Position Control of Hybrid Stepper Motor Using Brain Emotional Controller

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Energy Procedia 14 (2012) 1998 – 2004

1876-6102 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE).

doi:10.1016/j.egypro.2011.12.1200

Available online at www.sciencedirect.com

1 M. Khalilian et al/ Energy Procedia 00 (2011) 000–000

ICAEE: 27-28 December 2011, Bangkok, Thailand

Position Control of Hybrid Stepper Motor Using Brain

Emotional Controller

Mojtaba Khalilian

a,

*, Ali Abedi

b

, Adel Deris Zadeh

a

aDepartment of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran bDepartment of Electrical Engineering, Dolatabad Branch, Islamic Azad University, Isfahan, Iran

Abstract

In order to control the position of hybrid stepper motor and improve its performance, direct torque control strategy is adopted. The main idea of this paper is to present the implementation of an emotional controller for position control of hybrid stepper motor drive. The proposed controller is called Brain Emotional Learning Based Intelligent Controller (BELBIC). This controller is a computational model of emotional processing mechanism in the brain. The effectiveness of the proposed BELBIC controller-based hybrid stepper motor drive is verified by simulation results.

© 2011 Published by Elsevier Ltd.

Keywords: Hybrid stepper motor, direct torque control, BELBIC;

* Corresponding author. Tel.: +98-9133139315; fax: +98-3117771362.

E-mail addresses: m.khalilian@iaun.ac.ir, ali_abedi93@yahoo.com, adel_deriszadeh@iaun.ac.ir.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE).Open access under CC BY-NC-ND license.

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Stepper motors have been found a wide range of applications in machines and devices where robustness, accuracy and small size at a low cost are needed. A large range of stepper motors based on various operation principles have been developed for industrial applications. According to their operation rules, stepper motor can be classified into three types: variable reluctance, permanent magnet and hybrid. Variable reluctance stepper motors have salient poles on both stator and rotor with excitation coil on stator poles. In variable reluctance stepper motors, the torque is reluctance torque which is produced by the trend of rotor and stator poles to align them when the stator poles are excited. Another type of the stepper motors are permanent magnet stepper motors. These motors have salient poles carrying excitation coil on the stator. The torque in permanent magnet stepper motors is electromagnetic torque produced by the interaction of the stator currents and the rotor flux formed by the magnets. Hybrid stepper motors (HSM) have salient poles on both stator and rotor. The stator poles are toothed and carry excitation coils. The rotor teeth are magnetized by a permanent magnet and shape a number of pole pair. In hybrid stepper motors, torque is produced by both reluctance and electromagnetic effects. In practice, due to the large air gap introduced by the magnets, the electromagnetic torque is dominant as compare to the reluctance torque. Among various types of stepper motors, HSM are the most commonly used since they have the advantages of higher efficiency and torque capability over the other stepper motors [1]-[2].

Stepper motors with an open loop position control are very well suited to many filed of application, but they show a poor performance with respect to very precise motion control and high dynamic requirements. Applying the principle of field orientation, the dynamic performance of the stepper motor can considerably be improved and the stepper motor becomes a high-dynamic ac-servo [3]-[4]. At present direct torque control (DTC) strategy has been successful because it explicitly considers the variable structure nature of the voltage source inverter and uses few machine parameters, while being more robust to parameter uncertainty than field-oriented control. The DTC features fast responses, structural simplicity and robustness to modeling uncertainty and disturbances and thus this technique, can improve transient torque response of hybrid stepper motor [5].

Traditionally, conventional controllers like fixed-gain PI, PID were commonly used in control of hybrid stepper motor but, they are very sensitive to parameter variations, along with step changes of command speed and load disturbance. Therefore, researchers were attracted to utilize intelligent controllers for the HSM drive system. The design of intelligent controllers does not need the exact mathematical model of the system and they are able to handle any nonlinearity of arbitrary complexity. The Artificial Intelligence techniques, such as fuzzy logic, neural network and genetic algorithm have recently been applied widely in motor drives. The goal of artificial intelligence is to model human or natural intelligence in a computer so that a computer can think intelligently like a human being. One of the new types of artificial intelligent controllers is called the brain emotional learning based intelligent controller (BELBIC) and is developed from the computational model of emotion processing mechanism in brain. This type of controller is insensitive to noise and variations of parameters and has already been successfully implemented in some real time processes [6]-[8].

This paper is organized as follows; In Section2, the dynamic model of HSM in α-β stationary reference frame is presented. Section 3 describes the direct torque control principle for position control of HSM. In section 4 the structure of the emotional controller is explained. Some simulation results are provided in section 5. Finally, the conclusion is presented.

2. Model of hybrid stepper motor

The mathematical of the hybrid stepper motor is described by the following equations [9], [10]: ) N sin( . K dt di L i. R ua = a+ a −ω m θ (1)

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2000 Mojtaba Khalilian et al.\ / Energy Procedia 14 (2012) 1998 – 2004 ) N cos( . K . dt di L i. R ub= b+ b+ω m θ (2) )) N sin( . i ) N cos( . i( K Te = m b θ − a θ (3) ω − − = ω . B T T dt d .J e L m (4) s . p . 2 360 N θ = (5) Where R is winding phase resistance [Ω], L is winding phase inductance [H], Km is torque constant

[V.s/rad], J is total inertial momentum [kgm2], Bm is friction coefficient [Nms], θs mechanical step angle

in degree, p is Number of phases, N is the number of teeth on the rotor, Te is electromagnetic torque [Nm]

and TL is load torque [Nm].

3. Direct torque control

DTC is a sensorless technique which operates the motor without requiring a shaft mounted mechanical sensor. It is suitable for control of the torque and flux without changing the motor parameters and load. In this method torque and stator flux are directly controlled by two hysteresis controllers. The block diagram of direct torque control for HSM is shown in Fig. 1.The basic idea of DTC is to control the torque and flux linkage by selecting the voltage vectors properly using the switching table. Stator magnetic flux can be calculated using equation:

dt ) i R u ( t t t s s s

Δ + − = Ψ (6) R is small so stator flux linkage can be integral of stator voltage vectors. Thus, by selecting the proper voltage vectors, rotation and amplitude of stator flux linkage can be controlled. The torque equation of the hybrid stepper motor is [5]:

] 2 sin ). L L .( sin . L . . 2 [ L . L . 4 . p . 3 T r q s q d q d s ψ δψ δ ψ = (7)

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From equation (7), because Ψr is a constant, torque is proportional to amplitude of stator flux linkage

Ψs and δ. If amplitude of stator flux linkage is possibly kept invariable, electromagnetic torque in HSM is

determined by δ, thus quick dynamic response can be achieved by changing δ as fast as possible. So, control of flux and torque are by choosing proper voltage vectors. These voltage vectors are obtained from the switching table based on the flux and torque errors.

Fig. 1. The control system schematic diagram of HSM based on DTC

4. Brain emotional controller

BELBIC is a computational model based on the limbic system that imitate those parts of brain thought to be responsible for processing emotions like amygdala, the orbitofrontal cortex, the thalamus and sensory input cortex. The main plan is to use this computational model of emotional learning in control applications. BELBIC is divided into two parts: corresponding to the amygdala and orbitofrontal cortex (OFC). Amygdala receives connections from sensory cortices and the thalamus, while the OFC receives inputs from cortical areas and the amygdale only. The system receives a reinforcing signal (Emotional Cue). There is one A node for every stimulus to amygdale plus one additional node from thalamic stimulus. There is one single node for all outputs of the model, called E. This node simply sums the outputs from the A nodes, and then subtracts the inhibitory outputs from the O nodes, where O is OFC node for each of the stimuli [6]:

− = i i i i O A E (including Ath) (8)

Additionally, E′node sums the outputs from A except Ath and then subtracts it from inhibitory outputs

of the O nodes:

− = ′ i i i i O A E (not including Ath) (9)

The thalamic connection is calculated as the maximum over all stimuli S and becomes another input to the amygdaloid part:

) S max(

Ath = i (10)

Unlike other inputs to the amygdale, the thalamic input is not expected into the orbitofrontal part and can not be inhabited. For each A node, there is a connection weight V. Any input is multiplied by this weight to provide the output of the node.

i i

i S V

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2002 Mojtaba Khalilian et al.\ / Energy Procedia 14 (2012) 1998 – 2004

The connection weights Vi are tuned proportionally to the difference between the reinforcer (REW) and

the activation of the A nodes. The parameter is a learning rate parameter, between 0 (no learning) and 1 (instant adaptation). )) A REW .( S , 0 max( . V i i i i=α −

Δ (12)

The OFC model is similar to the amygdale model. It also adapts its output according to the sensory data S and the reinforcer (REW). Similarly, the learning rule in OFC is calculated as the difference betweenE′

and the reinforcing

)) REW E .( S .( Wi =β i ′− Δ (13)

Where Wi is the weight of OFC connection and β is OFC learning rate. It can be seen that the OFC

learning principle is very similar to the amygdale rule. The only difference between amygdale and OFC learning is that the OFC connection weight can be both increase and decrease as required tracking the desired inhibition. The OFC nodes values are then calculated as follows:

i i

i SW

O = (14)

Note that this system works at two levels: The amygdaloid part learns to predict and react to a given reinforcer. So, the OFC output is adjusted to minimize the discrepancy of the amygdale output and the reinforcer, which was exactly desired. The block structure of the emotional controller is shown in Fig. 2. For using BELBIC model as a controller for HSM drive, the sensory input and the emotional cue (reward) signals must be defined. In this work, according to the HSM characteristics, the following signals are selected as reward and sensory input signals respectively [6]:

CO . K dt .e . K e . K REW= 1 + 2

+ 3 , S=K4e. (15) In above equation, REW, CO, S and PO are emotional cue, controller output, sensory input, and plant output. The gains K1, K2, K3 and K4 should be tuned for designing a satisfactory controller [6]. The

structure of the position control configuration implemented in this paper is shown in Fig. 3.

Fig. 2. Basic block structure of the emotional controller Fig. 3. Control system configuration using BELBIC

5. Simulation Results

The drive system is simulated by Matlab software to validate the analysis. In simulation, reference position is set to 100 degree. The waveform of the speed of the motor is shown in Fig. 4. Position of the motor is illustrated in Fig. 5. Fig. 6 shows the motor torque. The load torque is 10N.m. Fig. 7 shows the stator current of hybrid stepper motor. The amplitude of stator flux linkage is shown on Fig. 8. Locus of stator flux is illustrated in Fig. 9. It can be seen that the flux vector amplitude is relatively constant and the trajectory is rounded.

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Fig. 4. Speed of HSM Fig. 5. Position of HSM

Fig. 6. Electromagnetic torque of HSM Fig. 7. Stator current of HSM

Fig. 8.Stator flux amplitude Fig. 9. Locus of stator flux

6. Conclusion

This paper has used an innovative emotional controller based on computational model of emotional learning of the brain, called BELBIC, in position control of hybrid stepper motor drives. The simulation results confirm that the proposed emotional controller is good in terms of fast response, no overshoot and zero steady-state error and thus, adaptive for high performance drive applications.

References

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