Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 1780710, 13 pages

http://dx.doi.org/10.1155/2016/1780710

## A Novel Online Multivariate Identification for Autotuning Speed Control in PMSM Drives

School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Luoyu Road, Wuhan 430074, China

Received 9 November 2015; Accepted 31 January 2016

Academic Editor: Haipeng Peng

Copyright © 2016 Ke 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

A novel online algorithm to identify the moment of inertia, viscous friction coefficient, and load torque of PMSM (Permanent Magnet Synchronous Motor) drives and a distinctive autotuning speed control scheme are presented. The proposed identification algorithm does not require motors run in a particular trajectory and only needs a short identification time. A Luenberger speed observer is introduced to eliminate noises which are generated by the detection of position signal and to improve the accuracy of identified parameters. Parameters of the speed controller are optimized by analyzing the mathematical model of the system and the formula of the PI controller. Compared to a standard recursive least squares method (RLSM) and traditional PI algorithm, the effectiveness of the proposed identification algorithm and autotuning speed control scheme are validated through simulations and experiments.

#### 1. Introduction

PMSM (Permanent Magnet Synchronous Motor) has been more and more popular in many industrial applications because of its advantageous features, simple structure, high torque-to-current ratio, high efficiency, and low maintenance cost [1–3]. Many PI (proportional-integral) speed control algorithms for PMSM drives are widely used in practical control applications owing to their simple control structure, ease of design, low cost, and effectiveness [4, 5]. However, parameters of speed controllers are highly vulnerable to parameter variations and external disturbances, such as load variation, speed change, external unpredictable disturbance, and mechanical parameters of the motor’s nonlinear change in PMSM drives. So it is important to identify the motor mechanical parameters and load torque for autotuning parameters of speed controller to run in the better condition [6, 7].

Many identification algorithms have been developed for PMSM drives such as identifying the moment of inertia of mechatronic servo systems based on the time average of a product of torque reference input [8] and using a full-order state observer [9]. They are offline algorithms. The identification algorithm which estimated inertia by using the speed observer needs the periodic test signal [10]. So algorithms [8–10] are not suitable for online identification in real-time. The recursive least square algorithm method (RLSM) and the Kalman filter have been used to estimate the moment of inertia [11, 12], but estimated value using RLSM has some oscillation on speed change and large error at low speeds. In addition, they also ignore the influence of the viscous friction coefficient. A reduced-order extended Luenberger observer has been used to estimate the moment of inertia and is not involved in the research of load torque [13].

The estimated values of mechanical parameters are used to optimize performance of the speed controller in real-time. Many autotuning control algorithms for PMSM drives have been studied. The fuzzy rules are using for autotuning PI gains in [14] and a hybrid control system is proposed in [15], which contains a PI controller and fuzzy controller in the steady state. However, both these methods use offline-tuning rules, which are not suitable for dealing with parameter variations of system. It will be very difficult to limit disturbances rapidly if adopting linear control methods in [16]. An adaptive PI controller for online-tuning PI gains is employed in [17]. But it does not show the performance of the speed controller under time-varying system uncertainties. A two-step estimation method, which is called in the sequel the steady-state response method (SSRM), is proposed in [18]. Unfortunately, the authors do not estimate the load torque and do not show the results at different speed.

In this paper, an online identification method which can simultaneously identify three mechanical parameters (the moment of inertia of the system, the viscous friction coefficient of the motor, and the load torque) and a distinctive autotuning speed control scheme are proposed, which adjusts the speed loop parameters using the identified parameters. The online identification algorithm does not require the motors run in a particular trajectory and only needs short identification time. The identified moment of inertia of the system is substituted into the Luenberger observer model to correct the effect of the model. The autotuning speed scheme can be transformed by comparing the PI transfer function and the formula of mathematical model of PMSM. At last, by comparing their performance of the RLSM and conventional PI speed controller, the effectiveness of the identification algorithm and the proposed control scheme has been verified.

The organization of this paper is as follows. First, the structure of speed control loop is given in Section 2. Then, Section 3 presents the identification algorithm and autotuning speed control scheme adopted in this paper. In Section 4, experiments are shown and the analysis of results is demonstrated. At last, Section 5 gives the conclusions of this paper.

#### 2. The Scheme of Speed Control Loop

The research object is the model of a surface-mounted PMSM. The FOC (Field Oriented Control) is a very practical and effective control strategy for PMSM drives [19–23]. Theoretically, the FOC for a PMSM drive allows the motor torque to be controlled independently with the flux like DC motor operation. In other words, the torque and flux are decoupled from each other. Also, the structure of cascade control loops mainly comprises two current loops and a speed loop. Two PI algorithms are used in the two current loops, respectively. Usually, the -axis reference current id is forced to . If the two current loops work well, the output id satisfies . Considering that the motor is the SPMSM, the -axis and -axis inductance satisfy . No reluctance torque is present and then the -axis current will be controlling the motor electromagnetic torque. So, the mathematical model of a SPMSM can be simplified and modeled as Figure 1 and expressed as The angular acceleration, which is obtained by approximating the derivation and applying Euler’s rule, can be computed as follows: where is 1 ms; it is also the system sampling time and the control cycle of the speed controller.