Design and Implementation of LCL Filter-Based Electric Machine Emulator With Disturbance Compensation

The electric machine emulator (EME), using digital simulation and power electronics to emulate the characteristics of actual machines, can greatly accelerate the testing of electric drives. However, most existing EMEs are based on typical L filter and linear controller, which causes control conflicts and bandwidth limitation. To address this issue, this paper presents an EME based on LCL filter with passive damping for a three-phase permanent magnet synchronous motor. To improve the dynamic emulating accuracy, a dual closed-loop deadbeat predictive current control algorithm is proposed, which is computationally efficient and easy to implement. The system stability is analyzed in the discrete domain, and the parameter constraints of the filter are obtained. Then, two unknown input observers are designed to compensate for the disturbance currents and voltages caused by modeling errors. Moreover, instead of the empirical method, a theoretical one considering the harmonic suppression, bandwidth, stability and resonance is presented for filter design. Finally, the performance of the proposed EME is validated through simulation and experimental results under various conditions such as machine start-up, torque step change, and speed reversal.

Internal resistances of L m and L e . T s Sampling time of the EME.
The associate editor coordinating the review of this manuscript and approving it for publication was Akshay Kumar Saha . u cd , u cq dq-axis voltages of the filter capacitance. u ed , u eq dq-axis voltages of the emulating converter. u ld , u lq dq-axis disturbance voltages. u md , u mq dq-axis voltages of the motor drive unit.
In the RTS, the machine model takes the terminal voltages of the MDU as input and calculates the reference currents as output to the interface controller. Then, the command voltages of the EC are calculated, and the actual currents are reached by controlling the terminal voltages of the IF.
Emulating accuracy is the key concern since the EME is used to replace the actual machine to test and validate the performance of the MDU [14]. As the controlled main component, the IF is not only used for harmonic suppression, but also determines the structure of the interface control algorithm (ICA) and system bandwidth. Therefore, the IF is of great significance to the emulating accuracy. Three types of IFs have been presented in EMEs, namely, L, LC and LCL filters [4], [15]. Among them, the LC filter may only be found in generator emulators [16], [17] despite better filtering capability than the L filter. The main reason is that the LC filter is asymmetric, which cannot be applied to the EME operating in four quadrants.
The L filter has been most widely used in EMEs. The main advantage of the L filter is that a simple linear proportionalintegral (PI) controller can be adopted as the ICA since it is a first-order system. EMEs based on PI controller have been developed in [8], [12], [18], [19], in which acceptable accuracy can be reached in the low-frequency region, whereas the dynamic performance in the high-frequency region is distorted because the low-pass filter (LPF) characteristic of the PI controller narrows system bandwidth [20]. In [10], feedforward control is added to the PI controller to extend system bandwidth, but the problem has not been thoroughly overcome. Besides, as shown in Fig. 1, control conflicts may arise due to the same currents being controlled by both the MDU and EME. To avoid the conflicts, [5] recommends that the current loop bandwidth of the EME needs to be at least five times higher than that of the MDU, which may impose a high cost and demand for the EME.
Open-loop current control (OLCC) has also been proposed for L filter-based EME [21], in which the command voltages of the EC are directly calculated through the machine and IF models, thus resolving control conflicts and improving dynamic response. In [22] and [20], an OLCC based on direct impedance regulation is presented, where the differential operation is eliminated to improve robustness. Nevertheless, the accuracy of the EME based on open-loop control deeply depends on accurate modeling and hardware implementation. Thus, unacceptable deviations from the actual machine may occur due to inevitable modeling errors and nonlinearities of the converter. Also, the inductance of the L filter can only be adjusted within a limited range since small values are ideal for high bandwidth while higher values are more effective for harmonic suppression [23], which further compromises the emulating accuracy and hinders its application.
The LCL filter seems to be the most suitable IF for EME. It can completely eliminate control conflicts because the addition of the capacitor branch decouples the current loop of the EME from that of the MDU [5]. Also, the performance of the PHIL system with the L and LCL filters is compared in [23], concluding that the LCL filter is better both in time domain and frequency domain. However, there are few EME literatures involving LCL filter due to its complex structure and cumbersome control. In [24], the EME with LCL filter is presented to test the performance of the inverter for elevator applications, in which a predictive algorithm is directly deduced based on backward difference and model inversion. Moreover, the LCL filter-based load emulator is proposed in [15], where the linear quadratic regulator (LQR) based on state feedback control is designed to improve the transient VOLUME 10, 2022 response. Nevertheless, both aforementioned ICAs are developed in abc frame, which not only introduces time-varying ac errors but also requires higher-bandwidth controller. Meanwhile, these algorithms suffer from a common problem that inevitable adverse factors such as the resonance, time delay and parameter uncertainty are not taken into account, leading to poor robustness and stability. In addition, unlike in gridconnected systems [25], [26], the LCL filter in EMEs have an impact not only on harmonic suppression, but also on system stability and bandwidth. Yet, there is no universal method presented for the parameter design of the LCL filter in EMEs.
In this paper, the LCL filter with passive damping is chosen as the IF. The comparison of the existing EMEs and the proposed EME is presented in Table 1, and the main contributions of this paper are further detailed as follows.
1) A dual closed-loop deadbeat predictive current control (DDPCC) based on dq frame is proposed, which effectively improves the dynamic accuracy of the EME. Also, the parameter constraints obtained based on the analysis in the discrete domain ensure the system stability, thereby further improving the practicability of the algorithm.
2) The parameter sensitivity of the ICA is analyzed in detail. On this basis, two unknown input observers (UIOs) are designed to compensate for the disturbance currents and voltages introduced by modeling errors. Thus, the system robustness is considerably enhanced. 3) A universal approach based on theoretical analysis rather than engineering experience is proposed, which comprehensively considers the harmonic suppression, bandwidth, stability and resonance.
Therefore, the proposed EME takes the emulating accuracy, stability and robustness into account, so that it is operative for various complex working conditions. The rest of this paper is structured as follows. Section II presents a detailed design and in-depth analysis for the EME. Sections III and IV are to validate the proposed EME through simulations and experiments, respectively. Section V concludes this paper.

II. DESIGN AND ANALYSIS OF THE EME
The overall schematic of the proposed EME in this paper is shown in Fig. 2. Compared with Fig. 1, the MDU and  EME are powered by two independent DC sources instead of the rectifier or power converter. Besides, the LCL filter with passive damping is chosen as the IF, and a high-bandwidth DDPCC is proposed as the ICA to improve dynamic performance of the EME. In addition, the PMSM is selected as the target motor to be emulated in this paper, for it is widely used in electric drive systems due to high efficiency, high power density and small size.

A. MACHINE MODEL
The accuracy of the machine model has a significant impact on the emulating accuracy. Various machine models, including mathematical models and look-up tables based models extracted from finite element analysis (FEA), have been implemented in real-time systems. Mathematical models are popular in electric drives due to their low computational effort, but the nonlinear characteristics of the machine cannot be taken into account. In this paper, a high-fidelity and computationally efficient look-up tables based machine model presented in [27] is used, which considers both the magnetic saturation and spatial harmonics.
For the aforementioned machine model, the flux linkage and torque functions of d-and q-axis currents and the rotor position are initially extracted by the FEA for a prototype PMSM. Subsequently, the current maps versus d-and q-axis flux linkages at different rotor positions are obtained by the inverse solution [27]. The resultant look-up tables of d-and q-axis currents and torque at 0 • rotor position are shown in Figs. 3 and 4.

B. PROPOSED INTERFACE CONTROL ALGORITHM
The system bandwidth not only affects the dynamic accuracy, but also determines the performance of the EME at high operating speed. Considering the multi-pole characteristic of the LCL filter, linear PI control is no longer applicable since very limited bandwidth is available. Besides, the dynamic performance will be distorted at high operating speed due to the LPF characteristic, which further narrows the operating speed range. As the predictive control with high bandwidth is excellent for controlling multiple-input multiple-output systems, a novel DDPCC-based ICA in dq frame is proposed to reach an accurate emulation.

1) DYNAMIC EQUATION OF THE INTERFACE FILTER
For simplicity, the single-phase LCL filter shown in Fig. 5 is initially analyzed. The dynamic equation of the single-phase filter is derived as follows.
Equation (1) is subsequently extended and transformed to dq frame by Park transform as follows.
According to (2) and (3), the currents i m = i md i mq T flowing through the MDU is not directly regulated by the terminal voltages u e = u ed u eq T , but controlled by the currents i e = i ed i eq T flowing through the EC. Inspired by the idea of backstepping control, in which the complex nonlinear control system is decomposed into several subsystems by introducing virtual control variables [28], [29], the current control of the LCL filter-based EME can also be decomposed into two simple subsystems, one to adjust the currents i m to track the reference ones i * m by accurately calculating the desired currents i * e , and the other to force the currents i e to track the desired by exactly controlling the command voltages u * e . That is to say, the currents i * e are selected as the intermediate control variables. However, different from backstepping control, the control law here can be directly derived without constructing the Lyapunov function since the system described by (2) and (3) is linear. In other words, derivative operations, Lyapunov function calculations, and complex gain tuning are all avoided. Thus, the proposed algorithm is computationally efficient and easy to implement.

2) DPCC FOR THE CURRENTS FLOWING THROUGH THE MDU
The prediction equation of the currents flowing through the MDU is obtained by forward Euler discretization of (2) as where and u m,k = u md,k u mq,k T , u c,k = u cd,k u cq,k T .
For deadbeat control, the predictive currents are assumed to be equal to the references output by the machine model as According to (4) and (5), the reference currents flowing through the EC can be derived as

3) DPCC FOR THE CURRENTS FLOWING THROUGH THE EC
Similarly, the prediction equation of the currents flowing through the EC is derived by discretizing (3) as where Likewise, the following assumption is established.  According to (7) and (8), the command voltages of the EC can be expressed as

4) DELAY COMPENSATION
In practice, the terminal voltages obtained at current moment will be applied at next moment, which may weaken the robustness of the algorithm. Thus, the delay should be compensated, and the voltage equation is accordingly updated as k+1 and i e,k+1 are calculated by (4) and (7), respectively. In addition, considering the time constant of the capacitance is much larger than that of the inductance due to the presence of the damping resistance, u c,k+1 ≈ u c,k is established when the sampling time is short enough.
As a result, the diagram of the proposed DDPCC with delay compensation is shown in Fig. 6, where the reference currents i * m,k flowing through the MDU are initially derived from machine model (see Fig. 2), and subsequently, the reference currents i * e,k flowing through the EC are calculated by (6) based on i * m,k and the variables measured by sensors. Simultaneously, the currents i m,k+1 and i e,k+1 are predicted by (4) and (7), respectively, to compensate for the unit delay. These variables are then entered into (10) to calculate the command voltages u * e,k , which will be ultimately modulated by PWM generator to drive the converter (see Fig. 2).

C. STABILITY ANALYSIS
System stability is a prerequisite for the operation of the EME. For the backstepping control, the system stability is ensured by constructing the Lyapunov function while obtaining the control law. However, the proposed DDPCC algorithm is directly deduced based on the linear system described by (2) and (3), so inappropriate system parameters may lead to a remarkable increase in prediction errors and thus cause system instability. Moreover, since the LCL filter is a thirdorder system, the unexpected resonance may cause further augmented prediction errors, thus increasing the tendency of system instability. Therefore, this section presents a detailed stability analysis, and the constraints on system parameters are obtained accordingly.
As shown in Fig. 6, the terminal voltages u m of the MDU are sampled to calculate the predictive currents along with desired currents i * e . According to Shannon sampling theorem, the sampling time of the EME needs to be at least twice as high as that of the MDU. In fact, the sampling time of the EME is typically three to five times higher than that of the MDU to reach an accurate emulation, which means T s is quite small. In this case, [30] indicates that the cross-coupling term ω e T s has little impact on system stability. To explain it, the tracking errors of the outer-and inner-loop controllers are defined as Based on (2) and (11), we can geṫ where t ∈ [k, k + 1]. When the sampling time T s is small enough (T s 1/ω e ), it is reasonable for low-and medium-speed emulated motors to suppose that the system variables, except for the pulsewidth voltage u md , remain constant in one control cycle, i.e., i md,t = i md,k , i mq,t = i mq,k , and ω e,t = ω e,k . On this basis, (12) can be simplified as (13) by substituting (6) into it.
Obviously, the cross-coupling term ω e,t i mq,t is cancelled out by the control term ω e,k i mq,k inż 1 , as well as inż 2 . Taking the outer current loop in Fig. 6 as an example, when the Lyapunov function is designed as V 1 = z 2 1 /2 + z 2 2 /2, the resultanṫ V 1 = z 1ż1 + z 2ż2 clearly does not contain cross-coupling term, which means that this term has almost no effect on system stability. It should be noted that this conclusion still holds for other forms of Lyapunov functions since V 1 is positive definite throughout. The same finding can be obtained from the inner current loop. Furthermore, according to (13), it may be difficult to directly acquire stability conditions since constructing the proper Lyapunov function is cumbersome. Actually, according to the expressions of coefficient matrices A m , B m , C m , A e , B e , and C e , the system can be considered as a single-input single-output one by ignoring the cross-coupling term, which contributes to a simpler analysis method. In this way, coefficient matrices can be simplified as The voltage equation with i * m,k as input can be expressed as (15) by substituting (4), (6), (7) and (14) into (10). where According to (15), the block diagram of the EME current loop is shown in Fig. 7, where the EC is assumed to be an ideal component and u i,k is neglected for simplicity as it has no effect on the analysis. Subsequently, the transfer function from i * m,k to i m,k can be obtained as According to Jury criterion for discrete system, the stability conditions can be expressed as where A(z) = a 3 z 3 + a 2 z 2 + a 1 z + a 0 . As described in Section II-E, the parameters of the LCL filter satisfy L m = L e and R m = R e , which means Furthermore, considering R m R d , the following relationship is satisfied.
Based on (21) and (22), the stability conditions can be rewritten as Eventually, the constraints is obtained by solving (23) as According to (24), when the sampling time T s is determined, the damping resistance R d should take on a value that is proportional to the inductance L m in order to achieve a stable operation. In other words, as the inductance increases, a larger damping resistance is required to ensure stability.
It should be noted that the above conclusion is obtained by simplifying the system to a single-input single-output one based on the premise that i mq,t and ω e,t remain constant within each control period. For low-and mediumspeed motors, it is completely operative due to the large mechanical time constant and large stator inductance. However, this premise will no longer hold for high-speed motors (T s 1/ω e is not satisfied) with the smaller inductance. For instance, for T s = 20 µs in this paper, when ω e > 5000 rad/s (i.e., 796 Hz in the electrical frequency and ω e T s > 0.1), the previous analysis may not be applicable. In this case, it may be more straightforward to resolve the stability conditions by constructing a proper Lyapunov function.

D. DISTURBANCE ANALYSIS AND SUPPRESSION
Since the proposed DDPCC is a model-based control method, the performance largely depends on the modeling accuracy of the IF. However, the IF is subject to parameter variation and uncertainty. For instance, the inductance decreases as the current rises, and the resistance increases as the temperature rises. According to (4), (6), and (7), the prediction and reference current errors caused by parameter mismatch can be represented based on the deviation matrices A m , B m , C m , A e , B e and C e as (25), (26), and (27), as shown at the bottom of the next page, respectively.
where u i , u o are defined as (16). As shown in Fig. 6, the prediction and reference current errors do not directly affect the emulating accuracy, but indirectly through the command voltages u * e . Therefore, it is necessary to derive the command voltage errors for further analysis. According to (10), the exact command voltages VOLUME 10, 2022 under parameter mismatch can be expressed as (28), shown at the bottom of the page. Further, the voltage errors can be derived as (29), shown at the bottom of the page, by substracting (10) from (28). Clearly, the errors can be divided into two parts, one is the error (defined as u il ) caused by the aforementioned disturbance currents (i.e., i * e,k , i e,k+1 and i m,k+1 ), and the other comes from the disturbance voltages (defined as u l ) generated by parameter mismatch (i.e., A e , B e and C e ) alone. As a result, the parameter mismatch initially introduces the disturbance currents, which in turn acts on the command voltages along with the disturbance voltages, thus deteriorating the emulating accuracy.
Figs. 8 and 9 quantitatively evaluate the effect of the parameter mismatch on the disturbance voltages, where the desired currents i * m are set as [i * md , i * mq ] = [0, 5] A, and the motor speed is stepped from 20 Hz to 150 Hz at 0.1 s. The rest of the configurations are the same as in Section III. As can be seen, the disturbance voltages caused by both resistance mismatch and inductance mismatch rise dramatically as the speed increases, indicating that disturbance suppression is crucial especially for high-speed operation. Moreover, the resistance mismatch only causes the offset errors, while the inductance mismatch not only produces the offset errors, but also leads to the violent fluctuation in disturbance voltages, which means that the waveform quality of the controlled currents will also deteriorate under the inductance mismatch.
Indeed, (29) also specifies the direction of disturbance rejection that we can counteract u il by compensating for disturbance currents, while offsetting disturbance voltages u l to completely eliminate the errors. Various disturbance estimation and attenuation methods have been developed, such as extended state observer [31], finite-time disturbance observer [29], nonlinear disturbance observer [32]- [34], and UIO [35], [36]. For these approaches, the estimated lumped disturbances are employed for feedforward compensation control. Among them, the UIO, integrating state feedback and disturbance evaluation, has become one of the most extensively investigated and applied methods due to its excellent ability to suppress disturbances and uncertainties. Therefore, the UIO is adopted here, and unknown input current observer (UICO) and unknown input voltage observer (UIVO) are presented to compensate for the disturbance currents and voltages, respectively.
Based on (2) and (3), the state-space form of the IF model can be derived aṡ where 82586 VOLUME 10, 2022 The UICO is first designed to compensate for disturbance currents to eliminate u il . Considering the errors between the reference model and the actual model, the deviation matrices A ms , B ms , and C ms can be defined as where A msf , B msf , and C msf are the coefficient matrices of the reference model. The dynamic equation with modeling errors can be obtained by substituting (32) into (30) aṡ (33) and the terms involving the model errors can be considered as unknown input disturbance currents i l = i ld i lq T as shown in (34).
The dynamic equation with modeling errors can be rewritten as (35) by substituting (34) into (33).
Based on the relationship between the disturbance currents i l and the measurable currents i m established in (35), the UICO is then designed as whereĩ m andĩ l denote the estimated variables, and the UICO gain H c = H c1 H c2 T is to drive the estimated variables to converge to the actual values. According to (36), the block diagram of the UICO is displayed in Fig. 10(a). In a similar way, the UIVO can be designed to compensate for disturbance voltages u l = u ld u lq T . Referring to (35), the dynamic equation with disturbance voltages can be derived aṡ The UIVO can then be designed based on the relationship between the disturbance voltages u l and the measurable currents i e as and the block diagram of the UIVO is shown in Fig. 10 The observed disturbance currents and voltages can then be used to compensate for the prediction and control errors caused by model uncertainty. Since the system described by (2) and (3) is updated to the one defined by (35) and (37), new prediction, reference and output equations can be obtained based on the same processing steps in Section II-B. Comparing these new equations with (4), (6), (7), and (10), we can get the compensated system variables as and the block diagram of the DDPCC with disturbance suppression is shown in Fig. 11.

E. PARAMETER DESIGN FOR LCL FILTER
As mentioned above, the IF has a direct effect on system bandwidth and harmonic suppression. Moreover, inappropriate filter parameters can lead to system instability according to (24). However, to our knowledge, no universal method has been presented for sizing the parameters of the LCL filter in EMEs. In this section, each component of the LCL filter is designed based on theoretical analysis.

1) FILTER INDUCTANCE
As shown in Fig. 2, the actual currents are driven to track the references by controlling the terminal voltages of the EC. Thus, the actual currents involve the higher-order harmonics caused by switching frequency and lower-order harmonics introduced by dead time. A large inductance, although effective for harmonic suppression, narrows the system bandwidth.
Here, the total inductance, L total = L m + L e , is first derived VOLUME 10, 2022 from the suppression of lower-order harmonics, while the inductance ratio, α = L m /L total , is determined by the suppression of higher-order harmonics. According to (1), when the internal resistances of the inductors are neglected, the transfer function from u e to i m can be expressed as (40) In the low-frequency region, the transfer function can be simplified to (41). In this case, the LCL filter is equivalent to a first-order system, which is also shown in Fig. 12(a).
In addition, as shown in Fig. 12(a), the LCL filter is more efficient at suppressing higher-order harmonics than the L filter for the same total inductance. Assuming that the lower-order harmonics introduced by the EC are the same as the MDU, the total inductance of the IF should be twice that of the actual machine to reach a close match, namely where In practice, the switching frequency of the EC is usually much higher than that of the drive inverter to achieve better dynamic performance and emulating accuracy, which means less dead time and fewer low-order harmonics. Considering the system bandwidth and harmonic suppression, the total resistance can be designed as Once the total inductance is determined, the suppression of higher-order harmonics depends on the inductance ratio. Based on (40), the bode diagrams of the LCL filter with different inductance ratios are shown Fig. 12(b), in which only the ratios in the range of [0 0.5] are considered due to the same results for α and 1-α. As shown in Fig. 12(b), the filter has the strongest suppression of high-frequency harmonics at α = 0.5, namely L m = L e . It should be noted that although the resonance peak is slightly higher for α = 0.5, it can be conquered by selecting the resonant frequency reasonably.

2) FILTER CAPACITANCE
The resonant frequency of the LCL filter can be expressed as Obviously, after the filter inductances are determined, the resonant frequency depends on the capacitance. As shown in Fig. 12, the resonant frequency should be positioned away the operating frequency region of the actual machine to avoid a significant increase in current harmonics. Besides, the resonance position should ensure that the harmonics at the switching frequency can be effectively attenuated. Thus, the resonant frequency can be selected as 5ω max < ω res < ω pwm /2 (46) The capacitance can subsequently be derived as

3) DAMPING RESISTANCE
As shown in Fig. 12(a), the resonance peak of the LCL filter can be considerably attenuated by the damping resistor in series with the capacitor, thus reducing the harmonics at the resonant frequency and improving system stability. Also, a larger damping resistance appears to be more efficient in this case, whereas it may lead to instability according to (24).
Considering the system stability and harmonic suppression at the resonant frequency, the damping resistance can be designed as Based on the previous analysis, the parameters of the LCL filter in this paper are designed as shown in Table 2.

III. SIMULATION RESULTS
The proposed EME based on LCL filter and DDPCC is first verified by simulations. The simulation topology is consistent with Fig. 2, where the drive inverter is operated with field-oriented control (FOC) in torque control command. The parameters of the EME test bench (i.e., the EME along with MDU under test) and target PMSM are shown in Table 2. To verify the steady-state and dynamic performance of the proposed EME over a wide operating point, a transient speed and torque load profile is designed as shown in Fig. 13, in which the motor is accelerated to 3000 r/min (i.e., ω e = 200 Hz) at start-up and stepped back to 1500 r/min (i.e., ω e = 100 Hz) at 0.15 s. Meanwhile, the torque steps from 5 N·m to 10 N·m at 0.1 s and steps back to 5 N·m at 0.2 s.
For comparison, the L filter-based EMEs with PI control [5] and OLCC [20] are also simulated respectively, and the results are shown in Fig. 14, in which the reference currents are calculated by the PMSM model. As shown in Fig. 14(a), the tracking errors of the L filter-based EME with PI control are as high as nearly 4 A and 0.8 A at machine start-up and high speed, respectively, which are much higher than those (0.76 A and 0.3 A) of the proposed EME. This is due to the distortion of high-frequency dynamic performance caused by the LPF effect of PI control. Besides, the tracking errors of the proposed EME are restricted to less than 0.2 A at low speed, which are still lower owing to the aforementioned control conflicts of the L filter-based EME.
As shown in Fig. 14(b), the tracking errors of the L filter-based EME with OLCC are apparently lower than that with PI control at machine start-up, since the OLCC can avoid control conflicts and greatly improve dynamic performance. However, the actual currents deviate significantly from the reference currents at both high and low speeds because the open-loop control cannot take into account the nonlinearities of the inverter, such as dead time and voltage drop. In fact, the tracking errors in this case are compensated by closed-loop current control of the MDU, so the actual currents can still match those of the target PMSM. Nevertheless, increased control requirements may result in the performance of the MDU not being convincingly verified. As shown in Fig. 14(c), both the steady-state and dynamic performance of the proposed EME are far superior to the other two cases, indicating that the proposed EME can reach a more accurate and reliable emulation. Furthermore, the target PMSM drive system where the actual motor rather than the EME is driven by the MDU is simulated and the currents are compared with the ones of the EME, as shown in Fig. 15. Not surprisingly, compared with the other two cases, the dq-axis current errors of the proposed EME are reduced by roughly half in most moments, which clearly gives stronger evidence that the proposed EME can achieve best emulating accuracy.
The comparison of the DDPCC with and without UIOs under parameter mismatch (R d = 1.6R d,real and L m = L e = 0.6L m,real = 0.6L e,real ) is carried out to verify the robustness. The reference disturbance currents and voltages are calculated by (49) and (50) presented in Appendix, respectively. As shown in Fig. 16, the d-and q-axis currents of the EME without UIOs certainly deviate from the references, while the disturbance currents and voltages can be exactly estimated by UIOs and compensated for modeling errors to maintain an accurate emulation. As expected, it can be found that the tracking errors caused by parameter mismatch is much larger at high speed. For this phenomenon, according to (49) and (50), the cross-coupling effect between d-axis and q-axis is enhanced at high speed, which amplifies the model errors caused by the inductance mismatch. Also, due to the high-frequency filtering effect of the capacitor branch, the current i mq −i eq flowing through this branch increases at high speed, resulting in a remarkable increase in tracking errors caused by the resistance mismatch. Therefore, the disturbance compensation is necessary for the emulation of highspeed motors. Moreover, since the mismatches of L m and L e are set to be the same in this case and the forms of the UICO and UIVO are similar, the curve shapes of the disturbance currents and voltages are semblable accordingly, as shown in Fig. 16(c). To further verify the performance of the proposed UIOs, the dq-axis currents and estimated voltages and currents for the EME with UIOs under resistance mismatch and inductance mismatch are shown in Figs. 17 and 18, respectively. In these two cases, the dq-axis currents can still be evidently kept around the references, and disturbance voltages and currents are effectively evaluated. Also, it can be found that the higher-order harmonics of the disturbance voltages and currents is not able to be estimated due to the limitation of the system bandwidth, but it is sufficient to ensure an acceptable system stability and accuracy.

IV. EXPERIMENTAL RESULTS
The performance of the proposed EME is further verified by the experimental setup shown in Fig. 19(a). The drive inverter of the MDU is built by IGBT modules and controlled by a digital signal processor (DSP) TMS320F28335, while the EC is composed of Silicon Carbide (SiC) modules to reach a higher switching frequency. Typhoon HIL 602+ device is chosen as the RTS, where the lookup tables-based PMSM model is implemented on FPGA with a time step of 1 µs, while the proposed ICA is realized on ARM Cortex A9 with a time step of 20 µs. The parameters of the target PMSM and VOLUME 10, 2022  EME test benches are listed in Table 2. The experiments are conducted under several transient conditions such as machine start-up, torque step change, and speed reversal. The results of the target PMSM test bench shown in Fig. 19(b) and the EME with the same topology but with abc frame-based model predictive control (MPC) [23] are also obtained for comparison. To fully validate the proposed EME, the FOC with speed control command is applied to the MDU.
The performance of the proposed EME without parameter mismatch is first verified. The current and speed responses of the actual PMSM, the EME with abc frame-based MPC, and the proposed EME under machine start-up are shown in Fig. 20. The operating speed is first set at 50 r/min, and then accelerated to 1200 r/min (i.e., ω e = 80 Hz) in 2 s. Meanwhile, the load torque is kept at 2 N·m. As can be seen, both the EMEs based on MPC and DDPCC can exactly emulate the fundamental current characteristics of the actual PMSM, and the corresponding speed errors can be controlled below 1% when the speed is greater than 400 r/min. However, the harmonic contents in the current of the EME based on MPC are much larger at low speed and low load, which leads to substantially increased higher-order current error (up to 1.8 A) and speed tracking errors (up to 6 r/min). This is partly due to the fact that the MPC based on abc frame is sensitive to phase current noise, which is sharply amplified for small currents. On the other hand, the time delay present in the system inevitably deteriorates the robustness. Whereas, the dq framebased DDPCC with delay compensation thoroughly conquers these defects, thus achieving a more accurate emulation with reduced current error (less than 1 A) and speed error (less than 3 r/min).
The comparison of the current responses under torque step increase is presented in Fig. 21 to further verify the transient and steady-state performance, where the load torque steps from 1 N·m to 6 N·m in 20 ms and the operating speed is kept at 2500 r/min (i.e., ω e = 166.7 Hz). As expected, the proposed EME can maintain a reliable and satisfactory emulation of the target motor at a higher operating speed, and the errors of phase currents are bound to less than 0.5 A in both transient and steady state. Furthermore, the phase currents of the MPC-based EME are clearly distorted relative to the target motor at both low and high loads. Actually, as the sampling time is constant, the increased speed leads to larger prediction errors in phase currents for abc frame-based MPC. As a result, the emulated currents exhibit pronounced time-varying ac errors, which is particularly noticeable at high load, as shown in Fig. 21(d). In contrast, the much lower current errors and more matched waveforms of the proposed EME provide a direct proof for its high bandwidth and high precision. Fig. 22 shows the transient current responses under torque step drop to further verify the dynamic performance of the proposed EME, where the load torque steps from 8 N·m to 4 N·m in 10 ms and the operating speed is kept at 2000 r/min (i.e., ω e = 133.3 Hz). Evidently, the current error of the proposed EME can be effectively limited to below 1 A throughout the entire transient process, which is halved compared to that (up to 2.1 A) of the MPC-based EME. Hence, the degraded waveform quality and increased emulating error explicitly confirm the previous analysis.
Moreover, the speed reversal experiment is carried out, and the results are shown in Fig. 23, in which the load torque is kept at 5 N·m and the operating speed is reversed from 600 r/min to −600 r/min (i.e., ω e from 40 Hz to −40 Hz)  in 2 s. In this case, although the steady-state performance of the MPC-based EME is improved owing to the reduction in the proportion of noise as the current amplitude increases, the significant current errors (up to 2.4 A) are produced during motor commutation due to the sharp changes in the amplitude and phase of the phase current, which results in an increased speed error (up to 6 r/min). Conversely, the current and speed responses of the proposed EME still closely match those of the actual PMSM, and its maximum speed error is below 4 r/min in transient state and less than 0.5% in steady state, proving that the proposed EME can reach an accurate emulation over a wide operating point. The robustness of the proposed EME is then verified under parameter mismatch. The results of resistance mismatch, inductance mismatch, and both resistance and inductance   The load torque steps from 3 N·m to 8 N·m at 0.3 s and the operating speed decreases from 1000 r/min to 600 r/min in 0.5 s at 0.8 s. Also, the tracking errors of the dq-axis currents in these cases at 1000 r/min and the load torque of 8 N·m is presented in Fig. 27. Under resistance mismatch, compared with the EME without UIOs, the maximum current error of the EME with UIOs is reduced from 1.6 A to 0.5 A as shown in Fig. 26(a) and (b), preliminary verifying the feasibility of disturbance compensation. Meanwhile, as shown in Fig. 24, the tracking errors of the EME without UIOs at high speed are much larger, which is because the increased current i mq − i eq promotes the modeling errors caused by the resistance mismatch according to (49) and (50).    As can be seen from Fig. 25, disturbance currents and voltages under inductance mismatch are not only affected by the load torque but also by the operating speed, which is determined by the terms ω e i m and ω e i e . In this case, the presence of UIOs is still able to lower the maximum tracking error from 1.3 A to 0.4 A. Further, since the disturbances generated by resistance mismatch and inductance mismatch are coupled to each other according to (49) and (50), it can be found that the addition of the inductance mismatch results in an evidently increased q-axis current deviation even with a smaller resistance mismatch by comparing Fig. 26 with Fig. 24. Again, the UIOs contributes to a remarkable reduction in tracking errors by approximately 78% (i.e., from 3.2 A to 0.7 A), which strongly proves the effectiveness of the UIOs.

V. CONCLUSION
In this paper, an EME based on LCL filter is presented to validate the performance of the MDU. A high-bandwidth DDPCC is proposed as the ICA in dq frame, which avoids control conflicts and greatly improves dynamic performance.
The system stability and robustness are then analyzed in detail, and the UICO and UIVO are designed to suppress the disturbance currents and voltages caused by modeling errors. Furthermore, a theoretical method is presented for filter design, in which the harmonic suppression, bandwidth, stability, and resonance are all considered to reach an accurate and stable operation. To validate the proposed EME, several transient operating conditions are dedicatedly designed, and both the torque control mode and the speed control mode are adopted by the MDU. The comparisons between the proposed EME and earlier studies are carried out systematically. Simulation and experimental results show that the proposed EME can achieve fast, accurate and reliable emulation for the actual machine over a wide operating point under steadystate, transient and parameter mismatch conditions.

APPENDIX
According to (2) and (