Modelling and verification for pitch angle of leveler machine in paddy fields based on time series analysis

Abstract: Attitude of the agricultural machinery working in paddy fields varies along with the roughness of the bottom layer, which has great influence on the efficiency and quality of the operation. There are different kinds of profiling systems designed for making the agricultural implements match up the unevenness of field surface, such as the leveler machine and wide sprayer. Basically, for most of the feedback control system, the system error received by the controller always lags one period behind the machine motion, which certainly affects the real-time control. However, the model predictive controller (MPC) can make the control decision in advance according to the predictive information, thus could improve the accuracy and responding rate of control system. The predictive model is the key and basic step for the design of MPC. In order to realize the height control for leveler machine with MPC in paddy field, the model identification technique and parameter estimation method for the pitch angle of the leveler machine are put forward respectively and verified by experiments. There are four main steps to identify the model which are sensor data pre-processing, model structure determination, parameters estimation, and residual diagnostic. By taking the difference to the non-stationary pitch angle data of the leveler machine, a set of stationary time series was ready for modeling. Based upon Akaike information criterion (AIC) rule, order of the model was simply determined. To start with, the popular RLS method is adopted to estimate the model parameter, but it was found that the pitch error between the predictive output of the model and measurements increased with time, because the RLS was failing to make full use of the newer data of the sensor. As a result, the Method of forgetting factor recursive least square (FFRLS) was utilized to estimate and update parameters of the model in real-time, and value of the FF () was adopted by carefully "trial and error" procedure. Finally, the ARMA (18, 17) was analyzed as the description of the pitch angle. The residual test was executed with the help of Matlab function which showed there was no autocorrelation in residuals, therefore the ARMA (18, 17) can be employed as the predictive model for the height control of leveler machine. The validity and accuracy of ARMA (18, 17) were further tested by comparing the model output with the measured pitch angles under 4 different practical conditions, which included crossing obstacles, crossing ditches, running on a slope and operating in the paddy field. The pitch angles were measured on-line by the attitude and heading reference system (AHRS, Mti-300) mounted on the leveler machine, and meanwhile, with the real-time pitch value, model parameters and predictive output were calculated using the proposed method at the same time. A good agreement was found between the output of model ARMA (18,17) and AHRS measurements on pitch angles. The maximum absolute error (MAE) and the root mean square error (RMSE) are both less than 0.2? in all experiment situations, which verifies the validity of ARMA (18,17) to be used as the predictive model for describing the pitch angle of the leveler machine, and the effectiveness of FFRLS algorithm to be used on real-time parameters estimation of time series models. Above all, the proposed method can offer an accurate predictive model for the design of MPC of the leveler machine in paddy fields. Besides, the error analysis shows that the model is accurate enough on pitch angle prediction, so this method could be developed further to apply it on many other agricultural machinery applications. The algorithm was designed and analyzed with the pitch angle series, but methods for creating the predictive model of the three-axis attitude still needs further study.