Design and implementation of a sliding-mode observer of the rotor flux and rotor speed in induction machines

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1 1 Design and implementation of a sliding-mode observer of the rotor flux and rotor speed in induction machines João Ferraz, Paulo Branco Phd. Abstract A sliding-mode observer for the rotor flux and speed of an induction motor is presented in this paper. It is also proposed another observer that is a modification of the original one to reduce the errors and improve the obtained speed results. The observer is used in a sensorless Indirect Field Oriented Control (IFOC). The original and modified observers are executed in an experimental platform that contains a digital signal processor (DSP) TMS320F2812, a 370W induction motor and an IGBT inverter. Experimental results show that the modified observer produces better results than the original, and globally the work produced good results. Index Terms Sensorless, Sliding-mode Observer, Rotor Speed, Rotor Flux, FOC, Induction Machine own cost. In this work, an adaptive sliding-mode observer that estimates the rotor flux and rotor speed is used and applied to an indirect FOC. We also propose a modification on the original observer to minimize the errors and improve its rotor speed estimation performance. The observer is fully developed based on sliding mode control theory [7] and the induction machine model [8] [9]. The observer is implemented in our laboratory and tested to a lot of drive conditions. The main components used in the experimental setup (Figure 1) are a Digital Signal Processor (DSP) (the TMS320F2812), a 370W induction motor, and an IGBT inverter. A PC is also needed, same as two variable resistors, a DC machine acting as load, an autotransformer and a 5Vdc feeder. I. INTRODUCTION The induction machine has many advantages comparing to others machines like its cheapness and robust construction and is usually the best solution for industry. In the last Century, the biggest barrier to the utilization of these types of machines was the difficult to control that operation [1] [2]. In the last four decades, a lot of techniques for control of induction motors has been developed, but due to the complexity of the process and the difficulties attached, this is still an open field of study where better results are constantly asked for. Actually, a commonly used technique to control the induction machine is the Field Oriented Control (FOC) [3] [4] which act on the stator currents to control the motor torque. This method needs the knowledge of the stator currents and the rotor position that is usually obtained by the integration of rotor speed [5]. The rotor speed can be measured with the utilization of sensors or by estimation (sensorless techniques). The utilization of sensors have many disadvantages [6] like the space needed to install it on motor, which is very reduced most situations, and forces a special construction of the motor what causes the solution to be more expensive, and also the bad operation due to motor vibrations or high temperature variations, possible mechanical failures of the sensor and its Figure 1 Experimental setup. II. CONSTANTS DEFINITION The following constants that are used along this paper are defined, ; ; ; ; ;

2 2 ; ; The rotor flux estimator is, ; ; ; ; (3) where Taking, - Stator resistance; - Rotor resistance; - Stator inductance; - Rotor inductance; - Mutual inductance; - Rotor speed; - Pole pairs number; The stator current is the measure quantity that is used to define the sliding mode surface. So, the Sliding mode condition is, (4) III. SLIDING MODE OBSERVER (5) A. Development Defining, is Flux Estimator Ψ r i s Current Estimator it comes, ; Ψ r i s i s i s. (6) ω Speed Estimator ω Considering the following Lyapunov function, Estimated Speed Figure 2 Connection of the estimators. (7) defining z as Based on the Sliding Mode Control Theory, it is defined the following expression: (1) it comes,, (8) (9) where, The derivative of Lyapunov function, can be expressed as,, (10) The stator current estimator is, Where (2). (11)

3 3 According the stability Lyapunov Law Where ;. (12). So it is imposed that. (13) The terms are defined as: Replacing. (21),, (14) Developing, which makes. (22). (15) Hence The modified rotor flux estimator becomes given by. (16). (23) This conducts to (17) IV. FIELD ORIENTED CONTROL (FOC) Finally the Sliding Mode Speed Estimator is obtained: B. Proposed Observer Modification (18) It is proposed the following modification to the rotor flux estimator. A new sliding-mode function is created, The control of asynchronous machines is classified as scalar or vector control. On scalar control only the amplitudes of flux, currents and voltages are considered. In vector control vectors are used to represent instant quantities. Based on DC machine behavior [5] the Field Oriented Control was created on 1973, and is a type of vector control. This method can be divided as direct and indirect. In this work we used the indirect FOC. This technique has the advantage of decoupling the flux and torque like the DC machine control and is presented on Figure 3.. (19) Hence, the new estimator becomes, (20)

4 4 ω ref Speed Controler i qs _ ref i qs _ ref Current Controler u qs _ ref u ds _ ref Clarke Transform u a _ ref dq u b _ ref abc u c _ ref PWM period P W M Vdc_ref i a i b i c Fig. 6 shows the measured and the estimated speed for a step variation of the reference. The estimated speed has a lot of delay on transients, but at stationary periods there are good results with some oscillations induced by sliding mode. Sensor/ Estimator M τ rψ r i ds dq i αs i a ω compensação Slip compensation de escorregamento i qs i βs abc i b Figure 3 Indirect Field Oriented Control (IFOC) V. RESULTS The main experimental results obtained are presented in this chapter. The first two graphs (Fig. 4 and Fig. 5) show the measured and estimated current for different reference speeds. For high speed values the estimator produces better results. Figure 6- Measured and Estimated Speed with a step increase at speed reference; Measured and Estimated Speed with a step decrease at speed reference Figure 4 Measured and estimated current for low speeds: 30rpm until 5s and raise to 90rpm until the end Fig. 7 shows the measured and estimated speed, the measured and estimated stator current (D component) and the estimated rotor flux (D component) of a step variation of speed reference from positive values (+450rpm) to negative values (-450rpm). The main conclusion taken from these results is that, at 4s, when the speed reference is changed, the estimated current has a variation during the transient and slowly goes again to the normal values. The estimated flux on transient goes near zero and reverses its phase, increasing slowly its amplitude to normal values (stationary period). Figure 5 Measured and Estimated Current for 1500rpm

5 5 Figure 8 Measured and Estimated Speed with the Motor under a variable Load Fig. 9 shows the results of estimated speed using the original and the modified flux estimator. It shows that the modification makes better results than the original, producing a smaller delay on transient period and maintaining good results on stationary period. (c) Figure 7 Speed change at 4s: 450rpm to -450rpm; Estimated and measured Current; (c) Estimated Flux The next test (Fig. 8) shows the measured and estimated speed taken with the motor coupled to a variable load. It shows a smoother speed variation, that makes a smaller delay on transient period. Figure 9 Measured Speed and Estimated speed using the Original flux estimator and the modified flux estimator with increase of reference speed; Measured Speed and Estimated speed using the Original flux estimator and the modified flux estimator with Positive and negative reference Speed

6 6 Finally, Fig. 10 shows the results of the application of Sliding-Mode Speed Observer on IFOC. It shows that the estimator has a very small initial delay and follows the reference very closely for positive and negative variations of speed reference. Figure 10 Speed reference and Estimated Speed using Observer on IFOC with Increase of reference speed until 750rpm at 5s and next a decrease of speed until zero (Positive Speeds); Speed reference and Estimated Speed using Observer on IFOC with increase of reference speed until -750 rpm at 4s, constant speed until 6s and next decrease of speed reference until zero (Negative Speeds) VII. REFERENCES 1. Leonhard, W. Control of Electrical Drives, Third Edition. s.l. : Springer-Verlag, Palma, João C.P. Accionamentos Electromecânicos de Velocidade Variável. s.l. : Fundação Calouste Gulbenkian, C.J.Bonano, L. Zhen, L.Xu. A direct field oriented induction machine drive with robust flux estimator for position sensorless control. s.l. : Proceedings of the IEEE Conference of the Industry Applications Society Annual Meeting, Vol.1, pp : , Béres, Z, Vranka, P. Sensorless IFOC of Induction Motor With Current Regulators in Current Reference Frame. s.l. : Industry Applications, Transactions on, vol. 37, no. 4, pp , Blaschke, F. The principle of field-orientation as applied to the Transvector closed-loop control K. Rajashekara, A. Kawamura,and K. Matsuse. Sensorless Control of AC Motors. s.l. : IEEE Press, Young, K. D. and U. Ozg. Sliding mode: Control engineering in practice. s.l. : Proceedings of the American Control Conference pp , Krause, P. C. Analysis of Electric Machinery. New York : McGraw-Hill, Maia, J. Controlo por Modo de Deslizamento da Posição de uma Máquina de Corrente Contínua". Lisboa : Dissertação de Mestrado, IST, VI. CONCLUSIONS The Speed Observer has a lot of delay to follow the measured speed at the transients, but after the stationary period it produces very good results. That delay is smaller when the motor is coupled to a load. The results also show that the proposed modification to the flux estimator produces better results than the original. Finally, the application of the Sliding Mode Observer on the IFOC is shows an estimated speed very close to the reference, so the work was successful.