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Real-Time Implementation of Bi Input-Extended Kalman Filter-Based Estimator for Speed-Sensorless Control of Induction Motors Murat Barut, Member, IEEE, Ridvan Demir, Emrah Zerdali, and Remzi Inan
Abstract—This paper presents the real-time implementation of a bi input-extended Kalman filter (EKF) (BI-EKF)-based estimator in order to overcome the simultaneous estimation problem of the variations in stator resistance Rs and rotor resistance Rr aside from the load torque tL and all states required for the speed-sensorless control of induction motors (IMs) in the wide speed range. BI-EKF algorithm consists of a single EKF algorithm using consecutively two inputs based on two extended IM models developed for the simultaneous estimation of Rr and Rs . Therefore, from the point of real-time implementation, it requires less memory than previous EKF-based studies exploiting two separate EKF algorithms for the same aim. By using the measured stator phase voltages and currents, the developed estimation algorithm is tested with real-time experiments under challenging variations of Rs , Rr , and tL in a wide speed range; the results obtained from BI-EKF reveal significant improvement in the all estimated states and parameters when compared with those of the single EKFs estimating only Rr or Rs . Index Terms—Extended Kalman filter, induction motors (IMs), load torque estimation, rotor and stator resistance estimation, sensorless control.
I. I NTRODUCTION
T
HE performance of speed-sensorless control of induction motors (IMs) relies upon how accurately state estimations of IM are performed. In fact, these estimations are adversely affected by the temperature and frequency-dependent variations of Rr and Rs as well as unknown load torque. Thus, for a successful speed-sensorless control application of IM, estimation algorithms must be robust against those variations; this fact can be discovered by inspecting the excellent papers such as [1]–[3]. Various estimation methods based on modified conventional methods [4], model reference adaptive system [5], neural network [6], sliding mode [7], and adaptive full-order Luenberger Manuscript received November 1, 2010; revised August 5, 2011 and September 13, 2011; accepted October 27, 2011. Date of publication December 7, 2011; date of current version June 19, 2012. This work was supported by the Scientific and Technical Research Council of Turkey (Türkiye Bilimsel ve Teknolojik Ara¸stırma Kurumu–TÜBÍTAK) under the research grant of EEEAG-108E187. M. Barut, E. Zerdali, and R. Inan are with the Department of Electrical and Electronics Engineering, Nigde University, 51245 Nigde, Turkey (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). R. Demir is with the Electrical and Energy Department, Bor Vocational School, Nigde University, 51700 Nigde, Turkey (e-mail: ridvandemir@ nigde.edu.tr). 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/TIE.2011.2178209
observer [8] have been proposed very recently in the literature. Among these studies, [4]–[6] are sensitive to the variations in Rr and Rs , while [7] and [8] are easily affected by the Rs or Rr variations, respectively; thus, they still need improved performance under both resistance uncertainties. On the other hand, Faiz and Sharifian [9] declare that the simultaneous estimation of Rr and Rs causes instability. Considering the studies [10]–[13], which attempt to perform both Rs and Rr estimations in a speed-sensorless case, reported so far, Karanayil et al. [10] do not present the result of Rr estimation together with that of Rs and angular velocity, ωm , in the speed-sensorless case. In [11], Rs and ωm estimations cannot be simultaneously conducted at no load or when the load torque is not sufficiently high, and a high-frequency signal is also injected on the magnetizing current command in order to perform Rr estimation. Moreover, the estimation algorithms in [12] and [13] are only applicable whenever the speed-sensorless control system is in steady state, which is declared by authors. On the other hand, extended Kalman filter (EKF)-based solutions have been also investigated by the studies such as in [14]–[17] for the simultaneous estimation problem of Rr , Rs , and ωm regardless of load conditions. For the solution of the problem, Barut et al. [14] and Bogosyan et al. [15] use braided EKF algorithms tested with real-time experiments while Barut et al. [16] utilizes switching EKF algorithm confirmed by simulations. For the same purpose, Barut [17] also introduces a novel estimation technique called as bi inputEKF (BI-EKF) which is only verified by some simulation tests. Both braided/switching EKF and BI-EKF provide an accurate estimation of an increased number of parameters than would be possible with a single EKF algorithm, but braided/switching EKF uses two separate EKF algorithms in a braided/switching manner while BI-EKF includes a single EKF algorithm with the consecutive operation of two inputs obtained from two extended IM models developed for the simultaneous estimation of Rr and Rs . In other words, BI-EKF includes a single standard EKF with consecutive use of two inputs calculated from the two extended IM models. Thus, it differs from the past EKFbased studies [14]–[16] involving the successive utilization of two EKF algorithms. Thus, BI-EKF technique has an important advantage over those studies [14]–[16] because it reduces by approximately two times the required memory area of the studies in [14]–[16] for embedding observer algorithm and it provides easier debugging and design than the studies in [14]– [16]. These advantages make BI-EKF more attractive from the
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engineering and real-time implementation points of view. As it is well known, nonideal behavior of inverters, processing errors of data acquisition devices, modeling errors, parameter uncertainties, and noise adversely affect the performance of any estimation algorithm in real-time experiments; thus, the realtime validation of BI-EKF algorithm is also important. The major contribution of this study is to verify BI-EKF algorithm in real time for the simultaneous estimation of Rr , Rs , and tL in addition to all states required for the speed-sensorless control of IMs via measuring stator phase voltages and currents. From this point of view, this is the first known study to perform the real-time application of the BI-EKF technique. Moreover, differently from [17], in this study, BI-EKF is conducted in a switching manner since the better results are obtained in this kind of manner, particularly during real-time experiments. For a more realistic approach, ac voltages are applied to the IM via a vector-controlled ac drive. The effectiveness of the BI-EKF technique is demonstrated not only by the real-time experiments but also by comparing its performance with single EKFs including only Rr or Rs estimation, without the need for signal injection. This paper is organized as follows. After the review of past studies related to the simultaneous estimation of Rr and Rs for speed-sensorless control of IMs in Section I, Section II presents the derivation of the extended IM models developed for Rr or Rs estimation. Next, Section III describes the BIEKF technique. The hardware configuration is explained in Section IV. Section V gives the experimental results and observations. Finally, the conclusions are listed in Section VI.
the states and inputs, Aei is the system matrix, ue is the control input vector, B e is the input matrix, wi1 is the process noise, hei is the function of the outputs, H e is the measurement matrix, and wi2 is the measurement noise. Based on the general expression in (1) and (2), the detailed state space representation of the extended IM models can be given as follows. 1) Model-1: The extended IM model developed for Rs estimation (Model-Rs ) ⎡ ⎤ ⎤ ⎡ ⎤ a1 0 isα (k) isα (k + 1) ⎢ isβ (k) ⎥ ⎢ 0 a1 ⎥ ⎢ isβ (k+1) ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎥
⎢ ϕrα (k) ⎥ ⎢ 0 0 ⎥ ⎢ ϕrα (k+1) ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎥ vsα (k) +w11 ⎢ ϕrβ (k+1) ⎥=Ae1 ⎢ ϕrβ (k) ⎥+⎢ 0 0 ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎥ vsβ (k) ⎢ ωm (k) ⎥ ⎢ 0 0 ⎥ ⎢ ωm (k+1) ⎥ ⎣ ⎣ ⎦ ⎦ ⎣ ⎦ ue tL (k+1) tL (k) 0 0 Rs (k+1) Rs (k) 0 0 ⎡
Be
xe1 (k)
(3) where Ae1 is defined as shown at the bottom of the page. The measurement equation is
1 isα (k) = 0 isβ (k)
0 1
0 0
0 0 0 0
0 x (k) + w12 . (4) 0 e1
0 0
He
Z(k)
2) Model-2: The extended IM model developed for Rr estimation (Model-Rr ) ⎡ ⎤ ⎤ ⎡ ⎤ a1 0 isα (k) isα (k+1) ⎢ isβ (k) ⎥ ⎢ 0 a1 ⎥ ⎢ isβ (k+1) ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎥
⎢ ϕrα (k) ⎥ ⎢ 0 0 ⎥ ⎢ ϕrα (k+1) ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎥ v (k) +w21 ⎢ ϕrβ (k+1) ⎥=Ae2 ⎢ ϕrβ (k) ⎥+⎢ 0 0 ⎥ sα ⎢ ⎢ ⎥ ⎥ ⎢ ⎥ vsβ (k) ⎢ ωm (k) ⎥ ⎢ 0 0 ⎥ ⎢ ωm (k+1) ⎥ ⎣ ⎣ ⎦ ⎦ ⎣ ⎦ ue tL (k+1) tL (k) 0 0 Rr (k+1) Rr (k) 0 0 ⎡
II. E XTENDED M ATHEMATICAL M ODELS OF THE IM BI-EKF algorithm uses two extended IM models in order to solve the simultaneous estimation problem of Rs and Rr together with ωm . The two rotor flux-based extended models in the discrete form, called Model-1 and Model-2, developed for this purpose can be given (as referred to the stator stationary frame) in the following general form:
(5)
xei (k + 1) = f ei (xei (k), ue (k)) + wi1 = Aei (xei (k)) xei (k) + B e ue (k) + wi1
(1)
Z(k) = hei (xei (k)) + wi2 (Measurement equation) = H e xei (k) + wi2 .
(2)
Here, i = 1 or 2 represents each model, xei is the extended state vector for both models, f ei is the nonlinear function of
⎡
1 − a1 Rs (k) − a3 0 ⎢ ⎢ a9 ⎢ ⎢ Ae1 = ˆ⎢ 0 ⎢ ⎢ −a11 ϕrβ (k) ⎣ 0 0
Be
xe2 (k)
0 1 − a1 Rs (k) − a3 0 a9 a11 ϕrα (k) 0 0
where Ae2 is defined as shown at the bottom of the next page. The measurement equation is
1 isα (k) = 0 isβ (k)
Z(k)
a4 −a5 ωm (k) 1 − a7 a10 ωm (k) 0 0 0
0 1
0 0
0 0 0 0
0 0
0 x (k) + w22 . (6) 0 e2
He
a5 ωm (k) a4 −a10 ωm (k) 1 − a7 0 0 0
0 0 0 0 0 0 0 0 1 −a12 0 1 0 0
⎤ 0 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎦ 0 1
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The coefficients in both models are as follows: a1 =
L2 T a3 , a2 = a1 m , a3 = a2 Rr , a4 = Lσ Lr Lm
a5 =
a1 Lm pp T , a6 = , a7 = a6 Rr , a8 = a6 Lm Lr Lr
a9 = a8 Rr , a10 = pp T, a11 = a8 a12 =
1.5pp JT
T a2 , a13 = , a14 = a1 Rs JT Lm
where pp is the number of pole pairs, Lσ = σLs is the stator transient inductance, σ = 1 − (L2m /Ls Lr ) is the leakage or coupling factor, Ls and Lr are the stator and rotor inductances, respectively, ϕrα and ϕrβ are the stator stationary axis components of rotor fluxes, vsα and vsβ are stator stationary axis components of stator voltages, isα and isβ are the stator stationary axis components of stator currents, JT is the total inertia of the IM and load, ωm is the rotor angular velocity, and T is the sampling time. In both models, the following conditions are true. 1) The main difference occurs due to the constant states Rs and Rr in xe1 and xe2 , respectively. 2) w12 in (4) and w22 in (6) are equal because of using the same measured state variables, isα and isβ . III. D ESCRIPTION OF BI-EKF A LGORITHM BI-EKF algorithm in this study uses a single EKF algorithm with switching between two inputs based on Model-Rr and Model-Rs for the simultaneous estimation of Rr and Rs aside from the unknown load torque, velocity, rotor fluxes, and stator current components; therefore, it significantly reduces the timeconsuming design stages and memory requirement, compared with previous studies such as in [14]–[16] which utilize two separate EKF algorithms. In other words, BI-EKF algorithm combines two separate EKF algorithms with two different IM models in a single EKF algorithm with consecutive switching of the inputs/terms of EKF equations which must be calculated for and special to each of the two different IM models in order to increase the number of parameter estimations that would be carried out by a single-standard EKF. Namely, the BI-EKF technique operates a single EKF algorithm via successively switching its input terms associated with the two IM models; That is why it is called BI-EKF. Here, “input” does not refer to the measurements. It refers to the inputs in switch1 in Fig. 1.
⎡
1 − a14 − a2 Rr (k) 0 ⎢ ⎢ a8 Rr (k) ⎢ ⎢ Ae2 = ˆ⎢ 0 ⎢ −a11 ϕrβ (k) ⎢ ⎣ 0 0
0 1 − a14 − a2 Rr (k) 0 a8 Rr (k) a11 ϕrα (k) 0 0
Fig. 1. Schematic view of the BI-EKF-based estimation technique.
Considering computation costs of both BI-EKF and past studies [14]–[16], although there is a little but not significant difference in favor of BI-EKF in simulations shown in [17], in real time, almost no difference is observed between their computation times due to the observer code conversion process from MATLAB/Simulink to the DS1104 controller (real time), which is automatically done by the universal experiment and instrumentation software of DS1104 known as “ControlDesk” in this study. It is also worth to note that the realization way of both BI-EKF and the other algorithms [14]–[16] will affect their computation times. However, from the engineering (or realtime implementation) point of view, BI-EKF has superiority over past studies using braided EKF or switching EKF in [14]– [16]. In particular, in spite of not showing significant difference between their computation burdens in real-time experiments, BI-EKF definitely has advantages in the following issues. 1) The cost of hardware platforms such as microprocessor, digital signal processor, and field-programmable gate array increases with the increase of the memory size/area required for embedding software algorithm. Thus, it is a
a13 Rr (k) −a5 ωm (k) 1 − a6 Rr (k) a10 ωm (k) 0 0 0
a5 ωm (k) a13 Rr (k) −a10 ωm (k) 1 − a6 Rr (k) 0 0 0
0 0 0 0 0 0 0 0 1 −a12 0 1 0 0
⎤ 0 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎦ 0 1
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big gain to appreciably reduce the memory requirements for braided or switching EKF via BI-EKF. 2) BI-EKF provides easier debugging and less time in the design stages than braided or switching EKF does since it includes fewer command lines than the others. On the other hand, BI-EKF such as the braided EKF in [14] and [15] or the switching EKF in [16] performs the simultaneous estimation of Rr and Rs in a speed-sensorless case, which is desired in the literature and industry. That shows why BI-EKF is important from the scientific point of view. In order to describe the BI-EKF technique, standard EKF equations can be given as follows: ∂f ei (xei (k), ue (k)) (7a) F ei (k) = ∂xei (k) x ˆ (k),u (k) ei
N i (k)
= F ei (k)P i (k)F Tei (k)
e
+ Qi
Experimental setup used for verifying BI-EKF algorithm.
values of isα , isβ , ϕrα , ϕrβ , ωm , and tL are updated to both inputs as initial values. Moreover, P i (k + 1) is stored as P i (k) for the usage of the next switching time.
(7b)
P i (k + 1) = N i (k) − N i (k)H Te −1 × Dξ + H e N i (k)H Te H e N i (k) (7c) xei (k), ue (k)) + P i (k + 1) x ˆei (k + 1) = fˆei (ˆ ˆei (k)) × H Te D−1 ξ (Z(k) − H e x
Fig. 2.
(7d)
where F ei is the function used in the linearization of the nonlinear models (3, 5). Qi is the covariance matrix of the system noise, namely, model error. Dξ is the covariance matrix of the output noise, namely, measurement noise. P i and N i are the covariance matrix of the state estimation error and extrapolation error, respectively. BI-EKF algorithm is constructed by examining the EKF equations (7a)–(7d) and using the following three remarks [17]. Remark 1: Equations (7b)–(7d) constitute the prediction and correction steps of the EKF algorithm. Remark 2: The inputs of (7b)–(7d), which must be changed for Model-1 or Model-2, are F ei , Qi , and fˆei because the elements of those matrices are calculated from each model. Remark 3: The inputs of (7b)–(7d), which must be the same for both models, are Dξ and H e due to using the same measurements (isα and isβ ). Moreover, the dimensions of N i , ˆei are identical for both models because of utilizing P i , and x the same-order models. Considering the aforementioned remarks, the schematic view of the BI-EKF-based estimation technique is given as in Fig. 1. The BI-EKF algorithm (see Fig. 1) consists of three parts: inputs for Model-Rr , inputs for Model-Rs , and standard EKF. In other words, the BI-EKF technique includes a single-standard EKF algorithm utilizing consecutively two different inputs derived from the extended models, Model-Rr and Model-Rs , one for the estimation of Rr and one for the estimation of Rr in this paper. The consecutive operation is performed at every n sampling time (n × T ) which is called as switching time, tswitch . During each tswitch , the same group of states (isα , isβ , ϕrα , ϕrβ , ωm , and tL ) are simultaneously estimated aside from one of the resistances. At the end of tswitch , the estimated value of Rr or Rs is used as a constant parameter in the other input for the estimation of the other resistance while the estimated
IV. H ARDWARE C ONFIGURATION The experimental setup used for verifying the BI-EKF algorithm is given in Fig. 2. Here, the IM is a squirrel-cage type of three phase, six pole, 380 V, 5.9 A, 2.2 kW, 22 N · m, and 940 r/min, the other specifications of which are presented in the Appendix. In order to load the IM, a Foucault brake of 30 N · m manually driven by a steplike variable dc source is utilized. The BI-EKF algorithm is implemented on a power PC-based DS1104 controller board processing floating-point operations at a rate of 250 MHz. The torque transducer of 50 N · m and the encoder of 5000 lines/rev are only used for the validation of tL and ωm (nm r/min) estimations, respectively; they are not utilized in the estimation algorithm. The phase voltages and currents are also measured by LV100-400 and LA55-P/SP1, respectively. For the performance evaluation of Rs estimation, a three-phase array resistor is connected in series to the stator windings of the IM; thus, it is aimed to show that the variations in Rs generated manually by the three-phase resistor are estimated via the BI-EKF algorithm. For a realistic evaluation, the IM is fed by an ac drive so that the BI-EKF algorithm is tested by taking the pulse-width modulated ac voltages and currents as inputs. Fig. 3 shows the ac voltages and currents referred to the stator stationary frame.
V. E XPERIMENTAL R ESULTS AND O BSERVATIONS To initialize the BI-EKF algorithm and achieve a desired estimation performance, the values of P i and Qi are determined experimentally by a trial-and-error method, which is usually done in previous studies such as [14], [15], [18], and [19], while Dξ is calculated by considering the measurement errors of the current sensors and the quantization error such as in [20]. For more clarification, the calculation of the elements of Dξ in this paper includes two steps in [20]: First, one is to determine the standard deviation of the stochastic noise/error of the current sensors, σsensor . For this purpose, data acquisition (measurement) with no current is done by one of the three samecurrent sensors, and then, a σsensor of 4.7 × 10−4 (A) is calculated by using the measured data which have almost Gaussian
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Fig. 3. Stator voltages applied to the IM through ac drive and the depicted stator currents. (a) Variation of vsα . (b) Variation of vsβ . (c) Variation of isα . (d) Variation of isβ .
distribution with zero mean. The second step is to obtain the standard deviation of the quantization noise/error √ of the 16-b analog–digital converters (ADCs), σADC = (1/ 3) × LSB = −5 16 7.35 × 10 √ (A), where ±LSB equals to (1/2 ) × Imax , and Imax = 2 × 5.9 is the maximum value of the current accepted by the current sensor. Finally, the resulting standard deviation, σmeasurement , is obtained as 2 2 2 σmeasurement = σsensor + σADC = 2.26 × 10−7 (A2 ).
(8)
In the light of the aforementioned evaluations, P i , Qi , and Dξ are given as follows: Q1=diag 10−11 A2 10−11 A2 10−12 (V.s)2 10−12 (V.s)2 10−12 (rad/s)2 10−13 (N.m)2 10−16 Ω2 Q2=diag 10−18 A2 10−18 A2 10−18 (V.s)2 10−18 (V.s)2 10−14 (rad/s)2 10−14 (N.m)2 10−15 Ω2 P i=diag 9A2 9A2 9(V.s)2 9(V.s)2 9(rad/s)2 9(N.m)2 9Ω2 2 2 Dξ=diag σmeasurement (A2 ) σmeasurement (A2 ) . To demonstrate the effectiveness of the BI-EKF algorithm, several scenarios are considered as follows: 1) performance of the conventional single EKFs using both Model-Rr and Model-Rs ; 2) performance of BI-EKF under Rs variations at 50% of the rated speed; 3) performance of BI-EKF under velocity and load torque reversal at the rated speed; 4) very low speed operation of the BI-EKF algorithm under Rs variations. Most of the scenarios are focused on the simultaneous estimation of Rr , Rs , and ωm together with tL specifically at and below 50% of the rated speed since estimation performances are usually deteriorated with decreasing angular velocity in the speed-sensorless case. In those scenarios, all initial values of the estimated states and parameters are taken as zero, and the
Fig. 4. Experimental results of EKF-Rr for step-type Rs variations. (a) Variation of tind and tˆL . (b) Variation of nm and n ˆ m . (c) Variation of ˆ . (d) Variation of ϕ ˆrα and ϕ ˆrβ . (e) Variation of isβ and ˆisβ . R r
sampling time is 130 μs. The resulting estimation performances are given in Figs. 4–8. In these figures, tind and tˆL , nm and ˆ , and R ˆ s represent the induced n ˆ m , isβ and ˆisβ , ϕˆrα , ϕˆrβ , R r torque obtained from the torque transducer and estimated load torque, the measured and the estimated velocity, the measured and estimated β components of stator current, the estimated α and β components of the rotor flux, the estimated rotor resistance, and the estimated stator resistance, respectively. Note that only ˆisβ is demonstrated in all scenarios since the estimation performance of isα is similar that of isβ . A. Scenario I—Performance of the Conventional Single EKFs Using Both Model-Rr (see Fig. 4) and Model-Rs (see Fig. 5) In this scenario, the single EKF using Model-Rr , which is called as EKF-Rr , is tested under Rs variations while the
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Fig. 5. Experimental results of EKF-Rs for step-type Rr variations. ˆ m . (c) Variation of (a) Variation of tind and tˆL . (b) Variation of nm and n ˆ s . (d) Variation of ϕ R ˆrα and ϕ ˆrβ . (e) Variation of isβ and ˆisβ .
Fig. 6. Experimental results of BI-EKF for step-type Rs variations at 50% ˆm. of the rated speed. (a) Variation of tind and tˆL . (b) Variation of nm and n ˆ and R ˆ s . (d) Variation of ϕ (c) Variation of R ˆrα and ϕ ˆrβ . (e) Variation of isβ r and ˆisβ .
other EKF utilizing Model-Rs , which is referred to as EKFRs , is examined with the variations in Rr . In Fig. 4, illustrating the estimation performance of EKF-Rr , Rs is stepped up to its rated value (Rsn ) plus 2.5 Ω at 15.6 s by adding serial resistances externally to the stator windings and down to Rsn at 29 s, while the IM is running at 466 r/min under 14.3 N · m. Since EKF-Rr assumes Rs to be constant, notably high error ˆ , as seen in Fig. 4. occurs, particularly in n ˆ m , tˆL , and R r On the other hand, EKF-Rs is given a start with the proper value of Rr which is obtained from EKF-Rr including the accurate Rr value, and then, Rr is abruptly increased to its ) at 11.2 s and back to its proper one at 25.7 s, rated value (Rrn as seen in Fig. 5. The estimation errors occur in this figure ) used in EKF-Rs ; thus, it is because of the constant Rr (Rrn very clear that EKF-Rs needs the exact Rr values varying with
the rotor temperature and frequency in a squirrel-cage-type IM. Both real-time experiments, Figs. 4 and 5, show that EKF-Rr and EKF-Rs simultaneously require for precise values of Rs and Rr , respectively. B. Scenario II—Performance of BI-EKF Under Rs Variations at 50% of the Rated Speed (see Fig. 6) This scenario aims to test the BI-EKF algorithm for steptype Rs variations, as seen in Fig. 6. For this purpose, Rs is instantaneously increased to Rsn + 2.5 Ω at 12.7 s by adding a three-phase resistor externally to the stator side in series while the IM is loaded to 16.3 N · m and operating at 460 r/min; then; the resistor is removed from the stator windings at 30.1 s. ˆ s tracks the actual value of Rs Under these variations, since R
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Fig. 8. Experimental results of BI-EKF for very low speed operation under Rs variations. (a) Variation of tind and tˆL . (b) Variation of nm and n ˆm. ˆ s . (d) Variation of the estimated position of the rotor ˆ and R (c) Variation of R r flux with reference to the stator stationary axis. (e) Variation of isβ and ˆisβ .
Fig. 7. Experimental results of BI-EKF for the velocity and load torque ˆm. reversals. (a) Variation of tind and tˆL . (b) Variation of nm and n ˆ s . (d) Variation of fs and fr (e) Variation of ϕ ˆ and R ˆrα (c) Variation of R r and ϕ ˆrβ . (f) Variation of isβ and ˆisβ .
very quickly, consequently, all estimated states and parameters converge to the real ones. Thus, it is concluded that BI-EKF performs quite well in spite of the step-type variations in Rs . Fig. 6(c) also shows the switching nature of the BI-EKF ˆ is constant while Rs is estimated by algorithm; namely, R r using Model-Rs as an input in BI-EKF during tswitch and vice
versa, but the other estimations, for example, tˆL and n ˆ m , are continuously conducted for each tswitch as seen in Fig. 6(a) and (b). The blue “0” and “1” in Fig. 6 are compatible with the switch positions in Fig. 1, and each of them represents tswitch which is determined as 0.26 s (n × T = 2000 × 130 μs) based on the following procedure. 1) Tune P i and Qi until the desired estimation performance is achieved by using the BI-EKF algorithm with each input derived from Model-Rr or Model-Rs . 2) Then, increase tswitch = n × T (where n = 1, 2, 3 . . . and T is the sampling period) by increasing n until over all estimation performance is satisfied.
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C. Scenario III—Performance of BI-EKF Under Velocity and Load Torque Reversals at the Rated Speed (see Fig. 7) The effectiveness of the BI-EKF algorithm during reversing transients of the velocity and the load torque is demonstrated in this scenario, which also includes a very short term operation at zero speed. The resulting estimation performances are given in Fig. 7. The scenario is generated by changing linearly the input frequency from 50 to −50 Hz and vice versa, while the IM is operating at 956 r/min under 16.4 N · m. The duration of the transient is adjusted by the acceleration/deceleration rate of the ac drive. The obtained results illustrate that the BI-EKF algorithm follows very closely the velocity and load torque reversals as seen in Fig. 7(a) and (b). Also, the estimated Rr [see Fig. 7(c)] varying inherently with the variation of the load torque is in agreement with that of previous results in [21] and [22] which present Rr -rotor/slip frequency, fr , relationship. The variation of the load torque in Fig. 7(a) is due to the typical torque–speed characteristics of the Foucault brake used in the experiment. According to Proca and Keyhani [21], Rr varies as a function of fr (skin effect) and rotor temperature. To observe the rotor resistance dependence on fr in this study, slip compensation is also disabled in the ac drive. Later, fr is calculated for this scenario by using the measured stator frequency (fs ), nm , and the well-known equality as follows: nm . fr = fs − pp 60
(9)
Finally, the variation of fr and fs is shown in Fig. 7(d) which ˆ r verifies Rr − fr relationship, and Fig. 7(d) also reveals that R is a function of fr . D. Scenario IV—Very Low Speed Operation of the BI-EKF Algorithm Under Rs Variations (see Fig. 8) This scenario addresses the performance of BI-EKF under imposed Rs variations at 9 r/min which is ∼1% of the rated speed, as shown in Fig. 8. Here, Rs is stepped up to Rsn + 1.5 Ω at 16.5 s and down to Rsn at 33.2 s by connecting or disconnecting the serial three-phase array resistor to the stator windings, respectively, while the IM is operating at 9 r/min under 1.5 N · m. Later, the velocity ramps up from 9 to 703 r/min at 48 s, and consequently, the IM is also almost linearly loaded to 17.8 N · m in order to show the estimation performance of BI-EKF during the transition from very low speed to the high speed. In spite of this challenging scenario, the BI-EKF algorithm satisfactorily estimates step-type Rs variations and the rotor frequency-dependent Rr variations [21], [22] aside from the velocity, the load torque, and the rotor fluxes. Although the load torque is defined as a constant parameter in the extended IM models [see (3) and (5)], the IM is applied to the almost linearly varying load torque during the transition in order to force and see how the BI-EKF algorithm behaves; because of this challenge, it is observed that tˆL affects ˆ s , particularly at low speeds. On the other hand, because R of the torque–speed characteristics of the Foucault brake, the IM cannot be applied to high load torque at very low speed
operation (for example, at zero speed, eddy currents are not induced in the brake’s disk, and thus, no torque occurs); that is why no result is presented for this type of operation in this paper. In summary, the obtained results from Scenarios II, III, and IV prove the real-time feasibility of the BI-EKF algorithm and also reveal the superiority of BI-EKF over the conventional single EKFs which demand exact Rs or Rr values in Scenario I. Moreover, in the context of this study, it is observed that the BI-EKF technique enables observation of the uncertainties in both Rs and Rr as well as isα , isβ , ϕrα , ϕrβ , ωm , and tL in the speed-sensorless case for IMs without performing further theoretical analysis, as in [14] and [15]. However, it does not mean that BI-EKF leads to multiple parameter estimations for every IM model; this reality can only be discovered after simulation and/or real-time-based experiments which are mostly done in the literature of the standard EKF. It is also noticed that the switching order between Rr and Rs in Fig. 1 is not important at the beginning of the consecutive operation; however, the BI-EKF algorithm is given a start with Model-Rr in this study since the Rs value is more easily obtained from dc test than that of Rr . VI. C ONCLUSION In this paper, the BI-EKF-based estimation technique introduced very recently in one of the authors’ previous study [17] has been verified in real-time experiments to accomplish the following: 1) to solve the simultaneous estimation problem of the uncertainties associated with Rr and Rs , in addition to the load torque and all states required for the speedsensorless control via measuring stator phase voltages and currents; 2) to overcome the limited number of state and parameter estimations that would be possible with a single EKF algorithm. Each of the issues stated earlier is a persisting challenge in the literature of the speed-sensorless IM control and EKF, respectively. Inverter switching effects, signal acquisition errors, uncertainties in parameters, modeling errors, and noise are also known to give rise to performance deteriorations in the speedsensorless real-time control of IMs, particularly at very low speed range. Thus, under these concerns, it is really essential for validating the BI-EKF algorithm in real-time experiments. Moreover, this study experimentally confirms utilizing a single EKF algorithm with consecutive execution of two different inputs obtained from the extended models developed for the Rr and Rs estimations, instead of using two individual EKF algorithms, which has been done in the previous studies such as in [14] and [15] for the solution of the same problem. On the other hand, it takes time to determine the proper values of Qi used in the BI-EKF algorithm. In fact, the optimal determination or tuning [23] of the values of Q is still an open area to research in the literature of Kalman filter in order to avoid trial-and-error time-consuming tuning [24]; thus, the solution of this issue is currently in our consideration.
BARUT et al.: REAL-TIME IMPLEMENTATION OF BI-EKF-BASED ESTIMATOR FOR SPEED-SENSORLESS CONTROL OF IMs
TABLE I RATED PARAMETERS OF THE IM
A PPENDIX The rated parameters of the IM used in the real-time experiments are given in Table I. R EFERENCES [1] J. Holtz, “Sensorless control of induction machines—With or without signal injection?” IEEE Trans. Ind. Electron., vol. 53, no. 1, pp. 7–30, Feb. 2006. [2] J. Holtz, “Sensorless control of induction motor drives,” Proc. IEEE, vol. 90, no. 8, pp. 1359–1394, Aug. 2002. [3] J. W. Finch and D. Giaouris, “Controlled ac electrical drives,” IEEE Trans. Ind. Electron., vol. 55, no. 2, pp. 481–491, Feb. 2008. [4] C. Patel, R. Ramchand, K. Sivakumar, A. Das, and K. Gopakumar, “A rotor flux estimation during zero and active vector periods using current error space vector from a hysteresis controller for a sensorless vector control of IM drive,” IEEE Trans. Ind. Electron., vol. 58, no. 6, pp. 2334– 2344, Jun. 2011. [5] T. Orlowska-Kowalska and M. Dybkowski, “Stator-current-based MRAS estimator for a wide range speed-sensorless induction-motor drive,” IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1296–1308, Apr. 2010. [6] S. M. Gadoue, D. Giaouris, and J. W. Finch, “Sensorless control of induction motor drives at very low and zero speeds using neural network flux observers,” IEEE Trans. Ind. Electron., vol. 56, no. 8, pp. 3029–3039, Aug. 2009. [7] M. Hajian, J. Soltani, G. A. Markadeh, and S. Hosseinnia, “Adaptive nonlinear direct torque control of sensorless IM drives with efficiency optimization,” IEEE Trans. Ind. Electron., vol. 57, no. 3, pp. 975–985, Mar. 2010. [8] I. Vicente, A. Endemaño, X. Garin, and M. Brown, “Comparative study of stabilising methods for adaptive speed sensorless full-order observers with stator resistance estimation,” IET Control Theory Appl., vol. 4, no. 6, pp. 993–1004, Jun. 2010. [9] J. Faiz and M. B. B. Sharifian, “Different techniques for real time estimation of an induction motor rotor resistance in sensorless direct torque control for electric vehicle,” IEEE Trans. Energy Convers., vol. 16, no. 1, pp. 104–109, Mar. 2001. [10] B. Karanayil, M. F. Rahman, and C. Grantham, “Online stator and rotor resistance estimation scheme using artificial neural networks for vector controlled speed sensorless induction motor drive,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 167–176, Feb. 2007. [11] H. Tajima, G. Guidi, and H. Umida, “Consideration about problems and solutions of speed estimation method and parameter tuning for speedsensorless vector control of induction motor drives,” IEEE Trans. Ind. Appl., vol. 38, no. 5, pp. 1282–1289, Sep./Oct. 2002. [12] I. J. Ha and S. H. Lee, “An online identification method for both statorand rotor resistances of induction motors without rotational transducers,” IEEE Trans. Ind. Electron., vol. 47, no. 4, pp. 842–853, Aug. 2000. [13] L. Zhen and L. Xu, “Sensorless field orientation control of induction machines based on a mutual MRAS scheme,” IEEE Trans. Ind. Electron., vol. 45, no. 5, pp. 824–831, Oct. 1998. [14] M. Barut, S. Bogosyan, and M. Gokasan, “Experimental evaluation of braided EKF for sensorless control of induction motors,” IEEE Trans. Ind. Electron., vol. 55, no. 2, pp. 620–632, Feb. 2008. [15] S. Bogosyan, M. Barut, and M. Gokasan, “Braided extended Kalman filters for sensorless estimation in induction motors at high-low/zero speed,” IET Control Theory Appl., vol. 1, no. 4, pp. 987–998, Jul. 2007. [16] M. Barut, S. Bogosyan, and M. Gokasan, “Switching EKF technique for rotor and stator resistance estimation in speed sensorless control of IMs,” Energy Convers. Manage., vol. 48, no. 12, pp. 3120–3134, Dec. 2007. [17] M. Barut, “Bi input-extended Kalman filter based estimation technique for speed-sensorless control of induction motors,” Energy Convers. Manage., vol. 51, no. 10, pp. 2032–2040, Oct. 2010. [18] E. S. de Santana, E. Bim, and W. C. do Amaral, “A predictive algorithm for controlling speed and rotor flux of induction motor,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4398–4407, Dec. 2008.
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[19] M. Barut, S. Bogosyan, and M. Gokasan, “Speed sensorless estimation for induction motors using extended Kalman filters,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 272–280, Feb. 2007. [20] E. Laroche, E. Sedda, and C. Durieu, “Methodological insights for online estimation of induction motor parameters,” IEEE Trans. Control Syst. Technol., vol. 16, no. 5, pp. 1021–1028, Sep. 2008. [21] A. B. Proca and A. Keyhani, “Identification of variable frequency induction motor models from operating data,” IEEE Trans. Energy Convers., vol. 17, no. 1, pp. 24–31, Mar. 2002. [22] M. Barut, S. Bogosyan, and M. Gokasan, “An EKF based estimator for speed sensorless vector control of induction motors,” Elect. Power Compon. Syst., vol. 33, no. 7, pp. 727–744, Jul. 2005. [23] K. Szabat and T. Orlowska-Kowalska, “Performance improvement of industrial drives with mechanical elasticity using nonlinear adaptive Kalman filter,” IEEE Trans. Ind. Electron., vol. 55, no. 3, pp. 1075–1084, Mar. 2008. [24] N. Salvatore, A. Caponio, F. Neri, S. Stasi, and G. L. Cascella, “Optimization of delayed-state Kalman-filter-based algorithm via differential evolution for sensorless control of induction motors,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 385–394, Jan. 2010.
Murat Barut (S’06–M’09) was born in Gaziantep, Turkey, in 1973. He received the B.Sc. degree in electronics engineering from Erciyes University, Kayseri, Turkey, in 1995, the M.Sc. degree in electrical and electronics engineering from Nigde University, Nigde, Turkey, in 1997, the Ph.D. degree (with Siemens Excellence Award) in computer and control engineering from Istanbul Technical University, Istanbul, Turkey, in 2005, and the Ph.D. degree in electrical and computer engineering from the University of Alaska Fairbanks, Fairbanks, in 2006. He is currently an Assistant Professor and the Head of Electrical Machine Division as well as the Head of Power Control Research Laboratory at Department of Electrical and Electronics Engineering, Nigde University. His current research interests include motion control, electrical drives, power electronics, mechatronics, and nonlinear observer and estimator design for electromechanical systems. Dr. Barut has been a Reviewer of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS since 2007 as well as of several other journals.
Ridvan Demir was born in Samsun, Turkey, in 1986. He received the B.Sc. and M.Sc. degrees in electrical and electronics engineering from Nigde University, Nigde, Turkey, in 2007 and 2011, respectively. From 2009 to 2011, he was a Researcher with the Power Control Research Laboratory, Department of Electrical and Electronics Engineering, Nigde University, and he is currently a Lecturer with the Department of Electrical and Energy, Bor Vocational School, Nigde University. His main research activity is focused on observer and estimator design for induction motor drive systems.
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Emrah Zerdali was born in Izmir, Turkey, in 1987. He received the B.Sc. degree in electrical and electronics engineering from Pamukkale University, Denizli, Turkey, in 2009 and the M.Sc. degree in electrical and electronics engineering from Nigde University, Nigde, Turkey, in 2011, where he has been working toward the Ph.D. degree in the Department of Electrical and Electronics Engineering since September 2011. He is currently a Research Assistant with the Faculty of Engineering, Department of Electrical and Electronics Engineering, Nigde University.
Remzi Inan was born in Denizli, Turkey, in 1987. He received the B.Sc. degree in electrical and electronics engineering from Pamukkale University, Denizli, in 2009 and the M.Sc. degree in electrical and electronics engineering from Nigde University, Nigde, Turkey, in 2011, where he has been working toward the Ph.D. degree in the Department of Electrical and Electronics Engineering since September 2011. He is currently a Research Assistant with the Faculty of Engineering, Department of Electrical and Electronics Engineering, Nigde University.
