Fuzzy PID Controller for Ride Comfort Enhancement of Tractor Operator during Tillage

doi:10.21203/rs.3.rs-1768019/v1

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Research Article

Fuzzy PID Controller for Ride Comfort Enhancement of Tractor Operator during Tillage

https://doi.org/10.21203/rs.3.rs-1768019/v1

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posted 23 Jun, 2022

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Tractors have become the most powerful tool in modern agriculture. Different type of implements is used to mechanize many agriculture tasks. But development of such tractors which can provide maximum comfort during tillage process is one of the design targets of manufacturing industries. This paper proposes a Fuzzy PID controller for seat of tractor operator while working in fields. The controller is designed with the objective to improve the ride quality of operator. Raw experimental data for acceleration at operator’s seat was measured by varying tractor forward speed and type of tillage implements. A model of tractor-implement system was developed and validated. The results of Fuzzy PID are presented graphically and compared with PID and passive system and it is found that Fuzzy PID controller has notable ability to suppress the amplitude of vibrations at driver seat of tractor.

PID Controller

Fuzzy logic

piezoelectric acceleration sensor

implements

Tractors or off road vehicles are exposed to different types of external varying disturbances because of rough farm conditions. Since most of the tractors are not provided any type of suspensions other than the damping effect of tire so these high amplitude vibrations are transmitted to the driver through seat, foot rest and steering wheel. The vibrations transmitted through seat are most harmful to the operators. Therefore it is the important topic of research to reduce the vibration levels at seat base to enhance the comfort level of operator. To provide the good road insulation, vehicle handling and road holding a well-controlled suspension system for seat is need of the hour for modern agriculture tractors. Since the conventional or passive suspension systems are made up of fixed spring stiffness and damping coefficients. Fixed spring stiffness and fixed damping coefficients limit the performance of suspension system. Therefore it is necessary to develop a suspension system with variable parameters. To achieve these active and semi-active suspension systems came into picture to provide the flexibility and to increase the range of suspension system.

Soil mobilization is done by tillage operations for crop production. It is the important task as it influences all other operations. Such operations are mostly performed by conventional plowing, harrowing and rotavators. For optimum crop production excessive mobilization is required by tillage operations but this excessive mobilization of soil increases vibration levels on the tractor. These vibrations are felt by operator through seat. So proper seat design is a crucial factor to improve the comfort levels to the operator [1, 2 and 3]. To design the damping system in seat of operator depends upon the excitation and source of vibration acting on the system. So it is important to know about the excitation source and level of vibrations [4 and 5]. The main source of vibrations to the operator’s seat of tractor during tillage is surface excitations to the tire from the fields. Therefore recording and analyzing the vibration levels and directions is important for seat designs.

Tractor implement set characteristics is an important factor for vibrations levels to the operator’s seat. Tractor implement set characteristics depends upon many factors such as forward travel speed, type of tillage implement, soil type, and tire inflation pressure. [6, 7 and 8] Excessive soil mobilization, incorrect ballast addition, extreme forward speed contributes towards vibration levels and due to excessive mechanical vibrations quality is always compromised [9].

Fuzzy PID controller is proposed in this paper to minimize the displacement of the vibrations at base of operator’s seat. Comparison between passive system and PID controlled system and Fuzzy PID is also presented to clearly visualize the reduction in amplitude of vibrations. The first part of paper presented the mathematical modelling of system and second part presented the design of a Fuzzy PID controller.

The experimental setup was developed to collect experimental data at base of driver’s seat during tillage with implements. The setup unit comprises of tri-axial accelerometer, data acquisition unit and fits and fixtures to mount the unit at seat base as shown in Fig. 1. The set up for the vibration measurement of agricultural tractor was designed with standards of ISO 2631-1, ISO 2631-5 and ISO 5008.

The acceleration sensors used for experimentation were piezoelectric accelerometers, the range of frequency is of 1 to 80 Hz and sensitivity is of vibration level of 0.05 m/s²and it has capability to measure vibrations upto 5 m /s²RMS with a crest factor as great as three without distortion and with an accuracy of ± 0.05 m/s² and sampling rate of data acquisition unit is 800 units/second. The accelerometer was fixed at base of tractor seat and the tractor was made to run at fields with tillage implements and data was recorded in data acquisition unit for further analysis.

Tractor-implement vibration model is developed for simulation as shown in Fig. 2 and mass of tractor with implements and moment of inertia relative to central axis is used to represent tractor body structure. Due to surface roughness front and rear tires of tractor are subjected to displacement excitations q_fz(t) and q_rz(t) respectively. Because there is a difference in amplitudes of qfz(t) and q_rz(t) therefore angular displacement with respect to centre of mass arises. Due to this angular displacement with respect to mass centre roll, yaw and pitch movements of tractor came into the picture.

The ground excitation relation between front and rear axles of the tractor-implement system at any instant i by considering the time lag between q_fz(t)and q_rz(t) can be expressed as

$${q}_{fzi}\left(t\right)={q}_{rzi}\left(t+\tau \right) \left(1\right)$$

Where qfzi(t) and q_rzi(t) are displacement excitations at front and rear axles respectively, Ʈ is time lag and can be calculated as

$$\tau =\frac{{l}_{bf}+{l}_{br}}{v} \left(2\right)$$

Where l_bf is distance of mass centre between chassis and front axle, l_br is the distance of mass centre between chassis and rear axle and v is the velocity of tractor-implement system.

The equations of motion can be expressed as

$$\left({M}_{T}+{M}_{I}\right)\ddot{z}={f}_{1}+{f}_{2}-\left({M}_{T}+{M}_{I}\right)g \left(3\right)$$

The displacement of wheels can be calculated as

$${z}_{1}=z+\left({l}_{1}+{l}_{3}\frac{{M}_{I}}{{M}_{T}+{M}_{I}}\right) \left(4\right)$$

${z}_{2}=z+\left({l}_{2}-{l}_{3}\frac{{M}_{I}}{{M}_{T}+{M}_{I}}\right) \left(5\right)$ The above equations are used to calculate the effect of tillage implement on displacement of wheels.

The mathematical model of tractor-implement system is shown in Fig. 3. The model represents a real system with parameters to passenger seat mass (m_s), force transmitted to the front left and right corner of tractor chassis (F_f1, F_f2 ),Tractor body mass (m_b) tyre stiffness (k_t), damping coefficients (c_t) vertical axle displacements (z_f1, z_f2, z_r1, z_r2). Road excitations have been represented by Z_r. Pitch and roll of tractor-implement system are represented by Ɵ and ϕ respectively.

The vibratory forces transmitted by each wheel at the point of contact between the axle and the wheel can be formulated as follows:

$${k}_{t}\left({z}_{a}-{z}_{R}\right)+{c}_{t}\left({\dot{z}}_{a}-{\dot{z}}_{R}\right) \left(6\right)$$

The governing dynamical equations for the forces transmitted to chassis are given as:

$${F}_{f1}={k}_{tf}\left({z}_{af1}-{z}_{Rf1}\right)+{c}_{tf}\left({\dot{z}}_{af1}-{\dot{z}}_{Rf1}\right) \left(7\right)$$

$${F}_{f2}={k}_{tf}\left({z}_{af2}-{z}_{Rf2}\right)+{c}_{tf}\left({\dot{z}}_{af2}-{\dot{z}}_{Rf2}\right) \left(8\right)$$

$${F}_{r1}={k}_{tr}\left({z}_{ar1}-{z}_{Rr1}\right)+{c}_{tr}\left({\dot{z}}_{ar1}-{\dot{z}}_{Rr1}\right) \left(9\right)$$

$${F}_{r2}={k}_{tr}\left({z}_{ar2}-{z}_{Rr2}\right)+{c}_{tr}\left({\dot{z}}_{ar2}-{\dot{z}}_{Rr2}\right) \left(10\right)$$

The linear accelerations of the points of force application to the tractor body may be computed as following:

$${\ddot{z}}_{afc}={\ddot{z}}_{cg}-{l}_{f}\ddot{\theta } \left(11\right)$$

$${\ddot{z}}_{a{r}_{1}}={\ddot{z}}_{cg}-{l}_{r}\ddot{\theta }+{t}_{1}\ddot{\varphi } \left(12\right)$$

$${\ddot{z}}_{ar2}={\ddot{z}}_{cg}-{l}_{r}\ddot{\theta }-{t}_{1}\ddot{\varphi } \left(13\right)$$

The linear accelerations of the joints between front axle and front wheels are indicated as follows:

$$\ddot{\alpha }=\frac{1}{{I}_{xxa}}\left({F}_{f1}{t}_{1}+{F}_{f2}{t}_{2}\right) \left(14\right)$$

Finally, the mathematical equations for the linear accelerations of the axles of front wheel joints can be computed as follows:

$${\ddot{z}}_{a{f}_{1}}={\ddot{z}}_{afc}+{t}_{1}\ddot{\alpha } \left(15\right)$$

$${\ddot{z}}_{af2}={\ddot{z}}_{afc}+{t}_{2}\ddot{\alpha } \left(16\right)$$

The source block or input is the signal generator representing the sine input with 0.01m amplitude and 35 Hz frequency and step function with the height of 1 unit up at 5 sec and 1 unit down at 7 sec for front wheel were selected. The time for step up and down for rear wheel was 8 sec and 10 sec respectively. At time t₀ and t_1, the road inputs applied to the front and rear wheels of modelled tractor, respectively. The time period of t₀ and t₁ is contemplated in relation to the distance between the front and rear axle (Wheel Base), WB, and the speed (v) of the tractor as:

$${t}_{1}-{t}_{2}=\frac{Wheel Base \left(WB\right)}{Velocity of tractor \left(v\right)} \left(17\right)$$

The developed Simulink model of disturbance input for front and rear wheel is presented in Fig. 4 (a) and (b) respectively.

Based on the actual parameters of tractor and implement simulink model was developed and is represented in Fig. 5.

The actual parameters of tractor and implement used for simulink model are represented in Table 1

Table 1

Parameters of full tractor- implement vibration model
Notations	Description	Values	Units
k_tf	Tractor Front tire stiffness	32,000	N/m
c_tf	Tractor front tire damping	980	N-s/m
k_tr	Tractor rear tire stiffness	31,000	N/m
c_tr	Tractor rear tire damping	1800	N-s/m
m_t	Mass of tractor	2,700	Kg
t₁	Distance of c.g.of tractor from left portion of chassis	0.81	M
t₂	Distance of c.g. of tractor from right portion of chassis	0.81	M
l_r	Distance of c.g. of tractor from rear portion of chassis	0.89	M
l_f	Distance of c.g. of tractor from front portion of chassis	1.32	M
I_xxt	MOI of tractor about x axis	590	kg-m²
I_yyt	MOI of tractor about y axis	1900	kg-m²
I_xxa	MOI of tractor front axle about the pivot point	4.5	kg-m²
m_s	Mass of seat	32	Kg
l_d	Longitudinal distance of seat from c.g. of tractor	0.67	M
k_s	stiffness of seat	7800	N/m
c_s	Damping of seat	128	N-s/m

PID Controller

The PID controller is consists of three main components which are proportional (P), integral (I), and derivative (D). The objective of proportional is to reduce the entire error and to follow the set point. The integral action improves the steady state error. The derivative is for rate of change of error and also reduces overshoot and oscillation. The algebraic sum of proportional, integral and derivative actions is used to control the process.

The output of PID controller is calculated in the time domain as;

$${f}_{c}={k}_{p}+{k}_{i}\int edt+{k}_{d}\frac{de}{dt} \left(18\right)$$

Where ${f}_{c}$ = Controlled damping force ${k}_{p}$ = Proportional gain,

${k}_{i}$ = Integral gain ${k}_{d}$ = Derivative gain

Simulation limits of 820 N to -820 N are used to limit controller force. The calculated parameters for PID controller are ${k}_{p}$= 4.4012, ${k}_{i}$= 91.87 and ${k}_{d}$= 180.

The PID controller is simple and commonly used for control of damping force to supress the amplitude of vibrations but scope of PID controller becomes limited when disturbances has varying conditions and PID controller has to retune. In tractor seat also disturbances vary continuously due to rough farm surface excitations. Gain values of PID controller have to change according to disturbances. To overcome this limitation self-tuned PID controller is used. To tune it Fuzzy logic is used. Membership function of Fuzzy logic was defined and accordingly fuzzification and de-fuzzification was performed. The designed controller needs to supply corresponding current used to control the process to an actuator or damper which will further apply force on vibrating seat base to supress the amplitude.

Fuzzy- PID Controller

There are three important functions of fuzzy logic controller;

Fuzzification: In fuzzification corresponding fuzzy sets with membership functions are represented according to input crisp data.
Fuzzy base rule: Fuzzy rules are defined in this step for input crisp data.
Defuzzification: The output crisp values are obtained from input data fuzzy base rules.

The proposed fuzzy PID controller gives the values of${ k}_{p}$, ${k}_{i}$ and ${k}_{d}$ using self-tuned fuzzy logic controller.

The simulation of tractor-implement model is carried out in MATLAB Simulink software. The actual parameters of tractor and implement are used to simulate the model. The model with Fuzzy PID controller is simulated using step input of 0.85 m. The Fig. 5 (a). shows the acceleration of tractor seat for passive system, PID controlled and Fuzzy-PID controlled output. The proposed Fuzzy-PID controller damp the road excitations compare to PID and uncontrolled systems in order to limit the seat displacement. In Fig. 5 (b). the combined results of simulated model are compared with uncontrolled output model and with PID model output are represented. The curves for uncontrolled output, PID controlled output and fuzzy –PID controlled output shows that amplitude of acceleration at seat base is reduced by maximum value in fuzzy –PID output as compared with PID controller followed by uncontrolled output. Time and frequency domain responses for developed model are represented in Fig. 5(c). It was observed that Fuzzy PID controlled output is much better than uncontrolled output and it reduces amplitude of acceleration at seat base by 18%.

In this paper experimental result has been used to develop a Fuzzy PID controller. The PID controller was tuned and simulated. The values of uncontrolled output and PID controlled output have been compared with Fuzzy PID output and it has been observed that Fuzzy PID controller gives good results for step and impulse road disturbances. It is understood that experimental results of response of force over varying current and displacement can be used to control actuator as current of a damper or actuator.

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No competing interests reported.

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Version 1

posted 23 Jun, 2022

You are reading this latest preprint version

Fuzzy PID Controller for Ride Comfort Enhancement of Tractor Operator during Tillage

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Version 1

Abstract

Figures

1. Introduction

2. Experimental Data Collection To Establish Vibration Behaviour At Seat

3. Dynamic Model Formation

4. Simulink Model Of Tractor Implement System

5. Controller Design Theory

6. Simulation Results

7. Conclusion

References

Competing Interests

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