A new intelligent adaptive mechanism for sensorless control of permanent magnet synchronous motor drive

Biologically Inspired Cognitive Architectures xxx (xxxx) xxx–xxx

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Biologically Inspired Cognitive Architectures journal homepage: www.elsevier.com/locate/bica

Research article

A new intelligent adaptive mechanism for sensorless control of permanent magnet synchronous motor drive ⁎

MD Qutubuddin , Narri Yadaiah Electrical and Electronics Engineering Department, Jawaharlal Nehru Technological University Hyderabad, College of Engineering, Kukatpally, Hyderabad, Telangana State 500085, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Emotions Mammalian brain Limbic system PMSM Motor parameters

This paper presents an intelligent adaptive mechanism for sensorless permanent magnet synchronous motor drive. The mammalian brain inspired intelligent controller named as brain emotional controller is introduced in adaptive mechanism of model reference adaptive system to estimate rotor speed, rotor position and for motor parameters identification. The brain emotional controller design includes certain parts of limbic system of mammalian brain. The brain emotion based adaptive mechanism is constructed with state tracking error of reference and adjustable models using Lyapunov function. Moreover, to control the speed of drive the brain emotional control based speed regulator is designed to achieve improved performance. The effectiveness of adaptive mechanism is verified using simulations and results obtained are analyzed by real time implementation using hardware-in-loop set up. The performance of proposed strategy is validated by operating at different operating and loading conditions. The results show the effectiveness and robustness of proposed brain emotional control strategy.

Introduction The advancements of modern control theory concepts have introduced different intelligent control techniques to solve nonlinear problems of industrial applications (Henson & Seborg, 1997; MurraySmith & Johansen, 1997; Rodriguez, Gutierrez-Garcia, & Ramos, 2016). Many intelligent controllers design is based on behaviour of different mammalian organs for which mammalian brain is responsible to finish the allocated task of an organ (Dancy, 2013; Hudlicka, 2014). The mammalian brain gives necessary signal to corresponding organ to attend the task very swiftly and more accurately (Larue, Poirier, & Nkambou, 2013; Taylor, 2010; Vallverdu et al., 2016). The limbic system of mammalian brain plays a vital role in decision making process of organ as it provides very fast and accurate signal in the form of emotions to finish a task, thus as per the neurobiological aspect it is called as centre of emotions (Lautin, 2002; Samsonovich, 2013). The process of emotional intelligence of Limbic system can be modeled and designed as a controller to obtain fast and accurate solution especially complex problems of engineering applications Moren and Balkenius developed a computational network for Limbic system to analyse behaviour of animals (Moren & Balkenius, 2000a, 2000b). Caro Lucas et al. modified and extended the network model to introduce brain emotional controller to find solution for complex nonlinear control

⁎

engineering systems (Lucas, Shahmirzadi, & Sheikholeslami, 2004). In design of brain emotional controller each part behaviour is modeled with a mathematical function with the inspiration of limbic system of mammalian brain which includes certain parts namely sensory cortex, thalamus, amygdala and orbitofrontal cortex (OFC). This controller is modified to solve the control problems of electrical drives and power systems (Dehkordi, Kiyoumarsi, Hamedani, & Lucas, 2011; Qutubuddin & Yadaiah, 2017; Soreshjani, Markadeh, Daryabeigi, Abjadi, & Karga, 2015). In this paper, Permanent Magnet Synchronous Motor (PMSM) drive which is a typical nonlinear system is considered for estimation and control. The brain emotional controller is introduced in adaptive mechanism to estimate rotor speed (ωr), rotor position (δ) and motor parameters identification i.e. resistance (Rs) and inductance (Ls). PMSM drive is gaining popularity due to its compact size and is used replacing other drives of same size. Developments in compact size magnet materials made to design PMSM drive for variety of industrial applications such as robotics, renewable energy applications, chemical industries process control, domestic applications and many more. The PMSM drive when operated with vector controlled algorithm which requires precise information about rotor speed and rotor position to synchronize with inverter to generate phase excitation pulses. The rotor information of PMSM drive can be measured by sensors and optical encoders, but in the case of sensorless applications these are absent, as

Corresponding author. E-mail addresses: [email protected] (M. Qutubuddin), [email protected] (N. Yadaiah).

https://doi.org/10.1016/j.bica.2018.04.003 Received 19 May 2017; Accepted 9 April 2018 2212-683X/ © 2018 Elsevier B.V. All rights reserved.

Please cite this article as: Qutubuddin, M., Biologically Inspired Cognitive Architectures (2018), https://doi.org/10.1016/j.bica.2018.04.003

Biologically Inspired Cognitive Architectures xxx (xxxx) xxx–xxx

M. Qutubuddin, N. Yadaiah

Nomenclature

Vd,Vq Id,Iq ωr ωr̂ δ Rd,Rq Ld ,Lq P Ψf

TL Te Bm Jm A O Si SC EC up uc

stator voltages reference currents rotor speed estimated rotor speed rotor position adjustable currents stator resistance per phase d-axis and q-axis inductance no. of Pole pairs of motor rotor magnetic flux linking the stator

load torque electromagnetic torque friction coefficient of motor moment of inertia of the motor and load amygdala orbitofrontal cortex sensory input sensory cortex emotional cue plant output controller output

the speed regulator is also designed with brain emotional controller strategy to reduce variations in stator phase winding currents and electromagnetic torque at different operating conditions. Fig. 1 shows structure of proposed technique, brain emotional controller used in adaptive mechanism and to control the speed of PMSM drive. The brain emotional controller has unique and simple designing which overcomes the complexity associated in other intelligent controllers. The input to brain emotional controller used in adaptive mechanism is fed from adjustable and reference models of MRAS technique, the reference model taken from plant i.e. motor and adjustable model is dynamic one in which estimated speed and parameters are variables. Further the estimated rotor speed is fed to control PMSM drive for sensorless application. This paper organized as follows: Section ‘Development of brain emotional controller’ deals with architecture of brain and focused in limbic brain and their associated parts to develop as a controller, Section ‘Brain emotional controller based adaptive mechanism’ explains about the adpative mechanism and significance to use brain emotional controller, the Section ‘Brain emotional controller based MRAS technique for PMSM drive’ the developed adaptive mechanism is applied to PMSM drive to verify the effectiveness, the results and discussions are explained in Section ‘Results and discussions’ and finally conclusions in Section ‘Conclusions’.

it occupies additional space for electronics converting circuit and frequent maintenance (Acarnley & Watson, 2006; Boldea, 2008). In sensorless control application rotor speed and rotor position is estimated rather than measured, which reduces space, cost and frequent maintenance. Different estimation techniques are readily available to implement out of which Model reference adaptive system (MRAS) is one of the promising, most popular and wide accepted technique (Kwon & Jin, 1999; Piippo, Hinkkanen, & Luomi, 2009; Sun, Xiaopeng, Bai, Wei, & Sun, 2016). MRAS construction includes reference model and adjustable model with suitable adaptive mechanism. The adaptive mechanism is designed with comparative output analysis of the reference and adjustable models using gradient, least square and Lyapunov approach. The adaptive mechanism of MRAS technique contains PI, Sliding mode controller (SMC) and artificial intelligent techniques. The PI and SMC controller’s performance is step fall at sudden load disturbance, speed variations and change in motor parameters. These variations impact on stator winding currents, deviations in stator voltages and in electromagnetic torque production. The SMC involves in chattering problem which creates noise, worsens the performance of machine and also requires additional hardware in real time implementation (Baik, Kim, & Youn, 2000; Foo & Rahman, 2010). The adaptive mechanism can modify with artificial intelligent (AI) techniques to obtain better performance but these models do not have exact mathematical relations. In case if the system stability is main concern the validation of AI techniques based adaptive mechanism has limitations of not ensuring the stability. The fuzzy logic controller based adaptive mechanism cannot be applied for the systems where stability is main concern due to lack of exact mathematical function (Chaoui & Sicard, 2012). The Neural networks based adaptive mechanism can be used to solve the problems but in training algorithm a fixed learning rate which converges speed and includes complex design structure (Elmas, Ustun, & Sayan, 2008). Other intelligent controllers ANFIS and Optimization techniques are proposed but they are shortfall in performance and also require extensive information of system which increases complexity in design (Jon, Wang, Luo, & Jong, 2017; Liu, Zhu, Zhang, & Zhang, 2008). In this paper, it is proposed to design and development brain emotional controller for three different major objectives (i) speed control of PMSM drive, (ii) estimation of state variables of PMSM (rotor speed and rotor position) and (iii) identification of motor parameters (Resistance and Inductance). These concepts are applied for sensorless vector control of PMSM drive. The design structure of brain emotional controller for said applications is alike but differs in selection of sensory signal and emotional cue or reward functions. The adaptive law for state variables and motor parameters is constructed with Lyapunov design approach (Sassano & Astolfi, 2013). In adaptive law the variable gain plays a major role which speeds up and slows down the adaptive mechanism performance which may limit overall performance of system. The brain emotional controller is designed for the variable gain used in adaptive mechanism to achieve improved performance. The estimated speed is given as feedback signal to control the drive where

Development of brain emotional controller The structure of brain emotional controller with Limbic system of mammalian brain, and parts associated to generate emotional signal is shown in Fig. 2. Amygdala plays a key role in limbic system to generate emotional signal with its connections to other parts of brain. The output of amygdala is considered as primary reinforce signal, further the response is processed in motor cortex with OFC to generate predicted emotional response to attend the task. Moren and Balkenius developed a computational network model to design limbic system with amygdala and OFC as main parts (Moren & Balkenius, 2000a, 2000b). The same component model has been considered in this paper to design brain emotional controller. The thalamus is designed in a superficial way for the sake of simplicity to onward transmission of sensory signal to amygdala and OFC. The emotional signal generation mechanisms is initiated by collecting inputs to controller and modify as sensory signal with a suitable function. The sensory signal is processed in sensory cortex, amygdala and OFC. The inputs to the amygdala are sensory cortex, emotional cue and sensory signal. Amygdala output response is very fast which needs to be conditioned with OFC to generate appropriate emotional signal response. The inputs to OFC are sensory cortex, sensory signal, emotional cue and resultant. The output of the controller is emotional response signal which is obtained from the outputs of amygdala and OFC. The emotional cue is reinforcing signal which trims amygdala and OFC response with appropriate weight to accord actual emotional response. The design 2

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Fig. 1. Proposed sensorless control of PMSM drive based on brain emotional controller.

speed controller. The sensory signal and emotional cue functions for adaptive mechanism to estimate rotor speed are obtained as

modelling of brain emotional controller is given as here under. The sensory signal (Si) can be represented with the function of f,

Si = f (e,up,uc )

(1)

f = (G1 + G2). x +

Si is processed with the function of g to achieve Sensory cortex.

SC = g (Si )

(2)

h = A.

∫ G3 uc

∫ x + B. uc + C. |x. uc |

(11) (12)

The function g is represented as

g = e Si

where x value obtained from adjustable model and reference model. G1, G2, and G3 are gain values of sensory signal function and A, B and C are gain values for emotional cue function respectively. The sensory signal and emotional cue functions for adaptive meR chanism to estimate motor parameter (a ̂ = L ) obtained as

(3)

The amygdala and OFC learning models designed as

A = Vi Si

(4)

ΔVi = α max(0,EC −Ai − 1 ) SCi

(5)

O = Wi Si

(6)

ΔWi = β (E ι−EC ) SCi

(7)

E ι = Ai −Oi

(8)

EC = h (e,uc,uP )

(9)

f = (G1R). x + G2R uc

(13)

h = AR . x + BR. uc

(14)

where x value obtained from adjustable model and reference model.

The output of the controller is emotional signal (E) which is derived as

E = A−O

(10)

where up is plant output and uc is controller output. A and O are outputs of amygdala and OFC, E is controller output, Vi and Wi are gain connections of amygdala and OFC. α and β are learning rates of amygdala and OFC respectively and Δ symbol represents variation in weights. E ι is resultant of controller, obtained from output of amygdala and OFC. In this paper emotional controller is used in adaptive mechanism of MRAS technique and as a speed controller in vector controlled PMSM drive. The selection of sensory signal and emotional cue functions of brain emotional controller are different for adaptive mechanism and for

Fig. 2. Mammalian Brain and Connections of Amygdala. 3

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linear time-varying systems for the purpose of deriving an adaptive mechanism. However, it is valid to initially treat ωr as a constant parameter of the models. Lyapunov function approach is established to design adaptive mechanism to estimate rotor speed and position. The motor Eqs. (21) and (22) can represent as

G1R, and G2R, are gain values of sensory signal function and AR, and BR are gain values for emotional cue function respectively. The sensory signal and emotional cue functions for adaptive me1 chanism to estimate motor parameter (b ̂ = L ) obtained as

f = (G1L). x + G2L uc

(14)

h = AL . x + BL. uc

(15)

R

ωr ⎤ Id ⎡− Id ⎡ ⎤ + 1 ⎡ Vd ⎤ p⎡ ⎤ = ⎢ L R ⎥ ⎢ Iq ⎥ I V −Ψ ω ⎢ ⎥ q L⎢ ⎣ ⎦ ⎢− ωr − L ⎥ ⎣ ⎦ ⎣ q f r⎥ ⎦ ⎦ ⎣

where x value obtained from adjustable model and reference model. G1L, and G2L, are gain values of sensory signal function and AL, and BL are gain values for emotional cue function respectively. The sensory signal and emotional cue functions for speed controller obtained as

f = K1. e + K2. uP + K3.

∫ uc dt

h = a. e + b. |e . uc | + c. YP

(23)

The above Eq. (23) is reference model and is represented as state space model

Ẋ = AX + BU

(24)

The adjustable model is represented with ωr̂ as adjusting parameter

(16)

R

ωr̂ ⎤ ⎡ Id̂ ⎤ Vd ⎤ 1 ⎡ Id̂ ⎤ ⎡ − p⎢ ⎥ = ⎢ L + ⎡ R ⎥⎢ ̂ ⎥ Vq−Ψf ωr ⎥ L⎢ Iq̂ Iq ̂ ω − − ⎢ ⎥ ⎦ ⎣ r ⎣ ⎦ ⎣ L ⎦⎣ ⎦

(17)

where e is value obtained from reference and actual speed, up is plant output and uc is controller output. K1, K2, and K3 are gain values for sensory signal function and a, b and c are gain values for emotional cue function respectively. The flow chart to design the brain emotional controller is shown in Fig. 3 the design process of controller is same for adaptive mechanism to estimate the speed, motor parameters and to control of PMSM drive the only difference is selection of sensory and emotional cue responses.

X ̇ = A  + BU X

R V pId = − Id + ωr Iq + d L L

(27)

Brain emotional controller based adaptive mechanism

R 1 pIq = −ωr Id− Iq + (Vq−Ψf ωr ) L L

(28)

The state space model of Eq. (25) can represent as

Eq. (25) can be written as

Mathematical modelling of PMSM machine

R 1 pId̂ = − Id̂ + ωr̂ Iq̂ + Vd L L

(29)

R 1 pIq̂ = −ωr̂ Id̂ − Iq̂ + (Vq−Ψf ωr ) L L

(30)

From Eqs. (27)–(30)

The mathematical modelling of PMSM machine is carried in synchronously rotor reference frame, the stator equation in rotor reference frame in d-q axis given by

Te =

3P [ψ Iq + (Ld −Lq) Id Iq] 2 f

Te = TL + Jm Pωr + Bm ωr

(18) (19) (20)

The above Eq. (18) can be rewritten in terms of currents to use in MRAS technique, the reference model and adjustable models are designed with currents and voltages of motor. The error of reference and adjustable models is fed as input for adaptive mechanism to estimate rotor speed and to identify motor parameters.

dId R V = −⎛ d ⎞ Id + ωr Iq + d dt Ld ⎝ Ld ⎠ ⎜

dIq dt

⎟

ϕf ωr Rq Vq = −⎛⎜ ⎞⎟ Iq−ωr Id− + L L Lq q ⎝ q⎠

(26)

Eq. (23) can be written as

The architecture of MRAS contains reference model and adjustable with an adaptive mechanism. The reference and adjustable models are designed using motor equations for which mathematical model of drive is required. Further, the reference and adjustable models are used to develop an adaptive mechanism using Lyapunov design approach.

R + PLq ωr Ld ⎤ Iq ⎡Vq ⎤ = ⎡ q ⎡ ⎤ + ⎡ Pωr ψf ⎤ ⎢ ⎢ ⎥ ⎢ ⎥ ⎣ 0 ⎥ ω L R − r q d + PLd ⎥ ⎦ ⎣Vd ⎦ ⎣ ⎦ ⎣ Id ⎦ ⎢

(25)

(21)

(22)

where ϕf = Lm i fr Ld = Lq = L and Rd = Rq = R. Adaptive mechanism to estimate speed The MRAS structure shown in Fig. 4, the output of reference model and adjustable model is used to design the adaptive mechanism to estimate the speed. It is important to ensure that the system will be stable and the estimated quantity will converge to the actual value for the adaptive mechanism. In general ωr is a variable, thus the models are

Fig. 3. Flow chart to design brain emotional controller. 4

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M. Qutubuddin, N. Yadaiah

ωṙ ̂ = KX T Xe Iq T εd ωr̂ (t )−ωr̂ (0) = K ⎡ ⎤ ⎡ ε ⎤ q ⎢ ⎣−Id ⎥ ⎦ ⎣ ⎦ ⎡ I −I ̂ ⎤ −Id ] ⎢ d d ⎥ ̂ ⎣ Iq−Iq ⎦ Ψf ωr̂ (t ) = K [Id Iq̂−Id̂ Iq + L (Iq̂−Iq)] + ωr̂ (0) = K [ Iq

(38)

Rotor angle estimation:

δ=

∫ ωr̂ dt

(39)

Fig. 4. MRAS structure to estimate the speed. R p (Id−Id̂ ) = − L Id + ωr Iq +

= pεd =

R − L (Id−Id̂ ) + R − L εd + ωr̂ εq

p (Iq−Iq̂ ) = −ωr Id− L Iq + R

(−

Vd − L

R ̂ I L d

1 + ωr̂ Iq̂ + L Vd

The variable K in Eq. (38) will fasters or slower down the speed adaptive law according to the required response. The variable K is obtained using brain emotional controller, the design of controller for adaptive mechanism and algorithm is giver here under:

)

(ωr −ωr̂ ) Iq + ωr̂ (Iq−Iq̂ ) + (ωr −ωr̂ ) Iq

Algorithm 1. Brain emotional controller design algorithm used in adaptive mechanism

(31)

(−ω ̂ I ̂−

1 (V −Ψf ωr )− L q

r d

R ̂ I L q

+

)

1 (V −Ψf ωr ) L q

Step 1: The controller design process start with the selection of input parameters to the controller i.e. sensory signal. The sensory signal (Si) is selected with Eq. (11) since the sensory signal contains x and uc are input variables. Step 2: The output of the sensory signal is processed in sensory cortex, amygdala and OFC. Firstly, the sensory signal is analyzed in sensory cortex (SC) to improve Si signal with Eq. (3). The SC signal is further processed in amygdala and in OFC for signal conditioning and to generate faster output of the controller i.e. emotional response. Step 3: The amygdala and OFC has a connection of emotional cue which is reward signal according to the required output response. The emotional cue is modeled with the Eq. (12). Step 4: Final output of the controller is based on the amygdala and OFC outputs, the amygdala (AG) are designed with Eq. (5) where it is function of amygdala gain, emotional cue, sensory cortex and learning rate (α). The max term in Eq. (5) makes output of amygdala monotonic i.e. never decreasing or a high values always. Step 5: The output of AG is trimmed with the help of OFC. The OFC is modeled in Eq. (6) with sensory signal, sensory cortex, emotional cue, and learning rate β. Step 6: The AG and OFC signals are processed in E to generate emotional response with Eq. (10) i.e. rotor speed (ωr) with Eq. (38) and rotor position (δ) with Eq. (39). If generated speed matches with required response of plant then process stops here otherwise goes to step1 and starts again.

R = − L (Iq−Iq̂ )−ωr̂ (Id−Id̂ )−Id (ωr −ωr̂ ) R pεq = −ωr̂ εd− L εq−Id (ωr −ωr̂ )

(32) From the Eqs. (31) and (32) R

ωr̂ ⎤ εd ⎡− εd 1 0 ⎤ ⎡ Iq ⎤ p ⎡ε ⎤ = ⎢ L ⎥ ⎡ ε ⎤ + (ωr −ωr̂ ) ⎡ q ⎣0 1⎦ ⎢ ⎣ ⎦ ⎢− ωr̂ − R ⎥ ⎣ q ⎦ ⎦ ⎣− Id ⎥ L⎦ ⎣

(33)

The above Eq. (33) is represented in state space form as follows

∼ X ⎛∵ ω ∼ = (ω ̂ −ω ) ⎡1 0 ⎤ ⎞ Ẋe = AXe −ω r r r r ⎣0 1 ⎦ ⎠ ⎝

(34)

Let us consider the model shown in Eq. (35) to derive the adaptive law to estimate the ωr . Consider the following Lyapunov function.

∼T ∼ ∼ ) = X T PX + tr ⎛⎜ ωr Pωr ⎞⎟ V (Xe ,ω r e e ⎝ K ⎠

(35)

where tr(P) denotes to trace of matrix P, K is the gain parameter and P = PT > 0 is chosen as solution for the Eq. (35) as follows.

PA + AT P = −Q

(36)

where P is positive definite The derivative of V is given by

∼̇ T Pω ∼ ∼T Pω ∼̇ ⎞ ω ⎛ω T r r + r V̇ = Ẋe PXe + XeT PẊe + tr ⎜ r K K ⎟ ⎠ ⎝

(37) Adaptive mechanism for parameters identification

∼̇ in Eq. (37), it becomes Substitute Xe and ω r ∼T ∼ X + tr ⎜⎛2 ωr PF1 ⎞⎟ V̇ = XeT (PA + AT P ) Xe −2XeT Pω r K ⎠ ⎝

The MRAS technique can be extended to identify the motor parameters, MRAS structure with adaptive mechanism for identification motor parameters shown in Fig. 5. The adaptive law is constructed by considering Lyapunov design approach. The motor mathematical model is considered to construct the adaptive mechanism with the assumptions of rotor speed (ωr) is regarded as fixed value. The reference model is represented as

∼ X = XTω ∼T PX = tr (ω ∼T PX T X ) 2XeT Pω r e e r r V̇ = −XeT Xe + 2tr ⎜⎛ ⎝

∼T PF ω 1 ∼T r −ωr PX T Xe ⎞⎟ K ⎠

In order to make V̇ negative the F1 is chosen as

R

ωr ⎤ Id ⎡− Id Vd 1 p⎡ ⎤ = ⎢ L ⎥ ⎡ I ⎤ + ⎡V −Ψ ω ⎤ I ⎢ q f r⎦ ⎥ ⎢ q⎦ ⎥ ⎢ q⎦ ⎥ ⎢− ωr − R ⎥ ⎣ L⎣ ⎣ L⎦ ⎣

ωṙ ̂ = F1 = KX T Xe In equilibrium condition ωr̂ = ωr and Xe = 0 The adaptive law is

R

where a = L , b = 5

1 L

(40)

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where P = PT > 0 and the solution for the Lyapunov Eq.

AmT P + PAm = −Q

(54)

The derivative V̇ is given by T ∼ ∼T ∼̇ ⎞ ⎛∼ Ȧ PAa A PAa + a V̇ = Xė T PXe + XeT PẊe + tr ⎜ a α1 α1 ⎟ ⎠ ⎝ T ∼ T ∼̇ ∼ ∼ ̇ ⎛ B PBb B PBb ⎞ ∼ + tr ⎜ b + b ,=XeT (PAm + AmT P ) Xe −2XeT PAa X α2 α2 ⎟ ⎝ ⎠ ∼T ∼T B b Pf2 ⎞ T ∼ ⎛ Aa Pf1 ∼T ∼ −2XeT PBb U + tr 2 Xe PAa X = X T Aa PXe +2 ⎜ α1 α2 ⎟ ⎝ ⎠ ∼T ∼ ∼T = tr (Aa PXe X T ) XeT PBb U = tr (B b PXe U T ) V̇ ∼ ∼ Bb Pf2 ∼T ⎞ ⎛ Aa Pf1 ∼T −Aa PXe X T + −B b PXe U T ⎟ = −XeT Xe + 2tr ⎜ α1 α2 ⎠ ⎝ ̇̂ T T ̇ where f1 = a ̂ = α1 Xe X and f2 = b = α2 Xe U

Fig. 5. MRAS structure for parameters identification.

Id Vd ⎤ −a ω Ẋ = ⎡− ω − ra ⎤ ⎡ ⎤ + b ⎡ Iq ⎥ Vq−Ψf ωr ⎥ r ⎢ ⎣ ⎦⎢ ⎣ ⎦ ⎦ ⎣

(41)

The above Eq. (41) is reference model and is represented as state space model

Ẋ = AX + BU

(42)

−a ω where A = ⎡− ω − ra ⎤,B = b r ⎣ ⎦ The adjustable model is represented as Vd ⎤ − a ̂ ωr ⎤ ⎡ Id̂ ⎤ ⎡ Id̂ ⎤ ̂⎡ p⎢ ⎥ = ⎡ ⎢ ̂ ⎥ + b ⎢Vq−Ψf ωr ⎥ ⎢− ωr − a ⎥ ̂ Iq̂ I ⎦ ⎣ ⎦⎣ q⎦ ⎣ ⎦ ⎣

(43)

X ̇ = A +B U X

(44)

pId = −aId + ωr Iq + bVd

(45)

pIq = −ωr Id−aIq + b (Vq−Ψf ωr )

(46)

̂d pId̂ = −a Î d̂ + ωr Iq̂ + b V

(47)

pIq̂ = −ωr Id̂ −a Î q̂ + b (̂ Vq−Ψf ωr )

(48)

̇ b ̂ = α2 (εd Vd + εq Vq−εq Ψf ωr )

(58)

)

Step 1: The controller design process start with the selection of input parameters to the controller i.e. sensory signal. The sensory signal (Si) is selected with Eq. (13) since the sensory signal contains x and uc are input variables. Step 2: The output of the sensory signal is processed in sensory cortex, amygdala and OFC. Firstly, the sensory signal is analyzed in sensory cortex (SC) to improve Si signal with Eq. (3). The SC signal is further processed in amygdala and in OFC for signal conditioning and to generate faster output of the controller i.e. emotional response. Step 3: The amygdala and OFC has a connection of emotional cue which is reward signal according to the required output response. The emotional cue is modeled with the Eq. (14). Step 4: Final output of the controller is based on the amygdala and OFC outputs, the amygdala (A) are designed with Eq. (5) where it is function of amygdala gain, emotional cue, sensory cortex and learning rate (α). The max term in Eq. (5) makes output of amygdala monotonic i.e. never decreasing or a high values always. Step 5: The output of A is trimmed with the help of OFC. The OFC is modeled in Eq. (6) with sensory signal, sensory cortex, emotional cue, and learning rate β. Step 6: The A and OFC signals are processed in E to generate emotional response with Eq. (10) i.e. with Eq. (58). If generated speed matches with required response of plant then process stops here otherwise goes to step1 and starts again.

(49)

= −ωr Id−aIq + (Vq−Ψf ωr ) b + ωr Id̂ + a Î q̂−b ̂(Vq−Ψf ωr ) ̂ Vq−Ψf ωr )−(a−a )̂ Iq−a ̂(Iq−Iq̂ ) = −ωr (Id−Id̂ ) + (b−b )(

̂ Vq−Ψf ωr )−(a−a )̂ Iq pεq = −ωr εd−a ε̂ q + (b−b )( (50)

(51)

The above Eq. (51) can represent in state space model as follows ∼ ∼ Ẋe = Am Xe −Aa X −Bb U (52) ∼ ∼ ̂ ̂ a Bb = b −b where Aa = a − Consider Lyapunov function

∼T ∼ ∼ ∼ ⎛ A PAa ⎞ ∼ ∼ ⎛⎜ Bb PBb ⎞⎟ V (Xe ,Aa ,Bb) = XeT PXe + tr ⎜ a + tr α1 ⎟ ⎝ α2 ⎠ ⎝ ⎠

(57)

(

= −aId + ωr Iq + Vd b + a Î d̂ −ωr Iq̂−Vd b ̂

Vd ⎤ εd −I − a ̂ ωr ⎤ εd ⎡ ⎤ + (a−a )̂ ⎡ d ⎤ + (b−b )̂ ⎡ p ⎡ε ⎤ = ⎡ I V −Ψ ω ⎥ ⎢ ⎢ ̂ ⎣ εq ⎦ ⎣ q⎦ ⎢ ⎣− q ⎥ ⎦ ⎦ ⎣ q f r⎥ ⎣− ωr − a ⎦

̂ a (0) ̂ ̂ −α1 (εd Id + εq Iq) a− = −α1 (εd Id + εq Iq) a ̂ = a (0)

Algorithm 2. To design brain emotional controller for identification of R motor parameter a ̂ = L

= −a ̂(Id−Id̂ ) + ωr (Iq−Iq̂ ) + Vd (b−b )̂ −Id (a−a )̂

p (Iq−Iq̂ )

(56)

(59) ̂ ̂ and b Λ are identified with Eqs. (57) and The motor parameters a Λ (59), where the variable gain parameters α1 and α2 are calculated using brain emotional controller strategy to speed up the adaptive mechanism.

Eq. (43) can be written as

pεd = −a ε̂ d + ωr εq + Vd (b−b )̂ −Id (a−a )̂

a ̇ ̂ = −α1 (εd Id + εq Iq)

̂ b (0) ̂ ̂ = α2 (εd Vd + εq Vq−εq Ψf ωr ) b ̂ = α2 (εd Vd + εq Vq−εq Ψf ωr ) + b (0) b−

 = ⎡− a ̂ ωr ⎤,B =b̂ where A ⎢− ωr − a ⎥ ̂ ⎣ ⎦ Eq. (40) can be written as

p (Id−Id̂ )

(55)

(53)

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Algorithm 3. To design brain emotional controller for identification of 1 motor parameter b ̂ = L

(

lesser toque ripples. In order to control rotor speed with respect to reference speed, the estimated rotor speed compared with reference speed and fed to brain emotional based speed controller. The control signal generated from speed controller is iq which is q-axis reference current value and id = 0 chosen for d-axis reference current, id and iq are processed to generate Vd and Vq signals with PI controller. Further, the current and the voltage signals are transformed with Clark and Park’s transformations for Space vector pulse width modulation technique to generate necessary gating pulses to inverter according to rotor position. The proposed brain emotional control based MRAS scheme is implemented considering the d-q axis voltages (Vd and Vq) and currents (id and iq) to estimate rotor speed and position with motor parameters identification. In the adjustable model of MRAS technique the motor parameters are not taken from the actual drive system, they are identified with adaptive mechanism and fed to the adjustable model to estimate the speed. The estimated speed and rotor position given as feedback signal to control the speed, stator phase currents and torque of PMSM drive. The brain emotional controller fed PMSM drive with adaptive mechanism is used to estimate speed and motor parameters identification. The brain emotional controller used as speed controller and in adaptive mechanism of MRAS technique for sensorless PMSM drive, which is implemented with different sensory input and emotional cue functions for adaptive mechanism and speed controller. The input of the controller is error signal which is modified as sensory signal with Eq. (11) for adaptive mechanism and with Eq. (13) for speed controller. The emotional cue is reinforce which adds the amygdala and OFC output to process appropriate emotional response signal with Eq. (12) for adaptive mechanism and with Eq. (14) for speed controller. The final output of the controller is emotional signal response (10) is processed with amygdala and OFC outputs. The amygdala (4) is modeled with gain (5), it has max term which makes the output of the amygdala always high and OFC (6) with gain value (7) trims the output of amygdala to give final output. The amygdala and OFC relations from (4)–(7) observed that two separate learning are carried out one gives amygdala very abrupt output which needs to trim further with other learning of OFC.

)

Step 1: The controller design process start with the selection of input parameters to the controller i.e. sensory signal. The sensory signal (Si) is selected with Eq. (15) since the sensory signal contains x and uc are input variables. Step 2: The output of the sensory signal is processed in sensory cortex, amygdala and OFC. Firstly, the sensory signal is analyzed in sensory cortex (SC) to improve Si signal with Eq. (3). The SC signal is further processed in amygdala and in OFC for signal conditioning and to generate faster output of the controller i.e. emotional response. Step 3: The amygdala and OFC has a connection of emotional cue which is reward signal according to the required output response. The emotional cue is modeled with the Eq. (16). Step 4: Final output of the controller is based on the amygdala and OFC outputs, the amygdala (A) are designed with Eq. (5) where it is function of amygdala gain, emotional cue, sensory cortex and learning rate (α). The max term in Eq. (5) makes output of amygdala monotonic i.e. never decreasing or a high values always. Step 5: The output of A is trimmed with the help of OFC. The OFC is modeled in Eq. (6) with sensory signal, sensory cortex, emotional cue, and learning rate β. Step 6: The A and OFC signals are processed in E to generate emotional response with Eq. (10) i.e. with Eq. (59). If generated speed matches with required response of plant then process stops here otherwise goes to step1 and starts again.

Brain emotional controller based mras technique for PMSM drive The PMSM drive in rotor flux oriented vector control scheme is chosen to implement MRAS sensorless technique. Fig. 6 shows configuration of PMSM drive, which provides better dynamic response with

Fig. 6. Block diagram of sensorless PMSM drive based on Brain Emotional Controller.

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Algorithm 4. Design of brain emotion based speed controller

currents during starting for a transient period and attains 5 A current according to the load supplied. Fig. 8 shows the observations of drive at sudden disturbance of load from 2 Nm to 5 Nm at 0.2 s, from the figures it is observed that before applying sudden disturbance of load the motor speed is constant at 300 rad/s, the rotor position also matches with actual position, when the sudden load applied at 0.2 s then disturbance in speed observed with a dip. There is deviation in rotor position when sudden load is applied. The electromagnetic torque developed settles to new value from 2 Nm to 5 Nm when load is applied at 0.2 s, the oscillations are observed during starting and no oscillations are found when sudden disturbance is applied. The stator winding currents draws 2 amps current with transient oscillations and when load is applied at 0.2 s the stator current windings draws 5 amps current without any transient variations The dynamic capability of brain emotional control based adaptive mechanism is observed in Fig. 9 by changing the speed setting from 300 rad/s to 200 rad/s at 0.2 s and applying sudden load disturbance from 2 Nm to 5 Nm at 0.4 s, Fig. 9(a) shows speed response where the estimated speed is same as that of actual speed and also traces the speed when change of speed is applied at 0.2 s with transient oscillation when change of speed is applied and when the sudden disturbance is applied at 0.4 s a small dip in speed is observed. The same observations are found for rotor position when speed setting changed at 0.2 s and at 0.4 s when sudden load disturbance is applied the small deviations in rotor position is observed. In the produced electromagnetic torque transient oscillations are found during starting and also for change in speed are applied. At 0.4 s when sudden load is applied electromagnetic torque settles to new torque without any oscillations. The stator currents response observed in Fig. 9 (d), when change of speed is applied oscillations in currents are observed at 0.2 s, when sudden disturbance is applied at 0.4 s, stator phase currents draws more current as per the load. In all the cases the motor parameters resistance and inductance are identified with the resistance as 2.857 Ω and inductor value as 8.0 mH as shown in Fig. 10.

Step 1: The design of controller starts with initiation of sensory signal function (Si) with Eq. (1). The signal is processed to thalamus to communicate with sensory cortex and amygdala. Step 2: The sensory signal is analyzed in sensory cortex (SC) with the functional Eq. (3). The SC faster the response of controller by generating appropriate signal for amygdala (A) and Orbitofrontal cortex (O). Step 3: Amygdala is designed with Eq. (5). The amygdala gain is modeled with emotional cue and learning rate (α). The max term makes in the learning Eq. makes the amygdala output always a high value. Step 4: The proper selection of emotional cue enhances the signal connection of amygdala and OFC to attain desired response. It is modeled with Eq. (18) and the signal is passed to A and OFC. Step 5: The amygdala’s response redressed by OFC learning model with Eq. (5). OFC gain is designed with EC, A, SC ad with learning rate β. Step 6: The A and OFC signals are processed in E to generate emotional response with Eq. (12). If generated emotional signal match with required response of plant then process stop here otherwise go to step1 and start again.

Results and discussions Simulation results The effectiveness of brain emotion controller for adaptive mechanism of MRAS technique for PMSM drive is firstly verified in Matlab/Simulink simulations with different tests such as constant speed, variable load and with variable speed and load. Fig. 7 shows results of PMSM drive is operated at constant speed of w = 300 rad/s with a load of 5 Nm, the estimated speed track with actual speed with small disturbances during start. The estimated and actual speed response of drive is very fast. The actual and estimated rotor positions are matched with fewer deviations. The electromagnetic torque against applied load of 5 Nm is observed in Fig. 7(c), the transient variation during start is observed and the produced torque fluctuates at 5 N m with less torque ripples. The stator winding takes high

Real-time results The simulation results are validated with real time implementation in hardware-in- loop (HIL) environment. The real time simulator

Fig. 7. Performance of PMSM drive at constant speed 300 rad/s. (a) Speed, (b) Rotor position, (c) electromagnetic torque and (d) stator phase winding currents. 8

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Fig. 8. Performance of PMSM drive at variable load at 0.2 s. (a) Speed, (b) Rotor position, (c) electromagnetic torque and (d) stator phase windings currents.

Fig. 9. Performance of PMSM drive at variable speed at 0.2 s and variable load at 0.4 s. (a) Speed, (b) Rotor position, (c) electromagnetic torque and (d) stator phase winding currents.

a) Resistance identification

b) Inductance identification

Fig. 10. Motor parameters identification. 9

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Fig. 11. Real-time set up model.

variations are found and settles new value of 5 N m when sudden load disturbance is applied. Fig. 14 shows dynamic capability of proposed technique, with variation of speed from 300 rad/s to 200 rad/s and load from 5 N m to 10 N m, in the estimated and actual speed response, similar observations are found when change in speed is applied and for change in load, a small dip in speed is found for both actual and estimated speed. The stator phase currents draw more current when load is applied for the sake of simplicity single phase current is shown. The actual and estimated rotor positions when the change in speed is applied variations are observed and there is no variation on rotor position when load is varied. In the electromagnetic torque when the speed is varied transient oscillations are observed when change in load is applied torque settles at a new value of 10 N m Fig. 15 shows identification of motor parameters resistance and inductance in real time implementation. The resistance is identified as around 2.875 Ohm and inductance as 0.008 H. The proposed brain emotional controller based MRAS sensorless technique results in offline and real time simulations shows that the estimated rotor speed and rotor position with identification of motor parameters gives almost alike response of actual responses of machine. In all test conditions, proposed estimation technique gives satisfactory performance in load disturbances with less current harmonics and torque ripples. Thus from the results brain emotional controller based MRAS sensorless control gives good performance from high speed to low speed and with variation of load.

contains Spartan 3 FPGA processor with 2.4 GHz with target computer configuration for performing parallel computations (Opal-RT). The proposed system for real time implementation set up model is shown in Fig. 11 consists of PMSM machine, MRAS technique and inverter circuit. The complete model is designed with a fixed time step of 15 µs, for every interval of time step the signal is modified. The Space vector PWM (SVPWM) technique has been used to design the switching signals of inverter. The switching signals are generated with the help of brain emotional controller based MRAS technique and speed controller. The estimated rotor speed signal is compared with the reference signal to generate control signal (Iq) which is further processed to generate switching signals for inverter. The output signals can be taken out side and is checked into oscilloscope and the same can be checked in the computer connected to target. The same tests of offline simulations are conducted in real time simulations to validate the results, Fig. 12 shows results at constant speed, in the actual and estimated speed there are some oscillations during start, the stator phase currents at starting draws high current. The rotor actual and estimated positions are matched and in electromagnetic torque there are more ripples observed compared to offline simulations. Fig. 13 shows, performance of PMSM at variable load, when the load is varied from 2 N m to 5 N m, the variations in speed response observed with oscillations in actual and estimated speed response. Accordingly, the stator phase windings draw more current when sudden load is applied. In rotor position, deviations are observed in actual and estimated signals and the produced electromagnetic torque transient

Fig. 12. Performance of PMSM drive at constant speed. (a) Actual Speed, (b) Estimated speed, (c) stator phase windings currents, (d) Actual Rotor position, (e) estimated rotor position and (f) electromagnetic torque. 10

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Fig. 13. Performance of PMSM drive at variable load. (a) Actual Speed, (b) Estimated speed, (c) stator phase windings currents, (d) Actual Rotor position, (e) estimated rotor position and (f) electromagnetic torque.

Fig. 14. Performance of PMSM drive at variable speed and variable load. (a) Actual Speed, (b) Estimated speed, (c) stator phase winding currents, (d) Actual Rotor position, (e) estimated rotor position and (f) electromagnetic torque.

a) Resistance identification

b) Inductance identification

Fig. 15. Real-time Motor parameters identification.

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Conclusions

actual speed and rotor position. The gains in brain emotional controller attribute for dynamic performances in all test conditions of drive.

This paper proposed a new intelligent technique for sensorless control of drive with MRAS technique based on brain emotional controller with parameters identification. Lyapunov design approach is followed to find the effective adaptive mechanism with brain emotional controller strategy for sensorless PMSM drive to estimate rotor speed and rotor position with motor parameters identification. The effectiveness of proposed controller has been verified successfully in real time against to offline simulations. In all test conditions applied on the drive, estimated speed and rotor position gives performances similar to

Acknowledgements The authors would like to thank Department of Science and Technology (DST) under CSRI Grant No. SR/CSRI/132/2013(G) and All India Council for Technical Education (AICTE) under AICTE Project-33 for their support to carry out this work and also Jawaharlal Nehru Technological University Hyderabad for providing facilities.

Appendix A See Table 1. Table 1 Specifications of PMSM. Rated power Rated speed No. poles Stator resistance Flux linkage Stator inductance Inertia Friction coefficient

200 W 300 rad/s 8 2.85 Ω 0.1584 Wb 8 mH 8e−4 kg m2 1.0e−4 NM-S

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