## 2 Materials and Methods
### Dynamic Compensation System Design  
The dynamic compensation system mainly consists of a six-degree-of-freedom platform, a seeding unit, a dynamic compensation mechanism, a dual-axis inclination sensor, and an industrial control computer. The industrial control computer loads excitation signals to the six-degree-of-freedom platform through RS232 to simulate the pose changes of the seeding unit during field operations. The dual-axis inclination sensor collects the inclination data of the seeding unit and transmits it to the industrial control computer via the CAN bus for analysis. The dynamic compensation mechanism is installed on the seeding unit, and the dynamic compensation is completed via a servo electric push rod and a linear displacement sensor. The compensation range of the system is \(-5\)-\(5\) cm, and the compensation speed is \(800\) mm/s. When the six-degree-of-freedom motion platform receives the loaded simulation signal through RS232, it simulates the field working state according to the pre-set waveform. The seeding tube falls from its ideal seeding position, and the dual-axis inclination sensor detects the changes of the \(x\) and \(y\)-axis angles of the seeding unit, which are transmitted to the control system via the CAN bus. The control system uses fuzzy PID control to drive the servo electric push rod to compensate for the deviation of the seeding tube. The displacement sensor detects whether the seeding tube has reached the predetermined position until the dynamic compensation of the seeding position is completed. The seeding position compensation system is mainly realized using two servo electric push rods for offset compensation. The servo electric push rod is driven by a servo motor (Panasonic, model MSMF0121V2M, rated speed \(3000\) r/min, rated power \(100\) W). Thedynamic equation and the electrical equation that the whole system satisfies during the movement are:  
\[\left\{ \begin{array}{l}U=E+IR_{1}+L_{1}\frac{\mathrm{d}I}{\mathrm{d}t}=K_{1} \frac{\mathrm{d}\theta_{1}}{\mathrm{d}t}+IR_{1}+L_{1}\frac{\mathrm{d}I}{\mathrm{d }t}\\ T=K_{2}I\\ T=T_{1}+T_{2}+T_{3}+T_{4}\\ T_{1}=J_{1}\frac{\mathrm{d}\omega}{\mathrm{d}t}\\ T_{2}=b_{1}\omega=K(\theta_{2}-\theta_{1})\\ T_{3}=J_{2}\frac{\mathrm{d}\omega}{\mathrm{d}t}\\ T_{4}=b_{2}\omega=K(\theta_{3}-\theta_{2})\\ Z=\theta_{3}R\\ \end{array} \right. \tag{1}\]  
where \(U\) is the armature voltage, V; \(I\) is the armature current, A; \(L_{1}\) is the armature inductance, H; \(R_{1}\) is the armature resistance, \(\Omega\); \(Z\) is the displacement of the pushrod, cm; \(J_{1}\) is the rotor inertia of the motor, kg\(\cdot\)m\({}^{2}\); \(J_{2}\) is the rotational inertia of the screw, kg\(\cdot\)m\({}^{2}\); \(\theta_{1}\) is the angle of rotation of the motor, rad; \(\theta_{2}\) is the angle of rotation of the screw, rad; \(T_{4}\) is the output torque of the screw, N\(\cdot\)m; \(T\) is the electromagnetic torque, N\(\cdot\)m; \(T_{1}\) is the inertia torque of the motor, N\(\cdot\)m; \(T_{2}\) is the friction torque of the motor, N\(\cdot\)m; \(T_{3}\) is the inertia torque of the load, N\(\cdot\)m; \(T_{4}\) is the frictional torque of the load, N\(\cdot\)m; \(b_{1}\) is the coefficient of viscous friction of the motor, N\(\cdot\)m\(\cdot\)s/rad; \(b_{2}\) is the coefficient of viscous friction of the load, N\(\cdot\)m\(\cdot\)s/rad; \(E\) is the motor counter-electromotive force, V; \(K_{2}\) is the motor torque coefficient, N\(\cdot\)m/A; \(K_{1}\) is the motor counter-electromotive force coefficient, V\(\cdot\)s/rad; \(K\) is the stiffness coefficient of the drive shaft, N\(\cdot\)m/rad; \(\omega\) is the motor angular velocity, rad/s; \(R\) is the unit angle telescopic displacement of the actuator, mm/rad.