Pneumatic servo control method and system based on extended state observation

Abstract

The invention discloses a pneumatic servo control method and system based on expansion state observation, and relates to the technical field of pneumatic servo system pressure control, and the method comprises the steps: building a piston-load power model and a cavity pressure model based on an air cylinder structure, i.e., related parameters; introducing reference mass to establish a load force reference model; obtaining total expected pressure based on the piston-load power model and the load force reference model; establishing a state space model based on the chamber pressure model; obtaining an extended state observation equation based on the state space model and the observer gain vector; obtaining a system state estimation value based on an extended state observation equation; a final control signal is obtained based on the total expected pressure and the system state estimated value; and adjusting the chamber pressure of the cylinder based on the final control signal to realize cylinder air pressure control. Precise control over the air pressure of the air cylinder is achieved, and then the precision, robustness and system stability of piston position control are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of pneumatic servo system pressure control, and more particularly to a pneumatic servo control method and system based on expansion state observation. Background Art

[0002] In modern industrial automation and manufacturing, pneumatic cylinders are widely used as actuators in various mechanical systems, particularly in fluid power transmission and hydraulic systems. They are used in scenarios such as pick-and-place movements and robotic manipulation, but these applications also place high demands on the speed and accuracy of their positioning control. Position servo control systems for pneumatic cylinders typically achieve precise control of piston position by regulating the air pressure within the chamber. This control method relies on the dynamic characteristics of the pneumatic system.

[0003] However, due to the compressibility of air and the delay in valve response, pneumatic position servo systems exhibit nonlinear dynamic equations. Furthermore, factors such as air leakage, load variations, and friction can introduce system uncertainties and disturbances, further increasing the control difficulty. To address these issues, researchers have developed various pressure control strategies. For example, pressure control is combined with position control to form a position servo system, with applications such as PI and PID controllers in related designs. However, while feedback linearization methods provide theoretical guidance, their effectiveness relies on precise mathematical models and lacks robustness to modeling uncertainties. Furthermore, open-loop pressure control has a simple structure but cannot compensate for disturbances and parameter changes. Closed-loop LQG self-tuning controllers can adapt to parameter changes, and intelligent controllers such as hybrid fuzzy PID are robust to parameter changes but lack the ability to cope with external disturbances. While sliding mode controllers (SMCs) can reduce the effects of disturbances and are effective in positioning control, they also have certain limitations.

[0004] In terms of controller design, the extended state observer (ESO) is used in the active disturbance rejection controller (ADRC) to estimate system states and generalized disturbances. It has shown good performance in motion control and is used in adaptive controllers and SMC due to its simple configuration and single tuning parameter. However, there has been insufficient consideration of air pressure dynamics in pneumatic actuator control.

[0005] Therefore, how to achieve precise control of cylinder air pressure and thereby improve the accuracy, robustness and system stability of piston position control is an urgent problem that needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a pneumatic servo control method and system based on expansion state observation, which realizes precise control of cylinder air pressure, thereby improving the accuracy, robustness and system stability of piston position control, while reducing valve excitation frequency and reducing valve loss, making the control system more feasible and practical in actual applications.

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

[0008] A pneumatic servo control method based on expansion state observation, comprising:

[0009] Establish a piston-load dynamic model and a chamber pressure model based on the cylinder structure and related parameters;

[0010] Introduce reference mass to establish load force reference model;

[0011] Obtaining a total desired pressure based on the piston-load dynamic model and the load force reference model;

[0012] establishing a state space model based on the chamber pressure model;

[0013] Obtaining an extended state observation equation based on the state space model and the observer gain vector;

[0014] Obtaining a system state estimate based on the expanded state observation equation;

[0015] obtaining a final control signal based on the total desired pressure and the system state estimation value;

[0016] The chamber pressure of the cylinder is adjusted based on the final control signal to achieve cylinder pressure control.

[0017] Preferably, the piston-load dynamic model is specifically:

[0018]

[0019] Among them, M P Indicates the piston mass, M L Indicates the load mass, represents the acceleration of the piston, β represents the viscous friction coefficient, Indicates the speed of the piston, F f (t) represents the Coulomb friction force, F L (t) represents the load force, P1(t) and P2(t) represent the absolute pressures of chamber 1 and chamber 2 in the cylinder, respectively, A1 represents the piston area separating chamber 1 and chamber 2, and A2 represents the area between A1 and A p The difference between A p Indicates the area on the right side of the piston rod in the cylinder, P a(t) represents atmospheric pressure.

[0020] Preferably, the chamber pressure model is specifically:

[0021]

[0022] in, represents the gas pressure of the i-th chamber, k represents the specific heat ratio, V i (t) represents the volume of the i-th chamber, R represents the difference between the specific heat capacity at constant pressure and the specific heat capacity at constant volume, T represents the temperature of the gas in the chamber, Represents the mass flow rate, P i (t) represents the absolute pressure of the i-th chamber, A i represents A1 or A2, and d(t) represents the external disturbance caused by air leakage.

[0023] Preferably, the load force reference model is specifically:

[0024]

[0025] in, represents the reference mass, represents the expected acceleration, represents the reference damping, represents the expected speed, represents the stiffness coefficient, x(t) represents the position of the piston, and x d Indicates the desired position.

[0026] Preferably, the total expected pressure is obtained by:

[0027] The expected force output is obtained based on the piston-load dynamic model and the load force reference model:

[0028]

[0029] Among them, F D (t) represents the desired force output, M represents the total mass of the piston and load;

[0030] Using anti-friction graphite pistons and neglecting Coulomb friction, the desired force output is converted to the desired pressure in each chamber:

[0031] F D (t) = P 1D (t)A1-P 2D (t)A2-P a (t)A P ;

[0032] P sum (t) = P 1D (t)+P2D (t);

[0033] Among them, P 1D (t) and P 2D (t) represents the desired pressure of chamber 1 and chamber 2, respectively, P a (t) represents atmospheric pressure, P sum (t) represents the total supply pressure parameter;

[0034] Based on the above formula, the expected pressure of chamber 1 and chamber 2 is obtained: P 1D (t) and P 2D (t);

[0035] Based on P 1D (t) and P 2D (t) together constitute the total desired pressure P D (t).

[0036] Preferably, establishing a state space model based on the chamber pressure model specifically includes:

[0037] The expansion state observer is obtained based on the chamber pressure model:

[0038] y (r) (t) = b(t)u(t) + f(t);

[0039] Where r = 1, y(t) = P(t), f(t) represents generalized interference,

[0040] Establish a state space model based on the extended state observer:

[0041]

[0042] in, represents the rate of change of the state variable, represents the interaction between state variables, X(t) represents the state variable, represents the effect of input on state variables, represents the correlation coefficient of the generalized perturbation derivative, represents the derivative of the generalized disturbance, y(t) represents the output pressure, and C = [1 0].

[0043] Preferably, the expanded state observation equation is specifically:

[0044]

[0045] in, represents the rate of change of Z(t) over time, Z(t) represents the estimated value of the system state, z1(t) represents the actual pressure estimate, z2(t) represents the generalized disturbance estimate, and L represents the observer gain vector.

[0046] Preferably, the final control signal acquisition method is:

[0047] The initial synovial surface s(t) is set based on the total desired pressure and the output pressure:

[0048] s(t)=e(t)=y(t)-P D (t);

[0049] Based on the initial sliding surface s(t), the initial control input u(t) is obtained:

[0050]

[0051] in, represents the approximate value of the generalized interference f(t), k SMC represents the stability coefficient, sgn(s(t))) represents the sign function of the sliding surface, and b represents the coefficient related to the dynamic characteristics of the system;

[0052] Based on the system state estimation value and the initial control input, the final control input u is obtained. ESMC (t):

[0053]

[0054] Among them, P ESMC Indicates the deviation from the pressure The intensity coefficient of the relevant control action, η ESMC Represents the function used to adjust the sign The intensity coefficient of the effect.

[0055] Preferably, based on the pressure deviation Construct a Lyapunov function:

[0056]

[0057] Based on the derivation of the Lyapunov function, we get:

[0058]

[0059] in, represents the rate of change of the actual pressure estimate z1(t);

[0060] Select the corresponding coefficient P ESMC and η ESMC , making This satisfies the system stability conditions.

[0061] A pneumatic servo control system based on expansion state observation includes: a first model building module, a desired pressure acquisition module, a second model building module, an estimated value acquisition module, a control signal output module and a control adjustment module;

[0062] The first model building module is used to establish a piston-load dynamic model and a chamber pressure model based on the cylinder structure, i.e., related parameters; and introduce a reference mass to establish a load force reference model;

[0063] The expected pressure acquisition module is configured to obtain a total expected pressure based on the piston-load dynamic model and the load force reference model;

[0064] The second model building module is configured to establish a state space model based on the chamber pressure model; and obtain an expanded state observation equation based on the state space model and an observer gain vector;

[0065] The estimated value acquisition module is used to obtain a system state estimated value based on the expanded state observation equation;

[0066] The control signal output module is configured to obtain a final control signal based on the total desired pressure and the system state estimation value;

[0067] The control and adjustment module is used to adjust the chamber pressure of the cylinder based on the final control signal to achieve cylinder pressure control.

[0068] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a pneumatic servo control method and system based on expansion state observation, which has the following beneficial effects:

[0069] 1. The present invention develops a sliding mode controller (SMC) based on an extended state observer (ESO) and combines it with an impedance control module to achieve precise control of cylinder pressure, thereby improving the accuracy, robustness and system stability of piston position control, while reducing the valve excitation frequency and the loss to the valve, making the control system more feasible and practical in actual applications.

[0070] 2. The proposed sliding mode controller based on an extended state observer (ESO) demonstrates superior performance in pressure control and position tracking. In position control, it achieves a smaller steady-state error, enabling more precise piston movement to the desired position. Furthermore, it outperforms a simple sliding mode controller in pressure regulation. For example, the ESO-based sliding mode controller effectively controls chamber pressure in response to parameter changes and external disturbances.

[0071] 3. It is more robust to system uncertainties and external disturbances. Under conditions of parameter changes (such as impedance parameter changes) and external disturbances (such as air leaks), the sliding mode controller based on the extended state observer can successfully drive the piston to the desired position and maintain stable pressure control, while traditional sliding mode controllers will produce steady-state errors and experience chattering under disturbances.

[0072] 4. The sliding mode controller based on the extended state observer generates fewer valve excitation signals, reducing valve wear. Furthermore, its controller gain is smaller than that of the active disturbance rejection controller and sliding mode controller, making it easier to implement in practical applications and reducing system requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0074] Figure 1 A flow chart of a pneumatic servo control method based on expansion state observation provided by the present invention.

[0075] Figure 2 This is a schematic diagram of the cylinder structure and force provided by the present invention.

[0076] Figure 3 Schematic diagram of the connection structure between the pneumatic valve and the chamber 1 provided by the present invention.

[0077] Figure 4 This is a schematic structural diagram of the pneumatic servo control system provided by the present invention.

[0078] Figure 5 A schematic structural diagram of a pneumatic servo control system based on expansion state observation provided by the present invention. DETAILED DESCRIPTION

[0079] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0080] Example 1

[0081] like Figure 1 As shown, an embodiment of the present invention discloses a pneumatic servo control method based on expansion state observation, comprising:

[0082] Establish a piston-load dynamic model and a chamber pressure model based on the cylinder structure and related parameters;

[0083] Introduce reference mass to establish load force reference model;

[0084] The total expected pressure is obtained based on the piston-load dynamic model and the load force reference model;

[0085] Establish a state space model based on the chamber pressure model;

[0086] The extended state observation equation is obtained based on the state space model and the observer gain vector;

[0087] Obtain the estimated value of the system state based on the expanded state observation equation;

[0088] Obtaining a final control signal based on the total desired pressure and the estimated value of the system state;

[0089] The chamber pressure of the cylinder is adjusted based on the final control signal to achieve cylinder pressure control.

[0090] Example 2

[0091] An embodiment of the present invention discloses a pneumatic servo control method based on expansion state observation, comprising:

[0092] The piston-load dynamic model and chamber pressure model are established based on the cylinder structure and related parameters.

[0093] Preferably, Figure 2 As shown, a cylinder consists of a piston, a piston rod, and two chambers. The difference in air pressure between the two chambers determines the position, force, and compliance of the piston.

[0094] The piston in the figure is tightly mounted inside the cylinder, precisely dividing it into two chambers: Chamber 1 and Chamber 2. A good seal is maintained between the piston and the cylinder wall, ensuring that the air pressure within the chambers effectively acts on the piston. One end of the piston rod is firmly connected to the piston, forming a stable, integrated structure. The other end is directly connected to the load, allowing the piston's linear motion within the cylinder to be transmitted unimpeded to the load. This allows the air pressure energy to be smoothly converted into the load's mechanical energy, driving the load to complete various desired operations.

[0095] In terms of force, the absolute pressure P1(t) in chamber 1 and the absolute pressure P2(t) in chamber 2 exert forces on the piston in different directions, and the difference between them is related to the load force F. L (t), Coulomb friction F f (t) and the resistance generated by the viscous friction coefficient β jointly determine the motion state of the piston.

[0096] Preferably, Figure 3 The figure shows the connection of two valves connected to chamber 1. Chamber 1 is connected to the outside world through these two valves. One valve (valve 1) is connected to the pressure tank through a supply path. When valve 1 is open (K1 = 1), compressed air in the pressure tank can flow smoothly into chamber 1, thereby increasing the air pressure in chamber 1. The other valve (valve 2) is connected to the atmosphere through an exhaust path. When valve 2 is opened (K2 = 1), the air in chamber 1 can be discharged to the atmosphere, reducing the air pressure in chamber 1. The opening and closing states of these two valves cooperate with each other to precisely control the changes in air pressure in chamber 1.

[0097] The connection between these two valves and chamber 1 is the key part to achieve pressure control of the pneumatic actuator. By controlling the opening and closing of valve 1 and valve 2, the air mass flow rate in chamber 1 can be adjusted. To control the air pressure P1(t) in chamber 1. Moreover, the change of air pressure in chamber 1 will be transmitted to the entire system through the piston, affecting the position of the piston and the movement of the load. Figure 1 The cylinder structure in the chamber forms a complete pneumatic actuator system, enabling precise control of actuator movement. The mutually exclusive design of the two valves ensures that air cannot flow into and out of chamber 1 at the same time, ensuring accurate and stable air pressure control.

[0098] Preferably, the piston-load dynamic model is specifically:

[0099]

[0100] Among them, M P Indicates the piston mass, M L Indicates the load mass, represents the acceleration of the piston, β represents the viscous friction coefficient, Indicates the speed of the piston, F f (t) represents the Coulomb friction force, F L (t) represents the load force, P1(t) and P2(t) represent the absolute pressures of chamber 1 and chamber 2 in the cylinder, respectively, A1 represents the piston area separating chamber 1 and chamber 2, and A2 represents the area between A1 and A p The difference between A p Indicates the area on the right side of the piston rod in the cylinder, P a (t) represents atmospheric pressure.

[0101] Preferably, assuming that compressed air (or gas) enters chamber 1 and is exhausted from chamber 2, the air pressure in each chamber is

[0102] Preferably, the chamber pressure model is specifically:

[0103]

[0104] in, represents the gas pressure of the i-th chamber, k represents the specific heat ratio, V i (t) represents the volume of the i-th chamber, i = {1, 2}, R represents the difference between the specific heat capacity at constant pressure and the specific heat capacity at constant volume, T represents the temperature of the gas in the chamber, Represents the mass flow rate, P i (t) represents the absolute pressure of the i-th chamber, A i represents A1 or A2, and d(t) represents the external disturbance caused by air leakage.

[0105] Reference mass is introduced to establish a load force reference model.

[0106] Preferably, mechanical impedance is defined as force divided by velocity. Therefore, if motion is the input and force is the output, an impedance equation can be constructed to derive force from motion. The impedance control module represents a mass-spring-damper behavior that regulates the relationship between force and displacement, velocity, and acceleration.

[0107] Preferably, the load force reference model is specifically:

[0108]

[0109] in, represents the reference mass, represents the expected acceleration, represents the reference damping, represents the expected speed, represents the stiffness coefficient, x(t) represents the position of the piston, and x d Indicates the desired position.

[0110] Preferably, It is a parameter introduced when constructing the load force reference model, which is used to describe the quality characteristics of the system under ideal conditions. Used to represent the damping characteristics of the system in the reference model, It reflects the stiffness characteristics of the system in the reference model and reflects the system's ability to resist deformation. d It represents the target position value preset by the control system, and x(t) is detected by the position sensor.

[0111] The total expected pressure is obtained based on the piston-load dynamic model and the load force reference model.

[0112] Preferably, the total expected pressure is obtained by:

[0113] The expected force output is obtained based on the piston-load dynamic model and the load force reference model:

[0114]

[0115] Among them, F D (t) represents the desired force output, and M represents the total mass of the piston and the load, i.e., M = M P +M L ;

[0116] Using anti-friction graphite pistons and neglecting Coulomb friction, the desired force output is converted to the desired pressure in each chamber:

[0117] F D (t) = P 1D (t)A1-P 2D (t)A2-P a (t)A P ;

[0118] P sum (t) = P 1D (t)+P 2D (t);

[0119] Among them, P 1D (t) and P 2D (t) represents the desired pressure of chamber 1 and chamber 2, respectively, P a (t) represents atmospheric pressure, P sum (t) represents the total supply pressure parameter;

[0120] Based on the above formula, the expected pressure of chamber 1 and chamber 2 is obtained: P 1D (t) and P 2D (t);

[0121] Based on P 1D (t) and P 2D (t) together constitute the total expected pressure P D (t).

[0122] Preferably, based on the formula:

[0123]

[0124] Rewritten as:

[0125]

[0126] F D (t) = P1(t)A1-P2(t)A2-P a (t)A p ;

[0127] Based on the above two formulas, enter the formula:

[0128] Ignore friction F f (t), we can get:

[0129]

[0130] Preferably, F L (t) is measured by a load cell, where M represents the total mass of the piston and the load, i.e., M = M P +M L .

[0131] Preferably, starting from the piston-load dynamics and load force reference model, the relationship between the desired pressure and the desired position is derived to obtain the chamber desired pressure P 1D (t) and P 2D (t), it is known that F D (t), A1, A2, A P 、P a (t) and P sum (t), substituting these values into the above equations, we can solve P 1D (t) and P 2D (t).

[0132] Optimally, the total desired pressure provides a precise reference signal for subsequent pressure control, enabling the controller to accurately adjust the chamber pressure according to the desired position, controlling the piston position at the desired location and achieving the goal of position control. Establishing a connection between position and pressure provides the foundation for the control strategy of the entire control system and serves as the front-end guiding part of the entire control process, ensuring that pressure regulation proceeds in the correct direction to achieve the desired position control effect.

[0133] Preferably, in the design of the controller, P 1D (t) and P 2D (t) is the internal reference signal of the controller. Although the controller ultimately regulates the total pressure P D (t), but in the actual control process, the controller needs to be based on P 1D (t) and P 2D (t) is used to adjust the valve status of chamber 1 and chamber 2 (i.e., control the rate of air inflow and outflow) to ensure that the pressure difference between the two air chambers can generate the required force.

[0134] A state-space model is established based on the chamber pressure model.

[0135] Preferably, establishing a state space model based on the chamber pressure model specifically includes:

[0136] The expansion state observer is obtained based on the chamber pressure model:

[0137] y (r)(t) = b(t)u(t) + f(t);

[0138] Where r = 1, y(t) = P(t), f(t) represents generalized interference,

[0139] Establish a state space model based on the extended state observer:

[0140]

[0141] in, represents the rate of change of the state variable, represents the interaction between state variables, X(t) represents the state variable, represents the effect of input on state variables, represents the correlation coefficient of the generalized perturbation derivative, represents the derivative of the generalized disturbance, y(t) represents the output pressure, and C = [1 0].

[0142] Preferably, Among them, A represents the side area of the piston, l represents the length of the cylinder, and since b min is a constant, b(t) is almost a constant, that is, b(t) = b, b represents a coefficient related to the dynamic characteristics of the system, which is related to the thermodynamic properties of the gas and the volume of the chamber.

[0143] Preferably, since b(t) varies with time, V i (t) is the volume of the air chamber, which varies with the piston position. Using b(t) directly would increase the complexity of the controller. By approximating b(t) as a constant b, the controller design can be simplified while still maintaining the accuracy of the model.

[0144] Preferably, Wherein, y(t)=P(t) represents the output pressure, and f(t)=x2(t).

[0145] Preferably, the pressure dynamics of the pneumatic actuator is modeled as a first-order differential equation that describes how the pressure P(t) varies with the mass flow rate. and the generalized disturbance f(t) changes, providing the basis for the subsequent state space model.

[0146] Preferably, the output pressure P(t) and the generalized disturbance f(t) are used as state variables. In the pneumatic actuator system, pressure is the key variable that needs to be controlled, and the generalized disturbance includes uncertainty factors inside and outside the system, which has an important impact on the dynamic behavior of the system. Through the definition of this output equation, the internal state of the system is linked to the measurable output, which facilitates the subsequent observer design based on output feedback and system performance analysis.

[0147] Preferably, the state variable x1(t) is selected as the pressure output y(t)=P(t); the state variable x2(t) is selected as the generalized disturbance f(t); based on the formula y (r) (t)=b(t)u(t)+f(t) we can get:

[0148] r=1, which means the first-order derivative of the output, represents the derivative of x1(t), represents the derivative of y(t);

[0149] Corresponding to the state equation:

[0150] The dynamics of the generalized perturbation f(t) is given by Description, which corresponds to the equation of state: represents the derivative of x2(t), represents the derivative of f(t);

[0151] The output y(t) is the state variable x1(t), so the output equation is: y(t) = x1(t).

[0152] The extended state observation equation is obtained based on the state space model and the observer gain vector.

[0153] Preferably, in order to enable the Zhang state observer ESO to effectively estimate the system state, a suitable observer gain vector is selected. In this embodiment, the observer gain vector L is: where ω o Represents the observer bandwidth, which is a positive real number. By adjusting the observer bandwidth ω o , which can affect the ESO's estimation performance of state variables.

[0154] Preferably, assuming that f(t) is differentiable, the extended state observation equation is obtained based on the state space model and the observer gain vector. The extended state observation equation is specifically:

[0155]

[0156] in, represents the rate of change of Z(t) over time, Z(t) represents the estimated value of the system state, z1(t) represents the actual pressure estimate, z1(t)≈P(t), z2(t) represents the generalized disturbance estimate, L represents the observer gain vector, z2(t)≈f(t).

[0157] Preferably, an ESO is constructed based on the chamber pressure model, and the state-space model is obtained by approximation, and then the ESO structure is designed. The main function of the ESO is to continuously update the estimate of the system state using the system input u(t), output y(t), and observer gain vector L, thereby achieving real-time observation and estimation of the system state estimate Z(t) (especially the generalized disturbance f(t)). This provides key interference estimation information for the subsequent sliding mode controller SMC to compensate for the interference, enabling the sliding mode controller SMC to more accurately adjust the control signal in the presence of uncertainty and interference, improving the robustness and stability of the system, and enhancing the control system's adaptability to complex actual working conditions.

[0158] The system state estimation is obtained based on the extended state observation equation.

[0159] The final control signal is obtained based on the total desired pressure and the system state estimate.

[0160] Preferably, the final control signal acquisition method is:

[0161] Set the initial synovial surface s(t) based on the total desired pressure and the output pressure:

[0162] s(t)=e(t)=y(t)-P D (t);

[0163] Based on the initial sliding surface s(t), the initial control input u(t) is obtained:

[0164]

[0165] in, represents the approximate value of the generalized interference f(t), k SMC represents the stability coefficient, sgn(s(t))) represents the sign function of the sliding surface, and b represents the coefficient related to the dynamic characteristics of the system;

[0166] Based on the system state estimate, the initial control input is integrated to obtain the final control input u ESMC (t):

[0167]

[0168] Among them, P ESMC Indicates the deviation from the pressure The intensity coefficient of the relevant control action, η ESMC Represents the function used to adjust the sign The two work together to adjust the control input to achieve stable control of the system and meet the expected performance.

[0169] Preferably, s(t) in the initial control input u(t) is replaced by Replace it with z2(t) and get the final control input u ESMC (t); By introducing the system state estimation value, the system state and generalized disturbance are estimated in real time, which reduces the estimation error of generalized disturbance in the classical sliding mode controller and improves the control accuracy.

[0170] Preferably, the Lyapunov function is obtained based on the initial synovial surface s(t): and its derivatives in,

[0171] when (η SMC is a positive number) the control system is stable, and the stability coefficient is set to k SMC =F+η SMC , where F is The boundary, Indicates average pressure.

[0172] Preferably, The volume V i (t) = Ax(t), pressure P(t) is the average pressure It is estimated that there are

[0173] Preferably, during the position control process, the sliding mode controller SMC continuously monitors the actual position of the piston and adjusts the control input according to the deviation from the desired position so that the piston can accurately follow the desired trajectory.

[0174] In the actual system, the sliding mode controller SMC obtains information such as piston speed, position and pressure through sensors, combines the known parameters of the system, calculates F, and then adjusts the controller parameters according to the value of F to optimize the control effect of the system and ensure that the system is stable in the presence of uncertainties (such as f(t) and The system can still operate stably and meet the control requirements under the condition of the difference between

[0175] Preferably, the design of the sliding surface determines the control target of the system, that is, to keep the system state on the sliding surface so that P(t) tracks P D(t), achieving precise control of pressure. The construction of Lyapunov function and its derivative analysis are used to prove the stability of the system.

[0176] Preferably, by integrating the system state estimation value output by the extended state observer ESO into the initial control input of the sliding mode controller SMC, and constructing a Lyapunov function based on the system state estimation value output by the extended state observer ESO for stability analysis, an effective combination of the extended state observer ESO and the sliding mode controller SMC is achieved, thereby improving the control performance of the pneumatic actuator servo system.

[0177] Preferably, the output of the extended state observer (ESO) is introduced into the initial control input design of the sliding mode controller (SMC). Based on the estimation of the generalized disturbance by the system state estimation value, the initial control input of the sliding mode controller (SMC) is adjusted to compensate for the influence of the disturbance on the system.

[0178] Preferably, z2(t) is a generalized disturbance estimate. Subtracting z2(t) from the final control input effectively offsets some of the generalized disturbance, improving the system's robustness to disturbances. For example, when the system is subject to generalized disturbances caused by air leaks or friction changes, the extended state observer (ESO) can estimate these disturbances in real time. The sliding mode controller (SMC) adjusts the control input based on the ESO estimate, enabling the system to better cope with disturbances and maintain stable performance.

[0179] Preferably, by calculating the pressure deviation The sliding surface can measure the difference between the current state and the desired state of the system based on the ESO's estimate of the system state, so that the SMC control strategy can be adjusted according to the information provided by the ESO. D When there is a deviation between (t), the sliding surface is not zero. The SMC will adjust the control input according to the state of the sliding surface to drive the system state closer to the desired state and achieve precise control of the piston position.

[0180] Preferably, based on the pressure deviation Construct a Lyapunov function:

[0181]

[0182] Based on the derivation of the Lyapunov function, we get:

[0183]

[0184] in, Represents the rate of change of the actual pressure estimate z1(t), which is used to analyze the convergence of the estimated pressure and the stability of the system;

[0185] Select the corresponding coefficient PESMC and η ESMC , making This satisfies the system stability conditions.

[0186] Preferably, in

[0187] Preferably, the stability analysis method based on ESO state estimation ensures that the ESO-SMC control system can operate stably in the presence of uncertainties and disturbances, providing a theoretical basis for reliable control of the system.

[0188] The chamber pressure of the cylinder is adjusted based on the final control signal to achieve cylinder pressure control.

[0189] Preferably, the SMC calculates the control input u based on the state estimation information provided by the ESO ESMC (t) to adjust the chamber pressure of the pneumatic actuator and, in turn, control the piston position. For example, during system operation, when the piston position changes or is subject to external disturbances, the ESO can quickly estimate the change in system state. The SMC adjusts the control input based on these estimates, enabling the system to respond quickly and maintain stable performance, achieving precise control of the piston position.

[0190] Preferably, through the above method, ESO and SMC are closely combined, giving full play to the ESO's estimation ability for system status and generalized disturbances and the SMC's robust control ability for uncertainty and disturbances, thereby improving the control accuracy and stability of the pneumatic actuator servo system under complex working conditions; the present invention can fully utilize the ESO's estimation ability for system status and disturbances and the control advantages of SMC, overcome the system's nonlinearity, uncertainty and external disturbances in actual operation, achieve high-performance control of the pneumatic actuator servo system, ensure the system operates stably and accurately, and meet the needs of practical applications.

[0191] Preferably, Figure 4 As shown in the figure, the expected position x d As the system's input signal, it is fed into the impedance control module. It represents the target piston position the system desires to achieve, providing goal guidance for the entire control process and determining the direction and magnitude of the system's subsequent control actions.

[0192] The impedance control module receives the desired position x d After that, according to its internal control logic, the output is the desired pressure P D This module plays a key role in the system in converting the desired position into the desired pressure, establishing a bridge between position and pressure, and providing a reference signal for subsequent pressure control, enabling precise adjustment of pressure regulation based on the desired position.

[0193] The control system receives the desired pressure P from the impedance control module D And the actual pressure P(t) and speed of the cylinder feedback Based on these input signals, the control system processes them using its internal ESO-based SMC algorithm and outputs a control signal u(t). Based on the difference between the desired pressure and the actual pressure and speed, the control system uses a controller algorithm to calculate the appropriate control signal to adjust the operating state of the pneumatic actuator, achieving precise control of pressure and position, ensuring the system tracks the desired position and operates stably.

[0194] The pneumatic actuator receives the control signal u(t) output by the control system and drives the actuator to work according to the signal, thereby generating the actual pressure P(t) and speed The pneumatic actuator is the system's actuating component, converting control signals into actual physical motion, changing the air pressure within the chamber, thereby driving the piston and achieving position control. Simultaneously, the actual pressure and velocity signals it provides feedback to the control system, forming a closed-loop control loop that enables the system to monitor and adjust its operating status in real time, improving control accuracy and stability.

[0195] The entire system forms a closed-loop feedback structure, starting with the desired position input, passing through the impedance control module, the control system, and the pneumatic actuator, and then feeding the actual actuator pressure and speed back to the control system, forming a complete signal circuit. This closed-loop structure enables the system to continuously adjust the control signal based on actual conditions to cope with various interferences and uncertainties, achieving precise control of the piston position, ensuring stable and accurate operation under different operating conditions, and meeting the requirements for fast and precise positioning of pneumatic actuators in industrial applications.

[0196] Example 3

[0197] Through simulation experiments, a comprehensive comparison of the ESO-based SMC and the classic SMC was conducted in terms of position tracking, pressure regulation, and robustness in the presence of external interference and parameter changes to verify the performance of the ESO-based SMC of the present invention:

[0198] Determine system parameter values, such as reference stiffness coefficients Total mass M = 0.1 kg, reference damping coefficient Reference quality factor Viscous friction coefficient β = 50 Ns / m, etc.

[0199] Reasonable selection of the parameters of the three controllers, such as ω in the ESO-based SMC o =1.5*10 4 、P ESMC =3*104 ,η ESMC =1*10 -5 wait.

[0200] Valve excitation frequency test: ESO-based SMC: The valve switches every 1.2ms, the excitation frequency is low, and the valve wear is reduced; classic SMC: The valve switches every 27μs, the excitation frequency is high, and it is easy to cause valve wear.

[0201] Pressure control accuracy test: ESO-based SMC: The pressure control error is 0.05kPa, showing extremely high control accuracy; classic SMC: The pressure control error is 5kPa, which is a large error.

[0202] Position tracking test: By comparing the output position and steady-state error (SSE) data, we can see that the average SSE of the ESO-based SMC is 2.5*10 -9 m, which is smaller than the average SSE of the classic SMC -1.7*10 -7 m, can track the desired position more accurately.

[0203] Pressure response test: When the reference position changes, the pressure controlled by the ESO-based SMC can accurately respond to the change and push the piston, while the SMC has pressure overshoot.

[0204] Robustness testing: A step disturbance representing a sudden air leak was added to the chamber pressure model. Despite the disturbance, the ESO-based SMC effectively compensated, maintaining the piston at the desired position and maintaining stable chamber pressure control. However, the SMC subsequently produced a steady-state error in the position output and significant control input chatter, demonstrating the ESO-based SMC's strong anti-interference capabilities.

[0205] Example 4

[0206] like Figure 5 As shown, a pneumatic servo control system based on expansion state observation includes: a first model building module, a desired pressure acquisition module, a second model building module, an estimated value acquisition module, a control signal output module and a control adjustment module;

[0207] The first model building module is used to establish a piston-load dynamic model and a chamber pressure model based on the cylinder structure and related parameters; a reference mass is introduced to establish a load force reference model;

[0208] An expected pressure acquisition module, configured to obtain a total expected pressure based on a piston-load dynamic model and a load force reference model;

[0209] The second model building module is used to establish a state space model based on the chamber pressure model; and obtain an expanded state observation equation based on the state space model and the observer gain vector;

[0210] An estimated value acquisition module is used to obtain a system state estimated value based on an expanded state observation equation;

[0211] A control signal output module, used for obtaining a final control signal based on a total desired pressure and a system state estimation value;

[0212] The control and regulation module is used to adjust the chamber pressure of the cylinder based on the final control signal to achieve cylinder pressure control.

[0213] Preferably, the functional implementation process of each module in this embodiment corresponds to the above method one by one, and will not be repeated here.

[0214] Example 5

[0215] Based on the same inventive concept, the present invention further provides a computer device, comprising a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus;

[0216] Memory for storing computer programs;

[0217] The processor, when used to execute the program stored in the memory, can implement a pneumatic servo control method based on expansion state observation as in embodiment 1 or 2.

[0218] The electronic device may include a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may invoke logic instructions in the memory to execute a pneumatic servo control method based on expansion state observation according to Embodiment 1 or 2.

[0219] In addition, the logical instructions in the above-mentioned memory can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0220] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a pneumatic servo control method and system based on expansion state observation, which has the following beneficial effects:

[0221] 1. The present invention develops a sliding mode controller (SMC) based on an extended state observer (ESO) and combines it with an impedance control module to achieve precise control of cylinder pressure, thereby improving the accuracy, robustness and system stability of piston position control, while reducing the valve excitation frequency and the loss to the valve, making the control system more feasible and practical in actual applications.

[0222] 2. The proposed sliding mode controller based on an extended state observer (ESO) demonstrates superior performance in pressure control and position tracking. In position control, it achieves a smaller steady-state error, enabling more precise piston movement to the desired position. Furthermore, it outperforms a simple sliding mode controller in pressure regulation. For example, the ESO-based sliding mode controller effectively controls chamber pressure in response to parameter changes and external disturbances.

[0223] 3. It is more robust to system uncertainties and external disturbances. Under conditions of parameter changes (such as impedance parameter changes) and external disturbances (such as air leaks), the sliding mode controller based on the extended state observer can successfully drive the piston to the desired position and maintain stable pressure control, while traditional sliding mode controllers will produce steady-state errors and experience chattering under disturbances.

[0224] 4. The sliding mode controller based on the extended state observer generates fewer valve excitation signals, reducing valve wear. Furthermore, its controller gain is smaller than that of the active disturbance rejection controller and sliding mode controller, making it easier to implement in practical applications and reducing system requirements.

[0225] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0226] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A pneumatic servo control method based on expansion state observation, characterized in that: include: Establish a piston-load dynamic model and a chamber pressure model based on the cylinder structure and related parameters; Introduce reference mass to establish load force reference model; Obtaining a total desired pressure based on the piston-load dynamic model and the load force reference model; establishing a state space model based on the chamber pressure model; Obtaining an extended state observation equation based on the state space model and the observer gain vector; Obtaining a system state estimate based on the expanded state observation equation; obtaining a final control signal based on the total desired pressure and the system state estimation value; The chamber pressure of the cylinder is adjusted based on the final control signal to achieve cylinder pressure control.

2. The pneumatic servo control method based on expansion state observation according to claim 1, characterized in that: The piston-load dynamic model is specifically: Among them, M P Indicates the piston mass, M L Indicates the load mass, represents the acceleration of the piston, β represents the viscous friction coefficient, Indicates the speed of the piston, F f (t) represents the Coulomb friction force, F L (t) represents the load force, P1(t) and P2(t) represent the absolute pressures of chamber 1 and chamber 2 in the cylinder, respectively, A1 represents the piston area separating chamber 1 and chamber 2, and A2 represents the area between A1 and A p The difference between A p Indicates the area on the right side of the piston rod in the cylinder, P a (t) represents atmospheric pressure.

3. The pneumatic servo control method based on expansion state observation according to claim 2, characterized in that: The chamber pressure model is specifically: in, represents the gas pressure of the i-th chamber, k represents the specific heat ratio, V i (t) represents the volume of the i-th chamber, R represents the difference between the specific heat capacity at constant pressure and the specific heat capacity at constant volume, T represents the temperature of the gas in the chamber, represents the mass flow rate, P i (t) represents the absolute pressure of the i-th chamber, A i represents A1 or A2, and d(t) represents the external disturbance caused by air leakage.

4. The pneumatic servo control method based on expansion state observation according to claim 3, characterized in that: The load force reference model is specifically: in, represents the reference mass, represents the expected acceleration, represents the reference damping, represents the expected speed, represents the stiffness coefficient, x(t) represents the position of the piston, and x d Indicates the desired position.

5. The pneumatic servo control method based on expansion state observation according to claim 4, characterized in that: The total expected pressure acquisition method is: The expected force output is obtained based on the piston-load dynamic model and the load force reference model: Among them, F D (t) represents the desired force output, M represents the total mass of the piston and load; Using anti-friction graphite pistons and neglecting Coulomb friction, the desired force output is converted to the desired pressure in each chamber: F D (t)=P 1D (t)A1-P 2D (t)A2-P a (t)A P ; P sum (t)=P 1D (t)+P 2D (t); Among them, P 1D (t) and P 2D (t) represents the desired pressure of chamber 1 and chamber 2, respectively, P a (t) represents atmospheric pressure, P sum (t) represents the total supply pressure parameter; Based on the above formula, the expected pressure of chamber 1 and chamber 2 is obtained: P 1D (t) and P 2D (t); Based on P 1D (t) and P 2D (t) together constitute the total desired pressure P D (t).

6. The pneumatic servo control method based on expansion state observation according to claim 5, characterized in that: Establishing a state space model based on the chamber pressure model specifically includes: The expansion state observer is obtained based on the chamber pressure model: y (r) (t)=b(t)u(t)+f(t); Where r = 1, y(t) = P(t), f(t) represents generalized interference, Establish a state space model based on the extended state observer: in, represents the rate of change of the state variable, represents the interaction between state variables, X(t) represents the state variable, represents the effect of input on state variables, represents the correlation coefficient of the generalized perturbation derivative, represents the derivative of the generalized disturbance, y(t) represents the output pressure, and C = [1 0].

7. The pneumatic servo control method based on expansion state observation according to claim 6, characterized in that: The expanded state observation equation is specifically: in, represents the rate of change of Z(t) over time, Z(t) represents the estimated value of the system state, z1(t) represents the actual pressure estimate, z2(t) represents the generalized disturbance estimate, and L represents the observer gain vector.

8. The pneumatic servo control method based on expansion state observation according to claim 7, characterized in that: The final control signal acquisition method is: The initial synovial surface s(t) is set based on the total desired pressure and the output pressure: s(t)=e(t)=y(t)-P D (t); Based on the initial sliding surface s(t), the initial control input u(t) is obtained: in, represents the approximate value of the generalized interference f(t), k SMC represents the stability coefficient, sgn(s(t))) represents the sign function of the sliding surface, and b represents the coefficient related to the dynamic characteristics of the system; Based on the system state estimation value and the initial control input, the final control input u is obtained. ESMC (t): Among them, P ESMC Indicates the deviation from the pressure The intensity coefficient of the relevant control action, η ESMC Represents the function used to adjust the sign The intensity coefficient of the effect.

9. The pneumatic servo control method based on expansion state observation according to claim 8, characterized in that: Based on pressure deviation Construct a Lyapunov function: Based on the derivation of the Lyapunov function, we get: in, represents the rate of change of the actual pressure estimate z1(t); Select the corresponding coefficient P ESMC and η ESMC , making This satisfies the system stability conditions.

10. A pneumatic servo control system based on expansion state observation, applied to a pneumatic servo control method based on expansion state observation according to any one of claims 1 to 9, characterized in that: include: a first model building module, a desired pressure acquisition module, a second model building module, an estimated value acquisition module, a control signal output module, and a control adjustment module; The first model building module is used to establish a piston-load dynamic model and a chamber pressure model based on the cylinder structure and related parameters; introduce a reference mass to establish a load force reference model; The expected pressure acquisition module is configured to obtain a total expected pressure based on the piston-load dynamic model and the load force reference model; The second model building module is configured to establish a state space model based on the chamber pressure model; and obtain an expanded state observation equation based on the state space model and an observer gain vector; The estimated value acquisition module is used to obtain a system state estimated value based on the expanded state observation equation; The control signal output module is configured to obtain a final control signal based on the total desired pressure and the system state estimation value; The control and adjustment module is used to adjust the chamber pressure of the cylinder based on the final control signal to achieve cylinder pressure control.

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