Control of induction motor drive without shaft encoder using model referencing adaptive system and to avoid torque jerks in transition at starting.

Khan, Mohammad Haseeb ; Amarnath, J.

Introduction

Traditionally, separately excited dc machines were the obvious choice for applications in adjustable speed drives, where independent torque and flux control is required. In dc machine, the torque can be controlled over a wide a range of speed by independent variation of field and armature currents. The dc machines also have the excellent dynamic performance over a wide range of operating conditions due to inherent decoupling between field flux and armature current. On the other hand, dc machines are inherently bulky and require frequent maintenance have low torque-to-weight ratio, in addition to commutation problems. Because of these limitations, attention has been diverted to develop induction motor drives. As induction motors are robust, less expensive, require less maintenance and have high torque-to-weight ratio.

The induction motor control is more complicated compared to separately excited dc motor control. This is due to nonlinear multivariable structure of induction motor. The aim of vector control is to decouple the torque and flux components of induction motors. For this, both the magnitude and phase angle of the current vector is to be controlled. With the vector control, the transient response characteristic of induction motor is similar to that of separately excited dc motor. Thus by placing a vector controller between induction motor and main controller, the motor can be forced to yield a fast torque response similar to that of separately excited dc motor [1].

Need for Sensor less Control

Volts/hertz (v/f) control and vector control are the most generally used control strategies of induction motor. In general v/f control method is used in fans, conveyors, centrifugal pumps, etc. where high performance and fast response is not needed. The v/f principle adjusts a constant Volts-per-Hertz ratio of the stator voltage by feed forward control. It serves to maintain the magnetic flux in the machine at desired level. The absence of closed loop control and the restriction to low dynamic performance make v/f controlled drives very robust. Scalar control is the technique in which the control action is obtained by the variation of only magnitude of control variables and disregards to control the coupling effect in the machine. The voltage of the machine can be controlled to control the flux and frequency, or slip can be controlled to control the torque. The control is provided by frequency and voltage reference generator with constant volt per hertz ratio [2,3].

Scalar control technique is somewhat simple to implement, but the inherent coupling effect results sluggish response and the system is easily prone to instability because of higher order system effect. The particular attraction of v/f-controlled drives is their extremely simple control structure, which favors an implementation by a few highly integrated electronic components. There is no direct or indirect control of torque and flux. The status of the rotor is ignored, i.e. no speed or position signal is feedback. These cost-saving aspects are especially important for applications at low power below 5 kW. Even though, the cost advantage makes v/f control very attractive for low power applications, while their robustness favors its use at high power when a fast response is not required. Constant Volts-per-Hertz control ensures robustness at the expense of reduced dynamic performance, which is adequate for applications like pump and fan drives, and tolerable for other applications. Although simple, this arrangement results in limited speed accuracy and poor torque response. The flux and torque responses are dictated by the response of the motor to the applied frequency and voltages are not under the control of the drive [4].

Sensor less control of induction motor is nothing but vector control without any shaft or position encoder [5-7]. The induction motor without speed sensor extract information of the mechanical shaft speed from measured stator voltages and currents at the motor terminals. By using the speed estimation techniques, the information of speed can be estimated and this information is feedback to control of the induction motor drive. One of such a technique is MRAS, [8,9] in which the information of speed can obtain by using the stator voltages and currents. The speed estimation by MRAS will give satisfactory operation at low speed also. But the speed estimation at very low speeds particularly at near zero speeds is a major challenge, because at very low speeds the estimation speed is not accurate.

When the induction motor is switched from standstill to sensorless vector control state in a very low speed control a jerk is generated during the transition period from stand still to sensorless vector control which can affect the performance of the induction motor [11]. To avoid this jerk during transition a high pass filter with feed forward control of stator flux is used.

Mathematical Modeling

Before going to analyze any machine it is very much important to obtain the machine in terms of equivalent mathematical equations. Traditional per phase equivalent circuit has been widely used in steady state analysis and design of induction motor, but it is not appreciated to predict the dynamic performance of the motor. The dynamic of considers the instantaneous effects of varying voltage/currents, stator frequency, and torque disturbance. The dynamic model of the induction motor is derived by using a two-phase motor in direct and quadrature axes. This approach is desirable because of the conceptual simplicity obtained with two sets of windings, one on the stator and the other in the rotor. The equivalence between the three phase and two phase machine models is derived from simple observation, and this approach is suitable for extending it to model an n-phase machine by means of a two phase machine.

The concept of power invariance is that the power must be equal in the three-phase machine and its equivalent two-phase model. Derivations for electromagnetic torque involving the currents and flux linkages are given. The differential equations describing the induction motor are nonlinear. For stability and controller design studies, it is important to linearize the machine equations around a steady state operating point to obtain small signal equations. In or adjustable speed drive, the machine normally constituted as element within a feedback loop, and therefore its transient behavior has to be taken into consideration. The dynamic performance of an ac machine is somewhat complex because the three phase rotor windings move with respect to the three phase stator windings.

The required transformation in voltages, currents, or flux linkages is derived in a generalized way. The reference frames are chosen to be arbitrary and particular cases, such as stationary, rotor and synchronous reference frames are simple instances of the general case. R.H. Park, in the 1920s, proposed a new theory of electrical machine analysis to represent the machine in d-q model. He transformed the stator variables to a synchronously rotating reference frame fixed in the rotor, which is called Park's transformation. He showed that all the time varying inductances that occur due to an electric circuit in relative motion and electric circuits with varying magnetic reluctances could be eliminated. In 1930s, H.C Stanley showed that time varying Inductances in the voltage equations of an induction machine due to electric circuits in relative motion can be eliminated by transforming the rotor variables to a stationary reference frame fixed on the stator. Later, G. Kron proposed a transformation of both stator and rotor variables to a synchronously rotating reference that moves with the rotating magnetic field.

It is understood that per phase equivalent circuit of the induction motor is only valid in steady state condition. Nevertheless, it does not hold good while dealing with the transient response of the motor. In transient response condition the voltages and currents in three phases are not in balance condition. It is too much difficult to study the machine performance of the machine by analyzing with three phases. In order to reduce this complexity the transformation of axes from 3-[PHI] to 2-[PHI] is necessary. Another reason for transformation is to analyze any machine of n number of phases, an equivalent model is adopted universally, that is 'd-q' model [3].

A symmetrical three-phase induction machine with stationary as-bs-cs axis at 2?/3 angle apart is considered. Our goal is to transform the three-phase stationary reference frame (as-bs-cs) variables into two-phase stationary reference frame ([d.sup.s]-[q.sup.s]) variables. Assume that [d.sup.s]-[q.sup.s] are oriented at [theta] angle. The voltages [V.sup.s.sub.ds] and [V.sup.s.qs] can be resolved into as-bs-cs components and can be represented in matrix from as in eq.1

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

The corresponding inverse relation is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

Here [v.sup.s.sub.os] is zero-sequence convenient to set [theta] = 0 so that [q.sup.s] axis is aligned with ds-axis. Therefore ignoring zero-sequence component, this can be simplified as

[V.sup.s.sub.qs] = 2/3 [[upsilon].sub.as] - 1/3 [[upsilon].sub.bs] - 1/3 [[upsilon].sub.cs] = [[upsilon].sub.as] (3)

2.3

[V.sup.s.sub.ds] = -1/[square root of (3)] [[upsilon].sub.bs] + 1/[square root of (3) [[upsilon].sub.cs] (4)

The terminal voltages are given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

Where p is the differential operator d/dt, and [v.sub.qs], [v.sub.ds] are the terminal voltages of the stator q axis and d axis. [V.sub.[alpha]], [V.sub.[[beta]] are the voltages of rotor [alpha] and [beta] windings, respectively. [i.sub.qs] and [i.sub.ds] are the stator q axis and d axis currents, respectively. [i.sub.[alpha]] and [i.sub.[beta]] are the rotor [alpha] and [beta] windings currents, respectively. [L.sub.qq], [L.sub.dd], [L.sub.[alpha][alpha]] and [L.sub.[beta][beta]] are the stator q and d axis winding and rotor ??and ??winding self-inductances, respectively [1].

The following are the assumptions made in order to simplify the eq. (5)

(i) Uniform air-gap

(ii) Balanced rotor and stator winding with sinusoidal distributed mmf.

(iii) Inductance in rotor position is sinusoidal and

(iv) Saturation and parameter changes are neglected

From the above assumptions the eq. (5) can be modified as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

Where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

By applying Transformation to the [alpha] and [beta rotor winding currents and voltages the eq. (6) after necessary modifications and simplifications can be written as in eq. (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

The stator and rotor flux linkages in the stator reference frame are defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9)

Since the rotor windings are short circuited, the rotor voltages are zero and hence from eq. (7), eq. (8) and eq. (9) we get the [i.sub.dr] and [i.sub.qr] equations as below

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

The electromagnetic torque of the induction motor in stator reference frame is given by

[T.sub.e] = 3/2 P/2 [L.sub.m] ([i.sub.qs][i.sub.dr] - [i.sub.ds] [i.sub.qr]) (11)

[T.sub.e] = 3/2 P/2 [L.sub.m]/[L.sub.r] ([i.sub.qs][[psi].sub.dr] - [i.sub.ds] [[lambda].sub.qr]) (12)

The electro-mechanical equation of the induction motor drive is given by

[T.sub.e] - [T.sub.L] = 2/p J [d[omega].sub.r]/dt (13)

From the above equations the motor model is developed in stationery frame of reference.

The Induction motor specifications are given in appendix.

Model Referencing Adaptive System (MRAS)

The sensorless vector controlled method used in the proposed model is MRAS. MRAS is a method that has two models in which one is known as adaptive model and the other is reference model. The reference model does not involve the estimation of the rotor speed and the adaptive model has the quantity to be estimated also known as adjustable model. In the proposed method the speed estimators are based on voltages and currents equations.

[FIGURE 1 OMITTED]

High Pass Filter (HPF)

In this paper the estimation of stator flux is done by using the proposed programmable HPF which reduces the dc-offset effects at low speeds and hence sensorless control at very low speeds can be obtained. Both the adjustable as well as reference models are augmented with high pass filter. When a High Pass Filter is used there is a time delay that can cause a jerk to generate during transition from standstill to sensorless control. This is compensated by using a high pass filter with feed forward control of stator flux and hence the jerk which is developed during transition from standstill to sensorless control can be avoided.

Results and Discussions

The simulation of Sensorless control of 3 Hp induction motor with specifications as shown in table.1 is done by using MATLAB-SIMULINK. As seen from the waveforms the drive switches to sensorless control mode from stand still when the torque command is applied at 0.4 seconds. The operation of the induction motor is seen very smooth by using sensorless control technique. The variation of speed is shown in fig.2. The variation of stator flux, direct and quadrature axes flux are shown in the fig.3, 4 and 5 respectively. Fig. 6 gives the variation of unit vector angle. As seen from the wave forms in Fig. 7 a jerk is generated at the time of transition when a high pass filter with feed forward control of stator flux is not used. By using high pass filter with feed forward control of stator flux estimation the jerk which is generated at the time of transition is reduced as seen from fig. 8

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

Conclusion

In this paper, Sensorless control of induction motor using Model Referencing Adaptive System (MRAS) technique has been used. Sensor less control gives the benefits of Vector control without using any shaft encoder. In this paper the mathematical model of the drive system has been simulated and the results are obtained. Simulation results of sensor less control of induction motor using MRAS technique were carried out by using Matlab/Simulink and from the analysis of the simulation results, performance of the drive have been presented and analyzed. By using MRAS speed is estimated, which is same as that of actual speed of induction motor. Thus by using sensorless control we can get the same results as that of vector control without shaft encoder thereby reducing the cost of drive and increasing the ruggedness of the motor at the same time achieving the fast dynamic response. In the proposed method, by using MRAS, a programmable high pass filter with feed ford ward control of Stator flux estimation is also used to estimate the stator flux so that jerk which is generated at the time of transition from stand still to sensorless control can be avoided. Also from the results it is observed that the transient response of the drive is fast. In the proposed method parametric changes have not been considered. The accuracy of the results can be improved further if the parametric changes are also considered.

Appendix

Induction Motor Specifications

Rotor Resistance    0.773 [[ohm]]/phase
Stator Resistance   0.8671 [[ohm]]/phase
Rotor Inductance    0.8 [mH]/phase
Stator Inductance   0.8 [mH]/phase
Mutual Inductance   25.6 [mH]/phase
Moment of Inertia   0.033 [Kg-[m.sup.2]]
Pole                2

References

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[9] S. Lassaad and M.Ben Hamed "An MRAS-based full order Luenberger Observer for Sensorless DRFOC of Induction Motors" ICGST-ACSE Journal, Volume 7, Issue 1, May 2007.

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(1) Mohammad Haseeb Khan and (2) J. Amarnath

(1) Royal Institute of Technology and Science, EEE Department, Chevella, RR Distt. A.P. India Email: [email protected]

(2) JNTU college of Engineering, EEE Department, JNT University, Kukatpally, Hyderabad, A.P. India E-mail: [email protected]