Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 5658983, 7 pages

https://doi.org/10.1155/2017/5658983

## The Loading Control Strategy of the Mobile Dynamometer Vehicle Based on Neural Network PID

College of Vehicle and Traffic Engineering, Henan University of Science and Technology, Luoyang 471003, China

Correspondence should be addressed to Liyou Xu; moc.anis@2002uoylx

Received 23 February 2017; Accepted 26 April 2017; Published 17 May 2017

Academic Editor: Antonios Tsourdos

Copyright © 2017 Xianghai Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

To solve the problems of low loading precision, slow response speed, and poor adaptive ability of a mobile dynamometer in a tractor traction test, a PID control strategy based on a radial basis function neural network with self-learning and adaptive ability is proposed. The mathematical model of the loading system is established, the algorithm of adaptive control is described, and the loading control method is simulated with MATLAB software. The system, which uses the NN-PID (neural network PID) control strategy, is used to test a YTO-MF554 tractor. Then, the proposed control strategy is validated. Results show that when the traction increases from 0 to 10 kN, the response time of the test system is 1.5 s, the average traction force in the stability range is 10.13 kN, and the maximum relative error of traction force is 2.2%. This control strategy can improve the response speed and steady-state accuracy and enhance the adaptive ability of the mobile dynamometer vehicle loading system. This study provides a reference for designing the adaptive controller of the mobile dynamometer vehicle loading system.

#### 1. Introduction

The loading process of mobile dynamometer vehicles presents many uncertainties in the tractor traction test. Frequently tuning the parameters is necessary for traditional control methods, thus disrupting the test. Moreover, the traditional system has low efficiency and accuracy. A considerable number of theories and practices have shown that the application of self-adaptable control technology to the test system will improve the efficiency and accuracy of the test system [1–4].

The adaptive control algorithm and its application have been studied by many local and international researchers. Locally, Wang et al. proposed the fuzzy adaptive PID control for the nonlinear and time-variant mobile dynamometer of an automobile [5]. He et al. expounded the output prediction of complex nonlinear systems based on the radial basis function (RBF) neural network and obtained well-predicted results [6]. Xia and Wang proposed a new method that combined the RBF neural network and single neuron PID. This method was applied to the speed control of a switched reluctance motor with good control effect [7]. Wang et al. applied RBF-PID to improve the temperature control of a thermal power plant [8]. Internationally, Anwar optimized PID controller parameters based on a genetic algorithm and achieved accurate real-time control for retarder loading [9]. Dash et al. expounded the application of the RBF neural network PID in controlling an electrical power unit [10]. D. L. Yu and D. W. Yu investigated the adaptive adjustment algorithm of RBF neural networks [11]. However, there are few studies on the adaptive control of loading for a mobile dynamometer vehicle in the tractor traction test.

In this study, the RBF neural network PID control strategy is used for the load control of the mobile dynamometer vehicle. The system output traction has a good follow effect in comparison with input load. And the output load for power wagon random loading system can reproduce the tractive load for tested tractor reasonably. This control strategy can improve loading precision and response speed and enhance the self-adaptive ability of the control system. This method can also provide a reference for the investigation of mobile dynamometer vehicle loading control.

#### 2. Mathematical Model of the Mobile Dynamometer Vehicle Loading System

The mobile dynamometer vehicle is modified with a YTO-1304 tractor. The tractor power take-off is connected to an electric eddy current retarder, which brakes the mobile dynamometer vehicle by loading the transmission system.

##### 2.1. Model of the Eddy Current Retarder

The eddy current retarder is mainly composed of front and rear rotor disks and eight excitation coils with an iron core between the disks. The following simplifications and assumptions are made when the loading torque of the retarder is calculated: the rotor disks are simplified as annular plates; the magnetic field that is produced by the coil is only distributed in the circular region and magnetic flux leakage is ignored; the relative permeability of the rotor disk is considered constant; and hysteresis losses and magnetic saturation are ignored. A detailed deduction is presented in [12], wherein the loading torque is denoted by the following:where is loading torque, N·m; is the number of magnetic pole pairs; is the resistivity of rotor disk, Ω·m; is the permeability of the vacuum, N·A^{−2}; is the number of turns of excitation coils; is the excitation current, A; is the magnetic core diameter of the excitation coil, m; is the angular velocity of the magnetic field changes, rad/s; is the relative magnetic permeability of the rotor disk; is the distance between the center of the magnetic pole and the center of the rotor disk, m; is the width of air gap m; and is the conversion rate ( usually takes 1.5).

Given that , the loading torque is simplified as follows:where , , and are parameters that are related to the structure and material of the eddy current retarder.

A simplified derivation of the retarder transfer function is as follows: the excitation coil of the eddy current retarder can be simplified as the resistance and inductance in series [13]. Therefore, the transfer function of the excitation voltage and current is as follows:where is the coil inductance of the eddy current retarder, H; is the coil resistance of the retarder, Ω; and is the excitation voltage, V.

A simplified method for establishing the transfer function of the DC dynamometer is based on [14]. The eddy current retarder with nonlinear properties can be simplified as a linear element with the assumption that the change rate of the excitation current is approximately constant when the excitation voltage changes. Combining (2) and (3) yields the transfer function of the retarder:In the formula, is a variable, which is related to the structure, material, and current change rate of the eddy current retarder.

##### 2.2. Model of Loading Transmission System

###### 2.2.1. Eddy Current Retarder

The moment of inertia of the rotor disk is considered in establishing the transfer function of the retarder. The retarder is a brake component, which is an external drive that provides power. The dynamic variables of the retarder are shown in Figure 1.where is the moment of inertia of the retarder rotor disk; kg·m^{2}; is the rotation angle of the retarder rotor disk rad; is the input torque of the retarder N·m; and is the loading torque of the retarder N·m.