1 Introduction

Modern automatic AC motor control systems currently competing with DTC [1] are commonly used. The DTC of the induction motor gives a good transient and steady state of operation. In DTC, the control mechanism is defined by means of torque and flux. However, the use of inverter modulation induces steady-state torque pulsations, which in turn raises the speed of noise. The other drawbacks to DTC are the complexity of controlling low speeds, high noise and also the absense of direct current control. The DTC approach was first proposed by I. Takahashi and T. Nouguchi [1] in the 1980s, and the authors concluded that DTC has a much lower control structure, is stable and provides fast dynamic response. The authors have explored various DTC control strategies [2]. A new strategy Space Vector Modulation (SVM) technique in DTC combines inverter hysteresis mode switching with dwell time-based switching. DTC-SVM operates at constant switching freequency [3]. A sensorless control increases the overall efficiency of the induction motor in terms of reducing complexity, hardware costs, increased robustness and productive speed. Flux estimators provide good efficiency at very low speed or zero speed  to high speed [4].

For the estimation  of the rotor speed of the IM drive [5], the MRAS with the Flux Observer is adapted. The estimation  of the observer's stator and rotor flux used as a reference method in the MRAS technique is very effective. The stator current and the calculation of the fluxes of the stator and rotor are two models used for the adaptive mechanism of the speed of the rotor. The usage of such a sensorless flux observer as a reference model in the MRAS method in this paper has resulted in sensitivity to parameter variations, simple and stable. The DTC-SVM-dependent IM drive is unreliable due to abrupt speed fluctuations, parameter variations and load disruptions influencing the speed of the rotor. The IM drive, therefore, requires a controller that reacts easily, accurately and precisely to all operating conditions [6]. Widespread focus on artificial and digital intelligent control methods, e.g. fuzzy logic controllers (FLCs), particle optimisation techniques, genetic algorithms, neural networks, etc. [7, 8], is applied throughout the design of speed controllers. They exhibit strong dynamic reaction, but in realistic implementations, they infuse architecture complexity and need the rapid processing of digital signal processors to conduct several controller computations [9]. Fuzzy logic controller (FLC) and neural network training need a broad data collection of parameters as the difficulty of computing grows [10, 11]. Wide testing data sets are needed to update the weight of the hybrid controllers.

In this paper, the BEIC, which is used as a speed controller, is suggested to address the drawbacks of current controllers, such as interface difficulty and quick reaction in the disrupted environment [12,13,14,15]. Lucas launched the BEIC in 2004 [16] and it was applied for the PMSM drive by M.A. Rahman [17]. Over the past year, this system has been used for a variety of modern control unit applications. The BEIC has been used to date in many industrial applications, including control plant applications [18, 19], aerospace launch vehicles [20], washing machines [21] and micro heat exchangers [22]. The BEIC configuration includes sensory input signals and emotional signals or rewards a feature that creates emotional signals. To minimise the torque ripples, to reduce the harmonics in the stator process of the winding and to obtain a quick reaction time of the speed signal, the emotional and sensory signals used have been changed and related to the IM drive. The findings obtained were related to the existing PI and FLC. Experimental work is done using an Op-RTDS (Real-Time Digital Simulator) in a hardware-in-loop process [23,24,25].

2 Architecture and advancement of brain emotional intelligent controller (BEIC) scheme

The formulation of the emotional intelligent controller of the bio-inspired brain is close to the configuration of the mammalian brain [12] as a consequence of the emotional reaction to the real activity of the mammalian brain. The purpose of the limbic brain is to generate emotions with related components, particularly thalamus, amygdala, orbitofrontal cortex and sensory cortex. Intelligent emotional reaction is very fast in decision-making relative to traditional controls. Thalamus is a component of the brain responsible for sensing and focusing on input from our senses and all the information that goes back and forth to the cortex. It plays a crucial function in feeling, alertness and memory.  A poor pre-processing of sensory feedback signals such as noise reduction or filtering may be achieved in the thalamus. The thalamus portion prepares the requisite sensory cortex inputs to be subdivided and differentiated. Amygdale is an almond-shaped brain formation with two amygdale’s located in the hippocampus towards the front of the temporal lobe. Amygdale is important to many feelings, learning and memory. Active specifically in the production of apprehension and anxiety in the decision-making phase, the orbital cortex plays a crucial function in the relationship with amygdala. The sensory cortex in the outermost layer of the brain senses the input and is isolated into two sensory cortexes, in particular the primary sensory cortex (PSC) and the secondary sensory cortex (SSC). PSC senses impulses from the muscles and prevents the operation of the neuronal signals. The details shall be submitted to the SSC and recorded to the part where the action is to be taken. Centred on the mechanism, Fig. 1 shows the process of BEIC.

Fig. 1
figure 1

Structure of BEIC

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In this paper, the torque ripple is assumed to be high and thus the speed regulation is decreased based on the error of the torque. The other roles are the rpm of the motor and the  estimated reference torque. Any of these signals are seen as negative feedback of the system. The proposed controller is equipped with sensory inputs Si, i = 1,…n and a single output. For each sensory  input (Si) there are two states in the brain's intelligent emotional controller, one connected to the orbitofrontal cortex output, OCt, and the other to the amygdala output, At components adorned in Fig. 1. Sensory signal (Si) is known to be a function, f. It includes error (e), plant output (zp) and controller output (Zc) represented as follows:

$$S_{i} = {\text{f}}(e,z_{{\text{p}}} ,z_{{\text{c}}} )$$
(1)
$$f = K_{1} .e + K_{2} .z_{{\text{p}}} + K_{3} .\int {z_{{\text{c}}} {\text{d}}t}$$
(2)

where K1, K2 and K3 are the sensory gains, and these are tuned in the experimentation premise. The sensory signal Si) is sent to the sensory cortex (SCt) and Amygdala it only the output of thalamus.

$${\text{SC}}_{t} = g(S_{i} )$$
(3)
$$g\left( {s_{i} } \right) = e^{{s_{i} }}$$
(4)

At and OCt, outputs are given by

$$A_{t} = V_{t} S_{i}$$
(5)

where Vt is the gain of At

$$\Delta V_{{\text{t}}} = \alpha \max \left({0},{\it {EC}} - {\it A}_{t(t - 1)} \right){\it {SC}}_{t}$$
(6)
$$V_{t} (t + 1) = V_{t} (t) + \Delta V_{i}$$

The orbitofrontal cortex output is expressed as

$${\text{OC}}_{t} = W_{t} S_{i}$$
(7)

where Wt is the gain of OCt

The At and OCt, learning process passes through the internal weight update

$$\Delta W_{t} = \beta \left( {E^{t(t - 1)} - {\text{EC}}} \right){\text{SC}}_{t}$$
(8)

where \(E^{t(t - 1)} = A_{{\text{t}}} (t - 1) - O_{{\text{t}}} (t - 1)\).

In the above, Δ symbol represents the variations in weights. α and β are the learning rates of At and OCt,.

The reward signal can be derived with function h as

$${\text{EC}} = h(e,\;Z_{p} ,\;Z_{c} )$$
(9)
$$H = K_{1} .e + K_{2} .\left| {e.z_{c} } \right| + K_{3} .z_{p}$$
(10)

EC has K1, K2 and K3 gains.

Over these components, the emotional signal output, Et, is obtained as the contrast between inhibitory Orbitofrontal Cortex and excitatory Amygdala nodal outputs as follows:

$$E^{t} = \sum {A_{t} - \sum {{\text{OC}}_{t} } }$$
(11)

The total derived emotional signal is expressed as

$$E = A - O$$
(12)

E is the resultant emotional signal of the controller.

The flowchart to design the brain emotional controller is shown in Fig. 2 [28] the design process of the controller is for control of DTC-SVM based IM drive.

Fig. 2
figure 2

Flow chart to design brain emotional intelligent controller

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3 MRAS speed  estimation for IM drive

Given the fact that a few schemes are accessible for the sensorless processing of IM drives, the MRAS is the mainstream and favoured scheme due to its easy execution and good performance. The model reference method takes advantage of the usage of multiple constructs to approximate the same state variables. It consists of a reference model (RM), an adjustable model or an adaptive mechanism (AM). RM will not depend on the speed of the rotor and AM will depend on the speed of the rotor. Both equations are used to measure state variables. The adaptive mechanism is used to produce the estimated speed Wr which is guided by an error between the measured state variables and the estimated state variables (Fig. 3).

Fig. 3
figure 3

MRAS estimator block diagram

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The outputs of RM and AM characterised by Ψr(1) and Ψr(2) are estimates the rotor flux space vector in stationary reference frame. The motor equations are (13), (14) by allowing the reference frame speed is stationary i.e. Wr = 0.

$$\underline{u}_{sn} = R_{s} \underline{i}_{s} + \frac{{{\text{d}}\underline{\psi }_{s} }}{{{\text{d}}t}}$$
(13)
$$0 = R_{{\text{r}}} \underline{i}_{{\text{r}}} + \frac{{{\text{d}}\underline{\psi }_{{\text{r}}} }}{{{\text{d}}t}} - j\omega_{{\text{r}}} \underline{\psi }_{{\text{r}}}$$
(14)

where Usn is the voltage vector.

The extraction of the rotor current and stator flux gives the estimation of the rotor flux.

$$\frac{{{\text{d}}\underline{{\psi_{{\text{r}}} }} }}{{{\text{d}}t}} = \frac{{L_{r} }}{{L_{m} }}\left[ {\underline{{v_{s} }} - R_{s} \underline{{i_{{\text{s}}} }} - \sigma L_{s} \frac{{{\text{d}}\underline{{i_{{\text{s}}} }} }}{{{\text{d}}t}}} \right]$$
(15)
$$\frac{{{\text{d}}\underline{\psi }_{{\text{r}}} }}{{{\text{d}}t}} = \left[ { - \frac{1}{{T_{{\text{r}}} }} + j\omega_{r} } \right]\underline{\psi }_{{\text{r}}} + \frac{{L_{m} }}{{T_{{\text{r}}} }}\underline{i}_{{\text{s}}}$$
(16)

where \(\sigma = 1 - ({{L_{m}^{2} } \mathord{\left/ {\vphantom {{L_{m}^{2} } {L_{s} L_{r} )}}} \right. \kern-\nulldelimiterspace} {L_{s} L_{r} )}}\), is,ir are the current vectors of stator and rotor, and Tr is the rotor time constant. Eq. (15) is utilised to compute the rotor flux vector based on the measured stator current and command voltage (or processed utilising PWM vectors) and is independent of the rotor speed, in this manner it might speak to the RM as shown in Fig. 3. Then again, in subsequent Eq. (16) requires stator currents and is dependent on the rotor speed. Eq. (16) represents the AM of Fig. 3.

The reference and adjustable model Eqs. (15, 16) represented in the form of matrix appear as

$$p\left[ {\begin{array}{*{20}c} {\psi_{{{\text{r}}^{x} }} } \\ {\psi_{{{\text{r}}^{y} }} } \\ \end{array} } \right] = \frac{{L_{r} }}{{L_{m} }}\left[ {\left[ {\begin{array}{*{20}c} {u_{{sn^{x} }} } \\ {u_{{sn^{y} }} } \\ \end{array} } \right] - \left[ {\begin{array}{*{20}c} {(R_{s} + \sigma L_{s} \rho )} & 0 \\ 0 & {(R_{s} + \sigma L_{s} \rho )} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {i_{\alpha s} } \\ {i_{\beta s} } \\ \end{array} } \right]} \right]$$
(17)
$$p\left[ {\begin{array}{*{20}c} {\psi_{{{\text{r}}^{x} }} } \\ {\psi_{{{\text{r}}^{y} }} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} { - \frac{1}{{T_{{\text{r}}} }}} & { - \omega_{r} } \\ {\omega_{{\text{r}}} } & { - \frac{1}{{T_{{\text{r}}} }}} \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\psi_{{{\text{r}}^{x} }} } \\ {\psi_{{{\text{r}}^{y} }} } \\ \end{array} } \right] + \frac{{L_{m} }}{{T_{{\text{r}}} }}\left[ {\begin{array}{*{20}c} {i_{\alpha s} } \\ {i_{\beta s} } \\ \end{array} } \right]$$
(18)

where \(p = \frac{{\text{d}}}{{{\text{d}}t}}\). The difference between the two rotor flux space vectors is used as speed tuning signal (error signal), which is tuned by an adaptation mechanism, results the estimated value of rotor speed and adaptive model of the error be less, gives better behaviour of the drive.

$$\omega^{{{\text{Esti}}}} = K_{p} \varepsilon + K_{i} \int {\varepsilon {\text{d}}t}$$
(19)

PI controller input is

$$\varepsilon = \psi_{{{\text{r}}^{y} }}^{(1)} \psi_{{{\text{r}}^{x} }}^{(2)} - \psi_{{{\text{r}}^{x} }}^{(1)} \psi_{{{\text{r}}^{y} }}^{(2)}$$
(20)

The PI controller parameters are Kp and Ki.

3.1 Reference  model

The estimation of stator currents for the reference model is shown by the accompanying conditions

$$\hat{i}_{s}^{x} = \frac{1}{{\sigma L_{s} }}\left( {\hat{\Psi }_{s}^{x} - K_{r} \hat{\Psi }_{r}^{x} } \right)$$
(21)
$$\hat{i}_{s}^{x} = \frac{1}{{\sigma L_{s} }}\left( {\hat{\psi }_{s}^{y} - K_{r} \hat{\psi }_{r}^{y} } \right)$$
(22)

The reference model is used and furthermore utilised for other variable estimation. The speed estimation of the adaptive observer is illustrated by the accompanying conditions

$$\frac{{{\text{d}}\hat{\psi }_{r}^{x} }}{{{\text{d}}t}} = - \frac{1}{{T_{{\text{r}}} }}\hat{\psi }_{r}^{x} - \hat{\omega }_{r} \hat{\psi }_{{\text{r}}}^{y} + \frac{{L_{m} }}{{T_{{\text{r}}} }}i_{{{\text{s}}^{x} }}$$
(23)
$$\frac{{{\text{d}}\hat{\psi }_{r}^{y} }}{{{\text{d}}t}} = - \frac{1}{{T_{{\text{r}}} }}\hat{\psi }_{r}^{y} - \hat{\omega }_{r} \hat{\psi } + \frac{{L_{m} }}{{T_{{\text{r}}} }}i_{{{\text{s}}^{y} }}$$
(24)

4 Modelling of induction motor (IM)

It is referred to a stationary reference frame used in the DTC strategy [17]. The stator flux is estimated in the real time at each sampling period ts. The discrete form of d, q components of stator flux and actual stator flux at each sampling period is shown in (25), (26), (27).

$$\psi_{ds} (k + 1) = \psi_{ds} \left( k \right) - t_{{\text{s}}} R_{{\text{s}}} i_{ds} \left( k \right) + t_{{\text{s}}} V_{ds} \left( k \right)$$
(25)
$$\psi_{qs} (k + 1) = \psi_{qs} (k) - t_{{\text{s}}} R_{{\text{s}}} i_{qs} (k) + t_{{\text{s}}} V_{qs} (k)$$
(26)
$$\psi_{{\text{s}}} (k + 1) = \sqrt {\psi_{ds}^{2} (k + 1) + \psi_{qs}^{2} (k + 1)}$$
(27)

In real-time implementation, \(\psi_{ds} (k + 1)\) and \(\psi_{qs} (k + 1)\) are estimated by the pure integrator. It causes integration drift and detuning effect. This low pass filter causes a problem of self-starting of the drive. The self-starting of drive is accomplished by using stator flux equations at stand-still are to be computed, therefore the standstill flux equations shown in (28), (29) are used up to the motor starts rotating and then the current model of the flux (25), (26), (27) is used.

$$\psi_{ds} (k + 1) = \psi_{ds} (k) - \sigma L_{{\text{s}}} i_{ds} (k) + \frac{{L_{m} }}{{L_{r} }}\psi_{dr} (k)$$
(28)
$$\psi_{qs} (k + 1) = \psi_{qs} (k) - \sigma L_{{\text{s}}} i_{qs} (k) + \frac{{L_{m} }}{Lr}\psi_{qr} (k)$$
(29)

where \(\sigma = 1 - ({{L_{m}^{2} } \mathord{\left/ {\vphantom {{L_{m}^{2} } {L_{s} L_{r} )}}} \right. \kern-\nulldelimiterspace} {L_{s} L_{r} )}}\).

The torque developed in the induction motor is expressed in (30), (31)

$$T_{e} = \frac{3}{2}\left( \frac{p}{2} \right)\frac{{L_{m} }}{{L_{r} L_{s} }}\left( {\psi_{{\text{s}}} } \right. \times \left. {\psi_{{\text{r}}} } \right)$$
(30)

The torque of the motor is estimated as

$$T_{e} (k + 1) = T_{e} (k) - \frac{3p}{4}\left( {\psi_{ds} (k)} \right.i_{qs} (k) - \left. {\psi_{qs} (k)i_{ds} (k)} \right)$$
(31)

5 Existing control schemes

  1. (i)

    PI controller The controller is designed for adjusting the speed control of IM drive to the given command speed. A variety of methods, such as the Ziegler-Nichols process, the trial-and-error method and the evolutionary techniques-based searching, can be used to pick the PI controller parameters Kp and Ki. The design of the PI controller includes a system speed loop that is illustrated by standardising the adjustments. The gain values Kp and Ki are determined by substituting the motor parameters ("Appendix") for the Final Transfer function. These gain values are calibrated on the trial-and-error basis, and the gain values are Kp  = 0.004 and Ki  = 0.08.

  2. (ii)

    Fuzzy Logic Controller (FLC) In terms of the proper formulation of the basic rule and the behaviour of the method under various operating circumstances, FLC is outlined as a linguistic mapping. Fuzzy input variables are to be considered as “error”, “change in error” and fuzzy output variables are quantized in lexical terms. By utilising the inference mechanism, fuzzy variables are processed on the basis of the set of rules in the table (5 × 5) as seen in Table 1. The Triangular Membership Function is selected to set the rules. The FLC rules for controlling the speed of the motor are set out in Table 1.

Table 1 Fuzzy associative memory matrix
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6 Simulation results, real-time simulations and hardware experiment verifications

The block diagram of the closed loop IM with the BEIC is shown in Fig. 4. The effects of the BEIC simulation are checked, and the results of the proposed control scheme are confirmed and correlated with the existing PI and FLC. A fractional h.p induction motor is used for simulation and experimental works. The parameters are shown in Appendix 1. Controller gains of DTC are tuned on trial-and-error basis.

Fig. 4
figure 4

Block diagram of IM with BEIC

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7 Offline Simulations

From the  figures shown in Fig. 5a–c,  the BEIC settles to command speed smoothly and rapidly without oscillations, whilst the PI and the FLC achieve command speeds with transient oscillations. The peak overshoot is also noticed. The speed reaction shown in Fig. 5a–c explicitly demonstrates that the speed response time of the BEIC IM drive is relatively much  lower to change the command speed 157 rad/s without peak overshoot and transient  oscillations. This technique confers on-load speed of 4.0 rad/s. The motor speed achieves its steady state with a fixed period of 0.18 s, and the set time of the fuzzy and PI controls is 0.24 s and 0.28 s, respectively. Variation of the stator phase current is detected by the Total Harmonic Distortion (THD) calculation, the BEIC gives THD of 7.35% and THD of 11.23% and THD of the FLC and Pl phase controller currents of 14.84%, respectively. The torque response to this strategy is shown in Fig. 5a-1, b-1, c-1. The Tmax and Tmin points are set at a period similar to the simulation time of 1 s at which the SVM DTC-based BEIC torque ripple is calculated.

Fig. 5
figure 5

Simulation results of IM drive with constant speed of 157 rad/s and sudden load disturbances of 0.36 N-m at 0.8 s (a) speed response with BEIC-based SVM DTC:(a-1) torque response with BEIC-based SVM DTC (a-2) Zoomed in torque response of BEIC-based SVM DTC (b) speed response with fuzzy-based SVM DTC: (b-1)torque response with fuzzy-based SVM DTC (b-2) Zoomed in torque response of fuzzy-based SVM DTC strategy (c) speed response with PI controller-based SVM DTC: (c-1) torque response with PI-based SVM DTC, (c-2) Zoomed in torque response with PI-based SVM DTC. Simulation results of IM drive with different speed tracking (0–50–100–200–300) rad/s (d) speed response with BEIC-based SVM DTC (d-1) speed response with fuzzy-based SVM DTC (d-2) speed response with PI-based SVM DTC

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Referring to the response of the torque ripple for three sets of data tips are taken as shown in Fig. 5a-2, b-2, c-2. The torque ripple (%\(\Delta T\)) is calculated by the averaging method as expressed in (32).

$$\% \Delta {\rm T} = \frac{1}{N}\left[ {\frac{{T_{{{\text{max}}1}} - T_{\min 1} }}{{T_{L} }} + \frac{{T_{\max 2} - T_{\min 2} }}{{T_{L} }} + ... + \frac{{T_{\max N} - T_{\min N} }}{{T_{L} }} - } \right] \times 100$$
(32)

N is the number of data tips, in the SVM strategy. The speed of IM is tracking with command speed values 50–150–250–300 rad/s at the time of intervals 0–1–2–3–4 s as shown in Fig. 5d, d-1, d-2 for BEIC, FLC and PI Controller. Figure 6a–c shows the simulation waveforms of D-Q axis flux of BEIC, fuzzy and PI controlled sensorless IM. Figure 6a-1, b-1, c-1 shows the estimated stator flux and Fig. 6a-2, b-2, c-2 shows the three phase currents; from these wave forms, it is observed that flux ripples reduced and the three phase currents obtained less fluctuations by using BEIC when compared with other controllers fuzzy and PI.

Fig. 6
figure 6

Simulation results of IM drive with constant speed of 157 rad/s and sudden load disturbances of 0.36 N-m at 0.8 s (a) d-q axis stator flux locus with BEIC-based SVM DTC: (a-1) stator flux with BEIC-based SVM DTC, (a-2) three phase currents (b) d-q axis stator flux locus with fuzzy-based SVM DTC, (b-1) stator flux with fuzzy-based SVM DTC, (b-2) three phase currents (c) d-q axis stator flux locus with PI-based SVM DTC: (c-1) stator flux with PI-based SVM DTC, (c-2) three phase currents

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7.1 Real-time simulations

The drive is performed at the command or reference  speed of 157 rad/s with change in load of 0.36 N-m and is added to the IM drive to observe the speed, torque and current harmonic distortion responses of BEIC. The speed of the three controllers is observed, as shown in Fig. 7a–c in a simulator in real time. The BEIC speed setting period is far smaller than the other two controllers at the command speed of 157 rad/s. The reaction of the torque is shown in Fig. 7a-1, b-1, c-1, respectively. It can be inferred from the statistics that torque ripples are often minimised with the usage of BEIC. The response of the torque ripple for three sets of data tips is taken as shown in Fig. 7a-2, b-2, c-2. IM speed tracks with command speed values of 50–150–250–300 rad/s at interval periods of 0–1–2–3–4 s as shown in Fig. 7d, d-1, d-2 for BEIC, FLC and PI Controllers. Figure 8a–c displays the D-Q axis flux waveforms of the BEIC, fuzzy and PI-regulated sensorless IM in real-time simulations (OP-RTDS). Figure 8a-1, b-1, c-1 displays the approximate stator flux, and Fig. 8a-2, b-2, c-2 shows three phase currents from these waveforms, it is found that the flux ripples are diminished, and the three phase currents are reduced with the usage of BEIC as opposed to other FLC and PI controllers.

Fig. 7
figure 7

Real-time results of IM drive with constant speed of 157 rad/s and sudden load disturbances of 0.36 N-m  at 0.8 s (a) speed response with BEIC-based SVM DTC: (a-1) torque response with BEIC-based SVM DTC (a-2) Zoomed in torque response of BEIC-based SVM DTC (b) speed response with fuzzy-based SVMDTC: (b-1) torque response with fuzzy-based SVM DTC (b-2) Zoomed in torque response of fuzzy-based SVM DTC (c) speed response with PI-based SVMDTC: (c-1) torque response with PI controller-based SVM DTC, (c-2) Zoomed in torque response with PI-based SVM DTC. Real-time results of IM drive with different speed tracking (0–50–100–200–300) rad/s (d) speed response with BEIC-based SVM DTC (d-1) speed response with fuzzy-based SVM DTC (d-2) speed response with PI-based SVM DTC.

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Fig. 8
figure 8

Real-time results of IM drive with constant speed of 157 rad/s and sudden load disturbances of 0.36 N-m  at 0.8 s (a) d-q axis stator flux locus with BEIC-based SVM DTC: (a-1) stator flux with BEIC-based SVM DTC, (a-2) three phase currents (b) d-q axis stator flux locus with fuzzy-based SVM DTC (b-1) stator flux with fuzzy-based SVM DTC, (b-2) three phase currents (c) d-q axis stator flux locus with PI-based SVM DTC: (c-1) stator flux with PI-based SVM DTC, (c-2) three phase currents

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The correlation tables are structured. Table 2 provides the speed settling time of the IM in offline mode and OP-RTDS. The observation of Table 2 illustrates that the speed settling time of BEIC-based IM in (OP-RTDS) simulator is 0.22 s against the offline simulation time 0.18 s.

Table 2 Speed settling time of various controllers of constant speed at 157 rad/s
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Table 3 shows the torque response of BEIC, FLC and PI control of IM in offline and (OP-RTDS) simulator. The BEIC gives less torque ripples, i.e. 9.98 in simulation and 12.6% in (OP-RTDS) simulator.

Table 3 Comparison of torque response characteristics
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In Table 4, the phase current THD of BEIC is 8.89% and 7.35% at OP-RTDS and offline, respectively, as against the fuzzy logic controller at 13.09% and 11.23% and for PI controller at 17.02% and 14.84%. From Figs. 5, 6, 7, 8 and Tables 2, 3, 4, it can be concluded that BEIC offers better performance in all applications.

Table 4 Comparison of current harmonics distortion
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8 Experimental results

Experimental testing on the BEIC by a motor-driven induction motor is carried out in the OPAL-RT (Op-RTDS) digital hardware simulator in real time. It includes the Spartan 3 FPGA 2.4 GHz cpu. The method of closed loop access between plant algorithms and control algorithms is referred to as rapid control prototyping (RCP) [26, 27]. Complexities in fast-processing microcontrollers and digital signal processors (DSPs) are removed by utilising an RCP-based experimental configuration and creating a reconfigurable basis for validating control strategies. The DTC signals from the mathematical simulation model and the plant control signals are accessed via HIL. In real time, general purpose Op-RTDS input/output (I/O) data acquisition modules access analogue and digital signals in RCP experimental configuration. Figure 9a displays the diagrammatic representation of the RCP-based Op-RTDS configuration for the IM drive. Op-RTDS executes real-time executions with an improvement pace of 100 MHz and performs PWM operations. The further activity of OP5142 is the generation of real-time digital events and time stamped operations to make it appropriate for high-precision PWM, switching signals to plant operations, even if high switching frequency is needed for the inverter. The OP5142 FPGA card transforms soft-line computed PWM signals to power signals in real time. The Op-RTDS has a multi-core capacity PC. Simulink.mdl computations are performed in each of these cores. Op-RTDS and host PC are connected in hand-shaking mode as shown in Fig. 9a. The experimental photograph is displayed in Fig. 9b of the document.

Fig. 9
figure 9

a Diagrammatic representation of the RCP-based Op-RTDS setup for induction motor drive b Experimental photograph

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Control methods are built in real time using the Simulink/Matlab block sets in the OP-RTDS simulator. The final model is obtained by using OPAL-RT, library and RT cases, along with the Simulink Library modules. The proposed Matlab model comprises an induction motor, a controller and an inverter. This has to be proven in the simulator by partitioning into two subsystems, the master and the console. The signal that takes the activity to real time is produced with each time interval. The planned induction motor drivers are run in real time.

Figure 10 shows the experimental results of speed and torque of proposed BEIC-based IM drive with constant speed of 157 rad/s. The load torque TL = 0.36 N-m  is applied on the DC generator connected with suitable number of lamps.

Fig. 10
figure 10

Performance of DTC-based sensorless control of IM drive using different controllers in experimental results (OP-RTDS) with constant speed of 157 rad/s and applied load of 0.36 N-m  a speed and torque responses of BEIC-based SVM DTC, b d-q axes flux and stator flux of BEIC-based IM drive, c speed and torque of fuzzy-based IM drive, d d-q axes flux and stator flux of fuzzy-based IM drive, e speed and torque of PI-based SVM DTC, f d-q axes flux and stator flux of PI-based IM drive

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In this experimental analysis, switching frequency fs = 19 kHz and real-time step of Ts = 4 μs are chosen. Figure 10a illustrates the zoomed in response of speed and torque of the BEIC-based IM drive under loaded condition. By using outgoing channels of op-RTDS, the speed and torque magnitude are measured in terms of voltage.

The actual torque ripple corresponding to this 60mv, which is calculated by using (32), is equal to 9.98% under loaded condition. From Fig. 10a, the voltage corresponding to the droop in speed is equal to 3.4 V on 1:10 scale. Then, the actual speed droop is 3.4 × 10 = 34 rad/s. The experimental stator flux and D-Q axis flux response are illustrated in Fig. 10b–c shows the experimental speed and torque results of fuzzy logic control-based SVM DTC under dynamic load conditions, it is noticed that the speed droop is 4.3 V and it corresponds to speed drop of 43 rad/s. Torque ripple voltage in this strategy is 100 mV and its equivalent steady-state torque ripple is equal to be 12.26% and the experimental stator flux and D-Q axis flux response for the same is illustrated in Fig. 10d. The experimental speed and torque are observed. From Fig. 10e, the voltage corresponding to the droop in speed is equal to 4.9 V. Then, the actual speed droop is 49 rad/s. Torque ripple voltage in this strategy is 120 mV, and its equivalent steady-state torque ripple is found to be 15.6% for the PI Control-based IM and is shown in Fig. 10e and the experimental stator flux and D-Q axis flux response for the same strategy are observed in Fig. 10f. Comparison of the BEIC, FLC and PI controllers is tabulated in Table5.

Table 5 Comparison of experimental results
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9 Conclusions

In this paper, the BEIC was effectively executed in OP-RTDS loop hardware (HIL) for SVM DTC-based IM drive under different test conditions, and the execution of the drive is analysed. The BEIC controller achieves dynamic efficiency in terms of less time-settling without any decreased peak over-shoots, a decrease in stator phase current harmonics and a reduction in electromagnetic torque, and the BEIC provides improved results compared with the eisting controllers, i.e. FLC and PI controllers. This makes BEIC excellent robustness, fast auto-learning, powerful and  easily adapted.