parameter optimization stage of the sliding mode controller; the integral time absolute error is used as the evaluation index in the parameter optimization stage of the pressure observer, and its specific expression is as follows: ， In the formula: f 1 and f 2 are the objective functions for optimizing the parameters of the sliding mode controller and the pressure observer respectively, e 1 is the displacement control error of the piston, T is the test duration.

5. The pressure sensing fault-tolerant control and parameter optimization method for the pneumatic position servo system according to claim 1, characterized in that The specific content of the step S44 is as follows: S441: Set the basic parameters of the new improved sparrow search algorithm and initialize them; S442: Randomly initialize the positions of the sparrow population in the search space; S443: Calculate the fitness value of each sparrow individual, and find the optimal position and the worst position; S444: Divide the discoverers and joiners in the sparrow group; S445: Update the positions of the discoverers using the new discoverer position update formula; S446: Update the positions of the joiners using the new joiner position update formula; S447: Divide the warners in the sparrow group; S448: Update the positions of the warners using the warner position update formula; S449: If the number of iterations reaches the maximum number of iterations, output the optimized control parameters, otherwise execute step S443; In the step S445, the new discoverer position update formula is as follows: ， where: r 1 and r 2 are random numbers within the range [0, 1]; I is a random number in the set {1, 2}; n is the current iteration number; Q is a random number that follows the standard normal distribution, ST represents the safety threshold and is a random number within the range [0.5, 1]; L is a 1× matrix where all elements are equal to 1, and d and d is the dimension of the search space; X n i,j is the i value of the n th sparrow after j iterations on the SX dimension; A solution randomly selected from the target set generated by the improved sparrow algorithm has the following specific expression: ， Where: FP i is the target set of the i-th sparrow; m is the number of the sparrow population; F i is the i fitness value of the i-th sparrow, X best is the location of the individual with the optimal fitness value; In the step S446, the new joiner position update formula is as follows: ， In the formula: X worst is the worst position in the current sparrow population; X p is the best position of the discoverer; r 3 is a random number within the range [0, 1]; N is the maximum number of iterations; A is a 1× d matrix with each value randomly assigned 1 or -1, and A * = A T ( AA T ) -1 ; r 4 is a random number subject to a Gaussian distribution, and its specific expression is as follows: ， In the formula: r 5 is a random number within the range [-2, 2]; In the step S448, the warner position update formula is as follows: ， where: K is a random number within the range [-1, 1]; β represents the update step size and is a random number following the standard normal distribution; f i is the fitness value of the i th sparrow individual; f g and f w are the global best fitness value and the global worst fitness value respectively; ε is a value equal to 1E - 50.

6. The pressure sensing fault tolerance control and parameter optimization method for the pneumatic position servo system according to claim 5, characterized in that In the step S447, the warners are selected using a random selection strategy, and the number of warners is determined by the non-linear adaptive factor, and its specific expression is as follows: ， Where: SD is the number of early warning personnel, SD max and SD min are the maximum and minimum values of the number of early warning personnel respectively, N is the maximum number of iterations, round is the rounding function.

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