Mathematical Problems in Engineering

Volume 2014 (2014), Article ID 568986, 8 pages

http://dx.doi.org/10.1155/2014/568986

## Online Identification Methods of Load Rotary Inertia and Torque in Radar Servo System

^{1}School of Energy Science and Engineering, University of Electronic Science and Technology of China, Sichuan 611731, China^{2}School of Electrical and Information Engineering, Xihua University, Sichuan 610039, China^{3}Dongfang Electric Corporation DEC R&D Centre, Sichuan 611731, China

Received 27 September 2014; Revised 9 December 2014; Accepted 10 December 2014; Published 31 December 2014

Academic Editor: Xinkai Chen

Copyright © 2014 Yong Chen 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

In radar servo system, the load is usually subject to movement and gust, which may cause instability of the system. In this paper, the online identification methods of load rotary inertia and torque in radar servo system are proposed, respectively. The radar servo system is based on synchronous motor. The load rotary inertia of the system is identified online by a disturbance observer. Moreover, a reduced order Luenberger observer is designed to observe the variation of the load torque and velocity online. The simulation models are established to verify the proposed disturbance observer for the load rotary inertia and the reduced order Luenberger observer for the load torque and velocity.

#### 1. Introduction

In radar servo system, the revolution of the load is usually subject to movement and gust, which may cause instability of the load rotary inertia and torque. Therefore, the stability of the servo controller is facing higher requirements. If the parameters of the controller in the speed loop do not match the load rotary inertia, the dynamic response of the system may become slow and even cause oscillation [1]. Furthermore, the load torque is also subject to the disturbance of gust torque. In some cases, the value of the gust torque is very big and uncertain. As a result, the descent of the revolution speed at the transient state in the radar system is big and thus the target tracking is adversely affected [2]. In order to enhance the dynamic and static characteristics and the disturbance rejection ability of radar servo system, online identification of the load rotary inertia and torque is a premise [3].

As for the research on the online identification of load rotary inertia, a speed response method for AC servo system was proposed in [4]. By modifying the output current limitation value of the speed controller, the speed response value and response time under different current limitation values are obtained, and then the rotary inertia is calculated. This method may affect the normal operation of the motor in practice and is not applicable to identify the rotary inertia online. In addition, a model reference adaptive method for permanent magnet synchronous motor (PMSM) was presented in [5] to estimate the rotary inertia. However, both the speed response method and the model reference adaptive method neglect the effect of the viscous friction of the rotor. Comparatively, the online identification method of the rotary inertia based on disturbance observer (DOB) considers the external disturbance and friction, respectively [6, 7]. More methods on load torque and speed are extended Kalman filters for PM synchronous motors [8], recursive input estimation for PMSM [9], and robust estimation based on singular perturbation theory [10]. Besides, disturbance is regarded as a constant or function in some papers [10, 11]. Nevertheless, the load torque in radar servo system is usually subject to the effects of gust and environment that are difficult to be defined as some noise in analysis. Therefore, it is necessary to propose an effective algorithm to directly identify the load torque and speed online. In this paper, according to the characteristics of radar servo system, a more practical online identification algorithm of rotary inertia based on DOB is proposed. The external disturbance and the friction of the model are estimated by the designed DOB and then the rotary inertia is identified. As far as the research on load torque and speed is concerned, Luenberger state observer can be employed to estimate the disturbance torque and a reduced order Luenberger load torque observer is designed to overcome the randomness of the disturbance torque.

This paper is organized as follows. In Section 2, motion equations of servo system are built. In Section 3, the load rotary inertia is identified online by a DOB. Then, a reduced order Luenberger observer is designed to observe the variation of the load torque in Section 4. In Section 5, the simulation models are established, and the DOB for the load rotary inertia and the reduced order Luenberger observer for the load torque are verified by simulations, respectively, in Section 6. Finally, this paper is concluded in Section 7.

#### 2. Motion Equations of Servo System

In -frame, the mathematical model of PMSM can be expressed as follows [1]:

The electromagnetic torque is given as where are the armature voltage of the -axis and -axis, are the armature current of the -axis and -axis, are the winding inductance of stator in -axis and -axis, is the winding resistance of stator, is the PM (permanent magnet) flux linkage; is the differential operator ; is the number of pole pairs of the rotor, and is the rotor electrical angular speed.

Motion equations of servo system are as follows [5]: where is the rotary inertia of the system, is the electromagnetism torque (i.e., driving torque), is the viscous friction coefficient of the rotor, and is the load torque.

Let be the disturbance torque which is an unknown value estimated by the disturbance observer. Then can be expressed as

In one sampling period, may be regarded as a constant, because the sampling frequency is much quicker than the variation of the disturbance torque in radar servo system. Hence, we have

From (3)–(5) the state equations can be got as where , , , , and .

For a PMSM with nonsalient pole structure, the -axis inductances are equal; that is, . The load rotary inertia and torque are identified online based on the field orientation control (FOC) system, where is controlled to be zero. The identification methods run in parallel with the vector control system. The block diagram of the whole system is shown in Figure 1.