A model predictive control algorithm-based positioning control method for a pneumatic system

Abstract

The application discloses a kind of based on model predictive control algorithm's pneumatic system positioning control method, comprising: the hardware composition and action principle of pneumatic system are analyzed, the mathematical model of pneumatic system is divided into the mass flow equation of gas, the mathematical equation of slide valve, piston force balance equation, based on above-mentioned three equations construction pneumatic system slide valve opening and system output mathematical model;Valve core is analyzed to find the midpoint position of making the stable inaction of both sides of cylinder, design pneumatic system setting process, according to setting process determines the various parameters of pneumatic system slide valve opening and system output mathematical model;Based on the setting process of design, design pneumatic system model predictive controller, this method designs pneumatic system model predictive controller, suppresses each kind of disturbance in system, inside and outside, realizes to pneumatic system and carries out good control.

Description

Technical Field

[0001] This invention relates to the field of pneumatic system position tracking technology, and in particular to a pneumatic system positioning control method based on model predictive control algorithm. Background Technology

[0002] In industrial automation control, various types of actuators are used, making them an indispensable component of automatic control systems. The function of an actuator is to receive control signals from the controller, change the magnitude of the controlled medium, and thus maintain the controlled variable at the required value or within a certain range. Pneumatic actuators use compressed air as their power source, receive control signals from the controller, and act on the controlled object to regulate the quantity, ensuring system stability and achieving good performance indicators. Although hydraulic and electric actuators have developed rapidly in recent years and have a wide range of applications, they have certain requirements regarding environmental conditions and auxiliary equipment. In comparison, pneumatic actuators are more suitable for working in harsh industrial control environments. Pneumatic actuators are relatively reliable and are one of the most widely used branches of actuators. Pneumatic actuators use lower working pressure air sources, and because their structural size cannot be too large, the total thrust of the pneumatic actuator corresponding to the valve cannot be very large. Pneumatic actuators are widely used in water treatment, transportation, automation, and many other fields. The pneumatic actuators described in this article are mainly used for valve control in industrial settings, with compressed air as the transmission medium. Taking thermal power plants as an example, pneumatic actuators are widely used in various valve control systems, such as boiler bypass dampers and inlet / outlet valves.

[0003] Model predictive control (MPC) is an advanced control method that optimizes the future output of a system by controlling the input. This is achieved by solving an optimization problem at each sampling time step, with the goal of finding the appropriate input signal that minimizes a certain cost function. As a model-based closed-loop optimization control strategy, MPC algorithms are known for their three key predictive control elements: an internal predictive model, a reference trajectory, and a control algorithm. They are also widely referred to as predictive models, rolling optimization, and feedback control. Extensive literature indicates that MPC algorithms do not require very high accuracy in the model structure of the controlled object, making them more suitable for systems with large time delays and inertia. Simultaneously, they offer good control performance. Compared to traditional classical control algorithms and optimal control strategies, predictive control is more suitable for industrial process control with uncertainties and large time delays. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention discloses a positioning control method for a pneumatic system based on a model predictive control algorithm, specifically including the following steps:

[0005] The hardware structure and operating principle of the pneumatic system are analyzed, and the mathematical model of the pneumatic system is divided into the mass flow equation of the gas, the mathematical equation of the slide valve, and the force balance equation of the piston. Based on the above three equations, a mathematical model of the slide valve opening degree and system output of the pneumatic system is constructed.

[0006] Analyze the spool valve core to find the midpoint position that makes the cylinder stable and without movement on both sides, design the pneumatic system tuning process, and determine the parameters of the pneumatic system spool valve opening and the system output mathematical model based on the tuning process;

[0007] Design a predictive controller for a pneumatic system based on the tuning process of the design.

[0008] Furthermore, based on the gas mass flow equation, the mathematical equation of the slide valve, and the piston force balance equation, a mathematical model of the pneumatic system slide valve opening and system output is constructed as follows:

[0009]

[0010] Among them, Q ma The mass flow rate of gas flowing into cylinder a is denoted as x; the valve core opening is denoted as P. a With P b P represents the air pressure in air chambers a and b. s y is the air source pressure; y is the cylinder piston displacement; ΔP m =ΔP a -ΔP b V a0 =V b0 =V0; R is the gas constant, which depends only on the type of gas; S is the cross-sectional area of ​​the output shaft; F f is the frictional force on the piston; m is the mass of the cylinder piston and steel shaft; T0 is the initial temperature of the cylinder.

[0011] Furthermore, the pneumatic system tuning process is designed, and the specific process for determining the parameters of the pneumatic system slide valve opening and the system output mathematical model based on the tuning process is as follows:

[0012] By controlling the slide valve to reach its maximum opening, the intake of air on the shaft side and the exhaust of air on the non-shaft side are controlled. The cylinder piston moves to the non-shaft side to the maximum opening, and the cylinder opening value at this time is obtained.

[0013] By controlling the slide valve to achieve the maximum reverse opening, the intake on the shaftless side and the exhaust on the shaft side are controlled. The cylinder piston moves towards the shaft side to the maximum opening, and the cylinder opening value at this time is obtained.

[0014] Control the intake air on the axial side and the exhaust air on the non-axial side. When the cylinder opening reaches 50%, the reset valve core returns to the midpoint position. At this time, there is no gas flow in either air chamber, and the cylinder is stable and does not move.

[0015] Gradually increase the valve opening to control the cylinder to move to both sides, and obtain the relationship between different valve openings and cylinder movement speed;

[0016] After completing the required spool valve opening degree test, if there are abnormal parameters, the test should be repeated; if the parameters meet the ideal curve, this step should be skipped.

[0017] By detecting the dead zone of the valve core at different opening degrees of the spool valve, the midpoint of the valve core that can maintain the stable position of the cylinder can be determined.

[0018] Based on the relationship between the valve opening degree and the cylinder operating speed, the specific parameters of the cylinder mathematical model are calculated.

[0019] Furthermore, when designing a predictive controller for aerodynamic systems:

[0020] By clarifying the constraints of the aerodynamic system, and designing a model to predict the cost function of the controller solution process:

[0021] The various constraints of the pneumatic system are as follows:

[0022]

[0023] in: It controls the input increment; It is a constraint output quantity; It is the controller output;

[0024] The optimal control output of the model predictive controller is obtained by solving the cost function.

[0025] The cost function is:

[0026]

[0027] Where Γ y,i Γ represents the weight of the cylinder opening degree in the objective function as a performance penalty for command position tracking. u,i The weights of the penalty term for the steady change of the control quantity are defined as p, where p is the prediction time domain and m is the control time domain.

[0028] By employing the above technical solutions, this invention provides a pneumatic system positioning control method based on model predictive control algorithms. This method uses both the air source pressure and the valve opening as input signals to the pneumatic system mathematical model, and the actual position output of the cylinder as the output, forming the MISO mathematical model of the pneumatic system. The pneumatic system tuning process provided by this invention, for systems with unknown valve openings, can effectively find the unknown midpoint of the valve core that will be stable, without requiring sensors to measure the valve core displacement. The model predictive control-based pneumatic system position tracking control method provided by this invention does not require a highly accurate system model, enabling control of systems with strong disturbances.

[0029] Based on the above reasons, this invention can be widely applied in fields such as pneumatic system positioning and control. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a diagram showing the overall structure of the pneumatic system in this invention.

[0032] Figure 2 This is a schematic diagram illustrating the operating principle of the slide valve-driven cylinder in this invention.

[0033] Figure 3 This is a basic conceptual diagram of the model predictive control algorithm in this invention.

[0034] Figure 4 This is a graph showing the position tracking control achieved by the algorithm described in this invention. Detailed Implementation

[0035] To make the technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention:

[0036] like Figure 1 The method for positioning control of an aerodynamic system based on model predictive control algorithm, as shown, specifically includes the following steps:

[0037] S1: Analyze the hardware structure and operating principle of the pneumatic system, and divide the mathematical model of the pneumatic system into the mass flow equation of the gas, the mathematical equation of the slide valve, and the force balance equation of the piston. Based on the above three equations, construct a mathematical model of the pneumatic system slide valve opening degree and system output.

[0038] S2: Analyze the spool valve core to find the midpoint position that makes the cylinder stable and without movement on both sides, design the pneumatic system tuning process, and determine the parameters of the pneumatic system spool valve opening and the system output mathematical model based on the tuning process;

[0039] The mathematical model for the relationship between the pneumatic system's valve opening and system output is as follows:

[0040]

[0041] Among them, Q ma The mass flow rate of gas flowing into cylinder a is denoted as x; the valve core opening is denoted as P.a With P b P represents the air pressure in air chambers a and b. s y is the air source pressure; y is the cylinder piston displacement; ΔP m =ΔP a -ΔP b V a0 =V b0 =V0; R is the gas constant, which depends only on the type of gas; S is the cross-sectional area of ​​the output shaft; F f is the frictional force on the piston; m is the mass of the cylinder piston and steel shaft; T0 is the initial temperature of the cylinder.

[0042] Furthermore, the pneumatic system tuning process is designed, and the specific process for determining the parameters of the pneumatic system slide valve opening and the system output mathematical model based on the tuning process is as follows:

[0043] By controlling the slide valve to reach its maximum opening, the intake air is controlled on the axial side while the exhaust air is controlled on the non-axial side. The cylinder piston moves to the non-axial side to the maximum opening, and the displacement sensor reads the value at this time.

[0044] By controlling the slide valve to reach the maximum reverse opening, the intake of air on the non-shaft side is controlled, while the exhaust of air on the shaft side is controlled. The cylinder piston moves to the maximum opening in the direction of the shaft side, and the value read by the displacement sensor at this time is obtained.

[0045] When the piston of the drive cylinder moves to a position of about 50% of its maximum displacement, the control system has axial air intake and no axial air exhaust. The reset valve core closes both air chambers until there is no gas flow in either air chamber and the cylinder is stable and does not move.

[0046] By gradually increasing the valve opening with a 4-pulse amplification, the cylinder is controlled to move to both sides, and the relationship between different valve openings and cylinder movement speed is obtained.

[0047] After completing the required spool valve opening test, if any parameters are abnormal, the test should be repeated. If the parameters conform to the ideal curve, skip this step.

[0048] By detecting the dead zone of the valve core at different opening degrees of the spool valve, the midpoint of the valve core that can be positioned to stabilize the cylinder can be determined.

[0049] Based on the relationship between the valve opening degree and the cylinder action speed, the specific parameters of the cylinder mathematical model are calculated.

[0050] S3: Design a predictive controller for a pneumatic system based on the tuning process of the design.

[0051] Since the past output y of the aerodynamic system is measurable, and the past control output u of the model predictive controller is known, based on these variable values ​​and the system's internal model, the model predictive control algorithm will calculate the appropriate future output trajectory, which will move the output y towards the set trajectory with optimal predictive behavior. This optimization of optimal predictive behavior is achieved by using the system model within the prediction time domain (N... p Within a certain control time domain range (N), it predicts future outputs to execute the operation. Furthermore, in the calculation of the input trajectory, it is assumed that the input trajectory is within a certain control time domain range (N). c After that, it remains constant. Once the optimal input trajectory is found, only the first element of that trajectory will be applied to the system. In the next time step, the entire process of measurement, output prediction, and input trajectory optimization will be repeated, while the prediction and control range will also be shifted forward by one time step.

[0052] The various constraints of the pneumatic system are as follows:

[0053]

[0054] in: It controls the input increment; It is a constraint output quantity; It is the controller output.

[0055] By solving the cost function to obtain the optimal control output of the model predictive controller, the future output of the system can be optimized. The typical form of the cost function considered by the model predictive control algorithm is given by the following equation:

[0056]

[0057]

[0058] Where r j (k+i), i = 1, 2, ..., p, represents the j-th component of the given reference input sequence; Γ y,i Γ is the weighting factor for the error of the i-th predictive control output; u,i The weighting factor of the control increment at the actual prediction time i.

[0059] The cost function J above consists of two summation terms. The first is the sum of prediction errors at time step k+i, where i = [1, 2, ..., p]. The second is the sum of incremental inputs Δu at time steps i = [1, 2, ..., m]. Matrix Γ y,i and Γ u,i It is a positive definite or semi-positive definite weighted matrix, which can be used as an optimization problem to adjust parameters and thus determine the closed-loop performance of the control algorithm.

[0060] The model predictive control algorithm can be summarized as finding the control input at the current sampling time in order to solve the following mathematical problem:

[0061]

[0062] in:

[0063]

[0064] Where Γ y,i Γ represents the weight of the cylinder opening degree in the objective function as a performance penalty for command position tracking. u,i The weights of the penalty term for the steady change of the control quantity are defined as p, where p is the prediction time domain and m is the control time domain.

[0065] This invention discloses a positioning control method for a pneumatic system based on a model predictive control algorithm. The method analyzes the hardware structure and operating principle of the pneumatic system, derives the mathematical model of the pneumatic system, designs the tuning process of the pneumatic system, and determines the specific parameters of the mathematical model based on the tuning results. The method also designs a model predictive controller for the pneumatic system to suppress various disturbances inside and outside the system, thereby achieving good control of the pneumatic system.

[0066] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A positioning control method for an aerodynamic system based on a model predictive control algorithm, characterized in that... include: The hardware structure and operating principle of the pneumatic system are analyzed, and the mathematical model of the pneumatic system is divided into the mass flow equation of the gas, the mathematical equation of the slide valve, and the force balance equation of the piston. Based on the above three equations, a mathematical model of the slide valve opening degree and system output of the pneumatic system is constructed. Analyze the spool valve core to find the midpoint position that makes the cylinder stable and without movement on both sides, design the pneumatic system tuning process, and determine the parameters of the pneumatic system spool valve opening and the system output mathematical model based on the tuning process; Design of a predictive controller for a pneumatic system based on the tuning process of the design; The specific process for designing the pneumatic system tuning procedure, and determining the parameters of the pneumatic system's valve opening and system output mathematical model based on the tuning process, is as follows: By controlling the slide valve to reach its maximum opening, the intake of air on the shaft side and the exhaust of air on the non-shaft side are controlled. The cylinder piston moves to the non-shaft side to the maximum opening, and the cylinder opening value at this time is obtained. By controlling the slide valve to achieve the maximum reverse opening, the intake on the shaftless side and the exhaust on the shaft side are controlled. The cylinder piston moves towards the shaft side to the maximum opening, and the cylinder opening value at this time is obtained. Control the intake air on the axial side and the exhaust air on the non-axial side. When the cylinder opening reaches 50%, the reset spool valve core returns to the midpoint position. At this time, there is no gas flow in either air chamber, and the cylinder is stable and does not move. Gradually increase the valve opening to control the cylinder to move to both sides, and obtain the relationship between different valve openings and cylinder movement speed; After completing the required spool valve opening degree test, if there are abnormal parameters, the test should be repeated; if the parameters meet the ideal curve, this step should be skipped. By detecting the dead zone of the valve core at different opening degrees of the spool valve, the midpoint of the valve core that can maintain the stable position of the cylinder can be determined. Based on the relationship between the valve opening degree and the cylinder action speed, calculate the specific parameters of the cylinder mathematical model; When designing a predictive controller for an aerodynamic system: By clarifying the constraints of the aerodynamic system, and designing a model to predict the cost function of the controller solution process: The various constraints of the pneumatic system are as follows: in: It controls the input increment; It is a constraint output quantity; It is the controller output; The optimal control output of the model predictive controller is obtained by solving the cost function. The cost function is: in This represents the weight of the cylinder opening degree penalty term for command position tracking performance in the objective function. To control the weight of the penalty term for steady changes in the quantity, To predict the time domain, To control the time domain.

2. The pneumatic system positioning control method based on model predictive control algorithm according to claim 1, characterized in that: Based on the gas mass flow equation, the mathematical equation of the slide valve, and the piston force balance equation, the mathematical model of the pneumatic system slide valve opening and system output is constructed as follows: in, denoted as , where is the mass flow rate of gas flowing into cylinder a; and is the valve core opening degree of the spool valve. and Let be the air pressure in air chamber a and air chamber b; y represents the air source pressure; y represents the cylinder piston displacement. ; R is the gas constant and depends only on the type of gas. This refers to the cross-sectional area of ​​the output shaft. ρ is the frictional force acting on the piston; m is the mass of the cylinder piston and steel shaft; This is the cylinder's initial temperature.

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