A New Current Model Flux Observer Insensitive To Rotor Time Constant And Rotor Speed For Dfo Control Of Induction Machine

A New Current Model Flux Observer Insensitive to Rotor Time Constant and Rotor Speed for DFO Control of Induction Machine

Habib-ur Rehman

Mustafa K. Guven

Adnan Derdiyok

Longya Xu

Department of Electrical Engineering The Ohio State University Columbus, Ohio 43210

Abstract:Direct Field Orientation (DFO) control f o r an induction machine is designed and implemented using a new sliding mode technique based current model flux observer. A close loop flux observer, based o n the current estimate error is constructed. The flux and current observers include a sliding function, which is derivative of the flux. Therefore, when the estimated current converges to the measured one, the sliding function itself is integrated to calculate the flux magnitude and angle. The flux angle is then used f o r the D F O control. The flux observer in this technique does not require any knowledge of the rotor time constant and the machine speed because both are included in the sliding mode function, thus making the proposed observer completely insensitive to any error in the rotor time constant or the machine speed information. Simulation and experimental results are presented to show the performance of the proposed observer f o r the D F O control of an induction motor drive system.

An on-line adaptation of the rotor time constant is necessary to keep the machine field oriented. Many on-line identification schemes have been designed [3]-[5]. These methods have provided some improvements, but are quite complex because they either require more parameters, or have hardware complications. DFO on the other hand is a feedback controller which is not sensitive to the rotor time constant, and at the same time can perform comparable to IFO. Therefore, the focus of this paper is to design a robust DFO drive system. DFO, as the name suggests, makes direct use of rotor flux information. The most practical approach, for the DFO control implementation is carried out by estimating the flux from the motor terminal quantities (stator voltages and currents) without adding flux sensors or additional hardware. This flux estimation, when using the voltage model flux observer [6, 71 is sensitive to the stator resistance and leakage inductance, and will also have difficulties at low speed due to integration. The current model flux observer is an alternative approach to overcome the problems of leakage inductance and stator resistance at low speed. However, it does not work well at high speed due I. Introduction to its sensitivity to rotor resistance. Jason [8, 91 combined the best accuracy attributes of the voltage model and curIndirect Field Orientation (IFO) and direct field orienrent model flux observers and designed a close loop flux tation control are the two most commonly used techniques observer which provides an automatic transition between for high performance induction machine drive systems. An the two most desirable open-loop flux observer models: IF0 is synthesized by properly controlling the slip frethe current model at low frequency to the voltage model quency, a necessary and sufficient condition for the field at high frequency. Problems of the stator resistance and orientation. However, an IF0 is very sensitive to the mathe rotor time constant variation are reduced, but not yet chine parameters, especially the rotor time constant (TT). completely eliminated, also an accurate speed information This is because the slip calculator is feedforward open loop is necessary for this technique. control by its nature. The effect of the deviation of T, from This paper proposes a sliding mode observer for rotor flux its actual value to the command value has been studied in and current estimation. A close loop observer based on the [I, 21.

0-7803-7067-8/01/$10.00 02001 IEEE

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current estimate error is designed and implemented. The derivative of the flux observer is equal to the designed sliding mode function. Therefore, when the current estimate error reaches zero, the sliding mode function can be integrated t o calculate the flux. The proposed observer does not require any speed information and is completely insensitive to the rotor time constant, thus can work very well both a t low and high speeds.

11.

Proposed Current Model Flux Observer

The machine model and the matrix S are presented in this form with a specific purpose in mind. It can be seen that the matrix S appears both in the current and flux equations of the machine. The current and flux equations by their nature have an advantage that the coupling terms between Q and ,O axes, both in the current and the flux equations are exactly the same. That is why the coupling terms can be replaced with the same sliding function both in current and flux observers. The current observer can be designed by replacing the matrix S with the proposed sliding function *,or in current equation (1):

The induction machine model, with the stator currents and rotor fluxes defined as the state variables, in the stationary a , L,3 coordinate system can be written as:

1 Lm 1 I,, = --- ,A, 0Ls Lr Tr 1

f f L , (RS +

and the equation for the flux observer can be written from equation (2) as:

1 L, + --wrApr0Ls Lr

&-) I,,

1

+ --&vas

where !Par = -uosign(sas),

!Por = -u,sign(sp,)

and Which can be represented in the matrix form as:

where k1 =

R, k3Lm , h=-, Lr

rJ=1-- L2,

LsLr ’

ffLS

I,,,, fopsand I,,,

1 ffL,

k3=--,

q = l/Tr = R,/L,,

T, is the rotor time constant and w, is the rotor electrical speed. Next define a matrix S as:

Io, are the observed and measured stator current components respectively. “Once the estimated current converges to measured one, the flux estimation is a mere integration of the sliding mode function without requiring a n y knowledge of the machine parameters or speed. ” This is a salient feature of the flux observer proposed in this paper. Two independent sliding functions, !POTand !Pp., are designed for the Q and ,B axes of the current observer respectively. These sliding functions are based on the error between the measured and estimated phase current. Therefore, the designed current and flux observers for the Q and ,B axes have no coupling between them. On the contrary, in the real machine equations we can see that there exists a coupling between the a and ,L3 axes of the current and flux equations. Especially in flux equations, the flux along the Q axis is a function of flux along the

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,6 axis and vice versa. The sliding mode function, when substituted into the observer equations, makes the current and the flux observer models totally decoupled. With this sliding mode function a and axes currents are estimated based on their self current errors i.e., the error between the observed and the measured current. The close loop current observer uses the measured current as feedback. As a result, there is no offset or drift problem in the current observer. In the flux equations there can be an offset because of the integration, but that is taken care of by using a low pass filter. When the estimation error trajectories reach the sliding surface (s, = 0) then, from (5) it is obvious that the observed currents will converge to the actual currents ( I,, = Ias and Ips = Ips). It is important to point out that this sliding surface equation selection guarantees that on the sliding surface, the observer will not be effected by any system parameter or disturbance (i.e. the current observer is invariant).

A.

Which implies that V

< 0 if

where

A =v B =v

+

L T

+ VLrnIas + VLrnIps,

w T X ~ T

-w T L T

X ~ T

By selecting large enough U, (found by the existence condition) the sliding mode (s, = 0) will occur. Solving s, = 0 for the discontinuity term yields the continuous equivalent control. However, the resulting equivalent control will depend on machine parameters and will be difficult to implement. Therefore, it is reasonable to assume that equivalent control is close to the slow component of the real control that can be derived by filtering out the high frequency components using a low-pass filter. The low-pass filter structure is implemented with

-

Observer Stability Analysis The stability of the overall observer structure is guar-

1

'ZOT -

qCYpT,

(6)

where p is the time constant of the filter and should be sufanteed through the stability of the current observer. The ficiently small to preserve the slow component undistorted Lyapunov function for the proposed sliding mode current but large enough to eliminate the high frequency compoobserver is chosen as: nents. The output of the low-pass filter will be equal to 1 the equivalent control on the sliding surface. v = -s:s,, 2

B. Flux and Position Estimation where s, = [ s a s , s p s ]T . The Lyapunov function is positive definite. This satF~~~the equivalent control concept [lo], it is assumed isfies the first Lyapunov stability condition. The second that the observed currents fa, and ips match with actual

v

condition is that the derivative of the sliding function must be less than zero i.e., V = SZS, < 0 with

h using ~ Equations ~ , (4)and (6), and ips. ~ currents the following can be written:

Then using (1)and (3) S, can be written as

Then using (4)and (7), flux can be estimated as:

[&] [ 31 =-

r r

i

Therefore,

--uos~gn (&) --uosign ( I p s ) ]-

[

JT

Note that this flux estimation is done only by using the sliding mode function without requiring any information on the right hand side of equation (7), thus making the proposed flux observer completely insensitive to the rotor itime constant or the rotor speed.

71 [Xx ]lf

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From the estimated flux, the flux angle can be calculated as:

--_0 AT

= 4x2.

1

1.5

2

2.5

3

Simulation and Experimental Results

” -100‘

I

I

I

I

I

I

I

0.5

1

1.5

2

2.5

3

3.5

“‘“I

I

I

I

I

I

I

1

1.5

2

2.5

3

0

+ c

2 0 c

A 5 H P induction machine and a flexible high performance Advanced Controller for Electric Machines (ACE) are used to validate the proposed algorithm. The ACE is a very high performance, rugged, rapid prototyping tool that implements advanced control algorithms and interfaces without any traditional programming. The user, through the graphical user interface, is able to change the various reference inputs and system parameters while the program is running in real time and observe the effects through the on-board data acquisition. The parameters of the machine, used to validate the proposed algorithm, are shown below.

220 Volts Lis = Li, = 1.9mH R, = 0.6 iCt

3.5

+,A:

The estimated flux angle is then used for current transformation from the synchronous to the stationary frame and vice versa, thus gauranting the drive under the filed orientation.

111.

0.5

14.8 Amps L , = 41.2mH R, = 0.412 iCt

5HP 1800 rpm 4 poles

p -

i I

35

(d) lime (sec.)

Figure 1: Simulation Results for a Triangular Speed Command Figures 2 through 4 prove that the proposed observer structure estimates the current, flux, and angle very well by using the designed sliding mode function. Results for the triangular speed command show the speed tracking, estimated and measured current, estimated flux and the sliding mode function which drives the estimated current to the measured one. Figures 3 and 4 show the proposed DFO control performance for a step and trapezoidal speed commands. Experimental results include the estimated and measured currents plotted on the top of each other proving the observer performance and its accuracy.

A . Simulation Results Figure 1 shows the simulation results for DFO control. The command speed and speed calculated from the machine model are plotted on the top of each other in Figure l(a). Figures l(b) and (c) show that the observed current and flux converge to those calculated from the machine model. Figure l(d) shows the sliding function, which is used to estimate the current and flux.

IV.

Conclusions

A robust sliding mode current model flux observer for DFO control of induction machine is designed and implemented. This observer does not require any knowledge of the machine speed and the rotor time constant because both the speed and the rotor time constant are included in the sliding mode function. Thus the proposed observer B. Experimental Results is not sensitive to any error in the speed information and The designed flux observer is tested for triangular, step the rotor resistance variation, problems commonly associand trapezoidal speed commands to validate the perfor- ated with the current model flux observer. The algorithm mance of proposed DFO control. The results shown in is simple to implement and is less computation extensive.

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1 tlme (sec:)

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Figure 3: Experimental Results for a Step Speed Command

time(sec)

Figure 2: Experimental Results for a Triangular Speed Command References

-

[I] K . B. Norciiii arid D . 1%’.No\,otny, “The influelice of

-Ef

5

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