Research and Application of Precision Fertilizer Application Algorithm Based on PSO Optimized Fuzzy PID Control

12 In irrigation’s process and fertilizer application in production of agri- 13 culture, the accuracy of fertilizer application and water maintains at a 14 relatively low level, which results in waste of soil slabbing and resources. 15 In this research, a fuzzy PID algorithm based on PSO optimization 16 is designed to control the fertilizer application process and irrigation 17 of the fertilizer applicator. Firstly, a mathematical model of the fer- 18 tilizer applicator is established according to the relevant modules and 19 corresponding parameters. Based on the MATLAB/Simulink platform, 20 the PID controller, the fuzzy PID controller and the controller pro- 21 posed in this article are constructed respectively, which can be applied 22 to the established transfer functions. The simulation outcomes demon- 23 strate that the response time of the control algorithm proposed in this 24 research is shortened to 30s, compared to fuzzy PID and PID, which 25 is 62.5% and 50% shorter respectively, and the overshoot of the control 26 algorithm in this article is nearly 0 of apart from the early oscillation. 27 In order to verify the algorithm’s reliability in practical application, this 28 research designs groups of diﬀerent pressure for the accuracy control 29 test , the test consequences illustrate that the fuzzy PID control based 30 on PSO optimization has excellent control eﬀect under each pressure. 31 The control accuracy is concentrated at around 2%, while PID con- 32 trol maintains around 20% and fuzzy PID control distributed at 10%. 33 The results show that the control algorithm proposed in this research 34 enhances the irrigation accuracy in the practical application process.

to the established transfer functions. The simulation outcomes demon-23 strate that the response time of the control algorithm proposed in this 24 research is shortened to 30s, compared to fuzzy PID and PID, which 25 is 62.5% and 50% shorter respectively, and the overshoot of the control 26 algorithm in this article is nearly 0 of apart from the early oscillation. 27 In order to verify the algorithm's reliability in practical application, this 28 research designs groups of different pressure for the accuracy control 29 test , the test consequences illustrate that the fuzzy PID control based 30 on PSO optimization has excellent control effect under each pressure. 31 The control accuracy is concentrated at around 2%, while PID con-32 trol maintains around 20% and fuzzy PID control distributed at 10%. 33 1 Introduction 38 Agriculture accounts for more than 65% of total water consumption, and 95%   Overall, this paper proposes to analyse the variable control section's com-

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The equilibrium equation for the motor drive voltage is shown in Eq(1).
Where U d (t) is the DC motor's drive voltage, R is the internal resistance, 127 I d (t) is the armature current and E(t) is the electric potential. The equation 128 for the output torque can be expressed as: where M (t) is the output torque of the DC motor and K is the DC motor 130 torque factor. The DC motor torque expression is given in Eq.
where (M )t is the torque of the load, J is the amount of rotational inertia 132 of the DC motor and w(t) is the speed of the DC motor.
where f is the coefficient of friction and is the angle of rotation of the 134 motor output.

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Combining the above equations yields.
Bringing the above equation into the voltage balance equation gives.
where K m is the inverse electric potential coefficient. The transfer function 138 between the DC motor's output angle and the input voltage is obtainable after 139 the Laplace inverse transformation as: By the series relationship between the parts, the output angle is used as the 141 reduction device's input reference, which increases the output torque by reduc- the input angle, which can be listed and written as follows.
where L denotes the lead of the guide rod and X is the output displacement. frequency, in summary, this voltage driving module's transfer function is: The modules are connected in parallel with each other and ks is the con-155 verter amplification factor. The transfer you function of the system can be 156 obtained as: The fertiliser application system parameters are listed in the table 1.

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Bringing the parameters into the mathematical model yields the transfer 159 function for this study as 160 G(s) = 0.048 9.9 × 10 −5 s 3 + 4.65 × 10 −4 s 2 + 2.87 × 10 −4 s (11) Determining the k p , k i and k d of the PID, either continuous control or analogue 167 control can be done by the PID controller, and its expression is: The control structure is schematically shown in Fig.2.   Table 2.

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The affiliation relationship between the two inputs and the output affiliation 213 relationship between the three optimised parameters is shown in Fig.4. The 214 fuzzy surface diagram of the optimised parameters is shown in Fig.5-Fig.7. 3.2 Design of a fuzzy PID controller based on particle 216 swarm optimization 217 PSO(particle swarm algorithm) has a strong ability to deal with continuous 218 problems, and is therefore suitable for parameter optimisation, while the PID 219 controller consists of three parameters: k p ,k i , k d .

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The PID controller is treated as a "black box", with these three parameters PID controller designed in this study is shown in Fig.8 .

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The flow of the basic particle swarm algorithm is as follows, Which can be 228 showon in Fig.9.

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(1) Particle swarm hyperparameters as well as random solutions are 230 initialised.   (2) Set the values of the PID control parameters, run the system and judge 232 whether the system performance indicators meet the requirements.

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(3) If the particle adaptation value at the current time is higher than all 234 previous ones, the optimal value is updated.

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(4) Iterate each particle, if the current particle is better than the best 236 position adaptation value in the swarm, then its as the population optimum.

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(5) The velocity and position of the particle are updated.  is taken as the result for the control model simulation.

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The system inputs a step signal with an amplitude of 10, then the fuzzy 278 language values corresponding to the compensation values k p , k i and k d from 279 the fuzzy controller are formed into individuals, and the initial population is 280 randomly generated, and the population is optimised by the particle swarm 281 operator, and the population is iterated to the maximum genetic generation.

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The particle swarm algorithm optimal individual iterative search process is PSO optimisation as the control algorithm for the variable control system.

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The system is tested indoors by setting target quantities through the control 309 terminal to respectively verify the relationship between flow rate and system valve. The platform for the precision fertiliser system is shown in Fig.11.  The accuracy test diagram is as follows.

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As is visible from the Fig.12-Fig. 14  in five measurements, and the average value is taken as the measurement data.

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The test outcomes reveal that PID control's fertiliser application accuracy is