An Emotional Learning Intelligent Direct Torque and Flux Controller Design for Induction Motor

Saeed Jafarzadeh, M. Sami Fadali Department of Electrical and Biomedical Engineering

University of Nevada, Reno Reno, NV, USA

Sjafarzadeh20@gmail.com

Cristian Lascu Department of Electrical Engineering University Politehnica of Timisoara

Timisoara, Romania

Abstract— The brain emotional learning based intelligent controller (BEBLIC) is a nonlinear controller motivated by the success in functional modeling of vigilance in control engineering applications. This paper investigates the application of this controller to induction motor (IM) drives. A BELBIC-based direct torque controlled (DTC) IM drive has been designed in which the torque controller and the stator flux magnitude controller are implemented as BELBICs in stator flux reference frame. The controllers include an exponential reward function which determines the controller dynamics. We present the controller design and investigate the drive performance. Extensive experimental results are presented and discussed. The results show that the BELBIC controller performs well.

Keywords: BELBIC, Electric Drives, Induction Motor.

I. INTRODUCTION

Emotion and cognition are two major aspects of human mental activity [1], [2]. Recently, there has been an increasing interest in the development of computational models for emotion. A computational model of the brain was proposed in [3], [4]. Later, this model was used as a controller and named the brain emotional learning based intelligent controller (BELBIC) [5].

Fig. 1 Computational model of emotional learning in the amygdala.

Motivated by the success in functional modeling of emotions in control engineering applications, a structural model for decision making and control engineering applications has been developed [3]. The computational model of emotional learning in the amygdala, based on

Moren and Balkenius model [6], is depicted in Fig. 1. The main parts that are responsible for performing the learning algorithms are orbitofrontal cortex and amygdala. The amygdala receives inputs from the thalamus and from cortical areas, while the orbitofrontal cortex receives inputs from the cortical areas and the amygdale only [7].

BELBIC is a nonlinear controller which has been successfully applied to various systems and has resulted in significant performance improvement. BELBIC is used in an intelligent autopilot control for a model of a helicopter in [8]. It also has been used in path tracking problems [9], [10]. The application of BELBIC in house appliances [11] is also reported. BELBIC with quadratic reward is also applied to control the motion of an omni-directional robot [12]. In [13], the authors present a uniform linear array adaptive antenna which uses BELBIC. BELBIC demonstrates superior performance in estimating the arrival direction of the incoming signals and performing adaptive beamforming, which is aimed at the receiving end. In [14], a neuro-fuzzy locally linear model tree system and BELBIC are applied to speed control of a switched reluctance motor. The real-time implementation of BELBIC is reported in [15], where BELBIC is used for an interior permanent-magnet synchronous motor drive.

The main contribution of this paper is the application of BELBIC for IM drives control. We implement the torque and the stator flux controllers as BELBICs in stator flux reference frame and discuss the drive performance based on experimental results. The controller dynamics is determined by the reward function contained within the controller. The paper presents design considerations and experimental results for a sensorless IM drive.

The paper is organized as follows. Section II discusses BELBIC and gives its equations. The IM controller design is described in Section III, and in Section IV we present the experimental results. Conclusions and future works are given in Section V.

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II. BELBIC

This section briefly reviews the theory of BELBIC controllers that is used in the remainder of the paper. A BELBIC controller is a multi-input-single-output system with sensory inputs , 1, … , , to be selected by the designer. The BELBIC controller also has two states for each sensory input. One of these two is related to amygdala’s output and another is related to the output of orbitofrontal cortex. Therefore the number of sensory inputs has a key role in BELBIC controller. Usually the sensory inputs are rich signals [5].

Consider the ith sensory input as s . The amygdala and orbitofrontal cortex outputs are:

(1)

(2)

where , are two states for the related sensory input, which are updated using the equations:

∆ . . 0, ∑ (3)

∆ . . ∑ ∑ (4)

In (3) and (4), and are positive design parameters. The max term in (3) is used to model the assumption of a non-forgetting amygdala. In other words, if the sensory input is positive, the amygdala’s output will remain positive. BELBIC control includes a reward function (rew in (3) and (4)) which, as the name implies, rewards desirable behavior by increasing the level of the control that yields it. Therefore the designer must define a reward function that has its maximum values in the most desirable regions of the state-space plane. The reward function could be either a frequency domain function or a time domain function.

Fig. 2 Block diagram of BELBIC IM drive.

As the amygdala acts as an actuator while the orbitofrontal cortex acts as a preventer, the BELBIC control effort is:

∑ ∑ (5)

where .

Since BELBIC is a single-output controller, multi-output systems require one BELBIC unit for each output. There are several tuning parameters for each sensory input. There is no

general algorithm for tuning these parameters and the parameter values are obtained by trial and error.

Fig. 3 Stator and rotor flux dynamics.

III. IM CONTROLLER DESIGN

To use BELBIC for an IM drive we implement two independent, decoupled controllers, one for stator flux control and the other one for torque control. This configuration simplifies the design and implementation by avoiding BELBICs with more than one sensory input. The sensory inputs for theses controllers are filtered flux magnitude and torque errors respectively, and .

(6)

(7)

(a)

(b)

Fig. 4 Response of the torque controller (a), and its time-zoom (b)

We implemented a BELBIC direct torque controller that produces the reference voltage vector, , in the stator flux reference frame.

, (8)

, (9)

where , , , are the controller states, with the update equations (3) and (4).

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(a)

(b)

(c)

Fig. 5 Startup and reversal: (a) estimated and real speed, (b) torque, (c) stator and rotor flux.

Next, the reference voltage is transformed to stator frame and realized through space vector modulation. The detailed block diagram of the drive system is shown in Fig. 2.

It can be seen from (8) and (9) that the control effort is mainly dependent on v and w. We use anti-windup limitation on these quantities to protect the motor against large voltages. The choice of and determines the learning speed and the speed of response of the IM. The values for these parameters in the experiments are 0.1, 0.1.

The reward function can be a frequency domain or a time domain function. The advantage of a frequency reward function is that its dynamics take the history of sensory inputs into account. On the other hand, time domain reward functions allow us to choose the location of the maximum of the reward function to coincide with the regions of high sensitivity. Since the sensory inputs are filtered errors, we use an exponential reward function with an exponent given by the negative of the square sensory input (10). We call this a bell-shaped reward function.

(10)

(a)

(b)

(c)

Fig. 6 Startup and low speed operation: (a) estimated and real speed, (b) torque, (c) stator and rotor flux.

IV. EXPERIMENTAL RESULTS

To evaluate the performance of the proposed controller, we implement BELBIC as a torque and flux controller for a sensorless IM drive and illustrate the experimental results for IM sensorless operation. The induction motor data and experimental setup are described in Appendix.

The dynamic response of the flux controller is shown in Fig. 3 which depicts the rotor and stator flux magnitudes at startup. The stator flux installation time is about 11 . Fig. 4 shows the performance of the torque controller, i.e. the torque response to a step command and its time-zoom view. The torque is ripple free and increases to its rated value (3 ) in about 2 , which is similar to other modern DTC techniques. The drive startup to 300 / and reversal are shown in Fig. 5. The startup to 300 rad/s followed by deceleration and operation at 3 rad/s is shown in Fig. 6. Both Figs 5 and 6 show real and estimated speed (a), torque (b), and flux magnitudes (c). The high and low speed operation is always very accurate and the controller response is fast in all situations.

To evaluate the controller’s performance in a wider speed range, the drive is subjected to a sinusoidal speed command with 50 Hz magnitude and period of 1 second. The results of

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this test are shown in Fig. 7. The controller is able to follow the sinusoidal speed command very well. This performance is kept almost intact at low and high speeds. The stator flux magnitude is also kept constant and without ripples.

(a)

(b)

(c)

Fig. 7 Startup and low speed operation: (a) estimated and real speed, (b) torque, (c) stator and rotor flux.

V. CONCLUSIONS

This paper introduces BELBIC control for sensorless induction motor drives. After briefly reviewing the theory of BELBIC controllers, we present the design of a BELBIC-based direct torque controller for IMs. The controller is implemented on the and axes in stator flux reference frame as two decoupled controllers, one for flux and one for torque. The controller complexity is relatively low and mimics the emotional behavior by using an embedded reward function. The main features of this controller are fast response, ripple-free operation, and simplicity. In addition, BELBIC turns out to be a flexible controller, since it has several tuning parameters which provide freedom in control design based on the desired performance.

We present experimental results for the IM in wide speed range sensorless operation. The results show that BELBIC is responsive and accurate in all situations investigated. The torque and flux are ripple free and their dynamic behavior is as fast as for other DTC techniques. It can be concluded that

BELBIC is a viable and practical alternative for IM drives control. Future efforts will be devoted to designing a BELBIC observer for IM drives.

Appendix – Experimental setup

The proposed controller has been experimentally tested on a 0.75 sensorless IM drive. The VSI is a 2.2 302 inverter from Danfoss Drives. The control was implemented in C++ on a TMS320F28335 DSP from Texas Instruments at a sampling and switching frequency of f 10kHz.

The IM nameplate data and parameters are: P0.75hp,U 240V,f 60Hz,p 2,T 3.1Nm, R 2.3Ω,R 2.5Ω, L L 0.25H,L 0.24H. Two currents and the dc link voltage were measured. A 2048-pulses encoder was used for speed monitoring only.

The stator flux, the rotor speed and torque are estimated using the state observer, which is a Kalman filter [16].

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[16] S. Jafarzadeh, C. Lascu and M. S. Fadali, “Square root unscented Kalman filters for state estimation of induction motor drives,” IEEE Energy Conversion Congress and Exposition, pp. 75-82, 2011.

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