Sliding-Mode Sensorless Control of Direct-Drive PM ... - IEEE Xplore

7 downloads 0 Views 1MB Size Report
convergence of the observer at high speeds in the flux-weakening region. As such, this sensorless control is suitable for domestic washing machine drives ...
582

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 45, NO. 2, MARCH/APRIL 2009

Sliding-Mode Sensorless Control of Direct-Drive PM Synchronous Motors for Washing Machine Applications Song Chi, Member, IEEE, Zheng Zhang, Fellow, IEEE, and Longya Xu, Fellow, IEEE

Abstract—A new sensorless field-oriented control of direct-drive permanent-magnet synchronous motors based on “sliding mode” has been studied and applied to domestic washing machine drives. To achieve speed control requirements for the application, a novel sliding-mode observer has been developed by applying the technique of feedback of the “equivalent control.” Armed with the developed algorithms, this observer is able to minimize the estimation error of rotor position at low speeds and guarantee fast convergence of the observer at high speeds in the flux-weakening region. As such, this sensorless control is suitable for domestic washing machine drives demanding wide-speed-range operation. The proposed sensorless control algorithms are implemented in a cost-effective digital controller and tested in a selected prototype washing machine. Both computer simulation and experimental results are illustrated for verification. Index Terms—Direct-drive permanent-magnet synchronousmotor (PMSM) control, sensorless, sliding-mode observer (SMO), washing machine drives, wide speed range.

I. I NTRODUCTION

O

VER THE past several years, various advanced sensorless controls of permanent-magnet synchronous motors (PMSMs) have been developed for industrial drives due to their high power density and high performance [1], [2]. To achieve field-oriented control, accurate rotor position of PMSM is essential for fast dynamic response, which can normally be obtained from a shaft-mounted optical encoder, resolver, or Hall sensors. Nevertheless, it is highly desirable to eliminate such sensors in order to reduce costs, save mounting space, and improve mechanical robustness and system reliability, which is crucial for many applications [3]. For these purposes, research works on sensorless controls of PMSM have been intensively conducted for decades. In general, major PMSM sensorless

Paper MSDAD-07-67, presented at the 2006 Industry Applications Society Annual Meeting, Tampa, FL, October 8–12, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Appliance Industry Committee of the IEEE Industry Applications Society. Manuscript submitted for review October 31, 2006 and released for publication May 30, 2008. Current version published March 18, 2009. S. Chi is with the Research and Engineering Center, Whirlpool Corporation, Benton Harbor, MI 49022 USA (e-mail: [email protected]). Z. Zhang is with Great Lakes Electric, Stevensville, MI 49127 USA (e-mail: [email protected]). L. Xu is with the Department of Electrical Engineering, The Ohio State University, Columbus, OH 43210 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2009.2013545

control techniques can be categorized into two approaches: 1) magnetic saliency detection and 2) back electromotive force (EMF) estimation. In the first category, rotor position is estimated by tracking inductance variations due to the magnetic saturation and/or effects of geometrical saliency of PM motors. Typical methods of magnetic saliency detection have been proposed, such as the “INFORM” method in [4] and the highfrequency signal injection method in [5]. For standstill and lowspeed operations of PM motors, the feasibility of this approach has been exclusively demonstrated. On the other hand, the back-EMF-based approach has been successfully applied in the applications that do not require full-load operation at standstill and very low speeds but do at comparatively higher speeds (above 5%–10% nominal speed). Included in this category are Luenberger observers [6], full-order state observer with feedback linearization [7], D-state observer [8], sliding-mode observers (SMOs) [9], etc. Recently, low-cost variable-speed motor drives have been increasingly applied into home appliances such as washing machines, dryers, dishwashers, and air conditioners. For washer drive applications, the direct-drive PM motor (DDPM) system represents an attractive solution because of its compactness and high dynamic performance. In a direct-drive washer, the rotor shaft is directly coupled to the basket or drum without belts, pulley, wheels, and gearbox anymore. Usually, a DDPM motor has multiple poles with pancake shape (i.e., short stack length) and is able to deliver the desired torque directly to the basket or drum within full speed range, which make them the best candidate for direct-drive applications. In addition, the directdrive architecture has benefits to meet the drive requirements of washing machines in both washing and spinning cycles. For domestic washing machine applications, there are a series of special torque–speed requirements of the drive system. For instance, in a washing cycle, a maximum torque is required for quick startup with full load; and then, a relatively smaller torque (i.e., rated torque) is needed to hold on the washing speeds. While in a spinning cycle, a high-power output, e.g., maximum and rated power, is needed to drive the basket or drum to reach the maximum speed. The operating speed range is quite large, which is normally from 10 : 1 to 40 : 1. In addition, both mechanical vibration and electric power oscillation are subject to occurrence due to the unevenly distributed laundry load inside the basket or drums, which result in control complexity. The unbalanced load must be detected in a right manner and managed in an appropriate way to limit the vibration and acoustic noise. Hence, sensing and diagnostic

0093-9994/$25.00 © 2009 IEEE

CHI et al.: SENSORLESS CONTROL OF DIRECT-DRIVE PMSMs FOR WASHING MACHINE APPLICATIONS

capabilities by using motor control information are becoming an extra but crucial requirement of motor drives. For DDPM motor drives, a few of sensorless control methods were studied, as previously reported in the literature [10]–[13]. A current-error-based estimation of rotor position was proposed for DDPM motor systems [10]. In this method, the estimator model is dependent on motor parameters, such as stator resistance and inductance; as a result, the estimation performance would be influenced by variations of motor parameters. Therefore, a compensation for the variation of stator resistance and back-EMF constant must be done to improve robustness. In addition, several gains have to be designed adaptive to operation conditions for both phase and magnitude estimations of back EMF. It is obvious that this method is too complicated to be easily implemented in low-cost DDPM systems. To reduce chattering components superimposed on the estimated back EMF, an iterative SMO was introduced in [12]. By iterating the calculation of observer for more than one time within a current sampling period, the error of the estimated rotor position angle can be reduced, particularly at high speeds, due to smaller ripples. However, this method inevitably increases the burden of computation and is subject to the limitation of updating frequency. Other than that, the estimation performance is hardly affected at low speeds. In order to improve low-speed estimation performance, a state filter was proposed in [13] to extract the back EMF of PMSM in the rotor reference frame. Two proportional– integral (PI) controllers must be used to estimate the rotor position angle and speed. Similarly, this method also requires the knowledge of accurate motor parameters. Moreover, the restriction of filter’s bandwidth makes it very challenging to tune both PI controllers and make them work properly over wide speed range. This paper presents a sensorless control of DDPM motor for domestic washing machines. First, requirements of washing machine drives are briefly reviewed after the introduction. Then, a novel SMO is proposed for the estimation of rotor position over wide speed range, including the deep flux-weakening region. In the observer, by selecting different feedback gains of equivalent control adaptive to speeds, the estimation error of rotor position can be minimized at low speeds, and the convergence of the observer can be accelerated at high speeds. Also, the overall field-oriented control of the DDPM drive system is discussed. The developed control algorithms are implemented in a cost-effective controller which consists of a digital signal processor (DSP). A series of experimental tests have been conducted on both a dynamometer bench and a prototype washer to evaluate the estimation performance of rotor position and system control robustness under specified operating conditions. Computer simulation and experimental results are finally provided to verify the sensorless control for DDPM drive systems. II. C ONFIGURATION AND R EQUIREMENTS OF W ASHING M ACHINE D RIVES Domestic washing machines can be generally categorized into two configurations: top- and front-load washers. A topload washer usually has an agitator or impeller to transfer motor torque (or mechanical actions) to the laundry inside the basket.

583

Fig. 1. Configuration of the top-load prototype washing machine with DDPM. (a) Prototype washer mechanical architecture. (b) Close-up of the washer basket with DDPM.

Fig. 2. Typical washing speed profile of a top-load washing machine.

While in a front-load washer, the tumbling action of the laundry is realized by driving its drum running at a specific constant speed. The configuration of a top-load prototype washer with a DDPM motor is shown in Fig. 1. As can be seen, the pancake motor is directly coupled with the impeller and other rotating mechanical parts. In general, a washing machine operates in two major cycles: washing and spinning cycles. As an example of washing cycle of the top-load washer, a specific speed profile is designed for each stroke to achieve washing functionality. A typical speed profile is shown in Fig. 2. From 0 to t1 is the ramp-up time

584

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 45, NO. 2, MARCH/APRIL 2009

B. SMO SMO (Fig. 4) is designed as   ˆi = A · ˆi + B · v ∗ + l · Z  eq + Z  s s s    = −K · sgn ˆis − is Z  −0.5, n < 180 r/min l= 1, n ≥ 180 r/min where Fig. 3. Typical torque and power versus speed requirements of a top-load washing machine.

during which the motor ramps up from zero to plateau speed. Then, the motor maintains at this speed for a period (namely, plateau time) until t2 and then decelerates and/or coasts until t3 . Ramp-up time is selected, depending on the laundry type and load level. Fig. 3 shows typical torque and power requirements of topload washing machines. A maximum torque is required in the washing cycle and is almost twice as big as the rated torque. The maximum torque normally occurs during fast acceleration. Meanwhile, the rated torque is required to keep the agitator or impeller running at predetermined washing speeds, which relates to steady-state operation. It should be noticed that since washers work most of the time in washing cycles at low speeds, the PM motor should endure the peak of temperature rise due to high phase currents and poor cooling conditions [3]. It implies that variation of stator resistance and back-EMF constant would be severe in washing cycles. On the other hand, to extract more water that is absorbed in wet clothes, a high-speed spinning (over 1000 r/min) is necessary to obtain large centrifugal force for water extraction.

 K=  is = vs∗

 =

i˙ s = A · is + B · (vs − es )

(1)

where 

  −Rs /Ls 1/Ls 0 B= 0 −Rs /Ls 0     v is = iαs vs = αs iβs vβs     eαs − sin(θr ) es = = Ke · ω r · eβs cos(θr ) A=

0 1/Ls



∗ vαs ∗ vβs





 eq , In (2), l is the feedback gain of the equivalent control Z and k, which is normally positive (k > 0), is the switching gain  The superscript “∗ ” denotes of the discontinuous control Z. a command voltage variable. Matrices A and B are the same as in (1).  eq can be obtained by applying a The equivalent control Z  as in low-pass filter (LPF) to the discontinuous control Z,   1  eq = Zeqα =  Z Z (3) Zeqβ pτc + 1 where

III. P OSITION S ENSORLESS C ONTROL OF PMSM

The dynamic equations of a PMSM without saliency in the stationary reference frame can be expressed in the matrix form as

iαs iβs

0 k 

  ˆi = ˆiαs . s ˆiβs

p= A. Mathematical Model of PMSM in the Stationary Reference Frame

k 0

d . dt

For the sake of simplicity, a first-order LPF is used in (3). It is noticed that the time constant τc of LPF should be designed properly according to the fundamental frequency of phase currents of PMSM. To cope with the chattering issue [3], [12], [14], the sign function, usually expressing the discontinuous control in the observer, is replaced by a saturation function, as shown in Fig. 5. When the magnitude of current error is less than E0 ,  changes to the linear saturation function as the control Z    = −ks · ˆis − is Z (4) where ks = k/E0 . Subtracting (1) from (2), we can obtain the dynamic slidingmode motion equation, as expressed in  eq + Z)  ˙ = A · S  + B · (es + l · Z S where

with Ls , Rs , and Ke referring to the stator inductance, resistance and back-EMF constant, respectively.

(2)

 = ˆis − is . S

(5)

CHI et al.: SENSORLESS CONTROL OF DIRECT-DRIVE PMSMs FOR WASHING MACHINE APPLICATIONS

Fig. 4.

585

Block diagram of the proposed SMO.

By substituting (4) into (5), we obtain  + B · es . ˙ = [A − (l + 1) · ks · B] · S S

Fig. 5.

Sketch of the saturation function.

 i.e., k, is large enough to guarantee If the switching gain of Z, the following: