FPGA-Based Custom Hardware-in-the-Loop Emulation of High-Power Induction Motor Drives with Sub-Microsecond Resolution Using NI LabVIEW FPGA

Figure 3 illustrates a three-phase full bridge diode rectifier (Zamiri et al., 2022) that generates a pulsating DC voltage with a six-pulse ripple (Lander, 1993). To reduce this ripple and improve DC output quality, filtering techniques such as RC circuits are used. The resulting capacitor voltage, known as the DC-link voltage, provides the DC power for the inverter stage, which drives the induction motor’s stator windings.

Figure 3.

Three phase diode rectifier circuit topology.

The DC-link voltage is calculated using the following equations, derived from the equivalent circuit of the diode rectifier.

(1) dVdcdt=1Cd[(VinR−VdcR−iload)] {{d{V_{dc}}} \over {dt}} = {1 \over {{C_d}}}\left[ {\left( {{{{V_{in}}} \over R} - {{{V_{dc}}} \over R} - {i_{load}}} \right)} \right]

Eq. (1) describes the pulsating DC voltage (V_in) at the rectifier output. R represents the total resistance of the DC-link, including the capacitor and the two diodes conducting at each moment. The load current, initially labelled i_load, is later redefined as i_in in part (B).

Figure 4 presents the schematic diagram of the VSI under investigation. A switching frequency of 5.7 kHz was employed in this study. Additional switching frequency and time-step conditions are analysed later in the experimental section. The following equations describe the input-output relationship, derived from the system’s transfer function (TF) and considering dependent and independent variables (Byoung-Kuk and Ehsani, 2001), (2) [vab,vbc,vca]=TF⋅Vdc \left[ {{v_{ab}},\;{v_{bc}},{v_{ca}}} \right] = TF \cdot {V_{dc}} (3) Iin=TF⋅[Ia,Ib,Ic]T {I_{in}} = TF \cdot {[{I_a},\;{I_b},{I_c}]^T} (4) TF=[SF1,SF2] TF = \left[ {S{F_1},S{F_2}} \right]

Figure 4.

Circuit configuration of the presented VSI. VSI, voltage source inverter.

The control logic embedded in the FPGA of the control board dictates the switching functions (SF_x) of the HIL system. This control logic produces gate signals that drive the switches of the stator-side VSI. Consequently, the output voltages of the rotor-side VSI, namely V_ao, V_bo and V_co, can be represented as: (5) Vao=(Vdc2⋅SF1−a)+Lon⋅d(ia⋅SF2−a)dt−(Ron⋅(ia⋅SF2−a)+Vf)Vbo=(Vdc2⋅SF1−b)+Lon⋅d(ib⋅SF2−b)dt−(Ron⋅(ib⋅SF2−b)+Vf)Vco=(Vdc2⋅SF1−c)+Lon⋅d(ic⋅SF2−c)dt−(Ron⋅(ic⋅SF2−c)+Vf) \matrix{ {{V_{ao}} = \left( {{{{V_{dc}}} \over 2} \cdot S{F_{1 - a}}} \right) + {L_{on}} \cdot {{d\left( {{i_a} \cdot S{F_{2 - a}}} \right)} \over {dt}} - \left( {{R_{on}} \cdot \left( {{i_a} \cdot S{F_{2 - a}}} \right) + {V_f}} \right)} \hfill \cr {{V_{bo}} = \left( {{{{V_{dc}}} \over 2} \cdot S{F_{1 - b}}} \right) + {L_{on}} \cdot {{d\left( {{i_b} \cdot S{F_{2 - b}}} \right)} \over {dt}} - \left( {{R_{on}} \cdot \left( {{i_b} \cdot S{F_{2 - b}}} \right) + {V_f}} \right)} \hfill \cr {{V_{co}} = \left( {{{{V_{dc}}} \over 2} \cdot S{F_{1 - c}}} \right) + {L_{on}} \cdot {{d\left( {{i_c} \cdot S{F_{2 - c}}} \right)} \over {dt}} - \left( {{R_{on}} \cdot \left( {{i_c} \cdot S{F_{2 - c}}} \right) + {V_f}} \right)} \hfill \cr }

This paper utilises signals SF₁ (+1 and −1 depending on the switch state in each leg (a, b, c) and SF₂ (+1 and 0 represent the voltage across the switching devices) acquired from the control board’s digital I/Os (IGBT Gate Signals). They combined a non-ideal Insulated Gate Bipolar Transistor (IGBT) switch model that encompasses the output voltages V_ao, V_bo, and V_co, which are subsequently used to derive the inverter’s line-to-line and phase voltages. By incorporating load currents, the switch currents are determined. The on-state resistance (R_on) and inductance (L_on) of the utilised IGBTs are considered, along with Vf and the forward voltage drop of the internal diode within the IGBT.

Given the system’s operation at low frequencies with rapid sampling, the Euler method provides sufficient accuracy, as established in studies on equation discretisation (Comanescu, 2012). Consequently, the forward Euler method was implemented to approximate the current’s rate of change, a critical factor in load control. This choice simplifies the process, avoiding the complexities of more advanced techniques such as zero-order hold (ZOH) or Tustin (Yanarates et al., 2023; Yushkova et al., 2021). The formula for this derivative is detailed in Eq. (6).

(6) di→abcdt=iabc(k+1)−iabc(k)Ts {{d{{\overrightarrow i }_{abc}}} \over {dt}} = {{{i_{abc}}\left( {k + 1} \right) - {i_{abc}}\left( k \right)} \over {{T_s}}}

Where T_s is the simulation time step. The inverter line to line voltages are expressed as: (7) Vab=Vao−VboVbc=Vbo−VcoVca=Vco−Vao \matrix{ {{V_{ab}} = {V_{ao}} - {V_{bo}}} \hfill \cr {{V_{bc}} = {V_{bo}} - {V_{co}}} \hfill \cr {{V_{ca}} = {V_{co}} - {V_{ao}}} \hfill \cr }

Calculation of the inverter’s phase voltage is achieved through: (8) Vno=13(Vao+Vbo+Vco) {V_{no}} = {1 \over 3}\left( {{V_{ao}} + {V_{bo}} + {V_{co}}} \right)

The phase voltages are given by: (9) Van=Vao−VnoVbn=Vbo−VnoVcn=Vco−Vno \matrix{ {{V_{an}} = {V_{ao}} - {V_{no}}} \hfill \cr {{V_{bn}} = {V_{bo}} - {V_{no}}} \hfill \cr {{V_{cn}} = {V_{co}} - {V_{no}}} \hfill \cr }

To determine the load currents (I_a, I_b, I_c ), consider that the load comprises the resistance and inductance of the induction machine’s stator. These currents are subsequently calculated within the model of the presented asymmetric machine. Importantly, the IGBT switch currents are derived by multiplying the calculated load currents by SF2.

(10) Is1=ia⋅SF2−aIs3=ib⋅SF2−bIs5=ic⋅SF2−c \matrix{ {{I_{s1}} = {i_a} \cdot S{F_{2 - a}}} \hfill \cr {{I_{s3}} = {i_b} \cdot S{F_{2 - b}}} \hfill \cr {{I_{s5}} = {i_c} \cdot S{F_{2 - c}}} \hfill \cr }

Finally, the inverter input current (i_in or i_load ) is derived from the switching currents using the following equations: (11) iin=iload=Is1+Is3+Is5iin=Ia⋅SF2−a+Ib⋅SF2−b+Ic⋅SF2−c \matrix{ {{i_{in}} = {i_{load}} = {I_{s1}} + {I_{s3}} + {I_{s5}}} \hfill \cr {{i_{in}} = {I_a} \cdot S{F_{2 - a}} + {I_b} \cdot S{F_{2 - b}} + {I_c} \cdot S{F_{2 - c}}} \hfill \cr }

The dynamic state-space equations of the induction machine can be derived from its dynamic equivalent circuit (Ong, 1998), as illustrated in Figure 5. The inverter’s output voltage space vector, expressed in the dq^s reference frame combined with the Euler method detailed in Eq. (6) for equation discretisation, is mathematically described by: (12) [VqssVdss]=23[1−12−12032−32][VanVbnVcn] \left[ {\matrix{ {V_{qs}^s} \cr {V_{ds}^s} \cr } } \right] = {2 \over 3}\left[ {\matrix{ 1 & { - {1 \over 2}} & { - {1 \over 2}} \cr 0 & {{{\sqrt 3 } \over 2}} & { - {{\sqrt 3 } \over 2}} \cr } } \right]\left[ {\matrix{ {{V_{an}}} \cr {{V_{bn}}} \cr {{V_{cn}}} \cr } } \right] (13) dΨqssdt=Ψqss(k+1)−Ψqss(k)Ts=ωb[Vqss+RsXls(Ψmqs−Ψqss)] {{d\Psi _{qs}^s} \over {dt}} = {{\Psi _{qs}^s\left( {k + 1} \right) - \Psi _{qs}^s\left( k \right)} \over {{T_s}}} = {\omega _b}\left[ {V_{qs}^s + {{{R_s}} \over {{X_{ls}}}}\left( {\Psi _{mq}^s - \Psi _{qs}^s} \right)} \right] (14) dΨdssdt=Ψdss(k+1)−Ψdss(k)Ts=ωb[Vdss+RsXls(Ψmds−Ψdss)] {{d\Psi _{ds}^s} \over {dt}} = {{\Psi _{ds}^s\left( {k + 1} \right) - \Psi _{ds}^s\left( k \right)} \over {{T_s}}} = {\omega _b}\left[ {V_{ds}^s + {{{R_s}} \over {{X_{ls}}}}\left( {\Psi _{md}^s - \Psi _{ds}^s} \right)} \right] (15) ios=ωbXls(vos−iosRs) {i_{os}} = {{{\omega _b}} \over {{X_{ls}}}}\left( {{v_{os}} - {i_{os}}{R_s}} \right) (16) dΨqr′sdt=Ψqr′s(k+1)−Ψqr′s(k)Ts=ωb[ωrωbΨdr′s+Rr′Xlr′(Ψmqs−Ψqr′s)] {{d\Psi _{qr}^{{\prime}s}} \over {dt}} = {{\Psi _{qr}^{{\prime}s}\left( {k + 1} \right) - \Psi _{qr}^{{\prime}s}\left( k \right)} \over {{T_s}}} = {\omega _b}\left[ {{{{\omega _r}} \over {{\omega _b}}}\Psi _{dr}^{{\prime}s} + {{R_r^{\prime}} \over {X_{lr}^{\prime}}}\left( {\Psi _{mq}^s - \Psi _{qr}^{{\prime}s}} \right)} \right] (17) dΨdr′sdt=Ψdr′s(k+1)−Ψdr′s(k)Ts=ωb[−ωrωbΨqr′s+Rr′Xlr′(Ψmds−Ψdr′s)] {{d\Psi _{dr}^{{\prime}s}} \over {dt}} = {{\Psi _{dr}^{{\prime}s}\left( {k + 1} \right) - \Psi _{dr}^{{\prime}s}\left( k \right)} \over {{T_s}}} = {\omega _b}\left[ {{{ - {\omega _r}} \over {{\omega _b}}}\Psi _{qr}^{{\prime}s} + {{R_r^{\prime}} \over {X_{lr}^{\prime}}}\left( {\Psi _{md}^s - \Psi _{dr}^{{\prime}s}} \right)} \right] (18) ior′=ωbXlr′(vor′−ior′Rr′) i_{{\rm{or}}}^{\prime} = {{{\omega _b}} \over {X_{lr}^{\prime}}}\left( {v_{or}^{\prime} - i_{or}^{\prime}R_r^{\prime}} \right) (19) Ψmqs=Xm(ΨqssXls+Ψqr′sXlr′) \Psi _{mq}^s = {X_m}\left( {{{\Psi _{qs}^s} \over {{X_{ls}}}} + {{\Psi _{qr}^{\prime s}} \over {X_{lr}^{\prime}}}} \right) (20) Ψmds=Xm(ΨdssXls+Ψdr′sXlr′) \Psi _{md}^s = {X_m}\left( {{{\Psi _{ds}^s} \over {{X_{ls}}}} + {{\Psi _{dr}^{{\prime}s}} \over {X_{lr}^{\prime}}}} \right) where the stator current and rotor current are expressed as: (21) iqss=1Xls(Ψqss−Ψmqs) i_{qs}^s = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {{X_{ls}}}}}\right.} \!\lower0.7ex\hbox{${{X_{ls}}}$}}\left( {\Psi _{qs}^s - \Psi _{mq}^s} \right) (22) idss=1Xls(Ψdss−Ψmds) i_{ds}^s = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {{X_{ls}}}}}\right.} \!\lower0.7ex\hbox{${{X_{ls}}}$}}\left( {\Psi _{ds}^s - \Psi _{md}^s} \right) (23) iqr′s =1Xlr′(Ψqr′s −Ψmqs) i_{qr}^{\prime s} = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {X_{lr}^{\prime}}}}\right.} \!\lower0.7ex\hbox{${X_{lr}^{\prime}}$}}\left( {\Psi _{qr}^{\prime s} - \Psi _{mq}^s} \right) (24) idr′s=1Xlr′(Ψdr′s−Ψmds) i_{dr}^{\prime s} = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {X_{lr}^{\prime}}}}\right.} \!\lower0.7ex\hbox{${X_{lr}^{\prime}}$}}\left( {\Psi _{dr}^{\prime s} - \Psi _{md}^s} \right) and the electromagnetic torque in per-unit, active and reactive power of stator and rotor can be calculated as follows: (25) Te=32P2⋅ωb(Ψdss⋅iqss−Ψqss⋅idss) {T_e} = {3 \over 2}{P \over {2 \cdot {\omega _b}}}\left( {\Psi _{ds}^s \cdot i_{qs}^s - \Psi _{qs}^s \cdot i_{ds}^s} \right)

Figure 5.

The equivalent circuit of a squirrel-cage induction machine in stationary dq coordinates.

The equation of motion, when expressed in per unit values based on the machine’s own base power and voltage, can be represented as: (26) 2Hd(ωr/ωB)dt=Tem+Tmech−Tdamp 2H{{d\left( {{\omega _r}/{\omega _B}} \right)} \over {dt}} = {T_{{\rm{em}}}} + {T_{{\rm{mech}}}} - {T_{{\rm{damp}}}}

Where H is inertia constant. This dimensionless parameter represents the ratio of the kinetic energy stored in the rotating mass at base speed to the machine’s rated power. Table 2 details the squirrel-cage induction machine parameters.

(27) H=jωbm22Sb H = {{j\omega _{bm}^2} \over {2{S_b}}}

Table 2.

Parameter	Symbol	Value
Nominal power	Pn	160 KW
voltage (line to line)	Vn	400 V
Nominal frequency	F	50 Hz
Pole	P	4
Speed	N	1500 RPM
Magnetizing inductance	Xm	0.0236 H
Stator resistor	Rs	0.0138 Ω
Rotor resistor	Rr′ R_r^{\prime}	0.0077 Ω
Base angular speed	ωb	314.1593 rad/s
Stator inductance	Xls	0.0487 H
Rotor inductance	Xlr′ X_{lr}^{\prime}	0.0478 H
Inertia	H	0.1901

The NI sbRIO9629, featuring an Intel Atom processor and Xilinx Artix-7 FPGA, functions as the 215 HP induction machine controller. It receives real-time signals via 16-bit analogue inputs, interfaces with relays and encoders through digital I/Os, and communicates with a host PC via Ethernet. The controller executes control algorithms at a 200 ns cycle, generating a selectable range of 5.7–200 kHz Pulse Width Modulation (PWM) signals for the HIL converter’s switches. The asynchronous operation of the controller and the HIL emulator, unlike synchronised real-time simulators, presents a risk of aliasing. Specifically, a large time step in the HIL emulator can generate aliased low-frequency components, potentially causing critical steady-state oscillations. To avoid this, the HIL system time step can be adjusted from 100 ns to 10 μs to avoid a lack of simulation regarding mathematical conversions and steady-state oscillations.

In a DC machine, the armature and field windings are designed to be orthogonal, creating perpendicular magnetic fields. Assuming negligible iron saturation, these fields interact minimally, allowing the developed torque to be expressed as: (28) Tem=kaϕ(If)Ia {T_{em}} = {k_a}\phi \left( {{I_f}} \right){I_a}

Where k_a is a constant coefficient, ϕ(I_f), the measured field flux by especial instrumentation, and I_a the armature current. Controlling torque in a three-phase induction motor is more complex than in DC machines due to the dynamic interaction of stator and rotor fields, which lack a fixed 90° orientation. Flux sensing issues at low speeds further complicate matters. Indirect field orientation control (IFOC) (Ong, 1998) provides a robust alternative. This control strategy eliminates the need for direct air-gap flux measurement. Instead, IFOC leverages a key principle, as long as the rotor flux linkage, λdr′e \lambda _{dr}^{{\prime}e} , remains constant, and the developed torque can be independently controlled by adjusting the q-axis component of the stator current (iqs′e) \left( {i_{qs}^{\prime e}} \right) . This relationship is mathematically described in Eq. (29) where, p=ddt p = {d \over {dt}} .

(29) Tem*=32p2LmLr′λdr′eiqse T_{em}^* = {3 \over 2}{p \over 2}{{{L_m}} \over {L_r^{\prime}}}\lambda _{dr}^{{\prime}e}i_{qs}^e

In practical IFOC, the rotor flux magnitude is precisely controlled by adjusting the d-axis stator current (idse) \left( {i_{ds}^e} \right) , as shown in Eq. (30). Maintaining proper field orientation involves regulating either the slip speed or the q-axis stator current (iqse) \left( {i_{qs}^e} \right) according to Eq. (31). With successful field orientation, the rotor flux linkage (λdr′e) \left( {\lambda_{dr}^{\prime e}} \right) aligns with the d-axis, and its rate of change is dictated by the rotor circuit time constant (Tr=rr′Lr′) \left( {{T_r} = {{r_r^{\prime}} \over {L_r^{\prime}}}} \right) .

(30) λdr*e=rr′Lmrr′+Lr′pidse \lambda _{dr}^{*e} = {{r_r^{\prime}{L_m}} \over {r_r^{\prime} + L_r^{\prime}p}}i_{ds}^e

Eq. (31) defines the slip speed relationship between d-q stator current components, ensuring precise alignment of the synchronously rotating reference frame with the rotor field. This alignment is critical for successful field orientation control in induction motors.

(31) ωsle=(ωe−ωr)=rr′Lr′iqseidse \omega _{sl}^e = \left( {{\omega _e} - {\omega _r}} \right) = {{r_r^{\prime}} \over {L_r^{\prime}}}{{i_{qs}^e} \over {i_{ds}^e}}

Decoupling algorithms are critical for improving induction motor control performance (Hazzab et al., 2006), as they compensate for the inherent cross-coupling between the d- and q-axis components of the machine model. This transformation effectively linearises the system, allowing independent control of flux and torque and enabling the use of classical control strategies such as Proportional–Integral (PI) controllers.

In this work, the PI controller gains were initially estimated using the Ziegler–Nichols open-loop tuning method and subsequently refined through simulation and experimental validation within the HIL environment to achieve stable operation, fast dynamic response, and minimal steady-state error.

Without the decoupling algorithm, the interaction between flux and torque components introduces non-linear effects that can result in slower transient response, increased oscillations, and reduced control accuracy, particularly under dynamic operating conditions. Although basic operation can still be achieved, the overall performance is significantly degraded.

This linearisation and tuning process contributes to improved system stability and smoother motor dynamics (Fateh Mehazzem et al., 2008). Key elements of the decoupling algorithm include: (32) VdsDecouple=−[ωslKLiqs+LmLrTrλdr′e] V_{ds}^{Decouple} = - \left[ {{\omega _{sl}}{K_L}{i_{qs}} + {{{L_m}} \over {{L_r}{T_r}}}\lambda _{dr}^{{\prime}e}} \right] (33) VqsDecouple=[ωslKLids+LmLrλdr′e] V_{qs}^{Decouple} = \left[ {{\omega _{sl}}{K_L}{i_{ds}} + {{{L_m}} \over {{L_r}}}\lambda _{dr}^{{\prime}e}} \right]

Where KL=Ls−Lm2(Lr+Lm) {K_L} = {L_s} - {{L_m^2} \over {\left( {{L_r} + {L_m}} \right)}} and Tr=LrRr′ {T_r} = {{{L_r}} \over {R_r^{\prime}}} . The general control structure of the converter is shown in Figure 8.

Figure 8.

General control structure of converter.

After the closure of the three-phase AC switch (either symmetric or asymmetric) and DC-link capacitor pre-charge (simulated with an initial value), the diode rectifier produces a 300 Hz DC voltage (Figure 10). With the DC link charged, the sbRIO9629 initiates the startup, driving the four-pole induction machine to 1500 RPM with a 157 rad/s setpoint (Figure 11). Upon reaching the setpoint, the system enters steady-state, ready for speed or torque variations. Figure 12 shows stator currents and rotor speed under a −500 N·m (73 kW) load torque.

Figure 10.

Full-wave bridge diode rectification of three-phase voltage. CH1 (orange) V_ab, CH2 (Cyan) V_bc, CH3 (Purple) V_ca, CH4 (Green) V_dc and MATH (〖−V 〗_ca). (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

Figure 11.

Induction machine’s start-up. CH1 (orange) I_a, CH2 (Cyan) Electromagnetic Torque, CH3 (Purple) V_dc, CH4 (Green) Speed. (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

Figure 12.

Stator current and speed in steady state operation. CH1(orange) I_a, CH2 (Cyan) I_b, CH3 (Purple) I_c, CH4 (Green) Speed (rad/s). (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

The primary goal of IFOC is to maintain motor controllability and DC link voltage stability under varying load conditions (TL). Figure 13 demonstrates this in a 215 HP induction machine HIL setup, showing the system’s response to a 900 N·m load application and removal. The results demonstrate the robustness and stability of the implemented IFOC system under varying load conditions. However, the observed speed ripple suggests that further improvement in speed regulation could be achieved through refined controller tuning or the implementation of additional filtering strategies.

Figure 13.

Load increase from 0 to 900 N·m. CH1 (orange) T_L, CH2 (Cyan) T_e, CH3 (Purple) V_dc, CH4 (Green) Speed (rad/s). (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

For a reference speed of 157 rad/s (1500 RPM), the measured mean speed is approximately 160 rad/s (1527 RPM), indicating a steady-state deviation. The instantaneous speed varies between 150 rad/s (1432 RPM) and 174 rad/s (1661 RPM), resulting in a speed ripple of approximately ±12 rad/s (±79 RPM). This relatively high ripple suggests that further refinement of the control loop parameters or the application of additional filtering techniques could improve speed regulation performance.

Another IFOC objective is effective torque control at low rotor speeds. Figure 14 shows that at 10 rad/s (95 RPM), a 900 N·m torque application, applied within approximately 8 s, causes a significant increase in stator current (I_a), while rotor speed and DC link voltage (V_dc) remain stable. This demonstrates the system’s ability to maintain stable operation and precise torque control at low speeds, crucial for demanding applications.

Figure 14.

Load increase from 0 to 900 N·m. CH1 (orange) T_L, CH2 (Cyan) T_e, CH3 (Purple) V_dc, CH4 (Green) Speed. (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

To evaluate the dynamic responsiveness of the motor controller, a load torque step response test was implemented. While typical operational scenarios involve gradual load torque variations, a step response provides a more rigorous assessment of the controller’s dynamic performance to react to sudden changes. The test involved an abrupt transition in load torque (T_L), changing from −100 N·m (equivalent to a power draw of 12 kW) to −500 N·m (equivalent to a power draw of 73 kW). This deliberate application of a significant load torque disturbance was designed to reveal the system’s dynamic behaviour under stress. Figure 15 illustrates the transient response of the load torque (T_L) and stator currents (I_abc) during this event. Furthermore, Figure 16 presents a broader view of the system’s response, displaying the DC link voltage (V_dc), phase voltage (V_an), load torque (T_L), and electromagnetic torque (T_e) as a function of time. Analysis of Figure 16 reveals a step response time of 3.6 ms, defined as the time required for the electromagnetic torque (T_e) to reach its final value (−500 N·m) following the load torque step change. This metric provides a quantitative measure of the controller’s ability to track the torque setpoint in response to a sudden disturbance. The zoomed-in view shown in Figure 16 corresponds to a magnified section of the same experimental data, included to highlight the transient behaviour immediately after the load torque step.

Figure 15.

Load torque step from 100 to 500 N·m. CH1 (orange) I_a, CH2 (Cyan) I_b, CH3 (Purple) I_c, CH4 (Green) T_L. (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

Figure 16.

Load increase from 100 to 500 N·m. CH1 (orange) T_L, CH2 (Cyan) T_e, CH3 (Purple) V_dc, CH4 (Green) Speed. (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

Variable frequency drives must adjust rotor speed under all conditions. As seen in Figure 17, with a −500 N·m (73 kW) load torque, a large speed set-point change from 10 rad/s to 157 rad/s is applied, followed by a reverse step change back to 10 rad/s. The results show no variation in DC link voltage or electromagnetic torque during these transitions. This demonstrates the system’s robustness in maintaining functionality and stability during significant speed variations under high load.

Figure 17.

Speed profile from 10 rad/s to 157 rad/s before decreasing back to 10 rad/s, all under 500 N·m load CH1 (orange) T_L, CH2 (Cyan) T_e, CH3 (Purple) V_dc, CH4 (Green-Probe 10X) Speed (rad/s). (Scale voltage: 100 V or Ampere per 1 V DAC on O-scope Probe 100X). DAC, digital to analogue converter.

As described in Section III, the inverter model offers the flexibility to choose between non-ideal switches (IGBTs) and ideal switches for the three-phase two-level inverter. Figure 18 illustrates the differences in phase voltages when non-ideal switches are employed (in absence of snubber), revealing voltage spikes caused by the inductance inherent in the non-ideal switch model. In real-world applications, such spikes, resulting from switching transients, are typically addressed using snubber circuits. The appearance of these spikes in the simulation emphasises the necessity of incorporating real-world non-idealities into the design and analysis of power electronic systems to ensure accurate modelling and reliable performance.

Figure 18.

Ideal and non-ideal switches in inverter. CH1 (orange) V_ao, CH2 (Cyan) V_bo, CH3 (Purple) V_co. (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

As illustrated in Figure 19 and detailed in section III, the control platform implements a programmable dead-time adjustment mechanism. The dead-time interval for the power switches is digitally tunable via firmware, operating within a 20 MHz control-loop clock. Adjustments are made in discrete steps of 50 ns, enabling precise synchronisation of the complementary gate signals. Capable of sub-microsecond simulation steps akin to established commercial HIL solutions (Typhoon HIL 602+), the custom-developed HIL system successfully detects and distinguishes these fine-grained timing variations. This allows the precise dead-time behaviour to be accounted for within the converter model, facilitating control optimisation and ensuring robust shoot-through protection.

Figure 19.

Dead-time parameter in inverter’s switches. CH1 (orange) S_(1_Controller), CH2 (Cyan) S_(1_Controller + deadtime),. (Scale voltage: 2 V digital input 3.3 V_dc).

Figure 20 shows the simulated rotary encoder’s A and B signals at four speeds, captured via oscilloscope and processed in MATLAB. The square wave frequencies range from 3.25 kHz (95 RPM) to 51.2 kHz (1500 RPM). These 40 MHz FPGA-generated signals, as described in Section III, provide real-time rotor speed feedback to the control board, ensuring accurate speed control.

Figure 20.

A and B signal of simulated rotary encoder. CH1 (orange) A, CH2 (Cyan) B. (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter

Table 4 provides a quantitative evaluation of the PI current controller’s tuning fidelity and the HIL system’s operational robustness across a range of time steps and switching frequency provided by the controller. This includes the unprecedented minimum of 100 ns time step achieved in this study for machine and converter modelling. This analysis is based on the mean absolute error (MAE) and root mean square error (RMSE) between the commanded references (iqs*e=200 A,ids*e=70 A) \left( {i_{qs}^{*e} = 200\;{\rm{A}},\;i_{ds}^{*e} = 70\;{\rm{A}}} \right) and measured currents references (iqsi and,idsi) \left( {i_{qs}^i\;{\rm{and}},\;i_{ds}^i} \right) defined by Eqs (34) and (35) for inner PI controller of the stator current.

To assess the impact of adopting a uniform time step across all subsystems, the effect of increasing the simulation time step is evaluated in Table 4. The results show that increasing the time step leads to significant degradation in current tracking accuracy and, in some cases, numerical instability. This indicates that a constant time-step approach either requires an extremely small time step for all subsystems—resulting in excessive computational burden—or leads to unacceptable accuracy loss. In contrast, the proposed multi-rate architecture enables higher accuracy while maintaining computational efficiency.

(34) MAE=1n∑i=tn|Idqsi−Idqs*e|n=200,000(n*Ts=20 ms) MAE = {1 \over n}\sum\limits_{i = t}^n {\left| {I_{dqs}^i - I_{dqs}^{*e}} \right|} n = 200,000\left( {n*{T_s} = 20\;{\rm{ms}}} \right)

(35) RMSE=1n∑i=tn(Idqsi−Idqs*e)2 RMSE = \sqrt {{1 \over n}\sum\limits_{i = t}^n {{{\left( {I_{dqs}^i - I_{dqs}^{*e}} \right)}^2}} }

To compare performance, a step-change in load torque from −100 N·m to −500 N·m was applied to the Typhoon HIL 602+ machine load settings. Figure 22 displays the resulting stator current, speed, and electromagnetic torque responses. When compared to the proposed HIL system’s response (Figure 23), the behaviour of both systems is remarkably similar, showing minimal differences. While both systems utilised the same control board and parameters, minor deviations are expected. These arise from inherent differences in model implementation details (due to confidentiality restrictions on the Typhoon system), solver algorithms used by the Typhoon HIL 602+, and variations in analogue input properties and calibrations. Consequently, two distinct interfaces and calibrations were necessary, introducing potential calibration errors in voltage and current feedback. Despite these factors, the results demonstrate a high degree of correlation between the two HIL systems.

Figure 22.

Torque load jump from −100 N·m to −500 N·m. CH1 (orange) T_L, CH2 (Cyan) Speed, CH3 (Purple) T_e and CH4 (Green) I_a. (Scale voltage: 100 V or Ampere per 1 V DAC). DAC, digital to analogue converter.

Figure 23.

Torque step response comparison test between NI custom made and Typhoon HIL. HIL, hardware-in-the-loop.

A rigorous comparative analysis was undertaken to validate the performance of the developed custom NI HIL system against the established industry-standard Typhoon HIL platform. This analysis focused on assessing the systems’ ability to handle dynamic speed variations with dissimilar user-defined setpoint changes under a consistent load. To this end, both systems were subjected to a speed ramp test, simulating a smooth acceleration from 10 rad/s (95 RPM) to 157 rad/s (1500 RPM) and a subsequent deceleration back to 10 rad/s, while maintaining a constant load torque of −500 N·m. This test was designed to evaluate the effectiveness of the IFOC drives in managing speed changes under a significant load. As evidenced in Figure 24, the NI HIL system exhibited a performance profile that closely mirrored that of the Typhoon HIL. Both systems demonstrated consistent and stable operation throughout the entire speed variation cycle, despite dissimilar user-defined setpoint changes, confirming the robust design and implementation of the custom NI HIL system.

Figure 24.

Speed variation 95 RPM to 1500 RPM then 95 RPM under −500 N·m mechanical Torque. CH1 (Blue) T_e, CH2 (Red) T_L, CH3 (Yellow) V_dc and CH4 (Purple) Speed. (Scale voltage: 100 V or Ampere per 1 V for Chanel one to three and DAC and 50 V per 1 V for CH4). DAC, digital to analogue converter.