# Metaheuristics Based Modeling and Simulation Analysis of New Integrated Mechanized Operation Solution and Position Servo System

Authors: Huixian Gao; Ahmed Kareem; Malik Jawarneh; Isaac Ofori; R. Raffik; Kakarla Hari Kishore
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Inadequate environmental protection is a problem, and to address it, the efficiency and quality grade of mechanical operations should be improved. A new comprehensive mechanized operation solution is proposed. The position control of a servo motor utilizing a PID (proportional, integral, derivative) controller and soft computing optimization approaches is explored in this paper. The essential technological realization techniques are reviewed and assessed, which serves as a reference for comprehensive mechanization solutions. The simulation model may be used to examine system features and explore control strategy by reflecting the characteristics of the actual system. A PID controller is designed by establishing a mathematical model based on the position servo system. It is verified that the PID control link is added to the pneumatic position servo control system. Through the comparison of the PID control experiment and PID control simulation data, the system can achieve high-precision position control, and the error is less than ±20 mm, meeting the requirements of rust removal and spraying design, and showing that the control system works stably and reliably to achieve high-precision simulation of the pneumatic position servo system.


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## Body

## 1. Introduction

Position servo control is an important part of the motion control system. It requires that the output position quantity completely duplicates the input position quantity and its changing trend, accurately controls the coordinate position of moving parts, and realizes fast and accurate motion. In other words, sufficient position control accuracy, position tracking accuracy, and fast enough tracking speed are taken as his main control objectives [1]. The regulating of a motor’s velocity and position based on a feedback signal is known as servo control. The velocity loop is the most basic type of servo loop. The velocity loop creates a torque command to lessen the error between the velocity command and velocity feedback. The process of providing actual torque in response to servo control loop torque commands is known as motor control. Because modifying PID controllers for positional control systems takes time, considerable effort has been spent on analysing the servo systems. Usually, servo systems require a controller in addition to speed control, which again is frequently handled by cascading or series linking a position loop and a speed loop. A single PID position loop is occasionally used to provide position and speed control in the absence of an explicit velocity loop [2, 3]. At present, the general motion servo control is still a widely used classical PID control method, and its advantage is a simple algorithm and easy to implement. Pneumatic servo technology has been used more and more widely in the field of automation production because of its advantages such as low price, simple structure, fast response speed, high power-volume ratio, and no pollution. Among them, the most widely used is the position servo system, and the model is the key to study the pneumatic servo system. According to the servo system regulation theory, the servo system is usually divided into an open-loop, semiclosed-loop, and closed-loop system [4]. Setting servo gains allows you to fine-tune (or correct) servo loops for each application. Stronger servo gains improve performance, but they also increase the danger of system instability. Low-pass filters are typically used in series only with a velocity loop to ease good adsorption difficulties [5, 6]. Open-loop systems have no measurement feedback. Semiclosed loop and closed-loop systems have measurement feedback links, in which the semiclosed loop system only the measuring element installed on the rotating shaft of the motor can detect the physical quantity related to angular displacement. The regular derusting and spraying maintenance of ships is an important part of the daily maintenance of ships, which is of great significance for prolonging the service life of ships and maintaining good operating conditions [7]. At present, manual derusting, physical derusting, and chemical derusting are mostly used. High-pressure water jet derusting and wall-climbing robot derusting have been gradually applied in recent years, but, from the overall situation, there are widespread problems such as low operating efficiency, poor environmental protection, and less than ideal process quality.Pressure regulators are available for a wide range of fluid, gas, and air applications. They occur in a variety of shapes and sizes, but they all have three functional aspects in common: a pressure-lowering or restricting valve, a pressure sensor component, and a temperature-reducing or restrictive control element. While a typical mechanical position control system consists of a double-acting pneumatic cylinder, one or more control valves, sensors, and controller hardware requirements (also known as a pneumatic servo system). The most common type of valve is a proportional valve, sometimes known as an on/off solenoid valve. A servomotor is a rotary actuator used in operations that demand precise control of rotational velocity, angular position, and acceleration. It is linked to a certain encoder. The proportional-integral-derivative (PID) controller has been used for decades due to its ease and efficacy [8, 9]. With the simplification of the model, a lot of important information about the system will be lost, resulting in the reduction of simulation accuracy. Long, Z. proposed the mathematical model of the control relationship of the hydraulic motor tracking servo motor and adopted the PID parameter setting combined control algorithm. The driver of the tracking control strategy is simulated based on the mathematical model. The results show that the main synchronization performance parameters of the hydraulic motor tracking servo motor composite drive control system are in good condition [10]. PID controllers are widely used in industry today. PID controllers make around 85–90 percent of all controllers used in the industry. Position control methods are highly unsustainable when utilised in a closed-loop configuration [11, 12]. Tong, X. R. et al. proposed a design scheme for a new real-time electronic countermeasures simulation system. The modeling and realization methods of each part of the whole simulation system are described, and the real-time performance of the system is realized. An electronic countermeasure simulation system is a key part of personal military training and can also make a realistic evaluation of the performance of modern equipment and technology [13].A dc servo motor is just a conventional dc motor with the few small manufacturing variations. DC servo motors must meet two physical criteria: low inertia and strong starting torque. Low inertia is achieved by decreasing the armature diameter and, as a result, the rotor length until the desired power output is obtained [14, 15]. A new comprehensive mechanization solution for hull derusting and spraying is proposed, and the key technology realization methods are discussed and analyzed, which provides a reference for a comprehensive mechanization solution for large hull derusting.


## 2. Position Servo Control System

### 2.1. Basic Principle of Position Servo

A servo motor is a motor that rotates with high precision. Servo motors sometimes have a control circuit that provides feedback on the current position of the motor shaft, allowing them to revolve with amazing accuracy. When you want to spin an object at a specific angle or distance, you use a servo motor. It is nothing more than a simple motor linked to a servo mechanism. According to the servo system regulation theory, the servo system is usually divided into open-loop, half closed-loop, and closed-loop systems. Open-loop systems have no measurement feedback. Semiclosed-loop and closed-loop systems have measurement feedback links, in which only the measuring elements installed on the rotating shaft of the motor in the semiclosed-loop system can detect physical quantities related to angular displacement [16, 17]. The open-loop system has no measurement feedback signal, and its accuracy is poor, while the semiclosed-loop and closed-loop systems can control the speed and position according to the results of the comparison between the detected feedback signal and the instruction signal, which has a higher control accuracy. The precision of the semiclosed-loop system is lower than that of the closed-loop system, but it is simpler and easier to adjust. Is a three-ring motion servo control system with a semiclosed loop. The outer loop is a position loop, and the inner loop contains a speed loop and a current loop. The working principle of position servo control is as follows: The actual position information of the photoelectric encoder feedback signal processing circuit is compared with the theoretical position information transmitted by the computer to obtain the following error. According to the following error, the digital quantity of the feed speed instruction is calculated by the position controller. The digital quantity is converted by D/A and used as the input speed instruction of the speed ring of the servo drive unit. The servo unit drives the coordinate axis to move and realizes the position control.


### 2.2. Mathematical Model of Position Servo Control System

According to the servo system regulation theory, the servo system is usually divided into open-loop, half closed-loop, and closed-loop systems. Open-loop systems have no measurement feedback. Semiclosed-loop and closed-loop systems have measurement feedback links, in which the semiclosed-loop system only the measuring element installed on the rotating shaft of the motor can detect the physical quantity related to angular displacement. The working principle of position servo control is as follows: the actual position information of the feedback signal processing circuit of the photoelectric encoder is compared with the theoretical position information transmitted by the computer to obtain the following error. According to the following error, the digital quantity of the feed speed instruction is calculated by the position controller [18]. The digital quantity is converted by D/A and used as the input speed instruction of the speed ring of the servo drive unit. The servo unit drives the coordinate axis to move and realizes the position control. The simplified position loop of the motion control system is shown in Figure 1.Figure 1
Simplified block diagram of the system.Among them,(1)Gs=KMsTs+1,Ghs=1−e−Tss,where T is the sampling period, TS is the time constant of the motor, and Km is the gain of the speed loop. Therefore, the open-loop transfer function is(2)GKs=KVsTs+1×1−e−Tss,TypeKV=KM×KD×KA,where KV is the open-loop gain of the system, KD is the digital-to-analog conversion gain, and KA is the gain of the measuring device.


### 2.3. Analysis of Position Servo PID Control Algorithm

PID control is one of the earliest developed control strategies. Because of its simple algorithm, convenient adjustment, good robustness, and high reliability, it is widely used in industrial control [19, 20]. PID (proportional, integral, and differential) control is based on classical control theory and is the most extensively used control approach in continuous systems. The schematic diagram of the PID control system is shown in Figure 2.Figure 2
Simulation PID control block diagram.In Figure2, Ki=Kp/TiKd=KPTd,ut represents the output of the controller, Kp represents the scale coefficient, Ti represents the integral time constant, and Td represents the differential time constant.(3)ut=Ket+1T∫0Tetdt+Tddetdt+u0t.The proportional gainKp is introduced to reflect the deviation signal of the control system in a timely manner. When the system deviation occurs, the proportional adjustment link immediately produces the adjustment effect, which makes the system deviation change rapidly to the decreasing trend. The integral function is introduced to eliminate the steady-state error of the system, improve the no-difference degree of the system, and ensure the realization of no-static tracking of the set value. The function of the differential link is mainly to improve the response speed and stability of the control system.Computer control is a kind of sampling control. It can only calculate the control quantity according to the deviation value of sampling time and carry out discrete control but cannot continuously output the control quantity and realize continuous control like an analog controller [9, 10]. Therefore, the integral and differential terms in the formula cannot be directly and accurately calculated in the computer but can only be approximated by the numerical calculation method. If T is the sampling period, the discrete sampling time point ikD is used to represent the continuous time T, and the sum is used to replace the integral; increment replaces differentiation. If the sampling period T is small enough, the approximate calculation will be quite accurate, and the controlled process is very close to the continuous control process. Therefore, the digital PID control algorithm can be obtained as follows:(4)ui=Kei+TT∑j=0iej+TdTei−ei−1+u0.The above control algorithm provides the positionui of the actuator each time the output, so it can be called the position-type PID control algorithm. Each output of this algorithm is related to the whole past state, and it is easy to generate large accumulated errors in calculation. In practice, an incremental PID control algorithm is often adopted, and the control quantity at the sampling time can be derived as follows:(5)Δui=ui−ui−1=Kej−ei−1+TTei+TdTei−2ei−1+ei−2=K⇒Δei+TdTΔ2ei.When the incremental algorithm is used, the control incrementuk of the computer output corresponds to the increment of the actuator position. Incremental PID is only a slight improvement on the algorithm, and there is no essential difference with positional PID. However, compared with the position-type PID, because it only outputs the control increment each time, that is, the change of the corresponding position of the actuator, the output change range is small, so when the processor fails, the production process will not be seriously affected. In addition, since its maximum output at each time is U (K) Max, no disturbance can be achieved when the control is switched from manual to automatic. The calculation workload is small, there is no need to add the calculation formula, only two historical data E (k−1) and E (k−2) are used, and the translation method is usually adopted to save the two historical data. According to the mathematical model of the position servo system, the PID control algorithm of MATLAB is compiled, and the simulation experiments of the typical input ramp input response and the unit step input response of the position servo controller are completed respectively. For the control system, in the case of not allowing overshoot, the best control effect can be obtained theoretically when the control parameters of the PID controller are respectively selected through experiments, as shown in Figure 3.Figure 3
Unit step input is the system output curve.In order to investigate the robustness of the PID control algorithm, when the system is running, change the open-loop gain of the transfer function of the control object, add a random component, and takeK=1+rand∗sinΔ. As can be seen from Figure 4, the PID control algorithm still maintains good dynamic characteristics. Through the analysis of the graph, it can be seen that it has a small following error, which is more important in the position servo control system, and directly determines the control accuracy of the control system.Figure 4
System output with gain K plus perturbation unit step input.


### 2.4. Mathematical Modeling of Rust Removal and Spraying

Dust removal followed by spraying is an important task for the proper functioning of the servo system. It can degrade motor efficiency and performance by overheating, polluting lubricants, hastening wear, and causing winding damage. Carbon dust is conductive, which means it might cause shorts if it gets into the wrong area. The control system of rust removal and spraying mainly includes three subsystems, which are pneumatic position servo system control, pneumatic pressure servo system control, and pneumatic angle control. Pneumatics enables rapid, high-force point-to-point motion. Servo pneumatics has the same speed and force capacities as standard pneumatics, but with the added benefit of greater positioning precision not just at stroke’s endpoints, but also in the middle. Servo pneumatics monitors and regulates air flow in addition to delivering position feedback, allowing for precise control of the force produced. Because the pneumatic angle control requires low precision, so it only needs to be controlled by the ordinary solenoid valve on and off, and the pneumatic pressure control and pneumatic position control are only different in the sensor feedback, so the following will be the establishment of the mathematical model of the pneumatic position servo system and pneumatic pressure control, and it is basically the same. Control technologies mainly include AC servo drive, pneumatic servo control, electronic parameter detection, and computer remote control. Table1 shows the main drivers and associated control objects.Table 1
Driver and associated control objects.
Control objectDrive the modeCharacteristicControl objectDrive the modeCharacteristicLevel shiftMotor driveServo/StepCylinder support forcePromotional pressure-force controlPromotional force controlVertical movementMotor driveServo/StepDerusting cylinder positionServo traffic-Location controlServo position controlIn Table1, the horizontal and vertical movements are driven and controlled by servo (or stepping), the cylinder support adopts proportional force control technology, and the position of the end-effector of the end manipulator of the rust-removing cylinder adopts pneumatic position servo control. The cylinder stroke is set as 2L, the middle position of the cylinder is set as the initial position, and the y displacement of this point is recorded as zero. At the same time, the right movement is set in the positive direction, and the left movement is set in the negative direction. The flow continuity equation is(6)qm1=ART1P1dydt+1+ykdp1dt,qm2=ART2P2dydt−1−ykdp2dt,where qm1,qm2 are the gas flow into cavity I and II, respectively; R is the gas constant; A is the cross-sectional area of the cylinder. The force balance equation of cylinder piston can be obtained from Newton’s second law.(7)md2ydt=P1A−P2A−Bfdydt−Fm−FI,where Fm is the friction force (N), which is composed of Coulomb friction force and static friction force; FI is the external load force (N). Ignoring the friction force, its incremental form is(8)AΔpm=md2Δydt2+BfdΔfdt+ΔFI.The flow equation of the throttle port of the pneumatic servo valve is(9)qm1=2k−1p1p2k+1/2kp1p21−k/k−11/2kRTspsAt,where pt is the pressure at the throttle (bar); Ts is the gas temperature at the valve inlet (K); At is the throttle port area mm2.tMATLAB is an excellent numerical calculation program produced by American Mathw Orks, which contains the authoritative and practical computer tools in the field of simulation-MATLAB/SIMULINK. The control simulation model was established by SIMULINK, and it includes four subsystems: control, large cavity pressure, small cavity pressure, and friction. The displacement and load can be set by step, and the PID control subsystem can select the PID parameters according to the positive and negative errors. When the absolute error is less than 0.5 mm, set the voltage in the center to limit the maximum output voltage and other functions; the pressure subsystem can choose the calculation formula of the flow of each throttle according to the control voltage. The friction subsystem is built according to the analysis principle of the friction force of the cylinder in 2.5 sections. The subsystem can calculate the friction force according to the positive and negative speed and whether the speed is zero, so as to achieve a more accurate simulation of the friction force of the cylinder. In the model, the atmospheric force acting on the piston rod is placed in the “load,” so that the simulation model can easily obtain the required simulation data of displacement, two-cavity pressure, and control voltage and realize the accurate simulation of the proportional direction flow valve-controlled cylinder pneumatic position servo system. The obtained simulation data were plotted by MATLAB. Simulation and experimental displacement response curves are similar. Since the maximum output voltage is set, the middle of the curve is approximately straight, and the speed is uniform when the curve rises. When the response approaches the target value, the curve has a transition curve under the action of the differential coefficient, indicating that the response velocity drops down. The pressure simulation curve of the large cavity and the experimental (relative pressure) curve have the same variation trend, both of which show that the initial pressure rapidly rises to the maximum value and then decreases to the steady-state value at a faster speed. Due to the complexity of the experimental situation, the experimental curve fluctuates greatly. The pressure curve of the small-cavity experiment has a process of decline at the beginning and then rises. The pressure curve of small cavity simulation also has a downward trend at the beginning, and then enters the rising stage, and is relatively stable after entering the steady state.


## 2.1. Basic Principle of Position Servo

A servo motor is a motor that rotates with high precision. Servo motors sometimes have a control circuit that provides feedback on the current position of the motor shaft, allowing them to revolve with amazing accuracy. When you want to spin an object at a specific angle or distance, you use a servo motor. It is nothing more than a simple motor linked to a servo mechanism. According to the servo system regulation theory, the servo system is usually divided into open-loop, half closed-loop, and closed-loop systems. Open-loop systems have no measurement feedback. Semiclosed-loop and closed-loop systems have measurement feedback links, in which only the measuring elements installed on the rotating shaft of the motor in the semiclosed-loop system can detect physical quantities related to angular displacement [16, 17]. The open-loop system has no measurement feedback signal, and its accuracy is poor, while the semiclosed-loop and closed-loop systems can control the speed and position according to the results of the comparison between the detected feedback signal and the instruction signal, which has a higher control accuracy. The precision of the semiclosed-loop system is lower than that of the closed-loop system, but it is simpler and easier to adjust. Is a three-ring motion servo control system with a semiclosed loop. The outer loop is a position loop, and the inner loop contains a speed loop and a current loop. The working principle of position servo control is as follows: The actual position information of the photoelectric encoder feedback signal processing circuit is compared with the theoretical position information transmitted by the computer to obtain the following error. According to the following error, the digital quantity of the feed speed instruction is calculated by the position controller. The digital quantity is converted by D/A and used as the input speed instruction of the speed ring of the servo drive unit. The servo unit drives the coordinate axis to move and realizes the position control.


## 2.2. Mathematical Model of Position Servo Control System

According to the servo system regulation theory, the servo system is usually divided into open-loop, half closed-loop, and closed-loop systems. Open-loop systems have no measurement feedback. Semiclosed-loop and closed-loop systems have measurement feedback links, in which the semiclosed-loop system only the measuring element installed on the rotating shaft of the motor can detect the physical quantity related to angular displacement. The working principle of position servo control is as follows: the actual position information of the feedback signal processing circuit of the photoelectric encoder is compared with the theoretical position information transmitted by the computer to obtain the following error. According to the following error, the digital quantity of the feed speed instruction is calculated by the position controller [18]. The digital quantity is converted by D/A and used as the input speed instruction of the speed ring of the servo drive unit. The servo unit drives the coordinate axis to move and realizes the position control. The simplified position loop of the motion control system is shown in Figure 1.Figure 1
Simplified block diagram of the system.Among them,(1)Gs=KMsTs+1,Ghs=1−e−Tss,where T is the sampling period, TS is the time constant of the motor, and Km is the gain of the speed loop. Therefore, the open-loop transfer function is(2)GKs=KVsTs+1×1−e−Tss,TypeKV=KM×KD×KA,where KV is the open-loop gain of the system, KD is the digital-to-analog conversion gain, and KA is the gain of the measuring device.


## 2.3. Analysis of Position Servo PID Control Algorithm

PID control is one of the earliest developed control strategies. Because of its simple algorithm, convenient adjustment, good robustness, and high reliability, it is widely used in industrial control [19, 20]. PID (proportional, integral, and differential) control is based on classical control theory and is the most extensively used control approach in continuous systems. The schematic diagram of the PID control system is shown in Figure 2.Figure 2
Simulation PID control block diagram.In Figure2, Ki=Kp/TiKd=KPTd,ut represents the output of the controller, Kp represents the scale coefficient, Ti represents the integral time constant, and Td represents the differential time constant.(3)ut=Ket+1T∫0Tetdt+Tddetdt+u0t.The proportional gainKp is introduced to reflect the deviation signal of the control system in a timely manner. When the system deviation occurs, the proportional adjustment link immediately produces the adjustment effect, which makes the system deviation change rapidly to the decreasing trend. The integral function is introduced to eliminate the steady-state error of the system, improve the no-difference degree of the system, and ensure the realization of no-static tracking of the set value. The function of the differential link is mainly to improve the response speed and stability of the control system.Computer control is a kind of sampling control. It can only calculate the control quantity according to the deviation value of sampling time and carry out discrete control but cannot continuously output the control quantity and realize continuous control like an analog controller [9, 10]. Therefore, the integral and differential terms in the formula cannot be directly and accurately calculated in the computer but can only be approximated by the numerical calculation method. If T is the sampling period, the discrete sampling time point ikD is used to represent the continuous time T, and the sum is used to replace the integral; increment replaces differentiation. If the sampling period T is small enough, the approximate calculation will be quite accurate, and the controlled process is very close to the continuous control process. Therefore, the digital PID control algorithm can be obtained as follows:(4)ui=Kei+TT∑j=0iej+TdTei−ei−1+u0.The above control algorithm provides the positionui of the actuator each time the output, so it can be called the position-type PID control algorithm. Each output of this algorithm is related to the whole past state, and it is easy to generate large accumulated errors in calculation. In practice, an incremental PID control algorithm is often adopted, and the control quantity at the sampling time can be derived as follows:(5)Δui=ui−ui−1=Kej−ei−1+TTei+TdTei−2ei−1+ei−2=K⇒Δei+TdTΔ2ei.When the incremental algorithm is used, the control incrementuk of the computer output corresponds to the increment of the actuator position. Incremental PID is only a slight improvement on the algorithm, and there is no essential difference with positional PID. However, compared with the position-type PID, because it only outputs the control increment each time, that is, the change of the corresponding position of the actuator, the output change range is small, so when the processor fails, the production process will not be seriously affected. In addition, since its maximum output at each time is U (K) Max, no disturbance can be achieved when the control is switched from manual to automatic. The calculation workload is small, there is no need to add the calculation formula, only two historical data E (k−1) and E (k−2) are used, and the translation method is usually adopted to save the two historical data. According to the mathematical model of the position servo system, the PID control algorithm of MATLAB is compiled, and the simulation experiments of the typical input ramp input response and the unit step input response of the position servo controller are completed respectively. For the control system, in the case of not allowing overshoot, the best control effect can be obtained theoretically when the control parameters of the PID controller are respectively selected through experiments, as shown in Figure 3.Figure 3
Unit step input is the system output curve.In order to investigate the robustness of the PID control algorithm, when the system is running, change the open-loop gain of the transfer function of the control object, add a random component, and takeK=1+rand∗sinΔ. As can be seen from Figure 4, the PID control algorithm still maintains good dynamic characteristics. Through the analysis of the graph, it can be seen that it has a small following error, which is more important in the position servo control system, and directly determines the control accuracy of the control system.Figure 4
System output with gain K plus perturbation unit step input.


## 2.4. Mathematical Modeling of Rust Removal and Spraying

Dust removal followed by spraying is an important task for the proper functioning of the servo system. It can degrade motor efficiency and performance by overheating, polluting lubricants, hastening wear, and causing winding damage. Carbon dust is conductive, which means it might cause shorts if it gets into the wrong area. The control system of rust removal and spraying mainly includes three subsystems, which are pneumatic position servo system control, pneumatic pressure servo system control, and pneumatic angle control. Pneumatics enables rapid, high-force point-to-point motion. Servo pneumatics has the same speed and force capacities as standard pneumatics, but with the added benefit of greater positioning precision not just at stroke’s endpoints, but also in the middle. Servo pneumatics monitors and regulates air flow in addition to delivering position feedback, allowing for precise control of the force produced. Because the pneumatic angle control requires low precision, so it only needs to be controlled by the ordinary solenoid valve on and off, and the pneumatic pressure control and pneumatic position control are only different in the sensor feedback, so the following will be the establishment of the mathematical model of the pneumatic position servo system and pneumatic pressure control, and it is basically the same. Control technologies mainly include AC servo drive, pneumatic servo control, electronic parameter detection, and computer remote control. Table1 shows the main drivers and associated control objects.Table 1
Driver and associated control objects.
Control objectDrive the modeCharacteristicControl objectDrive the modeCharacteristicLevel shiftMotor driveServo/StepCylinder support forcePromotional pressure-force controlPromotional force controlVertical movementMotor driveServo/StepDerusting cylinder positionServo traffic-Location controlServo position controlIn Table1, the horizontal and vertical movements are driven and controlled by servo (or stepping), the cylinder support adopts proportional force control technology, and the position of the end-effector of the end manipulator of the rust-removing cylinder adopts pneumatic position servo control. The cylinder stroke is set as 2L, the middle position of the cylinder is set as the initial position, and the y displacement of this point is recorded as zero. At the same time, the right movement is set in the positive direction, and the left movement is set in the negative direction. The flow continuity equation is(6)qm1=ART1P1dydt+1+ykdp1dt,qm2=ART2P2dydt−1−ykdp2dt,where qm1,qm2 are the gas flow into cavity I and II, respectively; R is the gas constant; A is the cross-sectional area of the cylinder. The force balance equation of cylinder piston can be obtained from Newton’s second law.(7)md2ydt=P1A−P2A−Bfdydt−Fm−FI,where Fm is the friction force (N), which is composed of Coulomb friction force and static friction force; FI is the external load force (N). Ignoring the friction force, its incremental form is(8)AΔpm=md2Δydt2+BfdΔfdt+ΔFI.The flow equation of the throttle port of the pneumatic servo valve is(9)qm1=2k−1p1p2k+1/2kp1p21−k/k−11/2kRTspsAt,where pt is the pressure at the throttle (bar); Ts is the gas temperature at the valve inlet (K); At is the throttle port area mm2.tMATLAB is an excellent numerical calculation program produced by American Mathw Orks, which contains the authoritative and practical computer tools in the field of simulation-MATLAB/SIMULINK. The control simulation model was established by SIMULINK, and it includes four subsystems: control, large cavity pressure, small cavity pressure, and friction. The displacement and load can be set by step, and the PID control subsystem can select the PID parameters according to the positive and negative errors. When the absolute error is less than 0.5 mm, set the voltage in the center to limit the maximum output voltage and other functions; the pressure subsystem can choose the calculation formula of the flow of each throttle according to the control voltage. The friction subsystem is built according to the analysis principle of the friction force of the cylinder in 2.5 sections. The subsystem can calculate the friction force according to the positive and negative speed and whether the speed is zero, so as to achieve a more accurate simulation of the friction force of the cylinder. In the model, the atmospheric force acting on the piston rod is placed in the “load,” so that the simulation model can easily obtain the required simulation data of displacement, two-cavity pressure, and control voltage and realize the accurate simulation of the proportional direction flow valve-controlled cylinder pneumatic position servo system. The obtained simulation data were plotted by MATLAB. Simulation and experimental displacement response curves are similar. Since the maximum output voltage is set, the middle of the curve is approximately straight, and the speed is uniform when the curve rises. When the response approaches the target value, the curve has a transition curve under the action of the differential coefficient, indicating that the response velocity drops down. The pressure simulation curve of the large cavity and the experimental (relative pressure) curve have the same variation trend, both of which show that the initial pressure rapidly rises to the maximum value and then decreases to the steady-state value at a faster speed. Due to the complexity of the experimental situation, the experimental curve fluctuates greatly. The pressure curve of the small-cavity experiment has a process of decline at the beginning and then rises. The pressure curve of small cavity simulation also has a downward trend at the beginning, and then enters the rising stage, and is relatively stable after entering the steady state.


## 3. Experimental Analysis

The hardware platform of the pneumatic servo position tracking control system is mainly composed of standard cylinder, proportional servo valve, displacement sensor, pressure sensor, data acquisition card, and industrial control computer. The cylinder is DSMI-40-270 vane swinging cylinder produced by FESTO Company in Germany. The diameter of the swinging cylinder is 40 mm, the stroke is 270, the maximum effective cross section of the proportional flow valve is 8mm2, the pressure sensor is Honeywell 4000PC, MLO2POT26002TLF displacement sensor (accuracy 0.5 mm), and the realization of A/D and D/A is completed by Advantage Microelectronics’s PCL-812PG data acquisition card. Compressed air is 0.51 MPa. When the system works, the industrial computer sends out the control signal that needs to be tracked and drives the servo valve after D/A conversion and amplification. The displacement sensor detects the angle signal of the rotation of the shaft and feedbacks it to the computer through A/D conversion and compares it with the specified input to obtain the deviation control quantity, so as to realize the continuous trajectory control. The proportional flow valve-controlled swing cylinder system described in the first two sections is used for simulation and experimental research.Values of parameters in the model:σ∗  = 0.528, Z=70×10−6kg⋅m2, θ10=θ20=100, T = 293K;Figure5 shows the comparison of the simulation results and experimental results of open-loop control. The experimental conditions are as follows: air supply pressure ps=0.51MPa, load moment of inertia J=112.78kg·cm2, and control quantity μ=0.4V.Figure 5
Dynamic process of angular displacement.It is clear from Figure5 that both curves are almost the same. This defines the efficiency of the proposed work. So, the model can well reflect the system characteristics and verify the correctness of the mathematical model of the system. The variation rule of the simulation curve and experiment curve is basically the same, which fully proves the effectiveness of the simulation model. The simulation model can reflect the characteristics of the actual system and can be used to analyze the system characteristics and study the control strategy.


## 4. Conclusions

Aiming at the position and pressure control problems of the pneumatic servo system involved in the ship hull derusting and spraying operation, the mathematical model of the pneumatic position servo system was established. Based on the principle of the original position servo system, the mathematical model of the system was established, and the PID controller was designed. Pneumatic position servo control system comprises PID control link, PID system experiment throughput, and PID control simulation data comparison. The simulation results show that the system has a fast response, no overshoot, and no shock, and the error accuracy is less than ±20 mm, which meets the requirements of precision and stability in the process of ship derusting and spraying. The simulation model can well reflect the system characteristics and verify the correctness of the mathematical model of the system. The simulation model can not only obtain the displacement simulation curve but also obtain the two-chamber pressure simulation curve of the cylinder, which can accurately realize the computer simulation of the pneumatic position servo system.



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*Source: 1466775-2022-06-18.xml*