Fractional PID controller in an active image stabilization system for mitigating vibration effects in agricultural tractors

Highlights

• An active image stabilization system was modeled for an agricultural machine.

• A method for tuning a fractional PID is presented for a closed-loop dynamic system.

• The fractional PID controller shows better performance than a classical PID.

• The model was evaluated using typical vibration data that was collected from a field experiment.

• Typical vibration components of agricultural machine were efficiently attenuated.

Abstract

Recent demands in sophisticated agricultural machinery require passive or active image sensors to be mounted on vehicle frames. The impact produced by vertical displacements due to tire-soil interaction and mechanical engine vibration causes oscillations that reduce the data quality of any activity performed by equipment such as a camera, spectroradiometer, or scanner laser. This paper presents the modeling and simulation of an active system for stabilization of oscillations using a fractional order PID (Proportional-Integral-Derivative) controller. A method for tuning the fractional order PID is presented for a closed-loop dynamic system. Experiments based on simulations are carried out to compare the performance of the active stabilization system with fractional and integer order PID controllers. Common excitation functions are used to assess the performance of the active stabilization system, along with some common vibration disturbances acquired by a field experiment with a tractor-implement set. The results show that the active stabilization system presents better performance, mitigating vibration displacements and accelerations through a closed-loop system with a fractional PID controller. Additionally, numerical results confirm the superior capacity of the fractional controller based system for attenuating the vibration disturbance compared to the classical PID system for different machinery operational conditions such as forward speed and load.

Introduction

In several agricultural applications, mechanical vibrations are frequently inconvenient due to oscillations that can significantly affect the desired outcome. Machine vision applications in agriculture are heavily dependent on the quality of acquired images in activities such as non-destructive measurements, visual navigation and behavioral surveillance (Barbedo, 2016, McCarthy et al., 2010). Occasionally, vibrating parts of the machinery that support the image acquiring sensor can blur images, which negatively affects the accuracy of machine vision systems (McCarthy et al., 2010). In addition, the development of autonomous agricultural vehicles and mobile agricultural robots requires more precise and advanced techniques to mitigate the effects of disturbances (Bayar et al., 2015, Mousazadeh, 2013, Reina et al., 2016, Zhang et al., 2016). Continuous vibrations can affect the outcome of applications as well as damage the mechanical and electronic components of those systems (Paraforos et al., 2014).

Novel civil and military vehicles require active suspension systems (ASS) for attenuating excitations caused by tire-soil interactions and engines. The active image stabilization system (AISS) is a type of ASS that applies techniques to eliminate, or reduce, unwanted fluctuations from mechanisms that apply movements in opposing vibrations of the vehicle where the image acquisition system is mounted (Zhao et al., 2015). In these systems, inertial sensors identify the vibrations and a controller drives an active stabilizing mechanism. The study of different control methods for design and deployment of controllers for AISS has been the focus of recent research (Gasteratos, 2009, Marichal et al., 2013, Zhao et al., 2015).

Some methods have been investigated to assess agricultural machinery properties in terms of vibrations to understand the effects on fatigue life (Paraforos et al., 2016) and operator safety (Cutini et al., 2016). Two types of approaches can be identified in these studies. One approach seeks to develop experimental methods to determine vibration characteristics and uses analysis parameters such as tire pressure, type of soil, type of agricultural operation, operation speed and type of agricultural machinery (Cuong et al., 2013, Cutini et al., 2016, Kang and Kaizu, 2011, Paraforos et al., 2016, Paraforos et al., 2014, Scarlett et al., 2007, Servadio et al., 2007). The other approach uses the analysis of numerical simulations based on dynamic models of agricultural vehicles to estimate vibration characteristics before real implementation, which avoids the cost of multiple prototypes (Melzi et al., 2014, Rabbani et al., 2011).

In addition to the studies to evaluate the effects of vibration on agricultural machineries, there are also proposals to diminish the damaging effects of vibrations. Bruce et al. (2001) performed experiments with a tractor equipped with a hydraulic active front axle suspension and an active three-point linkage shock absorber. The comparative analysis of the global acceleration transmitted through the tractor driving seat showed substantial attenuation for the tractor-implement system with an active vibration suppressor compared to the same system without the suppressor. De Temmerman et al. (2004) developed a model of a passive cab suspension for a self-propelled agricultural machine based on Lagrange’s equation. The model was evaluated by comparing the eigenfrequencies and vertical displacements for different vibration signals applied to the model and with an experimental test rig. Shamshiri and Ismail (2013) modeled and simulated a full-state feedback controller for a tractor electro-hydraulic active suspension. The simulations showed attenuation of the vertical displacements within a significantly shorter period of time compared to the uncontrolled system for step and sinusoidal disturbance inputs. However, among the different approaches, there are no specific investigations of the design of AISS for agricultural machinery, and significant challenges havenot been resolved before identifying reliable technologies for image acquisition, primarily for autonomous and robotic vehicles (Mousazadeh, 2013, Reina et al., 2016).

A promising methodology based on fractional order control has obtained positive results for the design of ASS. This methodology is based on fractional calculus (FC), which applies concepts of differential and integral calculus of non-integer order. Although FC dates back to the beginning of calculus theory, the usefulness of FC has been shown only in the last two decades, after the development of computers and numerical simulations. In recent years, FC has been shown to be useful in several applications, with control algorithms receiving considerable attention (Özbay et al., 2012, Silva and Machado, 2006, Tan et al., 2016).

The success of fractional algorithms in control engineering and the lack of studies in AISS for agriculture problems inspired this work, in which the performances of integer order (PID) and fractional order (FrPID) controllers are compared for an AISS operating on an agricultural machine. The investigation was performed using modeling and simulation to design and evaluate the performance of the controllers considering common vibration disturbances from agricultural machinery. The simulation of the model using PID and FrPID controllers generated results that are compared and discussed.

This paper is organized as follows: Section 2 describes how the AISS proposed in this work was modeled and simulated; Section 3 outlines the results obtained from the simulations, with the main aspects being presented and analyzed; and Section 4 states the main conclusions obtained from this study.