Trajectory planning and control strategy optimization design of double electric cylinder erecting device

The transition of the rocket from a horizontal to an erect state before its launch on the offshore platform is a crucial stage. Compared with erecting the rocket on the ground, higher servo control and synchronization accuracy are required for erecting it on the offshore platform. Most rocket erecting devices on offshore platforms rely on hydraulic drive systems, posing challenges due to their lower servo control accuracy and difficulties in achieving high-precision synchronization. The erecting process, trajectory planning, control system, and control strategies of rockets driven by a double electric cylinder erecting device are studied, aiming at the requirement of erecting rocket devices on offshore platforms. This paper commences by establishing the kinematic model of erecting the rocket with a double electric cylinder erecting device. It delves into the process and trajectory of the erection rocket with a double electric cylinder erecting device. Subsequently, the focus shifts toward designing the control system, while inclination and angular velocity sensors monitor the erection process. Finally, designing and demonstrating control strategies for a double electric cylinder erecting device, three different control strategies, master control, master-slave control, and cross-coupling control, are analyzed, and the cross-coupling control strategy is selected as the control strategy of the double electric cylinder offshore platform rocket erecting device.


Introduction
Existing offshore rocket launch erecting devices mostly use hydraulic drive systems.However, there are still many issues in hydraulic systems, such as "drips, leaks, runs, and emissions." [1]The electric cylinder is an actuator that provides linear motion and thrust.Compared with hydraulic drive systems, it has advantages such as high transmission efficiency, high positioning accuracy, reliability, safety, precise control, and good synchronization [2] .In comparison to the current offshore rocket launch erecting devices, an electric cylinder drive can better meet the driving requirements.
Trajectory planning is generally based on specific task requirements to obtain a time-variable curve that satisfies the system's kinematics and relevant constraints.The trajectory should smoothly connect the initial state of the system when it starts working and needs to have a certain smoothness for ease of tracking [3] .The traditional approach to trajectory planning involves considering the different advantages of various function curves and addressing the issue from the perspective of velocity or acceleration during system operation.By comprehensively considering them, a trajectory with good control performance is obtained while meeting certain indicators during system operation [4] .
The synchronous control of dual cylinders ultimately aims to keep the stroke error of the two cylinders within a certain accuracy range [5] , referred to as synchronization accuracy.Synchronization accuracy not only affects the equipment's positional accuracy but also influences the coordination of equipment operation [6] .
There are two main control methods for dual electric cylinders: mechanical connection methods and electric methods.The mechanical connection method uses a coaxial approach, which results in significant mechanical wear and low control precision [7] .The cross-coupled control structure was proposed by Koren to reduce the synchronization error and improve the synchronization control accuracy by detecting and compensating for the angular velocity or position signal difference of each motor [8] .On the basis of the cross-coupled control strategy, Kulkarni and Srinivasan adopted the optimal control scheme to further improve the performance of multi-axis coordinated control [9] .Tomizuka et al. have applied a feedforward adaptive control strategy to improve the system performance of a dual-axis motion control system under external interference [10] .

Composition of erecting device
The erecting device adopts the method of dual-cylinder erection using electric cylinders.The erecting frame employs a side-beam structure, achieving erection through two electric cylinders.The entire erecting device is positioned on a transport vehicle, enabling flexible transportation and the task of rapid, smooth erection.The device mainly consists of the erecting frame, support device, locking device, electric cylinders, connecting accessories, etc., as shown in Figure 1.The use of electric cylinders as the power source for the erecting device has several key advantages: 1) high dynamic response and precise position control; 2) a broad thrust range and longer stroke; 3) an extremely wide working temperature range; 4) low noise and vibration.
This study primarily focuses on the research of the dual-electric-cylinder erection trajectory planning, control system, and control strategies of the erecting device.

Analysis and trajectory planning of the erection process
The maximum erection angle for the rocket is 90°.According to the mathematical model analysis of the erecting device, when the elevation angle is less than 77°, as shown in Table 1. the electric cylinder provides thrust, and the load force on the electric cylinder is maximum at the initial stage of erecting.At 77°, the electric cylinder is not under force and experiences tension when exceeding 77°.
Table 1.Analysis of the erection process.

Working process Action Power supply type Angle of erection
Erecting Extend Thrust 0-77° Tension 77-90° Unstable motion intensifies mechanical component wear and leads to vibration and impact.To achieve smooth erecting, it is required that the function describing the erecting trajectory must be continuous, and its first derivative and second derivative should also be continuous.The trajectory planning is segmented into acceleration trajectory + uniform velocity trajectory + deceleration trajectory, as shown in Table 2, where the acceleration and deceleration trajectories adopt a fifth-order polynomial trajectory, and the speed setting value for the uniform velocity trajectory is 0.18°/s.The total motion time is set to 570 s, with acceleration and deceleration times both at 60 s.Fifth-order polynomial A fifth-order polynomial can be utilized for interpolation for the acceleration and deceleration phases with defined starting and ending points on the trajectory.
In the formula,  is the vertical angle, and t is the erecting time.Its constraint conditions are: The parameter table is shown in Table 3.
Figure 2 depicts the trajectory planning graph using a fifth-order polynomial.The angle curve planned by the fifth-order polynomial is smooth, with no acceleration impact during the erecting process.

Erection model analysis
The mathematical model of the erecting device's motion process is illustrated in Figure 3. ∆ represents the model of the erecting frame and rocket, Point C indicates the center of mass position, ∆  , ∆  , and ∆  represent the states before, during and after erecting, respectively.
Point O is the center of rotation during erecting, Points A and B are the electric cylinder's upper and lower hinge points, and θ is the lifting angle. ,  , and  represent the lengths of the electric cylinder before and after erecting.The farther the electric cylinder is from the lifting pivot point, the more energyefficient it is, but it requires a larger stroke.According to the installation space, the angle between the installation angle and the direction of the electric cylinder is 61.7°.The dual electric cylinders used in this study have an initial calculated length of L=3.927 m.

Control system scheme
The control system of the erecting device is depicted in Figure 4. Control commands are sent to the programmable logic controller (PLC) through operational buttons.After processing in the PLC, the instructions generate pulse control signals (four in total), each controlling the erecting cylinders 1, 2, and servo motors of the associated devices.Absolute value encoders are internally installed in the electric cylinders, and their feedback signals are processed by the PLC and transmitted to the upper computer.Tilt sensors and angular velocity sensors are mounted on the erecting frame, and their signals are processed by the controller before being transmitted to the upper computer for display, enabling the monitoring of the status of the erecting frame.The electrical control schematic of the electric cylinder in the erecting device is illustrated in Figure 5.After the system is ready, the erecting cylinder receives the driver's enable signal and reports the enable response signal to the driver.It then receives the upper computer's work command to release the holding brake of the motor, drive the servo motor to rotate, and drive the screw pair of the reducer and electric cylinder to rotate forward, extending the push rod of the electric cylinder.When the erecting cylinder is recovered, it receives the working instructions from the upper computer to drive the servo motor to reverse, driving the screw pairs of the reducer and electric cylinder to rotate in the opposite direction, causing the push rod of the electric cylinder to retract.

Control system software and hardware design
The control system's software section of the erecting device consists of two parts: the upper computer and the lower computer.The upper computer's hardware employs an industrial all-in-one machine, while the lower computer uses a PLC.The software system comprises monitoring and real-time control programs.The monitoring program, also known as the upper computer program, can be understood as the user interface program.The upper computer interface primarily displays the real-time operating status and parameters of the rust removal device, alarm information, and instructions.

Working principle of control system
Initially, the upper computer sends a signal to drive the electric cylinder to the lower computer through USB/PPI.Upon receiving the signal, the lower computer controls the central processing unit (CPU) to IOP Publishing doi:10.1088/1742-6596/2764/1/0120706 output corresponding pulse signals, which are sent to the servo drive of the respective motor.The motor servo controller processes the received pulse signals, subsequently outputting signals to the servo motor.Then, it drives the movement of the electric cylinder, causing the erecting cylinder to raise the erecting frame.The angular information from the motor's encoder is transmitted to the motor driver, processed, and then fed back to the PLC for status feedback.The signals from the inclinometer and angular velocity sensor are transmitted to the PLC and processed.Finally, the PLC sends the status information back to the upper computer through USB/PPI, completing the display of the electric cylinder and erecting frame status.

Dual motor master control structure
Both motors receive identical speed signals, achieving synchronous operation.The control structure is illustrated in Figure 6.Each motor has its complete closed-loop feedback, appearing similar to a parallel configuration.
There is no correlation between the two motors in the dual-motor master-command control mode.They operate purely based on their respective given signals.If any disturbance affects one motor during operation, it will not impact the operational state of the other motor.Its synchronization performance can only be reflected in the starting and ending stages.

Dual motor slave control structure
Taking the main motor as the control target, inputting the given speed signal, simultaneously obtaining the input speed signal from the main motor's output speed, and following the main motor's movement, the control structure is illustrated in Figure 7.Each motor has its complete drive control system, appearing similar to a series configuration.
The dual-motor master-slave control structure consists of two independent position servo systems.The main motor is responsible for executing given commands and completing expected actions, while the slave motor follows the main motor, providing assistance and support, achieving both synchronous operation and ample power supply.

Dual motor cross-coupling control structure
Comparing and subtracting the speed signals of two motors, we utilize this difference for feedback adjustment to correct synchronization errors, known as cross-coupling control.The driver controls the main shaft, simultaneously sending position commands to two slave shafts that need to be synchronized and aligned.The encoders of the two slave shafts couple their positions, adjusting their speeds to achieve positional synchronization.The control structure is depicted in Figure 8.The cross-coupling control structure combines the advantages of both the master command control mode and the master-slave control mode.Each motor is of equal importance, demonstrating good synchronization performance during the start and stop phases.Additionally, each motor is equipped with a speed compensator to compensate for synchronization errors caused by disturbances, effectively correcting deviations and enhancing the anti-interference capability of the dual-motor synchronous control system.
After comparing three synchronization control strategies, this design adopts the cross-coupling control strategy to achieve higher synchronization control precision.

Conclusions
An analysis and trajectory planning of the erecting process was conducted, with the overall trajectory comprising acceleration, constant speed, and deceleration phases.The acceleration and deceleration trajectories utilize fifth-degree polynomial trajectories, ensuring smooth and impact-free motion during the erecting process.
The system scheme and control strategy for the erecting device were determined.In combination with the double electric cylinder erecting system and the cross-coupling control, the approach involves comparing and subtracting the speed signals from the two motors.This method facilitates feedback adjustment, aiming to enhance the control accuracy for synchronously driving the two electric cylinders.

Figure 1 .
Figure 1.The basic composition of the erecting device.The use of electric cylinders as the power source for the erecting device has several key advantages: 1) high dynamic response and precise position control; 2) a broad thrust range and longer stroke; 3) an extremely wide working temperature range; 4) low noise and vibration.This study primarily focuses on the research of the dual-electric-cylinder erection trajectory planning, control system, and control strategies of the erecting device.
-time curve.b) Angle velocity-time curve.c) Angle acceleration-time curve.

Figure 2 .
Figure 2. The motion trajectory curve is programmed by a fifth-order polynomial.

Figure 4 .
Figure 4. Diagram of the erecting device control system.The electrical control schematic of the electric cylinder in the erecting device is illustrated in Figure5.After the system is ready, the erecting cylinder receives the driver's enable signal and reports the enable response signal to the driver.It then receives the upper computer's work command to release the holding brake of the motor, drive the servo motor to rotate, and drive the screw pair of the reducer and electric cylinder to rotate forward, extending the push rod of the electric cylinder.When the erecting cylinder is recovered, it receives the working instructions from the upper computer to drive the servo motor to reverse, driving the screw pairs of the reducer and electric cylinder to rotate in the opposite direction, causing the push rod of the electric cylinder to retract.

Figure 5 .
Figure 5. Schematic diagram of the control of the electric cylinder of the erecting device.

Figure 7 .
Figure 7. Diagram of dual-motor master-slave control mechanism.

Figure 8 .
Figure 8. Diagram of the cross-coupled control structure of two motors.The cross-coupling control structure combines the advantages of both the master command control mode and the master-slave control mode.Each motor is of equal importance, demonstrating good synchronization performance during the start and stop phases.Additionally, each motor is equipped with a speed compensator to compensate for synchronization errors caused by disturbances, effectively correcting deviations and enhancing the anti-interference capability of the dual-motor synchronous control system.After comparing three synchronization control strategies, this design adopts the cross-coupling control strategy to achieve higher synchronization control precision.

Table 3 .
Acceleration and deceleration phase parameter table.